A forced Landau-Stuart equation is studied in order to derive a low-dimensional model describing the temporal behavior of a paradigm open flow, the two-dimensional forced cylinder wake. Numerical results from the model exhibit several characteristics of circle maps, and compare qualitatively to previous experimental results for an oscillating cylinder wake. The low-dimensional model is also sho...

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation ǫ(p) = μ, a condition that ordinarily has the Fermi momentum pF as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative altera...

The Landau-Lifshitz-Gilbert Equation describes the dynamics of ferromagnetism, where strong nonlinearity and non-convexity are hard to tackle. Based on the work of S.Bartels and A.Prohl "Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation" ([4]), we present in this report a fully implicit finite element scheme with exchange and magnetostriction. We verify u...

Spin waves are waves of dynamical magnetization which can be excited in ferromagnetic materials. These waves can be thought of as slow electromagnetic waves. However, electromagnetic waves in a vacuum are described completely by Maxwell’s equations, and spin waves are not. To describe the dynamics of spin waves, one needs to consider the Landau-Lifshitz equation in addition to Maxwell’s equatio...

Global classical solutions near Maxwellians are constructed for the Boltzmann and Landau equations with soft potentials in the whole space. The construction of global solutions is based on refined energy analysis. Our results generalize the classical results in Ukai and Asano (Publ. Res. Inst. Math. Sci. 18 (1982), 477–519) to the very soft potentials for the Boltzmann equation and also extend ...

We derive heuristically an integro-differential equation, as well as a shell model, governing the dynamics of the Lowest Landau Level equation in a high frequency regime.

This is a non-linear diffusion equation, and the coefficients āi j, c̄ depend on the solution f . Here we are mainly concerned with the Gevrey class regularity for the solution of the Landau equation. This equation is obtained as a limit of the Boltzmann equation when the collisions become grazing (see [8] and references therein). Recently, a lot of progress has been made on the study of the Sob...

We examine a family of microscopic models of plasmas, with a parameter α comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previou...

Abstract. We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of [6, 7, 4], we propose a probabilistic interpretation of such a P.D.E. in terms of a nonlinear stochastic differential equation driven by a standard Brownian motion. We derive a numerical sch...