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The initial value problem for the binormal flow with rough data
(2015-12-31)
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 ...
Shell interactions for Dirac operators: On the point spectrum and the confinement
(2015-12-31)
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 ...
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0]
(2015-12-31)
[No abstract available]
An atomistic/continuum coupling method using enriched bases
(2015-12-31)
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 ...
A Mean-field model for spin dynamics in multilayered ferromagnetic media
(2015-12-31)
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 ...
Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions
(2015-12-31)
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 ...
The Vortex Filament Equation as a Pseudorandom Generator
(2015-08-01)
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 ...
The dynamics of vortex filaments with corners
(2015-07-01)
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 ...
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
(2015-05-01)
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 ...