Time-dependent Ginzburg-Landau parameter

We start from the time-dependent Ginzburg-Landau equation for a non-conserved order parameter 0... 

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... 

Abstract Dynamic response of microemulsions to shear deformation on the basis of two-order-parameter time dependent Ginzburg-Landau model is investigated by means of cell dynamical system approach. Time evolution of anisotropic factor and excess shear stress under steady shear flow is studied by changing shear rate and total amount of surfactant. As the surfactant concentration is increased. 

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]. 

One is the time-dependent Ginzburg-Landau equation which is described by a complex order parameter and vector potential. The other is the Langevin-type stochastic equation of motion for magnetic vortices in two and three dimensions, which is described in terms of vortex position variables. 

Close to the bifurcation point, one can generally derive a contracted description of the dynamics only in terms of the order parameter which is associated to the unstable mode. The corresponding equation of motion in many cases takes a form similar to the time-dependent Ginzburg-Landau equation (T.D.G.L.) familiar from the theory of equilibrium phase transition ... 

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 ... 

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 ... 

Analytic teclmiques often use a time-dependent generalization of Landau-Ginzburg ffee-energy fiinctionals. The different universal dynamic behaviours have been classified by Hohenberg and Halperin [94]. In the simple example of a binary fluid (model B) the concentration difference can be used as an order parameter m.. A gradient in the local chemical potential p(r) = 8F/ m(r) gives rise to a current j... 

The dynamical behavior of Ginzburg-Landau models is described by Langevin equations. In the simplest case, the equation of motion for a conserved order parameter field 0(r, /), which now depends on time / in addition to r, reads... 

To elucidate the time evolution of the concentration and orientation fluctuations during a SD, we introduce kinetic equations based on the time-dependent Landau-Ginzburg (TDLG) equations for concentration and orientational order parameters. 

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