Behavior Of Complex Systems Research Articles

Exploring Tsallis thermodynamics for boundary conformal field theories in gauge/gravity duality

Inspired by AdS/CFT interpretation Karch and Robinson (2015), we analyze thermodynamics for thermal boundary conformal field theories (CFT) that are dual to four-dimensional charged anti-de Sitter (AdS) black holes embedded in 11-dimensional M-theory-inspired models with AdS4×S7 space–time, employing the framework of Tsallis entropy. The latter is recognized as a nonadditive extension of the Boltzmann–Gibbs entropy that can satisfy the thermodynamic extensivity for black holes. Specifically, we consider AdS black holes in AdS4×S7 spacetime, interpreting the number of M2-branes as a thermodynamic variable. Using the Tsallis entropy enables us to highlight peculiar thermodynamic features, resorting to essential tools such as the chemical potential and Gibbs energy while examining phase transitions along iso-charge partitions. Then, we leveraged a class of geometrothermodynamic formalisms, including Weinhold, Ruppeiner, Quevedo I, and II metrics. Quevedo’s formulations provide richer information about phase transitions than the first two methods. Our study sheds new light on AdS black holes in a thermodynamically proper context, deepening our understanding of the role of non-extensivity in the critical behavior of such complex systems.

Effect of repulsive interaction and initial velocity on collective motion process.

Self-propelled collective motion is a highly complex phenomenon, necessitating advanced practical and theoretical tools for comprehension. The significance of studying collective motion becomes apparent in its diverse applications. For instance, addressing evacuation challenges in scenarios with multiple agents can be achieved through an examination of collective motion. Research indicates that the transition of individuals (such as birds, fish, etc.) from a state of rest to equilibrium constitutes a phase transition. Our interest of the issue is to delve into the nature of this transitional phase and elucidate the parameters that shape it. Hence, the primary aim of this paper is to grasp the kinetic phase transition by examining how initial velocity and repulsive interactions impact the dynamics of the system. To gain insight into the complex behavior of multi-agent systems, we apply an extended version of the classical Vicsek model. This extension includes an additional interaction zone, the repulsive zone, where particles repel each other at close range to avoid collisions. Our study uses numerical simulations to explore the system's behavior under various conditions. The focus of this study is the impact of initial velocity on the collective movement of particles. The importance of this research lies in comprehending how velocity affects the overall movement. The conclusion we can draw from these results is that the initial velocity affects both the noise and the density. The novelty of the work is the transition phase, yet it lacks universal characteristics because the critical noise depends on the initial velocity system and the repulsion radius zone. Notably, the repulsion radius and particle density play pivotal roles in achieving a phase transition from one equilibrium state to another aligned equilibrium state.

Effect of autaptic synapse on signal transmission performance of dressed Hodgkin–Huxley neuron

Astrocytes, which have complex relationships with neurons, are the most important biological arguments that support neurons in the performance of cognitive functions. Another important biological argument in nervous systems is autapse, a special type of synapse through which the neuron provides feedback to itself. It is well known that both astrocyte and autapse modulate neuron dynamics and they affect memory functions. Considering the idea that some cognitive brain functions occur through chaotic firings, more complex models in which structures such as astrocytes and autaptic synapses are included in the system are needed to better understand the neural system. In this study, the signal detection abilities of astrocyte-dressed Hodgkin–Huxley neurons which have electrical, excitatory, and inhibitory chemical autaptic synapses are examined separately under chaotic environmental conditions. The results show that astrocyte-supported neurons, especially those with electrical and excitatory-chemical autapse, exhibit a strong chaotic resonance for appropriate parameters. After the autaptic synapse, the astrocyte is a second modulator of the neuron’s signal detection success. Additionally, it is observed that autaptic time delay is more effective than autaptic conductance in modulating the signal transmission success of the neuron. For all autapse types, the parameter values at which the supportive effect of the astrocyte in the model is obtained are presented. Furthermore, multiple chaotic resonance is detected in neurons with electrical and excitatory chemical autapse when the autaptic delay is equal to integer multiples of the weak signal period. This is observed for neurons with inhibitory chemical autapse when half of the weak signal period is added to whole multiples of the weak signal period. We hope that our findings will shed light on the chaotic environment behavior of complex nervous systems interacting with astrocytes and autapse.

Stirring digital innovation in wood waste upcycling: system dynamics as a circular design decision-making methodology

Abstract The urgency to reduce climate-changing emissions and natural resources exploitation is pushing architecture and industrial design to explore viable options to innovate current practices on material use. In forest-based industries, in particular, wood upcycling is emerging as a pivotal investigation field, with a specific research agenda aimed at reducing the impacts generated by the rising demand of timber products and the actual incineration and landfilling rates. Indeed, the development of new technological solutions needs to account for energy and material flows, as well as for the environmental impacts and social and economic dynamics. Such a new complexity pushes towards a design approach that links digital technologies to circularity goals for a more comprehensive understanding of the forest-based resource management and the evalutation of alternative scenarios. In this paper, we propose System Dynamics (SD) as a methodology to provide a qualitative and quantitative framework to promote digital circular innovation in the wood industry. SD is a dynamic, multi-scale, multi-dimension and site-specific decision-making support tool wich helps designers, researchers and industrial stakeholders to understand and simulate the dynamic behavior and performances of complex systems within specific time and space parameters. The proposed SD for wood waste upcycling allows to model “stock and flow” scenarios, to simulate and compare the consequences of technological options on the system and to target their development in time - and space-based projections. This study outlines the first advances for the SD application to the Italian wood industry, and examines the consequences of the application of different circular strategies on a “business-as-usual” scenario.

Comparative Study of LSTM and ANN Models for Power Consumption Prediction of Variable Refrigerant Flow (VRF) Systems in Buildings

The optimized control of variable refrigerant flow (VRF) system requires an accurate time series forecast model for power consumption. Currently, physics-based and black-box models widely used for forecasting power consumption may not be able to capture the dynamic and non-linear behavior of such complex systems. This study presents a long-short-term memory (LSTM), deep learning-based model to accurately predict the power consumption of a VRF system with heat recovery units. The model training used one year of VRF system field test data. The feature selection through the Pearson correlation coefficient was implemented to improve the model's accuracy and computational efficiency. The sensitivity analysis of feature selection was performed by preparing three feature sets, including different levels of relationship with the predicted target. Additionally, the hyperparameters of the models were optimized by Bayesian optimization with the Tree-structured Parzen Estimator algorithm. The deep learning model, LSTM model, was compared to the baseline machine learning model, Artificial Neural Network (ANN) and decision tree. The results show that LSTM-30feat with input time step 4 has the best testing performance of Coefficient of the Variation of the Root Mean Square Error (CvRMSE) 23.3%. The best ANN model is ANN-10feat with input time step 8, which has a CvRMSE of 27.8% in testing and 13,569 trainable parameters. However, LSTM-10feat with input time step 4 has the CvRMSE of 24.8% in testing, and the trainable parameters are 1,809. A higher number of trainable parameters in models might result in increased memory usage on the computer and be computationally expensive.

Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles.

Understanding the behavior of complex molecular systems is a fundamental problem in physical chemistry. To describe the long-time dynamics of such systems, which is responsible for their most informative characteristics, we can identify a few slow collective variables (CVs) while treating the remaining fast variables as thermal noise. This enables us to simplify the dynamics and treat it as diffusion in a free-energy landscape spanned by slow CVs, effectively rendering the dynamics Markovian. Our recent statistical learning technique, spectral map [Rydzewski, J. J. Phys. Chem. Lett. 2023, 14(22), 5216-5220], explores this strategy to learn slow CVs by maximizing a spectral gap of a transition matrix. In this work, we introduce several advancements into our framework, using a high-dimensional reversible folding process of a protein as an example. We implement an algorithm for coarse-graining Markov transition matrices to partition the reduced space of slow CVs kinetically and use it to define a transition state ensemble. We show that slow CVs learned by spectral map closely approach the Markovian limit for an overdamped diffusion. We demonstrate that coordinate-dependent diffusion coefficients only slightly affect the constructed free-energy landscapes. Finally, we present how spectral maps can be used to quantify the importance of features and compare slow CVs with structural descriptors commonly used in protein folding. Overall, we demonstrate that a single slow CV learned by spectral map can be used as a physical reaction coordinate to capture essential characteristics of protein folding.

Soliton and lump and travelling wave solutions of the (3 + 1) dimensional KPB like equation with analysis of chaotic behaviors

Nonlinear evolution equations (NLEEs) have a wide range of applications in various fields, including physics, engineering, biology, economics, and more. These equations are used to describe complex systems that change over time, where the state or behavior of the system not only depends on the current situation, but may also be related to the past. A deep understanding of the solutions to NLEEs is of great significance for predicting and controlling the behavior of complex systems. The (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like (KPB-like) equation represents a partial differential equation that describes nonlinear wave phenomena in multi-dimensional spaces. This model is commonly employed in fields such as fluid dynamics, plasma physics, and nonlinear optics to study wave behaviors. This paper investigates the KPB-like equations, which have meaningful physical implications in describing nonlinear wave phenomena. Hirota bilinear method is employed to derive the bilinear form for the KPB-like equation and 1-soliton, 2-soliton, lump, and travelling wave solutions are studied to this kind of nonlinear model. In addition, the chaotic behaviors of soliton and lump solutions are explored via applying the Duffing chaotic system. To have a better understanding of dynamic structures, 3D, line, density and contour map plots of begotten results are displayed. Our results indicate the directness and effectiveness of the applied method for analyzing high-dimensional differential equations that arise in nonlinear science.

The analysis of the application of chaos and fractals

In 1963, Edward Norton Lorenz, the American meteorologist, proposed the chaos theory. Nonlinear systems exhibit diversity and multiscale characteristics, while chaos theory explains how deterministic systems can produce random results. These theories offer a new perspective to understand and describe complex systems and have found wide application in various fields such as physics, biology, meteorology, and economics. With advancements in computer technology, researches in chaos and fractals have also made significant progresses. This paper uses a literature review approach to provide a summary and synthesis of existing researches and literature. It briefly introduces the development of chaos and fractals and elaborates on their applications in daily life. It also analyzes the limitations of these theories and the challenges they are facing. By reviewing the core concepts of chaos and fractals such as mathematical principles and specific practices in different disciplines, this paper aims to enhance readers' understanding of the behavior of complex systems and to anticipate future development trends in chaos and fractals. This will help further promote the implementation and innovation of these theories in scientific research and practical applications, providing new ideas for theoretical development.

Probabilistic Performance-Pattern Decomposition (PPPD): Analysis framework and applications to stochastic mechanical systems

Numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as “solved” when a complete or partial probabilistic description on quantities of interest (QoIs) is determined. However, in the presence of complex system behavior, there is a critical need to go beyond computing probabilities. In fact, to gain a better understanding of the system, it is crucial to extract physical characterizations from the probabilistic structure of the QoIs, especially when the QoIs are computed in a data-driven fashion. Motivated by this perspective, the paper proposes a framework to obtain structuralized characterizations on behaviors of stochastic systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD). PPPD analysis aims to decompose complex response behaviors, conditional to a prescribed performance state, into meaningful patterns in the space of system responses, and to investigate how the patterns are triggered in the space of basic random variables. To illustrate the application of PPPD, the paper studies three numerical examples: (1) an illustrative example with hypothetical stochastic processes input and output; (2) a stochastic Lorenz system with periodic as well as chaotic behaviors; and (3) a simplified shear-building model subjected to a stochastic ground motion excitation.

Simulation experiment design for calibration via active learning

Simulation models often have parameters as input and return outputs to understand the behavior of complex systems. Calibration is the process of estimating the values of the parameters in a simulation model in light of observed data from the system that is being simulated. When simulation models are expensive, emulators are built with simulation data as a computationally efficient approximation of an expensive model. An emulator then can be used to predict model outputs, instead of repeatedly running an expensive simulation model during the calibration process. Sequential design with an intelligent selection criterion can guide the process of collecting simulation data to build an emulator, making the calibration process more efficient and effective. This article proposes two novel criteria for sequentially acquiring new simulation data in an active learning setting by considering uncertainties on the posterior density of parameters. Analysis of several simulation experiments and real-data simulation experiments from epidemiology demonstrates that proposed approaches result in improved posterior and field predictions.

Simulating Noise, Vibration, and Harshness Advances in Electric Vehicle Powertrains: Strategies and Challenges

This study examines the management of noise, vibration, and harshness (NVH) in electric vehicle (EV) powertrains, considering the challenges of the automotive industry’s transition to electric drivetrains. The growing popularity of electric vehicles brings new NVH challenges as the lack of internal combustion engine noise makes drivetrain noise more prominent. The key to managing NVH in electric vehicle powertrains is understanding the noise from electric motors, inverters, and gear systems. Noise from electric motors, mainly resulting from electromagnetic forces and high-frequency noise generated by inverters, significantly impacts overall NVH performance. This article details sources of mechanical noise and vibration, including gear defects in gear systems and shaft imbalances. The methods presented in the publication include simulation and modeling techniques that help identify and solve NVH difficulties. Tools like multi-body dynamics, the finite element method, and multi-domain simulation are crucial for understanding the dynamic behavior of complex systems. With the support of simulations, engineers can predict noise and vibration challenges and develop effective solutions during the design phase. This study emphasizes the importance of a system-level approach in NVH management, where the entire drivetrain is modeled and analyzed together, not just individual components.

