In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ...

A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to ...

In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ...

Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The ...

[No abstract available]

In this paper, we develop a mean-field model for describing the dynamics of spintransfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the ...

In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$ X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ...

This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the so-called binormal flow. The case of a regular polygon ...

The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ...