Related papers: The improved Ginzburg-Landau technique
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…
This paper presents a case study of the effects of increasing the order of a Ginzburg-Landau type expansion, by using the well known Gross-Neveu model in 1+1 dimensions as a test case. It is found that as the order of expansion increases,…
This paper discusses the theory and numerical method of two-scale analysis for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic materials. The novelty of this work can be summarized in three aspects: Firstly, the…
A continuum model for the phase separation and coarsening, observed in electrostatically driven granular media, is formulated in terms of a Ginzburg-Landau equation subject to conservation of the total number of grains. In the regime of…
In the paper we present an isothermal model for describing damage and fatigue by the use of the Ginzburg-Landau (G-L) equation. Fatigue produces progressive damage, which is related with a variation of the internal structure of the…
The study of critical phenomena and phase transitions is an important part of modern condensed matter physics. In this regard, the phenomenological Landau theory has been extraordinarily useful. Hereby we present an alternative theoretical…
Given the spectrum of a Hamiltonian, a methodology is developed which employs the Landau-Ginsburg method for characterizing phase transitions in infinite systems to identify phase transition remnants in finite fermion systems. As a first…
The statistical mechanics of 1D and 2D Ginzburg-Landau systems is evaluated analytically, via the transfer matrix method, using an expression of the ground state energy of the quartic anharmonic oscillator in an external field. In the 2D…
We study numerically the phase structure of the Ginzburg-Landau model, with particular emphasis on mass measurements. There is no local gauge invariant order parameter, but we find that there is a phase transition characterized by a…
We propose an analytical Landau-Ginzburg theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include electronic wave function of superconducting Cooper pairs,…
A novel mixed-hybrid method for Kirchhoff-Love shells is proposed that enables the use of classical, possibly higher-order Lagrange elements in numerical analyses. In contrast to purely displacement-based formulations that require higher…
This article introduces a dynamical Ginzburg-Landau phase transition/separation model for the mixture of liquid helium-3 and helium-4, using a unified dynamical Ginzburg-Landau model for equilibrium phase transitions. The analysis of this…
A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition.…
We study the Landau model for uniaxial incommensurate-commensurate systems of the I class by keeping Umklapp terms of third and fourth order in the expansion of the free energy. It applies to systems in which the soft mode minimum lies…
The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the…
The earlier-described cluster methods are used to generalize the Ginzburg-Landau gradient expansion for the free energy of an inhomogeneous alloy to the case of not small values of order parameters and variations of composition. The results…
The dynamical phase transition of a system with two coexisting competing order parameters is studied using the time-dependent-Ginzburg-Landau framework. The dynamics are induced by parameters capturing the physics of driving the system with…
We present numerical simulations of coupled Ginzburg-Landau equations describing parametrically excited waves which reveal persistent dynamics due to the occurrence of phase slips in sequential pairs, with the second phase slip quickly…
The critical behavior of the Ginzburg-Landau model is described in a manifestly gauge-invariant manner. The gauge-invariant correlation-function exponent is computed to first order in the $4-d$ and $1/n$-expansion, and found to agree with…