ISBN: 9780387743165 - stochastic ordinary and stochastic partial differential equations: transition from microscopic to macroscopic equations (stochastic modelling and applied probability, 58, band 58) (20 Ergebnisse)

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Buch. Zustand: Neu. 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.…

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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 472 pp. Englisch.…

Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Analyzes mathematical models of time-dependent physical phenomena on three levels including microscopic, mesoscopic and macroscopic.Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on .…

Buch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 472 pp. Englisch.…