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This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. The volume begins with an overview of analytical problems related to crowd modeling. Attention is then given to the importance of considering the social and psychological factors that influence crowd behavior ¿ such as emotions, communication, and decision-making processes ¿ in order to create reliable models. Finally, specific features of crowd behavior are explored, including single-file traffic, passenger movement, modeling multiple groups in crowds, and the interplay between crowd dynamics and the spread of disease.Crowd Dynamics, Volume 4 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19.  Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general.  Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system.  Chapters in this volume address these items, as well as offer perspectives for the future.

This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive equations for wide-ranging classes of materials. Derivations of results are detailed through careful proofs, and the contents have been developed to ensure a self-contained and consistent presentation.Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics ¿ such as reference and current configurations, transport relations, singular surfaces, objectivity, and objective time derivatives ¿ are covered in detail. A chapter on balance equations then develops the balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the balance laws in electromagnetism.Part II is devoted to the general requirements on constitutive models, emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed, and in this framework, detailed descriptions are given of solids (thermoelastic, elastic, and dissipative) and fluids (elastic, thermoelastic, viscous, and Newtonian).A wide of variety of constitutive models are investigated in Part III, which consists of separate chapters focused on several types of non-simple materials: materials with memory, aging and higher-order grade materials, mixtures, micropolar media, and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity, magnetoelasticity, and plasma theory.Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself, as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena, such as those occurring in hysteretic continua (e.g., plasticity, electromagnetism, and the physics of shape memory alloys).Mathematical Modelling of Continuum Physics will be an important reference for mathematicians, engineers, physicists, and other scientists interested in research or applications of continuum mechanics.

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across di¿erent ¿elds.Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic di¿erential equations.An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularlythe applications explored in the second half of the book.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. After providing a critical analysis of the current state of the field and an overview of the current research perspectives, chapters focus on three main research areas: pedestrian interactions, crowd control, and multiscale modeling. Specific topics covered in this volume include: crowd dynamics through conservation lawsrecent developments in controlled crowd dynamicsmixed traffic modelinginsights and applications from crowd psychology Crowd Dynamics, Volume 2 is ideal for mathematicians, engineers, physicists, and other researchers working in therapidly growing field of modeling and simulation of human crowds.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. After providing a critical analysis of the current state of the field and an overview of the current research perspectives, chapters focus on three main research areas: pedestrian interactions, crowd control, and multiscale modeling. Specific topics covered in this volume include: crowd dynamics through conservation lawsrecent developments in controlled crowd dynamicsmixed traffic modelinginsights and applications from crowd psychology Crowd Dynamics, Volume 2 is ideal for mathematicians, engineers, physicists, and other researchers working in therapidly growing field of modeling and simulation of human crowds.

This contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications.

This contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective.

A vital text that collates a wealth of previously dispersed material on the derivation and analysis of fluid models in plasma physics, this stimulating introduction to the topic deploys rigorous asymptotic analysis to justify classical physical approximations.

The third part further analyses the general structure of the classification diagram for variables and equations of physical theories.Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world.

This book offers a new approach to third-order aberrations theory. It presents the basic elements of third-order aberrations of optical telescopes, along with the necessary mathematical background, to design almost all optical combinations used in astronomy.

The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations.

This book presents the physical principles pertinent to the mathematical modeling of soft materials used in engineering, including man-made materials and biological tissues. It offers two theories of elasticity and their associated theories of viscoelasticity.

Valuable for its wide-ranging yet thorough approach to mechanics, this textbook succeeds in bridging the often daunting divide between classical analytical and modern differential geometries, and reflects the author's decades-long teaching experience.

This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective.

This volume explores the complex problems that arise in the modeling and simulation of crowd dynamics in order to present the state-of-the-art of this emerging field and contribute to future research activities.

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.

Exploring the use of cellular automata in modeling pattern formation in biological systems, the 2nd edition describes mathematical modeling approaches using cellular automata that can be used to study the dynamics of interacting cell systems in simulation and in practice. New chapters cover cell migration, tissue development, and cancer dynamics.

This book offers a unified presentation that does not discriminate between atmospheric and space flight.

In particular, the work covers active R filters, OTA-C filters, and switched-capacitor filters, including topics such as differential output opamps, sensitivity analysis for passive components, multiple-feedback techniques, double-sampling, and N-path filters.