The existence of two frequency regimes in a two-dimensional (2D) Rosenzweig–MacArthur ecological network is debated. semi-discrete approximation differentiates the regimes, each described by 2D complex Ginzburg–Landau equation. Using standard theory linear stability analysis, generalized expression for modulational instability growth rate derived mode. parametric study reveals its sensitivity t...

The initial-boundary value problem for the time-dependent Ginzburg-Landau equa, tions that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented. Keywords-Superconductivity, Timedependent Ginzburg-Landau equa...

We study solutions of the 2D Ginzburg-Landau equation −∆u + 1 ε2 u(|u| − 1) = 0 subject to “semi-stiff” boundary conditions: Dirichlet conditions for the modulus, |u| = 1, and homogeneous Neumann conditions for the phase. The principal result of this work shows that there are stable solutions of this problem with zeros (vortices), which are located near the boundary and have bounded energy in t...

In this paper we discuss correlation functions in certain A-twisted Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been discussed extensively in the literature, virtually no work has been done on A-twisted theories. In particular, we study examples of Landau-Ginzburg models over topologically nontrivial spaces – not just vector spaces – away from large-radius limits, so ...

We present some mathematical aspects of Landau-Ginzburg string vacua in terms of toric geometry. The one-to-one correspondence between toric divisors and some of (−1, 1) states in Landau-Ginzburg model is presented for superpotentials of typical types. The Landau-Ginzburg interpretation of non-toric divisors is also presented. Using this interpretation, we propose a method to solve the so-calle...

Block copolymer melts have been previously used to control the position and alignment of anisotropic nanoparticles. In this work, 2D 3D mesoscopic simulations are explore phase behavior block copolymer/nanoparticle systems. The method combines a time-dependent Ginzburg-Landau for polymer Brownian dynamics Rhomboidal spheroidal shaped particles simulated in two three dimensions, respectively. It...

In the asymptotic limit of a large Ginzburg-Landau parameter, we give a new asymptotic formula for the L-norm of the Ginzburg-Landau order parameter. The formula is valid in the bulk regime where the intensity of the applied magnetic eld is of the same order as the Ginzburg-Landau parameter and strictly below the second critical eld. Our formula complements the celebrated one of Sandier-Serfaty...

We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, Berglund-Hübsch, Givental, and HoriVafa. It can be done in more general situations, and provides partial resolutions when the above constructio...

{ In direct simulations of the anisotropic complex Ginzburg-Landau equation periodic defect chain structures are found. They develop spontaneously in a small parameter region, but once initialized their range of stable existence is rather large. We discuss diierent types found in diierent parameter regions.