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ISBN: 3039288806 3039288792 Year: 2020 Publisher: MDPI - Multidisciplinary Digital Publishing Institute
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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.
short- and long-range interactions --- living systems --- stress conditions --- learning --- symmetric interactions --- active particles --- conformist society --- kinetic equations --- kinetic models --- complex systems --- safety --- haptotaxis --- opinion dynamics --- multiscale modeling --- individualistic society --- CVaR --- kinetic theory --- social dynamics --- boundary conditions --- pattern formation --- crowd dynamics --- integro-differential equations --- scaling --- Efficient frontier --- cell movement --- vehicular traffic --- Crowd dynamics --- learning dynamics
Book
ISBN: 981193763X 9811937621 Year: 2022 Publisher: Singapore Springer Nature
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This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.
Boundary value problems. --- Chemotaxis --- Navier-Stokes equations. --- Mathematical models. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Chemiotaxis --- Chemotropism --- Biochemistry --- Growth --- Taxes (Biology) --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Problemes de contorn --- Quimiotaxi --- Models matemàtics --- Equacions de Navier-Stokes --- Navier-Stokes (Equacions) --- Dinàmica de fluids --- Equacions en derivades parcials --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Bioquímica --- Creixement --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Kármán --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Reaction-Diffusion --- Haptotaxis --- Navier-Stokes --- Cancer invasion --- Coral fertilization --- Sensity-suppressed motility --- Oncolytic virotherapy --- Foraging scrounging interplay
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