Entropy-driven phase transitions with influence of the field-dependent diffusion coefficient

Abstract

We present a comprehensive study of the phase transitions in the single-field reaction-diffusion stochastic systems with field-dependent mobility of a power-low form and the internal fluctuations. Using variational principles and mean-field theory it was shown that the noise can sustain spatial patterns and leads to disordering phase transitions. We have shown that the phase transitions can be of critical or non-critical character.

Properties of spatial arrangement of V-type defects in irradiated materials: 3D-modelling

“…To this end, we need to find a stationary solution of the corresponding Fokker-Planck equation satisfying the Langevin equation ( 11) [41]. As it was shown previously (see references [35,36,[42][43][44][45][46]) the functional of the stationary distribution of the vacancy concentration field has the explicit form…”

“…It is seen that the second term in the effective potential (13) serves as entropy contribution. It may lead to the so-called entropy-driven phase transitions [42,[45][46][47], phase decomposition [32,44] and patterning [35,36,43].…”

Universality and self-similar behaviour of non-equilibrium systems with non-Fickian diffusion

“…The presented formalism is general and can be applied to a large class of systems: semiconductors and metals, where the quantity depends on concrete material properties. Using these assumptions one can rewrite the total diffusion flux (7) through the free energy functional F [ρ] in the standard form…”

“…Nonlinear diffusion equation can be generalized by taking quasi-chemical reactions into account. In such a case, one arrives at nontrivial scenarios for nonequilibrium phase transitions [7], pattern formation [8] and delaying dynamics at phase separation processes [9]. For example, while studying the pattern formation phenomena on surfaces at deposition from a gaseous phase, one describes the corresponding system by reaction-diffusion model with field dependent diffusivity.…”

Pattern selection processes and noise induced pattern-forming transitions in periodic systems with transient dynamics

“…A considerable progress has been made through the study of problems related to fluid flow, solidification processes, formation of antiphase domain walls and grain boundaries, etc. The well known examples of pattern formation are: convective rolls in Rayleigh-Bénard cells [1][2][3], a Turing instability with spatio-temporal dynamics in chemical systems [4], formation of patterns on gelation surfaces [5], noise induced patterns in excitable systems [6,7] and formation of a semiconductor nanostructure [8], noise induced and sustained patterns in reaction-diffusion systems [9][10][11][12][13]. Also pattern formation processes can be induced by an external influence for example irradiation [14][15][16][17].…”