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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. Experts in various areas apply their unique
perspectives to specific aspects of crowd dynamics, covering the
topic from multiple angles. These include a demonstration of how
virtual reality may solve dilemmas in collecting empirical data; a
detailed study on pedestrian movement in smoke-filled environments;
a presentation of one-dimensional conservation laws with point
constraints on the flux; a collection of new ideas on the modeling
of crowd dynamics at the microscopic scale; and others. Applied
mathematicians interested in crowd dynamics, pedestrian movement,
traffic flow modeling, urban planning, and other topics will find
this volume a valuable resource. Additionally, researchers in
social psychology, architecture, and engineering may find this
information relevant to their work.
This monograph aims to lay the groundwork for the design of a
unified mathematical approach to the modeling and analysis of
large, complex systems composed of interacting living things.
Drawing on twenty years of research in various scientific fields,
it explores how mathematical kinetic theory and evolutionary game
theory can be used to understand the complex interplay between
mathematical sciences and the dynamics of living systems. The
authors hope this will contribute to the development of new tools
and strategies, if not a new mathematical theory. The first chapter
discusses the main features of living systems and outlines a
strategy for their modeling. The following chapters then explore
some of the methods needed to potentially achieve this in practice.
Chapter Two provides a brief introduction to the mathematical
kinetic theory of classical particles, with special emphasis on the
Boltzmann equation; the Enskog equation, mean field models, and
Monte Carlo methods are also briefly covered. Chapter Three uses
concepts from evolutionary game theory to derive mathematical
structures that are able to capture the complexity features of
interactions within living systems. The book then shifts to
exploring the relevant applications of these methods that can
potentially be used to derive specific, usable models. The modeling
of social systems in various contexts is the subject of Chapter
Five, and an overview of modeling crowd dynamics is given in
Chapter Six, demonstrating how this approach can be used to model
the dynamics of multicellular systems. The final chapter considers
some additional applications before presenting an overview of open
problems. The authors then offer their own speculations on the
conceptual paths that may lead to a mathematical theory of living
systems hoping to motivate future research activity in the field. A
truly unique contribution to the existing literature, A Quest
Toward a Mathematical Theory of Living Systems is an important book
that will no doubt have a significant influence on the future
directions of the field. It will be of interest to mathematical
biologists, systems biologists, biophysicists, and other
researchers working on understanding the complexities of living
systems.
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. In light of the recent
COVID-19 pandemic, special consideration is given to applications
of crowd dynamics to the prevention of the spreading of contagious
diseases. Some of the specific topics covered in this volume
include:Â - Impact of physical distancing on the evacuation
of crowds- Generalized solutions of opinion dynamics models- Crowd
dynamics coupled with models for infectious disease spreading-
Optimized strategies for leaders in controlling the dynamics of a
crowd Crowd Dynamics, Volume 3 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 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. In light of the recent COVID-19
pandemic, special consideration is given to applications of crowd
dynamics to the prevention of the spreading of contagious diseases.
Some of the specific topics covered in this volume include: -
Impact of physical distancing on the evacuation of crowds-
Generalized solutions of opinion dynamics models- Crowd dynamics
coupled with models for infectious disease spreading- Optimized
strategies for leaders in controlling the dynamics of a crowd Crowd
Dynamics, Volume 3 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 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 laws recent
developments in controlled crowd dynamics mixed traffic modeling
insights and applications from crowd psychology Crowd Dynamics,
Volume 2 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 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 laws recent
developments in controlled crowd dynamics mixed traffic modeling
insights and applications from crowd psychology Crowd Dynamics,
Volume 2 is ideal for mathematicians, engineers, physicists, and
other researchers working in the rapidly growing field of modeling
and simulation of human crowds.
The contents of this brief Lecture Note are devoted to modeling,
simulations, and applications with the aim of proposing a unified
multiscale approach accounting for the physics and the psychology
of people in crowds. The modeling approach is based on the
mathematical theory of active particles, with the goal of
contributing to safety problems of interest for the well-being of
our society, for instance, by supporting crisis management in
critical situations such as sudden evacuation dynamics induced
through complex venues by incidents.
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