相关论文: Magnetostatic problems in fractal domains

We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the…

The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional…

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD)…

The weak well-posedness, with the mixed boundary conditions, of the strongly damped linear wave equation and of the non linear Westervelt equation is proved in the largest natural class of Sobolev admissible non-smooth domains. In the…

Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on…

The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…

A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is…

We consider the Fast Fourier Transform (FFT) based numerical method for thin film magnetization problems [Vestg{\aa}rden and Johansen, SuST, 25 (2012) 104001], compare it with the finite element methods, and evaluate its accuracy. Proposed…

A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…

Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid…

Structural and static properties of a classical two-dimensional (2D) system consisting of a finite number of charged particles which are laterally confined by a parabolic potential are investigated by Monte Carlo (MC) simulations and the…

This paper proposes an efficient FDTD technique for determining electromagnetic fields interacting with a finite-sized 2D and 3D periodic structures. The technique combines periodic boundary conditions---modelling fields away from the edges…

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…

We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…

Despite multiple efforts, there exist many unsolved fundamental problems related with detection and analysis of internal polarization structure and related phase transitions in ferroelectric domain walls. Their solution can be very…

This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…

The imaging of magneto-dynamical processes has been, so far, mostly a two-dimensional business, due to the constraints of the available experimental techniques. In this manuscript, building on the recent developments of soft X-ray magnetic…

In this article, we provide a simple and systematic way to represent general (inhomogeneous) fractals that may look different at different scales and places. By using set-valued compression maps, we express these general fractals as…

We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on…