Browsing Linear and NonLinear Waves by Issue Date
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Relativistic Hardy Inequalities in Magnetic Fields
(Journal of Statistical Physics, 20141231)We deal with Dirac operators with external homogeneous magnetic fields. Hardytype inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ... 
Vortex filament equation for a regular polygon
(Nonlinearity, 20141231)In this paper, we study the evolution of the vortex filament equation,$$ X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give ... 
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
(Communications on Pure and Applied Analysis, 20150501)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 ... 
The dynamics of vortex filaments with corners
(Communications on Pure and Applied Analysis (CPAA), 20150701)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 socalled binormal flow. The case of a regular polygon ... 
The Vortex Filament Equation as a Pseudorandom Generator
(Acta Applicandae Mathematicae, 20150801)In this paper, we consider the evolution of the socalled 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 initial value problem for the binormal flow with rough data
(Annales Scientifiques de l'Ecole Normale Superieure, 20151231)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 ... 
An atomistic/continuum coupling method using enriched bases
(Multiscale Modeling and Simulation, 20151231)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 ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(IEEE Transactions on Magnetics, 20151231)In this paper, we present a meanfield model of the spinmagnetization coupling in ferromagnetic materials. The model includes nonisotropic diffusion for spin dynamics, which is crucial in capturing strong spinmagnetization ... 
Shell interactions for Dirac operators: On the point spectrum and the confinement
(SIAM Journal on Mathematical Analysis, 20151231)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 measurevalued potential. The ... 
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866876, DOI 10.1007/s1095501409150]
(Journal of Statistical Physics, 20151231)[No abstract available] 
A Meanfield model for spin dynamics in multilayered ferromagnetic media
(Multiscale Modeling and Simulation, 20151231)In this paper, we develop a meanfield 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 ... 
An IsoperimetricType Inequality for Electrostatic Shell Interactions for Dirac Operators
(Communications in Mathematical Physics, 20160601)In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell ... 
On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(Communications in Partial Differential Equations, 20160630)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... 
Discreteness of transmission eigenvalues for higherorder main terms and perturbations
(SIAM Journal on Mathematical Analysis, 20160701)In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higherorder main terms and higherorder perturbations. The coefficients of ... 
Spectral Transitions for AharonovBohm Laplacians on Conical Layers
(20160711)We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an AharonovBohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary ... 
Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type
(Advances in Mathematics, 20160901)We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ ... 
Hardy uncertainty principle, convexity and parabolic evolutions
(Communications in Mathematical Physics, 20160901)We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new logconvexity properties and the derivation of ... 
Reconstruction from boundary measurements for less regular conductivities
(20161001)In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $\nabla log\gamma$ in a Lipschitz ... 
A strategy for selfadjointness of Dirac operators: Applications to the MIT bag model and deltashell interactions
(20161221)We develop an approach to prove selfadjointness of Dirac operators with boundary or transmission conditions at a $C^2$compact surface without boundary. To do so we are lead to study the layer potential induced by the ... 
Spectral asymptotics for $\delta$interactions on sharp cones
(Journal of Mathematical Analysis and Applications, 2017)We investigate the spectrum of threedimensional Schr\"odinger operators with $\delta$interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...