Now showing items 1-20 of 52

• #### A Mean-field model for spin dynamics in multilayered ferromagnetic media ﻿

(Multiscale Modeling and Simulation, 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 ...
• #### Absence of eigenvalues of two-dimensional magnetic Schroedinger operators ﻿

(2018-01-01)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ...
• #### An atomistic/continuum coupling method using enriched bases ﻿

(Multiscale Modeling and Simulation, 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 ...
• #### An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators ﻿

(Communications in Mathematical Physics, 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 ...
• #### Asymptotic behaviour for fractional diffusion-convection equations ﻿

(2017-10)
We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...
• #### Asymptotic behaviour of neuron population models structured by elapsed-time ﻿

(Nonlinearity, 2019-01-04)
We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the ...
• #### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation ﻿

(2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...
• #### Discreteness of transmission eigenvalues for higher-order main terms and perturbations ﻿

(SIAM Journal on Mathematical Analysis, 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 ...
• #### An efficient multigrid strategy for large-scale molecular mechanics optimization ﻿

(Journal of Computational Physics, 2017-08-01)
Static mechanical properties of materials require large-scale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ...
• #### El efecto de Talbot: de la óptica a la ecuación de Schrödinger ﻿

(TEMat, 2017-07)
El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ...
• #### Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0] ﻿

(Journal of Statistical Physics, 2015-12-31)
[No abstract available]
• #### Existence of weak solutions for a general porous medium equation with nonlocal pressure ﻿

(submitted, 2017-10)
We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...
• #### Gaussian Decay of Harmonic Oscillators and related models ﻿

(Journal of Mathematical Analysis and Applications, 2017-05-15)
We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ...
• #### Hardy uncertainty principle, convexity and parabolic evolutions ﻿

(Communications in Mathematical Physics, 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 ...
• #### Hartree-Fock theory with a self-generated magnetic field ﻿

(Journal of Mathematical Physics, 2017-06-01)
We prove the existence of a ground state within the Hartree-Fock theory for atoms and molecules, in the presence of self-generated magnetic fields, with and without direct spin coupling. The ground state exists provided ...
• #### Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ ﻿

(Analysis & PDE, 2017-11)
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...
• #### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations ﻿

(Mathematische Nachrichten, 2017-06-20)
We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ...
• #### Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients ﻿

(Boundary Value Problems, 2017)
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ...
• #### Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions ﻿

(IEEE Transactions on Magnetics, 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 ...
• #### Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ﻿

(Mathematical Inequalities & Applications, 2017-07-18)
Let $I_{v}\left( x\right)$ be modified Bessel functions of the first kind. We prove the monotonicity property of the function \$x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ...