Browsing Linear and Non-Linear Waves by Issue Date
Now showing items 1-20 of 111
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Relativistic Hardy Inequalities in Magnetic Fields
Fanelli, L.
; Vega, L.; Visciglia, N. (2014-12-31)
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type 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
De la Hoz, F.; Vega, L. (2014-12-31)
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
(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 ... -
The dynamics of vortex filaments with corners
Vega, L. (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 ... -
The Vortex Filament Equation as a Pseudorandom Generator
De la Hoz, F.; Vega, L. (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 initial value problem for the binormal flow with rough data
Banica, V.; Vega, L. (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
Arrizabalaga, N.; Mas, A.; Vega, L. (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]
Fanelli, L.; Vega, L.; Visciglia, N. (2015-12-31)
[No abstract available] -
An atomistic/continuum coupling method using enriched bases
Chen, J.; García-Cervera, C.J.; Li, X. (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
Chen, J.; García-Cervera, C.J.; Yang, X. (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
Chen, J.; García-Cervera, C.J.; Yang, X. (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 ... -
An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
Arrizabalaga, N.; Mas, A.; Vega, L. (2016-06-01)
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
(2016-06-30)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 higher-order main terms and perturbations
García, A.; Vesalainen, E.V.; Zubeldia, M. (2016-07-01)
In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of ... -
Spectral Transitions for Aharonov-Bohm Laplacians on Conical Layers
(2016-07-11)We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm 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
(2016-09-01)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
Escauriaza, L.; Kenig, C.E.; Ponce, G.; Vega, L. (2016-09-01)
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 log-convexity properties and the derivation of ... -
Reconstruction from boundary measurements for less regular conductivities
García, A.; Zhang, G. (2016-10-01)
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 self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions
Ourmières-Bonafos, T.; Vega, L. (2016-12-21)
We develop an approach to prove self-adjointness 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
(2017)We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...