Now showing items 1-20 of 97

• #### 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 ...
• #### Absence of eigenvalues of two-dimensional magnetic Schr ̈odinger operators ﻿

(2017-10-17)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr ̈odinger operator possesses no point ...
• #### 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 ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### Asymptotic behaviour of some nonlocal equations in mathematical biology and kinetic theory ﻿

(2019-09)
We study the long-time behaviour of solutions to some partial differential equations arising in modeling of several biological and physical phenomena. In this work, the type of the equations we consider is mainly nonlocal, ...
• #### 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. ...
• #### 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 W1,8 around a carefully chosen, two term ansatz. Such knowledge ...
• #### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation ﻿

(2020-05-01)
We give the asymptotics of the Fourier transform of self-similar solutions for the modified Korteweg-de Vries equation. In the defocussing case, the self-similar profiles are solutions to the Painlevé II equation; although ...
• #### Bayesian approach to inverse scattering with topological priors ﻿

(2020)
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite ...
• #### Bilinear identities involving the $k$-plane transform and Fourier extension operators ﻿

(2019)
We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$-plane transform. As the estimates are $L^2$-based, they follow from ...
• #### Bilinear identities involving the k-plane transform and Fourier extension operators ﻿

(2019-11-30)
We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ...
• #### Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations ﻿

(2019-02)
We determine explicitly a boundary triple for the Dirac operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and \$\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda ...
• #### Carleman type inequalities for fractional relativistic operators ﻿

(2019-09-22)
In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ...
• #### Discreteness of transmission eigenvalues for higher-order main terms and perturbations ﻿

(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 ...
• #### Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions ﻿

(2017-04-28)
In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable ...
• #### Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics ﻿

(2021-07-30)
In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to ...
• #### An efficient multigrid strategy for large-scale molecular mechanics optimization ﻿

(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 ...