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Commit 3ac4146e by Joaquín Irazábal González
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doc: First version of the article on the journal template

parent 79d9678f
Showing with 2647 additions and 1306 deletions
Manuscript/wileyNJDv5_AMA.aux 0 → 100644
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\@writefile{toc}{\contentsline {chapter}{Fast design optimization of SLB dampers using FEM-calibrated surrogates: hysteresis prediction with LSTM and damage-constrained optimization}{1}{Doc-Start}\protected@file@percent }
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\citation{Hirt1974}
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WileyNJDv5_Template/wileyNJDv5_AMA.bbl → Manuscript/wileyNJDv5_AMA.bbl
...@@ -6,40 +6,6 @@ Hirt CW, Amsden AA, Cook JL. An arbitrary {L}agrangian-{E}ulerian computing ...@@ -6,40 +6,6 @@ Hirt CW, Amsden AA, Cook JL. An arbitrary {L}agrangian-{E}ulerian computing
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\documentclass[AMA,Times1COL]{WileyNJDv5} %STIX1COL,STIX2COL,STIXSMALL
\articletype{Article Type}%
\received{Date Month Year}
\revised{Date Month Year}
\accepted{Date Month Year}
\journal{Journal}
\volume{00}
\copyyear{2023}
\startpage{1}
\raggedbottom
\begin{document}
\title{Fast design optimization of SLB dampers using FEM-calibrated surrogates: hysteresis prediction with LSTM and damage-constrained optimization}
\author[1]{Author One}
\author[2,3]{Author Two}
\author[3]{Author Three}
\authormark{FIRST \textsc{et al.}}
\titlemark{FAST DESIGN OPTIMIZATION OF SLB DAMPERS USING FEM-CALIBRATED SURROGATES: HYSTERESIS PREDICTION WITH LSTM AND DAMAGE-CONSTRAINED OPTIMIZATION}
\address[1]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
\address[2]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
\address[3]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
\corres{Corresponding author Author One, This is sample corresponding address. \email{authorone@gmail.com}}
\presentaddress{This is sample for present address text this is sample for present address text.}
%\fundingInfo{Text}
%\JELinfo{ejlje}
\abstract[Abstract]{The geometric optimization of shear-link beam (SLB) dampers subjected to cyclic loading is a key challenge in seismic engineering, due to the strongly nonlinear and history-dependent nature of their mechanical response. High-fidelity finite element method (FEM) simulations provide detailed insight into hysteretic behavior and internal damage mechanisms, but their computational cost hinders their direct use within optimization loops. In this work, a surrogate-based optimization framework is proposed, leveraging FEM-calibrated datasets as ground truth for both global response and internal damage indicators that are not directly accessible through experimental testing.
FEM simulations are conducted for SLB dampers with increasing geometric complexity, considering configurations with two, three, and five windows, and are used to generate dedicated datasets spanning the relevant design space. Long Short-Term Memory (LSTM) neural networks are employed to predict hysteretic force–displacement curves, explicitly accounting for the loading history and memory effects inherent to cyclic response. Geometric optimization is then performed using surrogate models based on supervised learning algorithms, including tree-based and neural approaches, as well as Radial Basis Function (RBF) approximations. The different surrogate strategies are systematically compared in terms of predictive accuracy and computational efficiency.
The results highlight a clear trade-off between accuracy and computational cost across the considered surrogate models, enabling practical guidelines for their selection depending on the design scenario and available computational resources. Overall, the proposed methodology demonstrates the feasibility of fast and reliable surrogate-assisted optimization pipelines for the seismic design of SLB dampers, significantly reducing computational effort while preserving predictive fidelity.}
\keywords{Hysteresis, Long Short-Term Memory (LSTM), surrogate modeling, supervised learning, radial basis functions, structural optimization, FEM-calibrated models, shear-link dampers}
\jnlcitation{\cname{%
\author{Taylor M.},
\author{Lauritzen P},
\author{Erath C}, and
\author{Mittal R}}.
\ctitle{On simplifying ‘incremental remap’-based transport schemes.} \cjournal{\it J Comput Phys.} \cvol{2021;00(00):1--18}.}
\maketitle
\renewcommand\thefootnote{}
\footnotetext{\textbf{Abbreviations:} ANA, anti-nuclear antibodies; APC, antigen-presenting cells; IRF, interferon regulatory factor.}
\renewcommand\thefootnote{\fnsymbol{footnote}}
\setcounter{footnote}{1}
\section{Introduction}\label{sec1}
\subsection{Motivation and engineering problem}\label{sec1_1}
Shear-link beam (SLB) dampers are widely used as passive energy dissipation devices in seismic-resistant structures due to their ability to undergo stable inelastic deformations while limiting damage to the primary structural system. Their design aims at maximizing energy dissipation capacity and ductility under cyclic loading, while simultaneously controlling local damage levels to ensure reliability, durability, and predictable failure mechanisms.
Experimental testing plays a fundamental role in characterizing the global hysteretic response of SLB dampers. However, laboratory campaigns present inherent limitations when addressing design optimization problems. On the one hand, internal state variables such as local plastic strains, stress triaxiality, or damage indicators cannot be directly measured with sufficient spatial resolution. On the other hand, the high cost and logistical complexity of experimental programs severely restrict the number of geometric configurations that can be explored, making systematic optimization impractical.
In this context, high-fidelity finite element method (FEM) simulations constitute a powerful alternative. Advanced nonlinear FEM models enable detailed representation of cyclic plasticity, geometric nonlinearity, and damage evolution, providing access to both global response quantities and local indicators governing failure mechanisms. Moreover, FEM simulations allow the systematic generation of data across a wide range of geometric parameters, making them particularly suitable as a foundation for data-driven optimization strategies.
\subsection{Main challenges}\label{sec1_2}
Despite their advantages, the direct use of FEM models within optimization loops remains computationally prohibitive. The cyclic response of SLB dampers is characterized by pronounced hysteresis and strong memory effects, where the force–displacement relationship depends not only on the instantaneous deformation but also on the full loading history. Accurately capturing such behavior requires fine temporal discretization and sophisticated constitutive models, resulting in simulation times that can span several hours per configuration.
Furthermore, purely data-driven approaches face intrinsic limitations when applied to this class of problems. Models trained on limited datasets often exhibit poor extrapolation capabilities when queried outside the domain covered by the training data, which is particularly critical in design optimization scenarios. As a consequence, there is a clear need for surrogate modeling techniques that are both computationally efficient and sufficiently reliable to approximate complex nonlinear responses, while remaining consistent with the underlying physics captured by FEM simulations.
\subsection{Contributions of this work}\label{sec1_3}
This paper proposes a surrogate-assisted optimization framework for SLB dampers subjected to cyclic loading, combining FEM-calibrated datasets with advanced machine learning techniques. The main contributions of the work can be summarized as follows:
Generation of high-fidelity FEM datasets for SLB dampers with increasing geometric complexity, considering configurations with two, three, and five windows.
Prediction of hysteretic force–displacement curves using Long Short-Term Memory (LSTM) neural networks, explicitly accounting for history-dependent effects.
Geometric optimization based on surrogate models, including supervised learning algorithms—such as Random Forest (RF), Gradient Boosting Trees (GBT), XGBoost, Support Vector Regression (SVR), and Multilayer Perceptrons (MLP)—as well as Radial Basis Function (RBF) approximations.
A systematic comparison of the different surrogate strategies in terms of predictive accuracy and computational cost.
An adaptive validation and feedback strategy, where selected optimized designs are verified through additional FEM simulations and incorporated into the dataset when necessary \cite{Hirt1974}.
\section{Numerical simulation and ground truth generation}\label{sec2}
This section describes the finite element modeling strategy adopted to generate the reference datasets used in this study. The numerical simulations are designed to accurately capture the cyclic hysteretic behavior of shear-link beam (SLB) dampers, as well as relevant internal indicators associated with damage and energy dissipation. The resulting FEM outputs constitute the ground truth employed for training, validation, and comparison of the surrogate models considered in the subsequent sections.
\subsection{Geometry of SLB dampers}\label{sec2_1}
The study considers SLB dampers with increasing geometric complexity, focusing on configurations featuring two, three, and five shear windows. These layouts are representative of typical design solutions and allow the influence of geometric complexity on both structural response and surrogate modeling performance to be systematically assessed.
The geometry of each damper is parameterized through a reduced set of design variables. In particular, the thicknesses of the shear windows, denoted as tw, are treated as independent parameters, enabling local stiffness and plastic deformation patterns to be controlled. Additionally, the thickness of the surrounding frame, tf, is included as a global design variable, governing the overall stiffness and load transfer capacity of the device. This parameterization provides sufficient flexibility to explore a wide range of feasible geometries while maintaining a manageable dimensionality of the design space.
\subsection{Cyclic loading protocols}\label{sec2_2}
All numerical simulations are performed under displacement-controlled loading conditions, where the relative displacement is imposed by an idealized actuator. This choice ensures stable numerical convergence and allows the hysteretic response of the dampers to be directly characterized in terms of force–displacement relationships.
The applied loading histories follow cyclic protocols with progressively increasing displacement amplitudes, which are commonly adopted in the assessment of energy dissipation devices. Such protocols are particularly suitable for capturing stiffness degradation, strength evolution, and cumulative damage effects under repeated loading. The specific sequence of displacement amplitudes is adapted to the height of each damper configuration, ensuring comparable deformation demands across the different geometric layouts.
\subsection{Finite element outputs and quantities of interest}\label{sec2_3}
For each simulated configuration, the FEM model provides both global and local response quantities. At the global level, the primary quantity of interest is the hysteretic force–displacement curve, which characterizes the energy dissipation capacity and overall nonlinear behavior of the damper under cyclic loading.
In addition to the global response, internal indicators related to damage and deformation localization are extracted from the simulations. In particular, the triaxial failure damage map (TFDMap) is employed to quantify the proximity to failure at critical regions of the device. Furthermore, a local distortion measure associated with the deformation of the shear windows is evaluated, as it is directly related to the activation of plastic mechanisms responsible for energy dissipation. These quantities provide essential information for defining damage-based constraints in the subsequent optimization process.
\subsection{Design of the simulation dataset}\label{sec2_4}
The numerical campaign is designed to ensure a systematic and sufficiently uniform exploration of the geometric design space. The values of the geometric parameters are sampled using a quasi-random strategy, enabling efficient coverage of the admissible domain while avoiding clustering of samples in restricted regions.
The resulting dataset is explicitly divided into two subsets. A first subset is used for training the surrogate models, while a second subset is reserved for validation purposes and includes configurations not seen during the training phase. This separation allows the generalization capability of the surrogate models to be rigorously assessed and provides a consistent basis for evaluating their performance in both prediction and optimization tasks.
(Figure \ref{fig1} and \ref{fig2})
\begin{figure*}[t]
\centerline{\includegraphics[width=\textwidth,height=9pc,draft]{empty}}
\caption{This is the sample figure caption.\label{fig1}}
\end{figure*}
\begin{align*}
s(nT_{s}) &= s(t)\times \sum\limits_{n=0}^{N-1} \delta (t-nT_{s}) \xleftrightarrow{\mathrm{DFT}} S \left(\frac{m}{NT_{s}}\right) \nonumber\\[3pt]
&= \frac{1}{N} \sum\limits_{n=0}^{N-1} \sum\limits_{k=-N/2}^{N/2-1} s_{k} e^{\mathrm{j}2\pi k\Delta fnT_{s}} e^{-j\frac{2\pi}{N}mn}
\end{align*}
\begin{figure*}
\centerline{\includegraphics[width=342pt,height=9pc,draft]{empty}}
\caption{This is the sample figure caption.\label{fig2}}
\end{figure*}
\section{Hysteresis prediction using LSTM models}\label{sec3}
Accurate prediction of hysteretic force–displacement curves is a key requirement for surrogate-based optimization of SLB dampers. The nonlinear cyclic response of these devices is inherently history-dependent, as stiffness, strength, and energy dissipation mechanisms evolve with the accumulated deformation and loading direction. In this work, Long Short-Term Memory (LSTM) neural networks are adopted to model such behavior, as they are specifically designed to capture temporal dependencies and memory effects in sequential data.
\subsection{Problem formulation with memory effects}\label{sec3_1}
The objective of the hysteresis prediction task is to estimate the resisting force
F(t)
F(t) at a given time step as a function of the displacement history and the geometric characteristics of the damper. Unlike monotonic or memoryless systems, the force response of SLB dampers under cyclic loading cannot be uniquely determined from the instantaneous displacement alone.
Two key aspects justify the explicit inclusion of memory effects. First, the response depends on the loading direction, as unloading and reloading paths differ from the initial loading branch. Second, the amplitude and sequence of previous cycles influence stiffness degradation, plastic deformation accumulation, and energy dissipation capacity. As a result, an appropriate formulation must account for both the temporal evolution of the displacement signal and the geometric parameters governing the mechanical behavior of the device.
\subsection{Sequential representation of the input signal}\label{sec3_2}
To enable sequence-based learning, the input to the LSTM model is formulated as a time series of feature vectors. At each discrete time step t, the input vector is defined as $x_t=[u_t, \dot{u}_t, c_t, A_t, \theta]$, where $u_t$ denotes the imposed displacement, $\dot{u}_t$ its associated velocity or loading direction indicator, $c_t$ the cycle index, $A_t$ the maximum displacement amplitude reached in the current cycle, and $\theta$ the set of geometric parameters defining the damper configuration. This representation combines instantaneous kinematic information with cycle-level descriptors and fixed geometric features.
The output of the network is the corresponding resisting force $F_t$. Two prediction strategies are considered: an autoregressive formulation, in which the force is predicted sequentially at each time step, and a many-to-many formulation, where the full force–displacement curve is predicted as a sequence given the input displacement history.
\subsection{LSTM architectures considered}\label{sec3_3}
Different LSTM-based architectures are explored to assess their suitability for hysteresis prediction. A standard many-to-many LSTM architecture is employed as a baseline model, enabling direct mapping between input and output sequences of equal length. This architecture is particularly effective for reproducing complete hysteretic loops once the loading protocol is specified.
To improve generalization across different loading histories, an encoder–decoder architecture is also considered. In this configuration, the encoder processes the input displacement sequence and compresses the relevant temporal information into a latent representation, which is then decoded into the corresponding force response. This approach facilitates the handling of variable-length sequences and differing loading protocols.
Optionally, attention mechanisms can be incorporated into the decoder to enhance interpretability and to emphasize critical portions of the loading history, such as displacement reversals or peak amplitudes. Although not essential for all cases, attention-based models provide additional insight into the temporal regions that most strongly influence the predicted response.
\subsection{Training and validation strategy}\label{sec3_4}
Prior to training, all input and output variables are normalized to ensure numerical stability and to prevent scale imbalances from biasing the learning process. The networks are trained using loss functions based on mean absolute error (MAE) or mean squared error (MSE), optionally augmented with additional penalties to emphasize accurate prediction of force peaks, which are particularly relevant for energy dissipation assessment.
To rigorously evaluate generalization performance, the dataset is split at the level of complete simulations rather than individual time steps. Entire hysteretic responses corresponding to specific geometric configurations are reserved for validation, ensuring that no temporal segments of a given simulation appear simultaneously in both training and validation sets. This strategy prevents data leakage and provides a realistic assessment of predictive capability for unseen configurations.
\subsection{Advantages and limitations}\label{sec3_5}
The use of LSTM models for hysteresis prediction offers several advantages. By construction, LSTMs explicitly capture memory effects and temporal dependencies, enabling high-fidelity reproduction of complex hysteretic behavior under cyclic loading. This makes them particularly well suited for modeling systems where the response is governed by accumulated deformation and loading history.
However, these benefits come at the cost of increased model complexity and training time. LSTM networks typically require larger datasets and careful tuning to achieve stable performance, and their extrapolation capabilities remain limited when applied outside the range of training data. Consequently, while LSTMs provide an accurate tool for hysteresis prediction, they are best employed as part of a broader surrogate-based framework rather than as standalone optimization models.
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\section{Geometric optimization using surrogate models}\label{sec4}
Within each optimization iteration, a large number of candidate geometries are evaluated using the surrogate models, allowing rapid estimation of objective and constraint functions. Based on these surrogate predictions, the most promising candidate designs are identified and retained for further exploration. This surrogate-assisted DE framework enables efficient identification of optimal or near-optimal geometries while drastically reducing the number of costly FEM simulations required.
\subsection{Problem formulation}\label{sec4_1}
The geometric optimization problem is formulated in terms of a set of design variables and performance objectives. The design variables are defined as $\theta={t_{wi}, t_f}$, where
$t_{wi}$ denotes the thickness of the i-th shear window and $t_f$ represents the thickness of the surrounding frame. This parameterization allows local deformation mechanisms and global stiffness characteristics to be simultaneously controlled.
The optimization objectives are twofold. On the one hand, the goal is to minimize damage indicators derived from the FEM simulations, thereby ensuring structural integrity and limiting the risk of premature failure. On the other hand, the objective is to maximize the deformation capacity of the device, quantified through distortion measures directly related to energy dissipation under cyclic loading. These competing objectives reflect the fundamental trade-off between performance and safety in the design of energy dissipation devices.
To ensure physically admissible solutions, constraints are imposed based on damage-related quantities. Candidate designs exceeding prescribed thresholds of damage indicators are considered infeasible and are penalized or excluded from the optimization process. This constraint-based formulation ensures that optimized geometries satisfy both performance and reliability requirements.
\subsection{Surrogate models}\label{sec4_2}
The computational cost of direct FEM evaluations motivates the use of surrogate models to approximate the relationship between geometric parameters and response quantities. Two classes of surrogate approaches are considered in this study.
The first class comprises supervised machine learning models, including Random Forest (RF), Gradient Boosting Trees (GBT), XGBoost, Support Vector Regression (SVR), and Multilayer Perceptrons (MLP). These models are trained on the FEM-generated datasets to predict damage indicators and distortion-related quantities as functions of the geometric design variables. Their flexibility and ability to capture nonlinear relationships make them suitable for modeling complex response surfaces.
As an alternative, Radial Basis Function (RBF) approximations are employed as a direct interpolation-based surrogate. RBF models provide smooth functional representations of the design space and are characterized by very low computational cost at inference time. Their performance, however, depends strongly on the density and coverage of the available data, particularly in higher-dimensional parameter spaces.
\subsection{Optimization algorithm}\label{sec4_3}
The exploration of the design space is performed using the Differential Evolution (DE) algorithm, a population-based evolutionary optimization method well suited for nonlinear and nonconvex problems. DE operates through iterative mutation, crossover, and selection steps, enabling robust search without requiring gradient information.
Within each optimization iteration, a large number of candidate geometries are evaluated using the surrogate models, allowing rapid estimation of objective and constraint functions. Based on these surrogate predictions, the most promising candidate designs are identified and retained for further exploration. This surrogate-assisted DE framework enables efficient identification of optimal or near-optimal geometries while drastically reducing the number of costly FEM simulations required.
\section{Numerical validation and adaptive feedback}\label{sec5}
To assess the reliability of the surrogate-assisted optimization framework, selected optimized designs are subjected to additional finite element simulations. This validation stage serves a dual purpose: verifying the accuracy of surrogate predictions for previously unseen configurations and providing a mechanism for adaptive refinement of the surrogate models when necessary.
\subsection{FEM validation of optimized designs}\label{sec5_1}
A subset of candidate geometries identified as optimal by the surrogate-based optimization process is re-evaluated using high-fidelity FEM simulations. For each selected design, the FEM results are directly compared with the corresponding surrogate predictions.
The comparison focuses on both global and local response quantities. At the global level, the predicted hysteretic force–displacement curves are evaluated against their FEM counterparts to assess the accuracy of the surrogate models in reproducing energy dissipation and cyclic response characteristics. At the local level, damage-related indicators extracted from the FEM simulations are compared with the surrogate-based estimates, enabling verification of the constraint satisfaction and safety margins associated with the optimized designs.
This validation step provides a quantitative measure of the surrogate model performance in the vicinity of the optimal solutions, which is critical for ensuring the practical applicability of the proposed optimization framework.
\subsection{Adaptive retraining strategy}\label{sec5_2}
An adaptive feedback mechanism is introduced to enhance the robustness of the surrogate models. A predefined admissible error criterion is established for both global response quantities and damage indicators. When the discrepancy between surrogate predictions and FEM results for a validated design exceeds this threshold, the surrogate model is considered insufficiently accurate in that region of the design space.
In such cases, the newly generated FEM simulation is incorporated into the existing dataset, and the surrogate models are retrained to account for the additional information. This iterative enrichment of the training data progressively improves surrogate accuracy in regions of interest, particularly near optimal or constraint-active designs. The adaptive retraining strategy thus ensures that the optimization process remains reliable while minimizing the total number of high-fidelity FEM simulations required.
\section{Comparative assessment of supervised surrogate models and RBF approaches}\label{sec6}
This section presents a systematic comparison between supervised machine learning surrogate models and Radial Basis Function (RBF) approximations when employed within the proposed optimization framework. The comparison focuses on predictive accuracy, computational efficiency, and practical usability, with the objective of identifying the most suitable surrogate strategy for different design scenarios.
\subsection{Predictive accuracy}\label{sec6_1}
The predictive performance of the surrogate models is first assessed in terms of their ability to reproduce FEM-derived damage indicators and performance-related quantities. For each surrogate approach, the error in damage prediction is evaluated using validation cases not included in the training dataset. Particular attention is given to configurations near constraint boundaries, as accurate damage estimation in these regions is critical for reliable optimization.
In addition to damage-related quantities, errors in performance metrics associated with deformation capacity and energy dissipation are analyzed. The results show that supervised learning models generally provide higher predictive accuracy across the explored design space, especially in cases involving complex geometric configurations or strong nonlinear interactions between design variables. RBF models, while capable of accurately interpolating within densely sampled regions, exhibit increased sensitivity to data sparsity and dimensionality, which can lead to larger prediction errors in less populated areas of the design space.
\subsection{Computational cost}\label{sec6_2}
Computational efficiency is evaluated by analyzing both training and inference times. Supervised learning models typically require a non-negligible training phase, the cost of which depends on model complexity, hyperparameter tuning, and dataset size. However, once trained, their inference time remains relatively low and largely independent of the number of training samples.
In contrast, RBF models are characterized by minimal training effort and extremely fast inference, making them attractive for scenarios where rapid evaluation of candidate designs is required. Nevertheless, the computational cost of RBF approaches tends to increase with the dimensionality of the problem and the number of basis functions needed to adequately represent the response surface. As a result, scalability becomes a limiting factor for RBF models when applied to high-dimensional design spaces or when extensive datasets are employed.
\subsection{Practical implications and model selection}\label{sec6_3}
The comparative results highlight that the choice of surrogate model should be guided by the specific requirements of the design problem. For low-dimensional problems with limited but well-distributed datasets, RBF models offer an efficient and reliable solution, providing fast evaluations with minimal implementation complexity. Conversely, for higher-dimensional problems or scenarios involving complex nonlinear interactions, supervised learning models demonstrate superior robustness and accuracy, albeit at the cost of increased training time.
When rapid design iterations are required and computational resources are constrained, RBF approaches may be preferable, provided that the design space is adequately sampled. In contrast, when predictive fidelity and generalization are critical—particularly near damage thresholds—supervised surrogate models represent a more reliable choice. These insights provide practical guidance for selecting appropriate surrogate strategies in surrogate-assisted optimization of SLB dampers.
\section{Discussion}\label{sec7}
The results presented in this study highlight the inherent trade-offs involved in surrogate-assisted optimization of SLB dampers under cyclic loading. In particular, the balance between predictive accuracy, computational efficiency, and robustness emerges as a central aspect governing the selection and deployment of surrogate models within practical design workflows.
A clear trade-off between accuracy and computational speed is observed across the different surrogate strategies. Supervised learning models generally provide higher predictive fidelity, especially in regions of the design space characterized by strong nonlinearities and near active damage constraints. This improved accuracy comes at the expense of increased training effort and model complexity. In contrast, Radial Basis Function approaches offer extremely fast evaluation times and minimal training overhead, but their performance is strongly dependent on the density and distribution of the available data, as well as on the dimensionality of the design space. As a consequence, robustness with respect to extrapolation and sparse sampling becomes a limiting factor for purely interpolative methods.
The role of feature engineering is particularly relevant in this context. By incorporating physically meaningful descriptors—such as geometric parameters directly linked to deformation mechanisms and damage evolution—supervised surrogate models are able to capture complex response patterns with relatively compact representations. This contrasts with purely interpolative approaches, where predictive capability relies primarily on local proximity in the input space and rapidly degrades as dimensionality increases. The results indicate that informed feature selection, grounded in the underlying mechanics of the problem, is a key enabler for achieving reliable surrogate performance in high-dimensional optimization tasks.
The use of LSTM models for hysteresis prediction further complements the surrogate-based optimization framework. LSTMs are shown to be highly effective in reproducing history-dependent force–displacement relationships, explicitly accounting for memory effects that cannot be captured by static surrogate models. However, their computational cost and data requirements make them less suitable as direct optimization surrogates. Instead, LSTMs are best regarded as a complementary tool, providing accurate hysteresis predictions and insight into cyclic response behavior, while supervised or interpolative surrogates are employed for fast evaluation within optimization loops.
From a broader perspective, the proposed framework has important implications for computer-aided design in structural and seismic engineering. By combining high-fidelity FEM simulations, data-driven surrogates, and evolutionary optimization, the methodology enables systematic exploration of complex design spaces that would otherwise be inaccessible using conventional approaches. This paradigm supports more informed design decisions, facilitates performance-based optimization under realistic loading conditions, and contributes to the development of efficient and reliable workflows for the design of energy dissipation devices in seismic applications.
\section{Conclusions}\label{sec8}
This study has presented a surrogate-assisted framework for the geometric optimization of shear-link beam (SLB) dampers subjected to cyclic loading, combining high-fidelity finite element simulations with data-driven modeling and evolutionary optimization techniques. Based on the results obtained, the following conclusions can be drawn:
High-fidelity FEM simulations provide a reliable and information-rich ground truth for characterizing both global hysteretic response and internal damage-related quantities, enabling the systematic generation of datasets suitable for surrogate modeling and optimization.
Long Short-Term Memory (LSTM) neural networks are shown to be effective in predicting hysteretic force–displacement curves, successfully capturing the memory effects and history dependence inherent to cyclic structural response.
Surrogate-based optimization strategies significantly reduce computational cost compared to direct FEM-driven approaches, making accelerated geometric optimization of SLB dampers feasible without compromising predictive fidelity.
Radial Basis Function (RBF) models offer an ultra-fast surrogate alternative when the design space is well sampled and of limited dimensionality, whereas supervised learning models provide greater robustness and accuracy for higher-dimensional or more complex optimization problems.
Clear practical recommendations can be established regarding surrogate selection, depending on dataset size, design space complexity, and computational constraints, supporting informed decision-making in engineering design workflows.
Overall, the proposed methodology demonstrates the potential of integrating FEM-calibrated surrogates, sequence-based learning, and evolutionary optimization to enable efficient and reliable design of energy dissipation devices for seismic applications.
\paragraph{Fourth level head}
Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque
augue sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id, sapien. Nullam at lectus. In sagittis
ultrices mauris. Curabitur malesuada erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod.
Aenean vel lectus. Nunc imperdiet justo nec dolor.
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
\subparagraph{Fifth level head.}
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra
tortor. Sed fringilla justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue
est scelerisque sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas
urna mi, suscipit in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl.
Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed
lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc
purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet.
In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus.
Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam
porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis.
Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque.
