Stochastic Ordinary and Stochastic Partial Differential Equations : Transition from Microscopic to Macroscopic Equations

Peter Kotelenez

ISBN 10: 1489986588 / ISBN 13: 9781489986580

Edité par Springer, Springer, 2014

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - The present volume analyzes mathematical models of time-dependent physical p- nomena on three levels: microscopic, mesoscopic, and macroscopic. We provide a rigorous derivation of each level from the preceding level and the resulting me- scopic equations are analyzed in detail. Following Haken (1983, Sect. 1. 11. 6) we deal, 'at the microscopic level, with individual atoms or molecules, described by their positions, velocities, and mutual interactions. At the mesoscopic level, we describe the liquid by means of ensembles of many atoms or molecules. The - tension of such an ensemble is assumed large compared to interatomic distances but small compared to the evolving macroscopic pattern. . . . At the macroscopic level we wish to study the corresponding spatial patterns. ' Typically, at the mac- scopic level, the systems under consideration are treated as spatially continuous systems such as uids or a continuous distribution of some chemical reactants, etc. Incontrast,onthemicroscopiclevel,Newtonianmechanicsgovernstheequationsof 1 motion of the individual atoms or molecules. These equations are cast in the form 2 of systems of deterministic coupled nonlinear oscillators. The mesoscopic level is probabilistic in nature and many models may be faithfully described by stochastic 3 ordinary and stochastic partial differential equations (SODEs and SPDEs), where the latter are de ned on a continuum. The macroscopic level is described by ti- dependent partial differential equations (PDE's) and its generalization and simpl- cations. In our mathematical framework we talk of particles instead of atoms and mo- cules. The transition from the microscopic description to a mesoscopic (i. e.

N° de réf. du vendeur 9781489986580

Détails bibliographiques

• Titre: Stochastic Ordinary and Stochastic Partial Differential Equations : Transition from Microscopic to Macroscopic Equations
• Éditeur: Springer, Springer
• Date de parution: 2014
• Langue: anglais
• ISBN à 10 chiffres: 1489986588
• ISBN à 13 chiffres: 9781489986580
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 26 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 26 millimètres de profondeur
• Poids: 709 grammes

A propos de ce titre

Synopsis

Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.

Présentation de l'éditeur

This book analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail.