Time-dependent Ginzburg-Landau TDGL

Equation (60) is called the time-dependent Ginzburg-Landau (TDGL) equation. 

Dynamical Self-Organization. When the parameter X passes slowly through X (l),the bifurcation picture of the previous section accurateiy describes the system. However, in Fucus, and probably in many other examples, this time scale separation between the characteristic time on which X varies and the time to obtain the patterned state does not hold. Thus a dynamical theory allowing for the interplay of these two time scales is required to characterize the developmental scenario. A natural formalism to describe this process is that of time dependent Ginzburg-Landau (tdgl) equations used successfully in other contexts of nonequilibrium phase transitions (27). 

To elucidate the spatiotemporal emergence of crystalline structure and liquid-hquid phase separation in these polyolefin blends, we employ the time dependent Ginzburg-Landau (TDGL) equations pertaining to the conserved concentration order parameter and the nonconserved crystal order parameter. The spatiotemporal evolution of the nonconserved order parameter i/f, known as TDGL model-A equation (31,32), may be expressed as... 

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. 

When one applies an external flow to the microemulsion system, its mechanical response is deeply affected by its internal structure. Using a single-order-parameter time-dependent Ginzburg-Landau (TDGL) model, Mundy et al. have investigated rheological properties of microemulsions theoretically [2]. In their model, the order parameter represents the concentration difference between oil and water, and the presence of surfactants is taken into account through the surface tension parameter. Their work has been extended by Patzold and Dawson, and it was shown that the microemulsions behave in an essentially non-Newtonian manner [3]. 

Basically, the time-dependent Ginzburg-Landau (TDGL) equation [12] relates the temporal change of a phase order parameter to a local chemical potential and a nonlocal interface gradient. With respect to a non-conserved phase field order parameter, the TDGL model A equation is customarily described as ... 

TIME-DEPENDENT GINZBURG-LANDAU METHOD (TDGL)... 

TDGL Time-dependent Ginzburg-Landau method... 

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) ... 

One way to sample the fluctuations in the order parameter, and thus model tiieir effect upon the phase transition, is to propose a stochastic model for the order parameter field such as the time dependent Ginzburg-Landau model A (TDGL-A) dynamics ... 

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