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 ...
Read More
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.
Read Less
Add this copy of Stochastic Ordinary and Stochastic Partial Differential to cart. $112.32, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2007 by Springer.
Add this copy of Stochastic Ordinary and Stochastic Partial Differential to cart. $41.79, like new condition, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 2007 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
469 pp., Hardcover, inscribed by Kotelenez else LIKE NEW. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
Add this copy of Stochastic Ordinary and Stochastic Partial Differential to cart. $58.20, new condition, Sold by Media Smart rated 4.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 2007 by Springer.
