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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Stochastic Ordinary and Stochastic Partial Differential Equations
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Stochastic Ordinary and Stochastic Partial Differential Equations
Peter Kotelenez (Broschiert, Englisch)
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Beschreibung
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. 106,99 €
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Technische Daten
Erscheinungsdatum
18.09.2014
Sprache
Englisch
EAN
9781489986580
Herausgeber
Springer US
Serien- oder Bandtitel
Stochastic Modelling and Applied Probability
Sonderedition
Nein
Autor
Peter Kotelenez
Seitenanzahl
459
Einbandart
Broschiert
Buch Untertitel
Transition from Microscopic to Macroscopic Equations
Schlagwörter
Kotelenez, Macroscopic, Microscopic, Ordinary, Partial Differential Equations, Stochastic, Variance, partial differential equation
Thema-Inhalt
PBK - Mathematische Analysis, allgemein
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PHU - Mathematische Physik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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