Soliton, breather, lump, interaction solutions and chaotic behavior for the (2+1)-dimensional KPSKR equation

Nonlinear evolution equations are widely applied in various fields, and understanding their solutions is crucial for predicting and controlling the behavior of complex systems. In this paper, the (2+1)-dimensional Kadomtsev–Petviashvili–Sawada–Kotera–Ramani (KPSKR) equation is investigated, which has rich physical significance in nonlinear waves. Making use of Hirota’s bilinear form, soliton, breather and lump solutions of the (2+1)-dimensional KPSKR equation are derived. The interactions between lump solutions and exponential function, as well as between lump solutions and hyperbolic cosine function, are explored. Furthermore, the chaotic behavior of 1-soliton, 2-soliton, lump and interaction solutions are studied via applying the Duffing chaotic system. The physical structure and characteristics of begotten results are illustrated through 3D plots and corresponding two-dimensional profiles. These results indicate that the strategies utilized are more direct and effective, enriching the study of dynamics in high-dimensional nonlinear differential equations.

Modeling the Immune System Through Agent-based Modeling: A Mini-review

The immune system plays a critical role in protecting the human body against various pathogens and diseases. Understanding the complexity and dynamics of the immune system is essential for developing effective therapies and interventions. Agent-based modeling (ABM) has emerged as a powerful tool for simulating and studying the behavior of complex systems, including the immune system. This review examines the advantages, challenges, and applications of ABM in immune system modeling. ABM captures the complexity of immune cell behavior, spatial effects and stochasticity. It has been applied to study immune cell dynamics, immune responses to pathogens, immune cell migration, immunotherapies and immune system disorders. Challenges include parameterization, validation, and computational resource requirements. Future directions involve integrating multi-omics and single-cell data, incorporating machine learning, exploring multi-scale modeling, and developing user-friendly interfaces. ABM holds promise for enhancing our understanding of immune system dynamics and advancing diagnostics and treatments in immunology.

The analysis of chaos and fractals

Chaos and fractals are closely interconnected ideas in the field of mathematics. The behavior of complex systems is characterized by chaos, which is the result of excessive sensitivity to initial conditions, leading to unpredictable and random consequences. Fractals are geometric patterns that display self-similarity at many scales. This paper examines the complex connection between chaos and fractals using a method of theoretical analysis and a comprehensive examination of relevant literature. Studying the connection between chaos science and fractals can provide valuable insights into chaotic events in nonlinear dynamical systems. Furthermore, this investigation enables readers to understand the underlying fractal nature of such systems. Gaining insight into this correlation not only enhances comprehension of the fundamental principles that control intricate systems, but also provides opportunities for utilization in other domains, spanning from physics to biology and beyond.

Non-adiabatic dynamics of photoexcited cyclobutanone: Predicting structural measurements from trajectory surface hopping with XMS-CASPT2 simulations.

Over the years, theoretical calculations and scalable computer simulations have complemented ultrafast experiments, as they offer the advantage of overcoming experimental restrictions and having access to the whole dynamics. This synergy between theory and experiment promises to yield a deeper understanding of photochemical processes, offering valuable insights into the behavior of complex systems at the molecular level. However, the ability of theoretical models to predict ultrafast experimental outcomes has remained largely unexplored. In this work, we aim to predict the electron diffraction signals of an upcoming ultrafast photochemical experiment using high-level electronic structure calculations and non-adiabatic dynamics simulations. In particular, we perform trajectory surface hopping with extended multi-state complete active space with second order perturbation simulations for understanding the photodissociation of cyclobutanone (CB) upon excitation at 200nm. Spin-orbit couplings are considered for investigating the role of triplet states. Our simulations capture the bond cleavage after ultrafast relaxation from the 3s Rydberg state, leading to the formation of the previously observed primary photoproducts: CO + cyclopropane/propene (C3 products), ketene, and ethene (C2 products). The ratio of the C3:C2 products is found to be about 1:1. Within 700fs, the majority of trajectories transition to their electronic ground state, with a small fraction conserving the initial cyclobutanone ring structure. We found a minimal influence of triplet states during the early stages of the dynamics, with their significance increasing at later times. We simulate MeV-ultrafast electron diffraction (UED) patterns from our trajectory results, linking the observed features with specific photoproducts and the underlying structural dynamics. Our analysis reveals highly intense features in the UED signals corresponding to the photochemical processes of CB. These features offer valuable insights into the experimental monitoring of ring opening dynamics and the formation of C3 and C2 photoproducts.

Analyzing Convergence in Sequences of Uncountable Iterated Function Systems—Fractals and Associated Fractal Measures

In this paper, we examine a sequence of uncountable iterated function systems (U.I.F.S.), where each term in the sequence is constructed from an uncountable collection of contraction mappings along with a linear and continuous operator. Each U.I.F.S. within the sequence is associated with an attractor, which represents a set towards which the system evolves over time, a Markov-type operator that governs the probabilistic behavior of the system, and a fractal measure that describes the geometric and measure-theoretic properties of the attractor. Our study is centered on analyzing the convergence properties of these systems. Specifically, we investigate how the attractors and fractal measures of successive U.I.F.S. in the sequence approach their respective limits. By understanding the convergence behavior, we aim to provide insights into the stability and long-term behavior of such complex systems. This study contributes to the broader field of dynamical systems and fractal geometry by offering new perspectives on how uncountable iterated function systems evolve and stabilize. In this paper, we undertake a comprehensive examination of a sequence of uncountable iterated function systems (U.I.F.S.), each constructed from an uncountable collection of contraction mappings in conjunction with a linear and continuous operator. These systems are integral to our study as they encapsulate complex dynamical behaviors through their association with attractors, which represent sets towards which the system evolves over time. Each U.I.F.S. within the sequence is governed by a Markov-type operator that dictates its probabilistic behavior and is described by a fractal measure that captures the geometric and measure-theoretic properties of the attractor. The core contributions of our work are presented in the form of several theorems. These theorems tackle key problems and provide novel insights into the study of measures and their properties in Hilbert spaces. The results contribute to advancing the understanding of convergence behaviors, the interaction of Dirac measures, and the applications of Monge–Kantorovich norms. These theorems hold significant potential applications across various domains of functional analysis and measure theory. By establishing new results and proving critical properties, our work extends existing frameworks and opens new avenues for future research. This paper contributes to the broader field of mathematical analysis by offering new perspectives on how uncountable iterated function systems evolve and stabilize. Our findings provide a foundational understanding that can be applied to a wide range of mathematical and real-world problems. By highlighting the interplay between measure theory and functional analysis, our work paves the way for further exploration and discovery in these areas, thereby enriching the theoretical landscape and practical applications of these mathematical concepts.

الحلول شبه التحليلية لمعادلات فيشر الكسرية للزمن عبر الطريقة التكرارية الجديدة

إحدى الطرق الفعالة لحل المعادلات التفاضلية الجزئية غير الخطية ذات المشتقات الكسرية هي الطريقة التكرارية لتحويل سومودو الجديدة (NSTIM). إنه يبرع في حل الألغاز الرياضية الصعبة ويقدم معلومات ثاقبة حول سلوك معادلات فيشر ذات الكسر الزمني. الطريقة، التي تستخدم مشتقات كابوتو الحسية وWolfram في Mathematica، موثوقة وسهلة الاستخدام وتعطي تصويرًا مرئيًا للحل. أظهرت النتائج التحليلية أن الطريقة المقترحة فعالة وبسيطة في توليد حلول دقيقة لمعادلات فيشر الكسرية للزمن. أصبحت النتائج أكثر موثوقية وقابلة للتطبيق من خلال تضمين مشتقات كابوتو الحسية. تعتمد النمذجة الرياضية على فعالية وبساطة منهج NSTIM لحل معادلات فيشر ذات الكسر الزمني لأنها تتيح حلولاً دقيقة دون استخدام الكثير من قوة المعالجة. يعد نهج NSTIM أداة مفيدة للباحثين في مجموعة متنوعة من المجالات لأنه يوفر أيضًا إطارًا مرنًا يمكن تعديله بسهولة مع المعادلات التفاضلية الكسرية الأخرى. أصبح من الممكن الآن فحص ديناميكيات وسلوك الأنظمة المعقدة التي تحكمها معادلات فيشر الكسرية الزمنية بكفاءة وموثوقية، مما يفتح طرقًا بحثية جديدة. إن القدرة على حل معادلات فيشر ذات الكسور الزمنية بكفاءة وموثوقية باستخدام نهج NSTIM لها آثار مهمة على مجالات مختلفة مثل الديناميات السكانية والبيولوجيا الرياضية وعلم الأوبئة. يمكن للباحثين الآن تحليل انتشار الأمراض أو دراسة الديناميكيات السكانية للأنواع بدقة أعلى وجهد حسابي أقل. يمهد هذا التقدم في حل المعادلات التفاضلية الكسرية الطريق لرؤى أعمق حول سلوك وأنماط الأنظمة المعقدة، مما يؤدي في نهاية المطاف إلى تعزيز الفهم العلمي وتقديم إمكانيات جديدة للتطبيقات العملية.

