Dynamics of asymmetric dissipative systems : from traffic jam to collective motion / Yuki Sugiyama.
Sugiyama, Yuki.
2023
Q295 .S84 2023
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Title Dynamics of asymmetric dissipative systems : from traffic jam to collective motion / Yuki Sugiyama.
Author Sugiyama, Yuki.
ISBN 9789819918706 electronic book
9819918707 electronic book
9819918693
9789819918690
DOI https://doi.org/10.1007/978-981-99-1870-6
Published Singapore : Springer, 2023.
Language English
Description 1 online resource (xviii, 316 pages) : illustrations.
Item Number 10.1007/978-981-99-1870-6 doi
Call Number Q295 .S84 2023
Dewey Decimal Classification 003
Summary This book provides the dynamics of non-equilibrium dissipative systems with asymmetric interactions (Asymmetric Dissipative System; ADS). Asymmetric interaction breaks "the law of action and reaction" in mechanics, and results in non-conservation of the total momentum and energy. In such many-particle systems, the inflow of energy is provided and the energy flows out as dissipation. The emergences of non-trivial macroscopic phenomena occur in the non-equilibrium energy balance owing to the effect of collective motions as phase transitions and bifurcations. ADS are applied to the systems of self-driven interacting particles such as traffic and granular flows, pedestrians and evacuations, and collective movement of living systems. The fundamental aspects of dynamics in ADS are completely presented by a minimal mathematical model, the Optimal Velocity (OV) Model. Using that model, the basics of mathematical and physical mechanisms of ADS are described analytically with exact results. The application of 1-dimensional motions is presented for traffic jam formation. The mathematical theory is compared with empirical data of experiments and observations on highways. In 2-dimensional motion pattern formations of granular media, pedestrians, and group formations of organisms are described. The common characteristics of emerged moving objects are a variety of patterns, flexible deformations, and rapid response against stimulus. Self-organization and adaptation in group formations and control of group motions are shown in examples. Another OV Model formulated by a delay differential equation is provided with exact solutions using elliptic functions. The relations to soliton systems are described. Moreover, several topics in ADS are presented such as the similarity between the spatiotemporal patterns, violation of fluctuation dissipation relation, and a thermodynamic function for governing the phase transition in non-equilibrium stationary states.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Series Springer series in synergetics (Unnumbered)
Available in Other Form Dynamics of Asymmetric Dissipative Systems
Linked Resources Online Access
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Intro
Preface
Acknowledgment
Contents
Part I Basics of ADS and OV Models
1 Introduction to Asymmetric Dissipative Systems (ADS)
1.1 Background of ADS
1.1.1 Motivation
Basic Assumptions and Prospects
Non-equilibrium Dissipative Systems
Physical Properties in Emergence of Non-equilibrium Macroscopic Phenomena
1.1.2 Asymmetric Interactions in Dissipative System
Non-conservation of Momentum
Energy Flow Through a System and Non-equilibrium Stationary State
1.2 Minimal Model of ADS
1.2.1 Introducing the Optimal Velocity Model

1.2.2 Non-existence of Lagrangian
1.2.3 Examples of Phenomena Described by OV Model
1.3 ADS as a System of Active Matter
1.3.1 A Brief Review of Vicsek Model
Statistical Properties of Collective Motions
1.3.2 Comparing OV Model with Vicsek Model
Flocking Behaviours
Emergence of Solitary Objects
Macroscopic Approach and Statistical Properties
1.3.3 Importance of Asymmetry for Interactions in Flocking Behaviours
1.4 Overview of the Book
2 Optimal Velocity Model (OV Model)
2.1 Model
2.1.1 Single and Collective Motions

2.2 Homogeneous Flow Solution and its Stability
2.2.1 Linear Stability Analysis and Phase Transition
2.2.2 Dispersion Relation
2.3 Emergence of Instability Originating from Asymmetry
2.3.1 General OV Model
2.3.2 Linear Stability of General OV Model
2.3.3 Dispersion Relation for General OV Model
Coupled Oscillators with Viscous Force
Equivalence to Harmonic Oscillator System
Asymmetric Interaction without Dissipation
2.3.4 Particle Number Dependence in Linear Stability
2.4 Continuum System of OV Model
2.4.1 Continuation of Discrete System

2.4.2 Linear Stability Analysis
Note for Continuation of Asymmetry
2.4.3 Continuum System of General OV Model
2.5 Stability Change as Hopf Bifurcation
2.5.1 Hopf Bifurcation in Many-Particle System
2.5.2 Hopf Bifurcation Originating from Asymmetry
3 Cluster Flow Solutions
3.1 Moving Cluster
3.1.1 Spontaneous Emergence of a Moving Cluster
3.1.2 Non-equilibrium Stability of a Moving Cluster
Characteristic Time Interval
3.1.3 Profile of Cluster Flow Solution
Hysteresis Loop
Limit Cycle
3.1.4 Velocity of Moving Cluster

3.1.5 Statistical Properties of Cluster Flow
Distributions of Wave Numbers
Power Law Distributions for Sizes of Moving Clusters
3.2 Heaviside Step Function OV Model (Exactly Solvable Model 1)
3.2.1 Homogeneous Flow Solutions
Linear Stability Analysis
3.2.2 Construction of Cluster Flow Solution
Process of Escaping from a Cluster to a Fast Running Region
Process of Moving from a Fast Running Region to a Cluster
3.2.3 Exact Solutions of Cluster Flow
Induced Time Scale (Characteristic Time Interval)
Velocity of Moving Cluster
Hysteresis Loop and Limit Cycle
Process of Escaping from a Cluster to a Fast Running Region

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