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.     

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.     

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     

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     

Phase Transitions in Gravitational Allocation

Given a Poisson point process of unit masses (“stars”) in dimension d ≥ 3, Newtonian gravity partitions space into domains of attraction (cells) of equal volume. In earlier work, we showed the diameters of these cells have exponential tails. Here we analyze the quantitative geometry of the cells and show that their large deviations occur at the stretched-exponential scale. More precisely, the probability that mass exp(−R ^γ ) in a cell travels distance R decays like exp(-R^f_d(g)){\left(-R^{f_d(\gamma)}\right)} where we identify the functions f _d (·) exactly. These functions are piecewise smooth and the discontinuities of f^￠_d{f^{\prime}_d} represent phase transitions. In dimension d = 3, the large deviation is due to a “distant attracting galaxy” but a phase transition occurs when f ₃(γ) = 1 (at that point, the fluctuations due to individual stars dominate). When d ≥ 5, the large deviation is due to a thin tube (a “wormhole”) along which the star density increases monotonically, until the point f _d (γ) = 1 (where again fluctuations due to individual stars dominate). In dimension 4 we find a double phase transition, where the transition between low-dimensional behavior (attracting galaxy) and highdimensional behavior (wormhole) occurs at γ = 4/3.     

“Asymptotically non-minkowskian” bubbles with gravitational repulsion

It is usually assumed that spherical domain walls can be described by the same equation of state as planar domains. In this case, the spherical domain walls should also demonstrate gravitational repulsion, which would contradict the Birkhoff theorem. However, this theorem does not apply to solutions that are not described by Minkowskian geometry at infinity. In the thin-wall formalism, we consider the solution of the Einstein equations that describes a spherical domain wall with gravitational repulsion and which is “asymptotically non-Minkowskian.” Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 2, pp. 346–352, November, 1997.     

Conformal Geometry of Gravitational Plane Waves

By Brinkmann’s theorem the only Ricci flat and nonflat 4-manifolds admitting non-homothetic conformal vector fields are certain pp-waves. It seems that the converse direction was never completely clarified Which metrics really do occur? It is well known that the conformal group of a nonconformally-flat spacetime is atmost seven-dimensional and that seven is attained for certain pp-waves. Here we explicitly determine all solutions with a seven-dimensional conformal group. In other words We determine all Ricci flat Lorentzian manifolds admitting a seven-dimensional conformal group. They come in three particular families of gravitational plane waves. All of them are exact analytic solutions in terms of elementary functions. Furthermore, it turns out that Ricci flat Lorentzian manifolds with a six-dimensional conformal group are not necessarily real analytic.