相关论文: Geometric invariance from outer surfaces: Laplace-…
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in smooth three-dimensional domains is characterized by model problems inside the domain or on its boundary.…
We study the conditions of integrability when the boundary terms are considered in the variation of the geometric contribution of the Einstein-Hilbert action. We explore the emergent physical dynamics that is obtained when we make a…
The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili-Sire and…
For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between…
The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields. The quite large Hamiltonian matrix is transferred into the band-like…
We study the nonlinear evolution of the magnetic buoyancy instability in rotating and non-rotating gas layers using numerical solutions of non-ideal, isothermal MHD equations. The unstable magnetic field is either imposed through the…
The interplay between quantum geometry and electron correlation has emerged as a compelling paradigm in quantum many-body physics. Recent studies have highlighted the diagnostic utility of quantum geometry in identifying magnetic…
We study $\infty$-Ground states in convex domains in the plane. In a polygon, the points where an $\infty$-Ground state does not satisfy the $\infty$-Laplace Equation are characterized: they are restricted to lie on specific curves, which…
Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic…
The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and…
This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the…
Magnetic helicity is a quantity that underpins many theories of magnetic relaxation in electrically conducting fluids, both laminar and turbulent. Although much theoretical effort has been expended on magnetic fields that are everywhere…
Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…
We apply scattering theory on asymptotically hyperbolic manifolds to singular Yamabe metrics, applying the results to the study of the conformal geometry of compact manifolds with boundary. In particular, we define extrinsic versions of the…
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…
We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
We consider smooth bounded surfaces with a smooth boundary and a prescribed background metric g_0. We now consider all metrics g conformal to g_0 which have a prescribed volume M. We now minimize the first eigenvalue of the Laplace operator…
An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were…
We analyze the response of a type II superconducting wire to an external magnetic field parallel to it in the framework of Ginzburg-Landau theory. We focus on the surface superconductivity regime of applied field between the second and…