Vivamus eu dolor.
Nulla in ipsum. Praesent eros nulla, congue vitae, euismod ut, commodo a, wisi. Pellentesque habitant morbi
tristique senectus et netus et malesuada fames ac turpis egestas. Aenean nonummy magna non leo. Sed felis erat,
ullamcorper in, dictum non, ultricies ut, lectus. Proin vel arcu a odio lobortis euismod. Vestibulum ante ipsum primis
in faucibus orci luctus et ultrices posuere cubilia Curae; Proin ut est. Aliquam odio. Pellentesque massa turpis, cursus
eu, euismod nec, tempor congue, nulla. Duis viverra gravida mauris. Cras tincidunt. Curabitur eros ligula, varius ut,
pulvinar in, cursus faucibus, augue (Box~1).
Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed
lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc
purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet.
In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus.
Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam
porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis.
Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque.
Vivamus eu dolor.
\begin{boxwithhead}
{BOX 1\quad This is sample for Box head and text}
{\noindent This is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext. This is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext.}
\end{boxwithhead}
\begin{center}
\begin{table*}[!h]%
\caption{This is sample table caption.\label{tab1}}
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lllll@{}}
\toprule
&\multicolumn{2}{@{}l}{\textbf{Spanned heading$^{\tnote{\bf a}}$}} & \multicolumn{2}{@{}l}{\textbf{Spanned heading$^{\tnote{\bf b}}$}} \\\cmidrule{2-3}\cmidrule{4-5}
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} & {\textbf{Col4 head}} & \textbf{Col5 head} \\
\midrule
col1 text & col2 text & col3 text & 12.34 & col5 text\tnote{1} \\
col1 text & col2 text & col3 text & \hphantom{0}1.62 & col5 text\tnote{2} \\
col1 text & col2 text & col3 text & 51.809 & col5 text \\
\bottomrule
\end{tabular*}
\begin{tablenotes}%%[341pt]
\item[$^{\rm a}$] Example for a first table footnote.
\item[$^{\rm b}$] Example for a second table footnote.
\item {\it Source}: Example for table source text.
\end{tablenotes}
\end{table*}
\end{center}
Curabitur tellus magna, porttitor a, commodo a, commodo in, tortor. Donec interdum (Table~\ref{tab1}). Praesent scelerisque. Maecenas posuere sodales odio. Vivamus metus lacus, varius quis, imperdiet quis, rhoncus a, turpis. Etiam ligula arcu,
elementum a, venenatis quis, sollicitudin sed, metus. Donec nunc pede, tincidunt in, venenatis vitae, faucibus vel,
nibh. Pellentesque wisi. Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Etiam congue neque id dolor.
\begin{boxtext}%
{\noindent This is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext.}
\end{boxtext}
Nulla non mauris vitae wisi posuere convallis. Sed eu nulla nec eros scelerisque pharetra. Nullam varius. Etiam
dignissim elementum metus. Vestibulum faucibus, metus sit amet mattis rhoncus, sapien dui laoreet odio, nec ultricies
nibh augue a enim. Fusce in ligula. Quisque at magna et nulla commodo consequat. Proin accumsan imperdiet sem.
Nunc porta. Donec feugiat mi at justo. Phasellus facilisis ipsum quis ante. In ac elit eget ipsum pharetra faucibus.
Maecenas viverra nulla in massa (Table~\ref{tab2}).
Nulla in ipsum. Praesent eros nulla, congue vitae, euismod ut, commodo a, wisi. Pellentesque habitant morbi
tristique senectus et netus et malesuada fames ac turpis egestas. Aenean nonummy magna non leo. Sed felis erat,
ullamcorper in, dictum non, ultricies ut, lectus. Proin vel arcu a odio lobortis euismod. Vestibulum ante ipsum primis
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
\begin{table*}[!t]%
\centering %
\caption{This is sample table caption.\label{tab2}}%
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lllll@{\extracolsep\fill}}
\toprule
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} & \textbf{Col4 head} & \textbf{Col5 head} \\
\midrule
col1 text & col2 text & col3 text & col4 text & col5 text\tnote{$^\dagger$} \\
col1 text & col2 text & col3 text & col4 text & col5 text \\
col1 text & col2 text & col3 text & col4 text & col5 text\tnote{$^\ddagger$} \\
\bottomrule
\end{tabular*}
\begin{tablenotes}
\item[$^\dagger$] Example for a first table footnote.
\item[$^\ddagger$] Example for a second table footnote.
\item {\it Source}: Example for table source text.
\end{tablenotes}
\end{table*}
Below is the example \cite{Liska2010,Kucharik2003,Blanchard2015} for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list\footnote{This is an example for footnote.}:
\begin{itemize}
\item bulleted list entry sample bulleted list entry \cite{Lauritzen2011}, sample list entry text.
\item bulleted list entry sample bulleted list entry. bulleted list entry sample bulleted list entry. bulleted list entry sample bulleted list entry.
\item bulleted list entry sample bulleted list entry \cite{Klima2017}, bulleted list entry sample bulleted list entry \cite{Dukowicz2000}, sample list entry text. bulleted list entry sample bulleted list entry.
\item sample list entry text. sample list entry text.
\end{itemize}
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non
odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien
turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus.
Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the sample for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list:\vskip12pt
\noindent\textbf{Description sample:}
\begin{description}
\item[first entry] description text, description text \cite{Kucharik2011,Kucharik2014,Loubere2005}. description text, description text, description text, description text, description text.
\item[second long entry] description text, description text, description text, description text, description text, description text, description text.
\item[third entry] description text, description text, description text, description text, description text.
\item[fourth entry] description text, description text.
\end{description}
\noindent\textbf{Numbered list items sample:}
\begin{enumerate}[1.]
\item First level numbered list entry, sample numbered list entry.
\item First numbered list entry, sample numbered list entry. Numbered list entry \cite{Caramana1998}, sample numbered list entry. Numbered list entry, sample numbered list entry.
\begin{enumerate}[a.]
\item Second level alpabetical list entry. Second level alpabetical list entry. Second level alpabetical list entry \cite{Hoch2009}. Second level alpabetical list entry.
\item Second level alpabetical list entry. Second level alpabetical list entry \cite{Shashkov1996,Knupp1999,Knupp1999}.
\begin{enumerate}[i.]
\item Third level lowercase roman numeral list entry. Third level lowercase roman numeral list entry. Third level lowercase roman numeral list entry.
\item Third level lowercase roman numeral list entry. Third level lowercase roman numeral list entry. \cite{Kamm2000}
\end{enumerate}
\item Second level alpabetical list entry. Second level alpabetical list entry \cite{Taylor1937}.
\end{enumerate}
\item First level numbered list entry, sample numbered list entry. Numbered list entry, sample numbered list entry. Numbered list entry.
\item Another first level numbered list entry, sample numbered list entry. Numbered list entry, sample numbered list entry. Numbered list entry.
\end{enumerate}
\noindent\textbf{un-numbered list items sample:}
\begin{enumerate}[]
\item Sample unnumberd list text.
\item Sample unnumberd list text.
\item sample unnumberd list text.
\item Sample unnumberd list text.
\end{enumerate}
\section{Examples for enunciations}\label{sec4}
\begin{theorem}\label{thm1}
Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text.
\end{theorem}
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
\begin{proposition}
Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text.
\end{proposition}
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
\begin{definition}
Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text.
\end{definition}
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non
odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor.
Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien
turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus.
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam
vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi.
Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut
mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui.
Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui.
\begin{proof}
Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text.
\end{proof}
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
\begin{proof}[Proof of Theorem~{\rm\ref{thm1}}]
Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text.
\end{proof}
\begin{sidewaystable}%[h]
\def\d{\hphantom{0}}
\caption{Sideways table caption. For decimal alignment refer column 4 to 9 in tabular* preamble.\label{tab3}}%
\begin{tabular*}{\textheight}{@{\extracolsep\fill}lllllllll@{\extracolsep\fill}}%
\toprule
& \textbf{Col2 head} & \textbf{Col3 head} & \multicolumn{1}{l}{\textbf{10}} &\multicolumn{1}{l}{\textbf{20}} &\multicolumn{1}{l}{\textbf{30}} &\multicolumn{1}{l}{\textbf{10}} &\multicolumn{1}{l}{\textbf{20}} &\multicolumn{1}{l}{\textbf{30}} \\
\midrule
&col2 text &col3 text &\d0.7568&\d1.0530&\d1.2642&\d0.9919&\d1.3541&\d1.6108 \\
& &col2 text &12.5701 &19.6603&25.6809&18.0689&28.4865&37.3011 \\
3 &col2 text & col3 text &\d0.7426&\d1.0393&\d1.2507&\d0.9095&\d1.2524&\d1.4958 \\
& &col3 text &12.8008&19.9620&26.0324&16.6347&26.0843&34.0765 \\
& col2 text& col3 text &\d0.7285&\d1.0257&\d1.2374&\d0.8195&\d1.1407&\d1.3694* \\
& & col3 text &13.0360&20.2690&26.3895&15.0812&23.4932&30.6060\tnote{$\dagger$} \\
\bottomrule
\end{tabular*}
\begin{tablenotes}%%[\textheight]
\item[*] First sideways table footnote. Sideways table footnote. Sideways table footnote. Sideways table footnote.
\item[$^\dagger$] Second sideways table footnote. Sideways table footnote. Sideways table footnote. Sideways table footnote.
