Cargando…
Stochastic Ordinary and Stochastic Partial Differential Equations Transition from Microscopic to Macroscopic Equations /
This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely ma...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2008.
|
| Edición: | 1st ed. 2008. |
| Colección: | Stochastic Modelling and Applied Probability,
58 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-0-387-74317-2 | ||
| 003 | DE-He213 | ||
| 005 | 20220114235843.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2008 xxu| s |||| 0|eng d | ||
| 020 | |a 9780387743172 |9 978-0-387-74317-2 | ||
| 024 | 7 | |a 10.1007/978-0-387-74317-2 |2 doi | |
| 050 | 4 | |a QA299.6-433 | |
| 072 | 7 | |a PBK |2 bicssc | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 072 | 7 | |a PBK |2 thema | |
| 082 | 0 | 4 | |a 515 |2 23 |
| 100 | 1 | |a Kotelenez, Peter. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Stochastic Ordinary and Stochastic Partial Differential Equations |h [electronic resource] : |b Transition from Microscopic to Macroscopic Equations / |c by Peter Kotelenez. |
| 250 | |a 1st ed. 2008. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2008. | |
| 300 | |a X, 459 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Stochastic Modelling and Applied Probability, |x 2197-439X ; |v 58 | |
| 505 | 0 | |a From Microscopic Dynamics to Mesoscopic Kinematics -- Heuristics: Microscopic Model and Space-Time Scales -- Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit -- Proof of the Mesoscopic Limit Theorem -- Mesoscopic A: Stochastic Ordinary Differential Equations -- Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties -- Qualitative Behavior of Correlated Brownian Motions -- Proof of the Flow Property -- Comments on SODEs: A Comparison with Other Approaches -- Mesoscopic B: Stochastic Partial Differential Equations -- Stochastic Partial Differential Equations: Finite Mass and Extensions -- Stochastic Partial Differential Equations: Infinite Mass -- Stochastic Partial Differential Equations:Homogeneous and Isotropic Solutions -- Proof of Smoothness, Integrability, and Itô's Formula -- Proof of Uniqueness -- Comments on Other Approaches to SPDEs -- Macroscopic: Deterministic Partial Differential Equations -- Partial Differential Equations as a Macroscopic Limit -- General Appendix. | |
| 520 | |a This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation. A detailed analysis of the SODEs and (quasi-linear) SPDEs is presented. Semi-linear (parabolic) SPDEs are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids. A covariance analysis of the random processes and random fields as well as a review section of various approaches to SPDEs are also provided. An extensive appendix makes the book accessible to both scientists and graduate students who may not be specialized in stochastic analysis. Probabilists, mathematical and theoretical physicists as well as mathematical biologists and their graduate students will find this book useful. Peter Kotelenez is a professor of mathematics at Case Western Reserve University in Cleveland, Ohio. | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9780387520698 |
| 776 | 0 | 8 | |i Printed edition: |z 9780387743165 |
| 776 | 0 | 8 | |i Printed edition: |z 9781489986580 |
| 830 | 0 | |a Stochastic Modelling and Applied Probability, |x 2197-439X ; |v 58 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-0-387-74317-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||