S. B. Goryachev | Searcharxiv

arXiv1999

Reply to Comment on "Theory of Spinodal Decomposition"

Rutenberg [cond-mat/9411016] claimed erroneously that I incorrectly apply only global conservation constraint to systems with local conservation embodied by continuity equation [PRL vol.72, p.1850 (1994)]. I reply that my theory describes the order parameter (OP) evolution of all three types of systems: without conservation law, with global one and with local one. I explain that continuity equation is a differential form of global conservation law, taking into account the absence of OP production. It is a supplementary equation, but it contains an unknown variable - OP flux. In my theory OP flux can be always found from OP evolution equation and continuity one.

cond-mat↗

arXiv1997

Kinetics, Hydrodynamics and Stochastodynamics of Cellular Structure Coarsening

For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and macroscopic levels of approach are distinguished. At the microscopic level the cellular structure is describe by a probability distribution function in a phase space of cell coordinates and of cell sizes. A kinetic equation for the function is written and a development to a hydrodynamic equation of a mesoscopic cell medium is realised. It has the form of a diffusion-reaction equation with a negative "diffusion" coefficient and with a cell interface density playing the role of concentration. Its analysis reveals a new effect of macroscopic patterning in the cell medium: existence of space-correlated stochastic fluctuations of the cell interface density.

cond-mat↗