Discrete-to-continuum limit of magnetic forces: Dependence on the distance between bodies
type: Item
instance of: scholarly article
title: Discrete-to-continuum limit of magnetic forces: Dependence on the distance between bodies
zbMATH Open document ID: 1185.78006
author: Anja Schlömerkemper
author: Bernd Schmidt
published in: Archive for Rational Mechanics and Analysis
publication date: 2009-08-27T00:00:00Z
review text: The paper revisits a classical problem of the interaction between two solid magnetic bodies brought in the contact, in the case when the remaining distance between the bodies may be counted in terms of spacings of the intrinsic lattices which account for the magnetic properties of the bodies. It is relevant to mention that the first classical results concerning magnetic forces acting between macroscopic bodies were published by Augustin Cauchy in 1828. In the present paper, the authors present a rigorous analysis of the problem. In addition to the previously known long-range and short-range forces of the interaction between the two bodies, they derive an extra force, which is contributed to by the microscopic interactions between atomistic dipoles forming the magnetic lattices in the two bodies. This additional force exponentially decays as a function of the distance between the bodies, measured in units of the lattice period.
Mathematics Subject Classification ID: 78A30
zbMATH DE Number: 5598871
zbMATH Keywords: dipole-dipole forces
zbMATH Keywords: magnetostatics
zbMATH Keywords: Cauchy classics
reviewed by: B. A. Malomed
MaRDI profile type: Publication
full work available at URL: s00205-008-0134-4
OpenAlex ID: W2113614415
cites work: On the continuum theory of deformable ferromagnetic solids
cites work: Q4385502
cites work: Discrete-to-continuum limit of magnetic forces.
cites work: Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. I: Analysis
cites work: Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. II: Numerical simulation
cites work: About solutions of Poisson's equation with transition condition in non-smooth domains
cites work: Mathematical derivation of the continuum limit of the magnetic force between two parts of a rigid crystalline material
cites work: Q5437249
DOI: 10.1007/S00205-008-0134-4
description: scientific article; zbMATH DE number 5598871