\end{tablenotes}
\end{sidewaystable}
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra tortor. Sed fringilla
justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue est scelerisque
sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas urna mi, suscipit
in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl (Table~\ref{tab3}).
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam
vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi (Figure~\ref{fig3}).
Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut Curabitur tellus magna, porttitor a, commodo a, commodo in, tortor. Donec interdum. Praesent scelerisque. Mae-
cenas posuere sodales odio. Vivamus metus lacus, varius quis, imperdiet quis, rhoncus a, turpis. Etiam ligula arcu,
elementum a, venenatis quis, sollicitudin sed, metus. Donec nunc pede, tincidunt in, venenatis vitae, faucibus vel.
\begin{sidewaysfigure}
\centerline{\includegraphics[width=542pt,height=9pc,draft]{empty}}
\caption{Sideways figure caption. Sideways figure caption. Sideways figure caption. Sideways figure caption. Sideways figure caption. Sideways figure caption.\label{fig3}}
\end{sidewaysfigure}
Pellentesque wisi. \cite{Kucharik2012} Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Etiam congue neque id dolor.
\begin{algorithm}
\caption{\enskip Pseudocode for our algorithm}\label{alg1}
\begin{algorithmic}
\For each frame
\For water particles $f_{i}$
\State compute fluid flow \cite{Hirt1974}
\State compute fluid--solid interaction \cite{Benson1992}
\State apply adhesion and surface tension \cite{Margolin2003}
\EndFor
\For solid particles $s_{i}$
\For neighboring water particles $f_{j}$
\State compute virtual water film \\(see Section~\ref{sec3})
\EndFor
\EndFor
\For solid particles $s_{i}$
\For neighboring water particles $f_{j}$
\State compute growth direction vector \\(see Section~\ref{sec2})
\EndFor
\EndFor
\For solid particles $s_{i}$
\For neighboring water particles $f_{j}$
\State compute $F_{\theta}$ (see Section~\ref{sec1})
\State compute $CE(s_{i},f_{j})$ \\(see Section~\ref{sec3})
\If $CE(b_{i}, f_{j})$ $>$ glaze threshold
\State $j$th water particle's phase $\Leftarrow$ ICE
\EndIf
\If $CE(c_{i}, f_{j})$ $>$ icicle threshold
\State $j$th water particle's phase $\Leftarrow$ ICE
\EndIf
\EndFor
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm}
Donec et nisl at wisi luctus bibendum. Nam interdum tellus ac libero. Sed sem justo, laoreet vitae, fringilla at,
adipiscing ut, nibh. Maecenas non sem quis tortor eleifend fermentum. Etiam id tortor ac mauris porta vulputate.
Integer porta neque vitae massa \cite{Hirt1974,Benson1992}. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat. Class aptent
taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Vivamus rhoncus tincidunt libero.
Etiam elementum pretium justo. Vivamus est. Morbi a tellus eget pede tristique commodo \cite{Benson1992}. Nulla nisl. Vestibulum
sed nisl eu sapien cursus rutrum.
Pellentesque wisi. Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Etiam congue neque id dolor.
Donec et nisl at wisi luctus bibendum. Nam interdum tellus ac libero. Sed sem justo, laoreet vitae, fringilla at,
adipiscing ut, nibh. Integer porta neque vitae massa. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat.
Maecenas non sem quis tortor eleifend fermentum. Etiam id tortor ac mauris porta vulputate.
Integer porta neque vitae massa. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat. Class aptent
taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Vivamus rhoncus tincidunt libero.
Etiam elementum pretium justo. Vivamus est. Morbi a tellus eget pede tristique commodo. Nulla nisl. Vestibulum
sed nisl eu sapien cursus rutrum.
\begin{align}\label{eq23}
\|\tilde{X}(k)\|^2
&=\frac{\left\|\sum\limits_{i=1}^{p}\tilde{Y}_i(k)+\sum\limits_{j=1}^{q}\tilde{Z}_j(k) \right\|^2}{(p+q)^2} \nonumber\\
& \leq\frac{\sum\limits_{i=1}^{p}\left\|\tilde{Y}_i(k)\right\|^2+\sum\limits_{j=1}^{q}\left\|\tilde{Z}_j(k)\right\|^2 }{p+q}.
\end{align}
Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque
augue sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id, sapien. Nullam at lectus. In sagittis
ultrices mauris. Curabitur malesuada erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod.
Aenean vel lectus. Nunc imperdiet justo nec dolor.
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
\begin{align}\label{eq24}
\|\tilde{X}(k)\|^2
&=\frac{\left\|\sum\limits_{i=1}^{p}\tilde{Y}_i(k)+\sum\limits_{j=1}^{q}\tilde{Z}_j(k) \right\|^2}{(p+q)^2}\nonumber\\
& \leq\frac{\sum\limits_{i=1}^{p}\left\|\tilde{Y}_i(k)\right\|^2+\sum\limits_{j=1}^{q}\left\|\tilde{Z}_j(k)\right\|^2 }{p+q}.
\end{align}
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra
tortor. Sed fringilla justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue
est scelerisque sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas
urna mi, suscipit in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl.
Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed
lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc
purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet.
In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus.
Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam
porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis.
Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque.
Vivamus eu dolor.
\section{Conclusions}\label{sec5}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae,
felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec
vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus
sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel
leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur
auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
Duis eget orci sit amet orci dignissim rutrum.
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
%\backmatter
\bmsection*{Author contributions}
This is an author contribution text. This is an author contribution text. This is an author contribution text. This is an author contribution text. This is an author contribution text.
\bmsection*{Acknowledgments}
This is acknowledgment text. \cite{Kenamond2013} Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here.
\bmsection*{Financial disclosure}
None reported.
\bmsection*{Conflict of interest}
The authors declare no potential conflict of interests.
\bibliography{wileyNJD-AMA}
\bmsection*{Supporting information}
Additional supporting information may be found in the
online version of the article at the publisher’s website.
\appendix
\bmsection{Program codes appear in Appendix\label{app1}}
\vspace*{12pt}
Using the package {\tt listings} you can add non-formatted text as you would do with \verb|\begin{verbatim}| but its main aim is to include the source code of any programming language within your document.\newline Use \verb|\begin{lstlisting}...\end{lstlisting}| for program codes without mathematics.
The {\tt listings} package supports all the most common languages and it is highly customizable. If you just want to write code within your document, the package provides the {\tt lstlisting} environment; the output will be in Computer Modern typewriter font. Refer to the below example:
\begin{lstlisting}[caption={Descriptive caption text},label=DescriptiveLabel, basicstyle=\fontsize{8}{10}\selectfont\ttfamily]
for i:=maxint to 0 do
begin
{ do nothing }
end;
Write('Case insensitive ');
WritE('Pascal keywords.');
\end{lstlisting}
\bmsubsection{Subsection title of first appendix\label{app1.1a}}
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
\bmsubsubsection{Subsection title of first appendix\label{app1.1.1a}}
\noindent\textbf{Unnumbered figure}
\begin{center}
\includegraphics[width=7pc,height=8pc,draft]{empty}
\end{center}
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
\bmsection{Section title of second appendix\label{app2}}%
\vspace*{12pt}
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla (Figure~\ref{fig5}).
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
%== Figure 4 ==
%% Example for figure inside appendix
\begin{figure}[b]
\centerline{\includegraphics[height=10pc,width=78mm,draft]{empty}}
\caption{This is an example for appendix figure.\label{fig5}}
\end{figure}
\bmsubsection{Subsection title of second appendix\label{app2.1a}}
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non odio.
Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce sed justo
eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec
pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin et quam.
Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien turpis,
fermentum vel, eleifend faucibus, vehicula eu, lacus.
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
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Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut
mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui.
Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui.
\bmsubsubsection{Subsection title of second appendix\label{app2.1.1a}}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae,
felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec
vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus
sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel
leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur
auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
Duis eget orci sit amet orci dignissim rutrum (Table~\ref{tab4}).
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
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\begin{table*}[t]%
\centering
\caption{This is an example of Appendix table showing food requirements of army, navy and airforce.\label{tab4}}%
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}llllll@{\extracolsep\fill}}%
\toprule
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} & \textbf{Col4 head} & \textbf{Col5 head} & \textbf{Col6 head} \\
\midrule
col1 text & col2 text & col3 text & col4 text & col5 text & col6 text\\
col1 text & col2 text & col3 text & col4 text & col5 text & col6 text\\
col1 text & col2 text & col3 text& col4 text & col5 text & col6 text\\
\bottomrule
\end{tabular*}
\end{table*}
Example for an equation inside appendix
\begin{equation}
{\mathcal{L}} = i \bar{\psi} \gamma^\mu D_\mu \psi - \frac{1}{4} F_{\mu\nu}^a F^{a\mu\nu} - m \bar{\psi} \psi\label{eq25}
\end{equation}
\bmsection{Example of another appendix section\label{app3}}%
\vspace*{12pt}
This is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text
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\begin{equation}
\mathcal{L} = i \bar{\psi} \gamma^\mu D_\mu \psi
- \frac{1}{4} F_{\mu\nu}^a F^{a\mu\nu} - m \bar{\psi} \psi
\label{eq26}
\end{equation}
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\begin{center}
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\toprule
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\midrule
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col1 text & col2 text & col3 text \\
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\nocite{*}% Show all bib entries - both cited and uncited; comment this line to view only cited bib entries;
\bmsection*{Author Biography}
\begin{biography}{\includegraphics[width=76pt,height=76pt,draft]{empty}}{
{\textbf{Author Name.} Please check with the journal's author guidelines whether
author biographies are required. They are usually only included for
review-type articles, and typically require photos and brief
biographies for each author.}}
\end{biography}
\end{document}
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WileyNJDv5_Template/wileyNJDv5_AMA.tex deleted 100644 → 0
\documentclass[AMA,Times1COL]{WileyNJDv5} %STIX1COL,STIX2COL,STIXSMALL
\articletype{Article Type}%
\received{Date Month Year}
\revised{Date Month Year}
\accepted{Date Month Year}
\journal{Journal}
\volume{00}
\copyyear{2023}
\startpage{1}
\raggedbottom
\begin{document}
\title{Please insert your article title here}
\author[1]{Mark Taylor}
\author[2,3]{Author Two}
\author[3]{Author Three}
\authormark{TAYLOR \textsc{et al.}}
\titlemark{PLEASE INSERT YOUR ARTICLE TITLE HERE}
\address[1]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
\address[2]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
\address[3]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
\corres{Corresponding author Mark Taylor, This is sample corresponding address. \email{authorone@gmail.com}}
\presentaddress{This is sample for present address text this is sample for present address text.}
%\fundingInfo{Text}
%\JELinfo{ejlje}
\abstract[Abstract]{This is a generic template designed for use by multiple journals,
which includes several options for customization. Please
refer the author guidelines and author LaTeX manuscript preparation document for the journal to which you
are submitting in order to confirm that your manuscript will
comply with the journal’s requirements. Please replace this
text with your abstract. This is sample abstract text just for the template display purpose.}
\keywords{keyword1, keyword2, keyword3, keyword4}
\jnlcitation{\cname{%
\author{Taylor M.},
\author{Lauritzen P},
\author{Erath C}, and
\author{Mittal R}}.
\ctitle{On simplifying ‘incremental remap’-based transport schemes.} \cjournal{\it J Comput Phys.} \cvol{2021;00(00):1--18}.}
\maketitle
\renewcommand\thefootnote{}
\footnotetext{\textbf{Abbreviations:} ANA, anti-nuclear antibodies; APC, antigen-presenting cells; IRF, interferon regulatory factor.}
\renewcommand\thefootnote{\fnsymbol{footnote}}
\setcounter{footnote}{1}
\section{First level head}\label{sec1}
Please lay out your article using the section headings and the given body text is dummy text for layout purpose.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit \cite{Hirt1974}. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae,
felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec
vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus
sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel
leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur
auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
Duis eget orci sit amet orci dignissim rutrum.
\section{Another first level head}\label{sec2}
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus viverra
fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa ac
quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo \cite{Liska2010}. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa. Example for bibliography citation \cite{Taylor1937}, text \cite{Knupp1999,Kamm2000} inserted in text for your reference.
Quisque ullamcorper placerat ipsum. Cras nibh \cite{Kucharik2003,Blanchard2015}. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. (Figure \ref{fig1} and \ref{fig2}) Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congues
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
\begin{figure*}[t]
\centerline{\includegraphics[width=\textwidth,height=9pc,draft]{empty}}
\caption{This is the sample figure caption.\label{fig1}}
\end{figure*}
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
\begin{align*}
s(nT_{s}) &= s(t)\times \sum\limits_{n=0}^{N-1} \delta (t-nT_{s}) \xleftrightarrow{\mathrm{DFT}} S \left(\frac{m}{NT_{s}}\right) \nonumber\\[3pt]
&= \frac{1}{N} \sum\limits_{n=0}^{N-1} \sum\limits_{k=-N/2}^{N/2-1} s_{k} e^{\mathrm{j}2\pi k\Delta fnT_{s}} e^{-j\frac{2\pi}{N}mn}
\end{align*}
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non
odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor.
Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien
turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus.
\begin{figure*}
\centerline{\includegraphics[width=342pt,height=9pc,draft]{empty}}
\caption{This is the sample figure caption.\label{fig2}}
\end{figure*}
\subsection{Second level head}
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit, dictum
in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam vestibulum
fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi. Pellentesque
eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut mi mi, lacinia
sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui. Mauris nibh leo,
facilisis non, adipiscing quis, ultrices a, dui.
Morbi luctus, wisi viverra faucibus pretium, nibh est placerat odio, nec commodo wisi enim eget quam. Quisque
libero justo, consectetuer a, feugiat vitae, porttitor eu, libero. Suspendisse sed mauris vitae elit sollicitudin malesuada.
Maecenas ultricies eros sit amet ante. Ut venenatis velit. Maecenas sed mi eget dui varius euismod. Phasellus aliquet
volutpat odio. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque sit
amet pede ac sem eleifend consectetuer. Nullam elementum, urna vel imperdiet sodales, elit ipsum pharetra ligula,
ac pretium ante justo a nulla. Curabitur tristique arcu eu metus. Vestibulum lectus. Proin mauris. Proin eu nunc eu
urna hendrerit faucibus. Aliquam auctor, pede consequat laoreet varius, eros tellus scelerisque quam, pellentesque
hendrerit ipsum dolor sed augue. Nulla nec lacus.
\begin{quote}
This is an example \cite{Burton2013,Berndt2011,Kucharik2012} for quote text. This is an example for quote text. This is an example for quote text. This is an example for quote text \cite{Breil2015}. This is an example for quote text. This is an example for quote text. This is an example for quote text. This is an example for quote text. This is an example for quote text. This is an example for quote text \cite{Barth1997}. This is an example for quote text. This is an example for quote text. This is an example for quote text.
\end{quote}
\section{Example for another first level head}\label{sec3}
\subsection{Example for another second level head}
Suspendisse vitae elit. Aliquam arcu neque, ornare in, ullamcorper quis, commodo eu, libero. Fusce sagittis erat at
erat tristique mollis. Maecenas sapien libero, molestie et, lobortis in, sodales eget, dui. Morbi ultrices rutrum lorem.
Nam elementum ullamcorper leo. Morbi dui. Aliquam sagittis. Nunc placerat. Pellentesque tristique sodales est.
Maecenas imperdiet lacinia velit. Cras non urna. Morbi eros pede, suscipit ac, varius vel, egestas non, eros. Praesent
malesuada, diam id pretium elementum, eros sem dictum tortor, vel consectetuer odio sem sed wisi.
Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque
augue sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id, sapien. Nullam at lectus. In sagittis
ultrices mauris. Curabitur malesuada erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod.
Aenean vel lectus. Nunc imperdiet justo nec dolor.
\subsection{Second level head}
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
\subsubsection{Third level head}
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra tortor. Sed fringilla
justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue est scelerisque
sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas urna mi, suscipit
in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl.
\paragraph{Fourth level head}
Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque
augue sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id, sapien. Nullam at lectus. In sagittis
ultrices mauris. Curabitur malesuada erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod.
Aenean vel lectus. Nunc imperdiet justo nec dolor.
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
\subparagraph{Fifth level head.}
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra
tortor. Sed fringilla justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue
est scelerisque sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas
urna mi, suscipit in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl.
Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed
lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc
purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet.
In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus.
Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam
porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis.
Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque.
Vivamus eu dolor.
Nulla in ipsum. Praesent eros nulla, congue vitae, euismod ut, commodo a, wisi. Pellentesque habitant morbi
tristique senectus et netus et malesuada fames ac turpis egestas. Aenean nonummy magna non leo. Sed felis erat,
ullamcorper in, dictum non, ultricies ut, lectus. Proin vel arcu a odio lobortis euismod. Vestibulum ante ipsum primis
in faucibus orci luctus et ultrices posuere cubilia Curae; Proin ut est. Aliquam odio. Pellentesque massa turpis, cursus
eu, euismod nec, tempor congue, nulla. Duis viverra gravida mauris. Cras tincidunt. Curabitur eros ligula, varius ut,
pulvinar in, cursus faucibus, augue (Box~1).
Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed
lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc
purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet.
In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus.
Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam
porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis.
Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque.
Vivamus eu dolor.
\begin{boxwithhead}
{BOX 1\quad This is sample for Box head and text}
{\noindent This is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext. This is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext.}
\end{boxwithhead}
\begin{center}
\begin{table*}[!h]%
\caption{This is sample table caption.\label{tab1}}
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lllll@{}}
\toprule
&\multicolumn{2}{@{}l}{\textbf{Spanned heading$^{\tnote{\bf a}}$}} & \multicolumn{2}{@{}l}{\textbf{Spanned heading$^{\tnote{\bf b}}$}} \\\cmidrule{2-3}\cmidrule{4-5}
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} & {\textbf{Col4 head}} & \textbf{Col5 head} \\
\midrule
col1 text & col2 text & col3 text & 12.34 & col5 text\tnote{1} \\
col1 text & col2 text & col3 text & \hphantom{0}1.62 & col5 text\tnote{2} \\
col1 text & col2 text & col3 text & 51.809 & col5 text \\
\bottomrule
\end{tabular*}
\begin{tablenotes}%%[341pt]
\item[$^{\rm a}$] Example for a first table footnote.
\item[$^{\rm b}$] Example for a second table footnote.
\item {\it Source}: Example for table source text.
