Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems
Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems

Author: Nicola Bellomo

Publisher: MDPI

Published: 2020-05-29

Total Pages: 118

ISBN-13: 3039288792

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This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.

Contemporary Kinetic Theory of Matter
Contemporary Kinetic Theory of Matter

Author: J. R. Dorfman

Publisher: Cambridge University Press

Published: 2021-06-24

Total Pages: 667

ISBN-13: 1009038222

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Kinetic theory provides a microscopic description of many observable, macroscopic processes and has a wide range of important applications in physics, astronomy, chemistry, and engineering. This powerful, theoretical framework allows a quantitative treatment of many non-equilibrium phenomena such as transport processes in classical and quantum fluids. This book describes in detail the Boltzmann equation theory, obtained in both traditional and modern ways. Applications and generalizations describing non-equilibrium processes in a variety of systems are also covered, including dilute and moderately dense gases, particles in random media, hard sphere crystals, condensed Bose-Einstein gases, and granular materials. Fluctuation phenomena in non-equilibrium fluids, and related non-analyticities in the hydrodynamic equations are also discussed in some detail. A thorough examination of many topics concerning time dependent phenomena in material systems, this book describes both current knowledge as well as future directions of the field.

Kinetic Theory and Swarming Tools to Modeling Complex Systems--Symmetry problems in the Science of Living Systems
Kinetic Theory and Swarming Tools to Modeling Complex Systems--Symmetry problems in the Science of Living Systems

Author: Nicola Bellomo

Publisher:

Published: 2020

Total Pages: 118

ISBN-13: 9783039288809

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This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences--specifically mathematics--without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.

Active Particles, Volume 1
Active Particles, Volume 1

Author: Nicola Bellomo

Publisher: Birkhäuser

Published: 2017-04-06

Total Pages: 410

ISBN-13: 3319499963

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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. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

Physicomimetics
Physicomimetics

Author: William M. Spears

Publisher: Springer Science & Business Media

Published: 2012-01-05

Total Pages: 651

ISBN-13: 3642228046

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Standard approaches to understanding swarms rely on inspiration from biology and are generally covered by the term “biomimetics”. This book focuses on a different, complementary inspiration, namely physics. The editors have introduced the term 'physicomimetics' to refer to physics-based swarm approaches, which offer two advantages. First, they capture the notion that “nature is lazy', meaning that physics-based systems always perform the minimal amount of work necessary, which is an especially important advantage in swarm robotics. Second, physics is the most predictive science, and can reduce complex systems to simple concepts and equations that codify emergent behavior and help us to design and understand swarms. The editors consolidated over a decade of work on swarm intelligence and swarm robotics, organizing the book into 19 chapters as follows. Part I introduces the concept of swarms and offers the reader a physics tutorial; Part II deals with applications of physicomimetics, in order of increased complexity; Part III examines the hardware requirements of the presented algorithms and demonstrates real robot implementations; Part IV demonstrates how the theory can be used to design swarms from first principles and provides a novel algorithm that handles changing environments; finally, Part V shows that physicomimetics can be used for function optimization, moving the reader from issues of swarm robotics to swarm intelligence. The text is supported with a downloadable package containing simulation code and videos of working robots. This book is suitable for talented high school and undergraduate students, as well as researchers and graduate students in the areas of artificial intelligence and robotics.

Mathematical Modeling of Complex Biological Systems
Mathematical Modeling of Complex Biological Systems

Author: Abdelghani Bellouquid

Publisher: Springer Science & Business Media

Published: 2006-08-17

Total Pages: 194

ISBN-13: 0817643958

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This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.

Bulletin of the Atomic Scientists
Bulletin of the Atomic Scientists

Author:

Publisher:

Published: 1961-05

Total Pages: 88

ISBN-13:

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The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.

Modeling in Applied Sciences
Modeling in Applied Sciences

Author: Nicola Bellomo

Publisher: Springer Science & Business Media

Published: 2000-04-20

Total Pages: 438

ISBN-13: 0817641025

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Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis. Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations. An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications. This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process. Topics and Features: * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinetic traffic-flow models * Models of granular media * Large communication networks * Thorough discussion of numerical simulations of Boltzmann equation This new book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers, and postgraduates will find the book a modern and authoritative guide to the topic.

Philosophy of Complex Systems
Philosophy of Complex Systems

Author:

Publisher: Elsevier

Published: 2011-05-23

Total Pages: 951

ISBN-13: 0080931227

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The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on.Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years.-Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Nonlinear Dynamics in Complex Systems
Nonlinear Dynamics in Complex Systems

Author: Armin Fuchs

Publisher: Springer Science & Business Media

Published: 2012-09-22

Total Pages: 237

ISBN-13: 3642335527

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With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified. This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work. “This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.” “With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.” “What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.” (J.A.Scott Kelso, excerpts from the foreword)