The theory of spatiotemporal pattern in nonequilibrium systems. (English) Zbl 1097.82531
Summary: Stationary states and evolution of the spatially periodic and self-similar structures arising in the course of phase transformations are considered. Stationary inhomogeneous structures are studied in the framework of the thermodynamic approach, investigation of the dynamics of their formation is based on the field representation which makes it possible to describe behavior of the most probable values of stochastic variables. In the framework of unified conceptions, peculiarities of the behavior of thermodynamic, self-organizing and stochastic systems with multiplicative noise are studied. The concepts of the fractional integral and derivative are introduced which allow one to write the equation of evolution of an arbitrary system in a general form. Investigation of stationary inhomogeneous distributions is carried out by using the two- and one-component representations of the order parameter. A qualitative analysis based on the method of phase plane shows that under the transition from the disordered phase into the ordered one the harmonic distribution with a short period transforms into the step-like distribution with a long period.
MSC:
| 82B35 | Irreversible thermodynamics, including Onsager-Machlup theory |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
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