\end{tablenotes}
\end{table*}
\end{center}
Curabitur tellus magna, porttitor a, commodo a, commodo in, tortor. Donec interdum (Table~\ref{tab1}). Praesent scelerisque. Maecenas posuere sodales odio. Vivamus metus lacus, varius quis, imperdiet quis, rhoncus a, turpis. Etiam ligula arcu,
elementum a, venenatis quis, sollicitudin sed, metus. Donec nunc pede, tincidunt in, venenatis vitae, faucibus vel,
nibh. Pellentesque wisi. Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Etiam congue neque id dolor.
Donec et nisl at wisi luctus bibendum. Nam interdum tellus ac libero. Sed sem justo, laoreet vitae, fringilla at,
adipiscing ut, nibh. Maecenas non sem quis tortor eleifend fermentum. Etiam id tortor ac mauris porta vulputate.
Integer porta neque vitae massa. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat. Class aptent
taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Vivamus rhoncus tincidunt libero.
Etiam elementum pretium justo. Vivamus est. Morbi a tellus eget pede tristique commodo. Nulla nisl. Vestibulum
sed nisl eu sapien cursus rutrum.
\begin{boxtext}%
{\noindent This is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext this is sample for boxtext.}
\end{boxtext}
Nulla non mauris vitae wisi posuere convallis. Sed eu nulla nec eros scelerisque pharetra. Nullam varius. Etiam
dignissim elementum metus. Vestibulum faucibus, metus sit amet mattis rhoncus, sapien dui laoreet odio, nec ultricies
nibh augue a enim. Fusce in ligula. Quisque at magna et nulla commodo consequat. Proin accumsan imperdiet sem.
Nunc porta. Donec feugiat mi at justo. Phasellus facilisis ipsum quis ante. In ac elit eget ipsum pharetra faucibus.
Maecenas viverra nulla in massa (Table~\ref{tab2}).
Nulla in ipsum. Praesent eros nulla, congue vitae, euismod ut, commodo a, wisi. Pellentesque habitant morbi
tristique senectus et netus et malesuada fames ac turpis egestas. Aenean nonummy magna non leo. Sed felis erat,
ullamcorper in, dictum non, ultricies ut, lectus. Proin vel arcu a odio lobortis euismod. Vestibulum ante ipsum primis
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
\begin{table*}[!t]%
\centering %
\caption{This is sample table caption.\label{tab2}}%
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lllll@{\extracolsep\fill}}
\toprule
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} & \textbf{Col4 head} & \textbf{Col5 head} \\
\midrule
col1 text & col2 text & col3 text & col4 text & col5 text\tnote{$^\dagger$} \\
col1 text & col2 text & col3 text & col4 text & col5 text \\
col1 text & col2 text & col3 text & col4 text & col5 text\tnote{$^\ddagger$} \\
\bottomrule
\end{tabular*}
\begin{tablenotes}
\item[$^\dagger$] Example for a first table footnote.
\item[$^\ddagger$] Example for a second table footnote.
\item {\it Source}: Example for table source text.
\end{tablenotes}
\end{table*}
Below is the example \cite{Liska2010,Kucharik2003,Blanchard2015} for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list. Below is the example for bulleted list\footnote{This is an example for footnote.}:
\begin{itemize}
\item bulleted list entry sample bulleted list entry \cite{Lauritzen2011}, sample list entry text.
\item bulleted list entry sample bulleted list entry. bulleted list entry sample bulleted list entry. bulleted list entry sample bulleted list entry.
\item bulleted list entry sample bulleted list entry \cite{Klima2017}, bulleted list entry sample bulleted list entry \cite{Dukowicz2000}, sample list entry text. bulleted list entry sample bulleted list entry.
\item sample list entry text. sample list entry text.
\end{itemize}
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non
odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien
turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus.
Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the sample for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list. Below is the example for description list:\vskip12pt
\noindent\textbf{Description sample:}
\begin{description}
\item[first entry] description text, description text \cite{Kucharik2011,Kucharik2014,Loubere2005}. description text, description text, description text, description text, description text.
\item[second long entry] description text, description text, description text, description text, description text, description text, description text.
\item[third entry] description text, description text, description text, description text, description text.
\item[fourth entry] description text, description text.
\end{description}
\noindent\textbf{Numbered list items sample:}
\begin{enumerate}[1.]
\item First level numbered list entry, sample numbered list entry.
\item First numbered list entry, sample numbered list entry. Numbered list entry \cite{Caramana1998}, sample numbered list entry. Numbered list entry, sample numbered list entry.
\begin{enumerate}[a.]
\item Second level alpabetical list entry. Second level alpabetical list entry. Second level alpabetical list entry \cite{Hoch2009}. Second level alpabetical list entry.
\item Second level alpabetical list entry. Second level alpabetical list entry \cite{Shashkov1996,Knupp1999,Knupp1999}.
\begin{enumerate}[i.]
\item Third level lowercase roman numeral list entry. Third level lowercase roman numeral list entry. Third level lowercase roman numeral list entry.
\item Third level lowercase roman numeral list entry. Third level lowercase roman numeral list entry. \cite{Kamm2000}
\end{enumerate}
\item Second level alpabetical list entry. Second level alpabetical list entry \cite{Taylor1937}.
\end{enumerate}
\item First level numbered list entry, sample numbered list entry. Numbered list entry, sample numbered list entry. Numbered list entry.
\item Another first level numbered list entry, sample numbered list entry. Numbered list entry, sample numbered list entry. Numbered list entry.
\end{enumerate}
\noindent\textbf{un-numbered list items sample:}
\begin{enumerate}[]
\item Sample unnumberd list text.
\item Sample unnumberd list text.
\item sample unnumberd list text.
\item Sample unnumberd list text.
\end{enumerate}
\section{Examples for enunciations}\label{sec4}
\begin{theorem}\label{thm1}
Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text. Example theorem text.
\end{theorem}
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
\begin{proposition}
Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text. Example proposition text.
\end{proposition}
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
\begin{definition}
Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text. Example definition text.
\end{definition}
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non
odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce
sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor.
Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin
et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien
turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus.
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam
vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi.
Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut
mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui.
Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui.
\begin{proof}
Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text.
\end{proof}
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
\begin{proof}[Proof of Theorem~{\rm\ref{thm1}}]
Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text. Example for proof text.
\end{proof}
\begin{sidewaystable}%[h]
\def\d{\hphantom{0}}
\caption{Sideways table caption. For decimal alignment refer column 4 to 9 in tabular* preamble.\label{tab3}}%
\begin{tabular*}{\textheight}{@{\extracolsep\fill}lllllllll@{\extracolsep\fill}}%
\toprule
& \textbf{Col2 head} & \textbf{Col3 head} & \multicolumn{1}{l}{\textbf{10}} &\multicolumn{1}{l}{\textbf{20}} &\multicolumn{1}{l}{\textbf{30}} &\multicolumn{1}{l}{\textbf{10}} &\multicolumn{1}{l}{\textbf{20}} &\multicolumn{1}{l}{\textbf{30}} \\
\midrule
&col2 text &col3 text &\d0.7568&\d1.0530&\d1.2642&\d0.9919&\d1.3541&\d1.6108 \\
& &col2 text &12.5701 &19.6603&25.6809&18.0689&28.4865&37.3011 \\
3 &col2 text & col3 text &\d0.7426&\d1.0393&\d1.2507&\d0.9095&\d1.2524&\d1.4958 \\
& &col3 text &12.8008&19.9620&26.0324&16.6347&26.0843&34.0765 \\
& col2 text& col3 text &\d0.7285&\d1.0257&\d1.2374&\d0.8195&\d1.1407&\d1.3694* \\
& & col3 text &13.0360&20.2690&26.3895&15.0812&23.4932&30.6060\tnote{$\dagger$} \\
\bottomrule
\end{tabular*}
\begin{tablenotes}%%[\textheight]
\item[*] First sideways table footnote. Sideways table footnote. Sideways table footnote. Sideways table footnote.
\item[$^\dagger$] Second sideways table footnote. Sideways table footnote. Sideways table footnote. Sideways table footnote.
\end{tablenotes}
\end{sidewaystable}
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra tortor. Sed fringilla
justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue est scelerisque
sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas urna mi, suscipit
in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl (Table~\ref{tab3}).
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam
vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi (Figure~\ref{fig3}).
Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut Curabitur tellus magna, porttitor a, commodo a, commodo in, tortor. Donec interdum. Praesent scelerisque. Mae-
cenas posuere sodales odio. Vivamus metus lacus, varius quis, imperdiet quis, rhoncus a, turpis. Etiam ligula arcu,
elementum a, venenatis quis, sollicitudin sed, metus. Donec nunc pede, tincidunt in, venenatis vitae, faucibus vel.
\begin{sidewaysfigure}
\centerline{\includegraphics[width=542pt,height=9pc,draft]{empty}}
\caption{Sideways figure caption. Sideways figure caption. Sideways figure caption. Sideways figure caption. Sideways figure caption. Sideways figure caption.\label{fig3}}
\end{sidewaysfigure}
Pellentesque wisi. \cite{Kucharik2012} Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Etiam congue neque id dolor.
\begin{algorithm}
\caption{\enskip Pseudocode for our algorithm}\label{alg1}
\begin{algorithmic}
\For each frame
\For water particles $f_{i}$
\State compute fluid flow \cite{Hirt1974}
\State compute fluid--solid interaction \cite{Benson1992}
\State apply adhesion and surface tension \cite{Margolin2003}
\EndFor
\For solid particles $s_{i}$
\For neighboring water particles $f_{j}$
\State compute virtual water film \\(see Section~\ref{sec3})
\EndFor
\EndFor
\For solid particles $s_{i}$
\For neighboring water particles $f_{j}$
\State compute growth direction vector \\(see Section~\ref{sec2})
\EndFor
\EndFor
\For solid particles $s_{i}$
\For neighboring water particles $f_{j}$
\State compute $F_{\theta}$ (see Section~\ref{sec1})
\State compute $CE(s_{i},f_{j})$ \\(see Section~\ref{sec3})
\If $CE(b_{i}, f_{j})$ $>$ glaze threshold
\State $j$th water particle's phase $\Leftarrow$ ICE
\EndIf
\If $CE(c_{i}, f_{j})$ $>$ icicle threshold
\State $j$th water particle's phase $\Leftarrow$ ICE
\EndIf
\EndFor
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm}
Donec et nisl at wisi luctus bibendum. Nam interdum tellus ac libero. Sed sem justo, laoreet vitae, fringilla at,
adipiscing ut, nibh. Maecenas non sem quis tortor eleifend fermentum. Etiam id tortor ac mauris porta vulputate.
Integer porta neque vitae massa \cite{Hirt1974,Benson1992}. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat. Class aptent
taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Vivamus rhoncus tincidunt libero.
Etiam elementum pretium justo. Vivamus est. Morbi a tellus eget pede tristique commodo \cite{Benson1992}. Nulla nisl. Vestibulum
sed nisl eu sapien cursus rutrum.
Pellentesque wisi. Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Etiam congue neque id dolor.
Donec et nisl at wisi luctus bibendum. Nam interdum tellus ac libero. Sed sem justo, laoreet vitae, fringilla at,
adipiscing ut, nibh. Integer porta neque vitae massa. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat.
Maecenas non sem quis tortor eleifend fermentum. Etiam id tortor ac mauris porta vulputate.
Integer porta neque vitae massa. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in
faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat. Class aptent
taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Vivamus rhoncus tincidunt libero.
Etiam elementum pretium justo. Vivamus est. Morbi a tellus eget pede tristique commodo. Nulla nisl. Vestibulum
sed nisl eu sapien cursus rutrum.
\begin{align}\label{eq23}
\|\tilde{X}(k)\|^2
&=\frac{\left\|\sum\limits_{i=1}^{p}\tilde{Y}_i(k)+\sum\limits_{j=1}^{q}\tilde{Z}_j(k) \right\|^2}{(p+q)^2} \nonumber\\
& \leq\frac{\sum\limits_{i=1}^{p}\left\|\tilde{Y}_i(k)\right\|^2+\sum\limits_{j=1}^{q}\left\|\tilde{Z}_j(k)\right\|^2 }{p+q}.
\end{align}
Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque
augue sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id, sapien. Nullam at lectus. In sagittis
ultrices mauris. Curabitur malesuada erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod.
Aenean vel lectus. Nunc imperdiet justo nec dolor.
Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper
eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien
facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam
a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
\begin{align}\label{eq24}
\|\tilde{X}(k)\|^2
&=\frac{\left\|\sum\limits_{i=1}^{p}\tilde{Y}_i(k)+\sum\limits_{j=1}^{q}\tilde{Z}_j(k) \right\|^2}{(p+q)^2}\nonumber\\
& \leq\frac{\sum\limits_{i=1}^{p}\left\|\tilde{Y}_i(k)\right\|^2+\sum\limits_{j=1}^{q}\left\|\tilde{Z}_j(k)\right\|^2 }{p+q}.
\end{align}
Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra
tortor. Sed fringilla justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue
est scelerisque sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas
urna mi, suscipit in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl.
Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed
lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc
purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet.
In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus.
Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam
porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis.
Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque.
Vivamus eu dolor.
\section{Conclusions}\label{sec5}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae,
felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec
vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus
sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel
leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur
auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
Duis eget orci sit amet orci dignissim rutrum.
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
%\backmatter
\bmsection*{Author contributions}
This is an author contribution text. This is an author contribution text. This is an author contribution text. This is an author contribution text. This is an author contribution text.
\bmsection*{Acknowledgments}
This is acknowledgment text. \cite{Kenamond2013} Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here. This is acknowledgment text. Provide text here.
\bmsection*{Financial disclosure}
None reported.
\bmsection*{Conflict of interest}
The authors declare no potential conflict of interests.
\bibliography{wileyNJD-AMA}
\bmsection*{Supporting information}
Additional supporting information may be found in the
online version of the article at the publisher’s website.
\appendix
\bmsection{Program codes appear in Appendix\label{app1}}
\vspace*{12pt}
Using the package {\tt listings} you can add non-formatted text as you would do with \verb|\begin{verbatim}| but its main aim is to include the source code of any programming language within your document.\newline Use \verb|\begin{lstlisting}...\end{lstlisting}| for program codes without mathematics.
The {\tt listings} package supports all the most common languages and it is highly customizable. If you just want to write code within your document, the package provides the {\tt lstlisting} environment; the output will be in Computer Modern typewriter font. Refer to the below example:
\begin{lstlisting}[caption={Descriptive caption text},label=DescriptiveLabel, basicstyle=\fontsize{8}{10}\selectfont\ttfamily]
for i:=maxint to 0 do
begin
{ do nothing }
end;
Write('Case insensitive ');
WritE('Pascal keywords.');
\end{lstlisting}
\bmsubsection{Subsection title of first appendix\label{app1.1a}}
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
\bmsubsubsection{Subsection title of first appendix\label{app1.1.1a}}
\noindent\textbf{Unnumbered figure}
\begin{center}
\includegraphics[width=7pc,height=8pc,draft]{empty}
\end{center}
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
\bmsection{Section title of second appendix\label{app2}}%
\vspace*{12pt}
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et
vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla (Figure~\ref{fig5}).
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu
ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum
eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et
convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non,
pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio.
%== Figure 4 ==
%% Example for figure inside appendix
\begin{figure}[b]
\centerline{\includegraphics[height=10pc,width=78mm,draft]{empty}}
\caption{This is an example for appendix figure.\label{fig5}}
\end{figure}
\bmsubsection{Subsection title of second appendix\label{app2.1a}}
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non odio.
Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce sed justo
eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec
pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin et quam.
Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien turpis,
fermentum vel, eleifend faucibus, vehicula eu, lacus.
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam
vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi.
Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut
mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui.
Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui.
\bmsubsubsection{Subsection title of second appendix\label{app2.1.1a}}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae,
felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec
vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus
sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel
leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur
auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
Duis eget orci sit amet orci dignissim rutrum (Table~\ref{tab4}).
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
\begin{table*}[t]%
\centering
\caption{This is an example of Appendix table showing food requirements of army, navy and airforce.\label{tab4}}%
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}llllll@{\extracolsep\fill}}%
\toprule
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} & \textbf{Col4 head} & \textbf{Col5 head} & \textbf{Col6 head} \\
\midrule
col1 text & col2 text & col3 text & col4 text & col5 text & col6 text\\
col1 text & col2 text & col3 text & col4 text & col5 text & col6 text\\
col1 text & col2 text & col3 text& col4 text & col5 text & col6 text\\
\bottomrule
\end{tabular*}
\end{table*}
Example for an equation inside appendix
\begin{equation}
{\mathcal{L}} = i \bar{\psi} \gamma^\mu D_\mu \psi - \frac{1}{4} F_{\mu\nu}^a F^{a\mu\nu} - m \bar{\psi} \psi\label{eq25}
\end{equation}
\bmsection{Example of another appendix section\label{app3}}%
\vspace*{12pt}
This is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text this is sample for paragraph text
Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero,
pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna,
vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque
a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt
urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris.
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
\begin{equation}
\mathcal{L} = i \bar{\psi} \gamma^\mu D_\mu \psi
- \frac{1}{4} F_{\mu\nu}^a F^{a\mu\nu} - m \bar{\psi} \psi
\label{eq26}
\end{equation}
Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus
viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend
at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia
nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec
bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum
pellentesque felis eu massa.
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
\begin{center}
\begin{tabular*}{250pt}{@{\extracolsep\fill}lcc@{\extracolsep\fill}}%
\toprule
\textbf{Col1 head} & \textbf{Col2 head} & \textbf{Col3 head} \\
\midrule
col1 text & col2 text & col3 text \\
col1 text & col2 text & col3 text \\
col1 text & col2 text & col3 text \\
\bottomrule
\end{tabular*}
\end{center}
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit
amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat
quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor
vitae risus porta vehicula.
Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac
venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue
quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla
facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, evehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla.
Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer.
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit,
dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam
vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi.
Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut
mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui.
Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui.
\nocite{*}% Show all bib entries - both cited and uncited; comment this line to view only cited bib entries;
\bmsection*{Author Biography}
\begin{biography}{\includegraphics[width=76pt,height=76pt,draft]{empty}}{
{\textbf{Author Name.} Please check with the journal's author guidelines whether
author biographies are required. They are usually only included for
review-type articles, and typically require photos and brief
biographies for each author.}}
\end{biography}
\end{document}
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