Motion of magnetic domain walls

We consider the dynamics of one-dimensional micromagnetic domain walls in layers of uniaxial anisotropy. In the regime of bulk materials, i.e. when the thickness is assumed to be infinite, and the magnetostatic interaction terms appear as local quantities, explicit traveling wave solutions for the corresponding Landau-Lifshitz equation, known asWalker exact solutions, can be constructed. A natural question is whether this construction can be perturbed to the non-local regime of layers of finite thickness. Our stability analysis gives an affirmative answer. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gravitational field of a massive rotating spherical shell in RTG

We obtain a continuous solution describing the gravitational field of a massive rotating shell in the relativistic theory of gravity (RTG) in an approximation linear in expansion rate but arbitrary in the magnitude of the static gravitational field. We show that the coordinate-invariant dragging effect inside the shell may be used to define a global inertial coordinate system.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 315–319, February, 1996.     

Moving domain walls in magnetic nanowires

This paper investigates the reversal of magnetic nanowires via a perturbation argument from the static case. We consider the gradient flow equation of the micromagnetic energy including the nonlocal stray field energy. For thin wires and weak external magnetic fields we show the existence of travelling wave solutions. These travelling waves are almost constant on the cross section and can thus be seen as moving domain walls of a type called transverse wall.     

On the motion of magnetic domain walls

In certain regimes and for relative small applied fields, magnetic domain walls behave as mechanical particles in a viscous fluid. By analogy their dynamic can be described with an evolution equation of the form Mq̈ + β^–1 q̇ = H (1) where M and are the effective wall mass and wall mobility, and H is an applied forcing. These effective parameters depend on the particular geometrical configuration and dynamical model considered. We present a method that can be used to systematically estimate the wall mass and wall mobility in terms of the static wall geometry and various physical constants. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Localization of light particles on fermion-induced domain walls

We offer a possible explanation for the appearance of light composite fermions and Higgs bosons on a four-dimensional domain wall. The pattern of light particle trapping is attributed to a strong self-interaction of five-dimensional pre-quarks. We calculate the low-energy effective action which manifests the invariance under the so-called τ-symmetry. After that, we find a set of vacuum solutions that break the symmetry and the five-dimensional translational invariance. The induced relations between low-energy couplings for Yukawa and scalar field interactions allow us to make certain predictions for light particle masses and couplings themselves, which may provide a signature of the higher-dimensional origin of particle physics in the forthcoming experiments. Bibliography: 53 titles. Dedicated to our old friend Petr P. Kulish, in honor of his 60th birthday Published in Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 11–42.     

On the statics and dynamics of transverse domain walls in bilayer piezoelectric-magnetostrictive nanostructures

In this article, we investigate the static and dynamic properties of transverse Bloch domain wall in an isotropic, linearly elastic bilayer piezoelectric-magnetostrictive nanostructures under the influence of axial (driving), transverse magnetic fields and spin-polarized electric current. To be precise, we perform the analysis under the framework of the one-dimensional Extended Landau–Lifshitz–Gilbert equation in the presence of stresses generated by a piezoelectric actuator. First, we derive the magnetization profile in the two distant domains and then study the static magnetization profile in the sole presence of the applied transverse magnetic field. Next, we propose a new Walker’s type trial function and establish the analytical expressions of the dynamical quantities such as moving DW profile, velocity, displacement, and excitation angle by using a small angle approximation approach. Finally, we delineate the obtained analytical results with the aid of numerical illustrations.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

A new method for solving the eikonal equation in the spherical computing domain

In order to overcome the problem of singularities and nonuniform grids arising when solving eikonal equation in spherical coordinate systems, a spherical Cartesian coordinate system is defined and the Hamiltonian form of the eikonal equation according to this coordinate system is given. A modified velocity function that can transform spherical coordinate system–based eikonal equation into ones based on a spherical Cartesian coordinate system is deduced by using a differential geometric method where a layered distribution of the velocity function is assumed. After comparing the results of using this approach with the traditional method of solving eikonal equation based on a spherical coordinate system, the viability of the transformation to a spherical Cartesian coordinate system based on a modified velocity function is proven. Despite the assumption of a layered distribution of the velocity function, it is also proven that the method will hold for a velocity function under any three-dimensional distribution. The new method overcomes problems present in traditional approaches and opens up a new way of solving eikonal equation in a spherical computational domain.     

引力规范理论中的一类引力波方程

该文给出了Vierbein表述的局域Lorentz群引力规范理论中的一类引力波方程。证明了Bondi平面波方程和引力孤立波方程均被该类方程所包含,这些方程的解均为该类方程在一定条件下的特解。因而这些解是与量子场论协调一致的。     

Curved domain walls dynamics driven by magnetic field and electric current in hard ferromagnets

The propagation of curved domain walls in hard ferromagnetic materials is studied by applying a reductive perturbation method to the generalized Landau–Lifshitz–Gilbert equation. The extended model herein considered explicitly takes into account the effects of a spin-polarized current as well as those arising from a nonlinear dissipation.     

Gravitational experiments in space

Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 1, pp. 3–10, January, 1989.     

A domain decomposition method for solving the hypersingular integral equation on the sphere with spherical splines

We present an overlapping domain decomposition technique for solving the hypersingular integral equation on the sphere with spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O(H/δ), where H is the size of the coarse mesh and δ is the overlap size, which is chosen to be proportional to the size of the fine mesh. In the case that the degree of the splines is even, a better bound O(1 + log²(H/δ)) is proved. The method is illustrated by numerical experiments on different point sets including those taken from magsat satellite data.     

Entropic repulsion of an interface in an external field

We consider an interface above an attractive hard wall in the complete wetting regime, and submitted to the action of an external increasing, convex potential, and study its delocalization as the intensity of this potential vanishes. Our main motivation is the analysis of critical prewetting, which corresponds to the choice of a linear external potential. We also present partial results on critical prewetting in the two dimensional Ising model, as well as a few (weak) results on pathwise estimates for the pure wetting problem for effective interface models.Mathematics Subject Classification (2000): 60K35, 82B41, 82B27