9781489986580 - stochastic ordinary and stochastic partial differential equations: transition from microscopic to macroscopic equations (stochastic modelling and applied probability, band 58) von kotelenez, peter (3 Ergebnisse)
Sprache: Englisch
Verlag: Springer 2014
Serie: Stochastic Modelling and Applied Probability, Buch 15 von 30. Buch 15 von 30 - Stochastic Modelling and Applied Probability
- Softcover
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Weitere BilderSprache: Englisch
Verlag: Springer 2014
Serie: Stochastic Modelling and Applied Probability, Buch 15 von 30. Buch 15 von 30 - Stochastic Modelling and Applied Probability
- Softcover
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Taschenbuch. Zustand: Neu. Stochastic Ordinary and Stochastic Partial Differential Equations | Transition from Microscopic to Macroscopic Equations | Peter Kotelenez | Taschenbuch | Stochastic Modelling and Applied Probability | x | Englisch | 2014 | Springer | EAN 9781489986580 | Verantwortliche Person für die EU: Springer Verl…ag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Sprache: Englisch
Verlag: Springer, Springer 2014
Serie: Stochastic Modelling and Applied Probability, Buch 15 von 30. Buch 15 von 30 - Stochastic Modelling and Applied Probability
- Softcover
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Taschenbuch. 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 equat…ions 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.
