Soft and hard wall in a stochastic reaction diffusion equation

Asymmetric domain walls of small angle in soft ferromagnetic films

We focus on a special type of domain walls appearing in the Landau-Lifshitz theory for soft ferromagnetic films. These domain walls are divergence-free $S^2$-valued transition layers that connect two directions in $S^2$ (differing by an angle $2θ$) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such "asymmetric" domain walls in the limit $θ\to 0$. As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.

带软壁的紧束缚算符的边缘态

Edge states for tight-binding operators with soft walls

本研究针对带软壁的一维和二维周期紧束缚模型，证明壁位移时边缘模型会出现谱流，将其识别为布洛赫带并给出边缘态数量下界，为紧束缚体系边缘态研究提供理论支撑。

Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls

We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the…

A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

We study the Landau-Lifshitz model for the energy of multi-scale transition layers -- called "domain walls" -- in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors $m^\pm \in \mathbb{S}^2$ that differ by an angle $2α$. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence…

Vacuum energy density and pressure near a soft wall

Perfectly conducting boundaries, and their Dirichlet counterparts for quantum scalar fields, predict nonintegrable energy densities. A more realistic model with a finite ultraviolet cutoff yields two inconsistent values for the force on a curved or edged boundary (the "pressure anomaly"). A still more realistic, but still easily calculable, model replaces the hard wall by a power-law potential; because it involves no a posteriori modification of the formulas calculated from the theory, this model should be anomaly-free. Here we first set up the formalism and notation for the quantization of a …