Modeling Complex Living Systems: A Kinetic Theory and Stochastic Game Approach
Thesubjectofthisbookisthemodelingofcomplex systemsinthelife sciences constituted by a large number of interacting entities called active particles. Their physical state includes, in addition to geometrical and mechanical variables, a variable called the activity, which characterizes the speci?c living system to be modeled. Interactions among particles not only modify the microscopic state, but may generate proliferative and/or destructive phenomena. The aim of the book is to develop mathematical methods and tools, even a new mathematics, for the modeling of living systems. The background idea is that the modeling of living systems requires technically complex mathematical methods, which may be s- stantially di?erent from those used to deal with inert matter. The?rstpart ofthe bookdiscussesmethodological issues, namely the derivation of various general mathematical frameworks suitable to model particular systems of interest in the applied sciences. The second part presents the various models and applications. The mathematical approach used in the book is based on mathema- cal kinetic theoryfor active particles, whichleads tothederivation of evo- tion equations for a one-particle distribution function over the microscopic state. Two types of equations, to be regarded as a general mathematical framework for deriving the models, are derived corresponding to short and long range interactions.
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12 Classical Models of Kinetic Theory
13 Discrete Velocity Models
14 Guidelines for Modeling Living Systems
15 Purpose and Plan of the Book
Mathematical Structures of the Kinetic Theory for Active Particles
22 The Generalized Distribution Function
23 Modeling Microscopic Interactions
55 Critical Analysis and Further Developments
Mathematical Modeling of Vehicular Traffic Flow Phenomena
62 Scaling and Representation
63 A Survey of Continuous Kinetic Traffic Models
64 Discrete Velocity Models
65 On the Model by Delitala and Tosin
66 On the Modeling by Active Particle Methods
Complex Biological Systems Mutations and Immune Competition
24 Mathematical Frameworks
25 Some Particular Frameworks
26 Additional Concepts
Additional Mathematical Structures for Modeling Complex Systems
32 Models with MixedType Interactions
33 Models with Exotic Proliferations
34 Phenomenological Frameworks
35 Open Systems
Mathematical Frameworks for Discrete Activity Systems
42 Motivations for a Discrete States Modeling
43 On the Discrete Distribution Function
44 Mathematical Framework
45 Additional Generalizations
46 Critical Analysis
Modeling of Social Dynamics and Economic Systems
52 A Model by Bertotti and Delitala
53 Qualitative Analysis and Simulations
54 Some Ideas on Further Modeling Perspectives
72 Modeling the Immune Competition
73 Mathematical Structures for Modeling
74 An Example of Mathematical Models
75 Modeling Developments and Perspectives
Modeling Crowds and Swarms Congested and Panic Flows
82 The Representation of Crowds and Swarms
83 Modeling by Macroscopic Equations
84 Modeling by Kinetic Theory Methods
85 Looking Forward
Additional Concepts on the Modeling of Living Systems
92 Mathematical Problems
93 Looking for New Mathematical Structures
94 Additional Issues on Modeling
95 Speculations on a Mathematical Theory for Living Systems
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ability active particles activity variable additional analogous analyzed applied mathematicians assumption behavior Bellomo Boltzmann equation classical classical mechanics complex computational consider corresponding crowds and swarms defined Delitala denotes depends derivation described developed discrete velocity distribution function domain equilibrium evolution equation external actions field particle follows identified immune cells immune competition immune system individuals initial value problem instance interacting pairs interacting populations ith population large number living systems long range interactions macroscopic scale mathematical framework mathematical kinetic theory mathematical models mathematical problems mathematical structures methods microscopic interactions modeling approach modeling of microscopic modify Moreover number of particles obtained ordinary differential equations parameters phase space phenomena phenomenological probability density proliferative qualitative analysis research perspectives Section social classes space variable spatially homogeneous specific models strategy suitable technical term test particle theory for active tion traffic flow modeling value problem velocity variable
Page iii - USA wpaepmnas . epm . ornl . gov KR Rajagopal (Multiphase Flows) Department of Mechanical Engineering Texas A&M University College Station, TX 77843, USA KRaj agopaltaengr . tamu . edu Y.
Page iii - Advisory Editorial Board M.Avellaneda (Modeling in Economics) Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York, NY 1001 2, USA...
Page 216 - Prigogine, I. and Herman, R. (1971) Kinetic Theory of Vehicular Traffic. Elsevier, New York.
Page 214 - Biol., 37 (1998), 235-252. [JAa] JAGER E. and SEGEL L., On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math., 52 (1992), 1442-1468. [LAa] LACHOWICZ M., A system of stochastic differential equations modeling Euler and Navier Stokes hydrodynamic equations, Japan J.
Page 215 - Koch, AJ and Meinhardt, H. (1994) Biological pattern formation: from basic mechanisms to complex structures.
Page iii - Mathematiques pour ('lndustrie et la Physique Universite P. Sabatier Toulouse 3 118RoutedeNarbonne 31062 Toulouse Cedex, France degondOmip . ups-tlse . fr A. Deutsch (Complex Systems in the Life Sciences) Center for lnformation Services and High Performance Computing Technische Universita't Dresden 01062 Dresden, Germany andreas...