Attractors for Hopfield lattice model in weighted spaces

The investigation into the dynamic behavior of infinite lattice systems holds paramount significance in the realm of physical phenomena, particularly in mechanics. This intricate domain has captivated the attention of both mathematicians and physicists.In acknowledgment of the inherent noise prevalent in real-world environments, our study embraces this aspect by introducing a random term into our model. This deliberate inclusion of stochasticity engenders a novel perspective, giving rise to a stochastic lattice differential equation. This model proves to be a versatile tool for accurately characterizing spatial structures characterized by discrete components and the associated uncertainties that pervade them. This research elucidates the intricate interplay between lattice dynamics and environmental noise, shedding light on the complex behavior of such systems in a realistic context. Our result generalizes many results in three directions: extending the connections between the terms to non-linear, extending the connection neighborhood from 3 (as in most cases) to arbitrary value n, and extending the results that are in ℓ2 to ℓρ2.

Systems Engineering roles to handle emergent properties and behaviors in complex technical systems

AbstractEngineering projects for complex technical systems such as automobiles demand extensive requirement specifications and corresponding hierarchy levels in system architectures. Especially when considering emergent phenomena, such as total weight or aerodynamics, a closely networked collaboration of discipline‐specific and cross‐disciplinary roles is required. Further, in large organizations with a group structure, resulting functional and non‐functional contents need to be managed by distinct Systems Engineering roles. For example, the role “property manager” takes care of achieving overarching product properties, such as weight or aerodynamics, which cannot be directly fixed, but result from many specifications. This paper proposes new Systems Engineering roles and their application in a German Original Equipment Manufacturer (OEM). For validation, the roles have already been applied in everyday engineering projects at the OEM. The concept proved to be indispensable and transferable to other Systems Engineering projects.

Molecular Dynamic Simulations for Biopolymers with Biomedical Applications.

Computational modeling (CM) is a versatile scientific methodology used to examine the properties and behavior of complex systems, such as polymeric materials for biomedical bioengineering. CM has emerged as a primary tool for predicting, setting up, and interpreting experimental results. Integrating in silico and in vitro experiments accelerates scientific advancements, yielding quicker results at a reduced cost. While CM is a mature discipline, its use in biomedical engineering for biopolymer materials has only recently gained prominence. In biopolymer biomedical engineering, CM focuses on three key research areas: (A) Computer-aided design (CAD/CAM) utilizes specialized software to design and model biopolymers for various biomedical applications. This technology allows researchers to create precise three-dimensional models of biopolymers, taking into account their chemical, structural, and functional properties. These models can be used to enhance the structure of biopolymers and improve their effectiveness in specific medical applications. (B) Finite element analysis, a computational technique used to analyze and solve problems in engineering and physics. This approach divides the physical domain into small finite elements with simple geometric shapes. This computational technique enables the study and understanding of the mechanical and structural behavior of biopolymers in biomedical environments. (C) Molecular dynamics (MD) simulations involve using advanced computational techniques to study the behavior of biopolymers at the molecular and atomic levels. These simulations are fundamental for better understanding biological processes at the molecular level. Studying the wide-ranging uses of MD simulations in biopolymers involves examining the structural, functional, and evolutionary aspects of biomolecular systems over time. MD simulations solve Newton's equations of motion for all-atom systems, producing spatial trajectories for each atom. This provides valuable insights into properties such as water absorption on biopolymer surfaces and interactions with solid surfaces, which are crucial for assessing biomaterials. This review provides a comprehensive overview of the various applications of MD simulations in biopolymers. Additionally, it highlights the flexibility, robustness, and synergistic relationship between in silico and experimental techniques.