Time-dependent Ginzburg-Landau method

TIME-DEPENDENT GINZBURG-LANDAU METHOD (TDGL)... [Pg.160]

TDGL Time-dependent Ginzburg-Landau method... [Pg.491]

In order to describe the diffusive dynamics of composition fluctuations in binary mixtures one can extend the time-dependent Ginzburg-Landau methods to the free energy functional of the SCF theory. The approach relies on two ingredients a free energy functional that accurately describes the chemical potential of a spatially inhomogeneous composition distribution out of equilibrium and an Onsager coefficient that relates the variation of the chemical potential to the current of the composition. [Pg.38]

MSI) that uses the same time-dependent Ginzburg Landau kinetic equation as CDS, but starts from (arbitrary) bead models for polymer chains. The methods have been summarized elsewhere. Examples of recent applications include LB simulations of viscoelastic effects in complex fluids under oscillatory shear,DPD simulations of microphase separation in block copoly-mers ° and mesophase formation in amphiphiles, and cell dynamics simulations applied to block copolymers under shear. - DPD is able to reproduce many features of analytical mean field theory but in addition it is possible to study effects such as hydrodynamic interactions. The use of cell dynamics simulations to model non-linear rheology (especially the effect of large amplitude oscillatory shear) in block copolymer miscrostructures is currently being investigated. ... [Pg.232]

Mesoscopic methods include several field-based approaches such as cell dynamical systems (CDS), mesoscale density functional theory (DFT), and self-consistent field (SCF)" theory. Most of these methods are related to the time-dependent Ginzburg-Landau equation (TDGL) ... [Pg.209]

As in the case of homogeneous systems, there are two kinds of stochastic descriptions for reaction-diffusion systems as well the master equation approach and the stochastic differential equation method. Until now we have dealt with the first approach however, stochastic partial differential equations are also used extensively. Most often partial differential equations are supplemented with a term describing fluctuations. In particular, time-dependent Ginzburg-Landau equations describe the behaviour of the system in the vicinity of critical points (Haken, 1977 Nitzan, 1978 Suzuki, 1984). A usual formulation of the equation is ... [Pg.172]

The mesoscopic regime lies between discrete particles and finite element representations of a continuum. Examples of mesoscopic field-theoretic methods are complex Langevin technique (CLT), time-dependent Ginzburg-Landau (TDGL) approach, and dynamic density functional theory (DDFT) method. [Pg.421]