相关论文: Maxwell meets Korn: A New Coercive Inequality for …
This paper extends the univariate Theory of Connections, introduced in (Mortari,2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface,…
We study the massless Maxwell system on fixed sub--extremal Kerr-Newman exteriors. In the weak Kerr--Newman regimes with $0<|a|\le c_a M$, $0<|Q|\le c_Q M$, and $c_a,c_Q \in (0,1) $, we prove non--degenerate boundedness, Morawetz /…
The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including both tensor and non-tensor computational regions. First, we extend the existing…
We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding…
In classical treatment of Maxwell equations, the initial and boundary conditions are introduced by mathematical consideration rather than strictly using the Maxwell equations. As a result, the initial and boundary conditions are not logic…
We show that the following generalized version of Korn's second inequality with nonconstant measurable matrix valued coefficients P ||DuP+(DuP)^T||_q+||u||_q >= c ||Du||_q for u in W_0^{1,q}({\Omega};R^3), 1<q<{\infty} is in general false,…
We establish Korn's interpolation inequalities and the rigidity results of the strain tensor of the middle surface for the parabolic and elliptic shells and show that the best constant in Korn's inequalities scales like $h^{3/2}$ for the…
We show that Kondratev's theory for corner domains can be extended to scalar transmission problems between two polygonal materials if the contrast ratio between the two materials is different from -1.
We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^\alpha$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes…
We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which…
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
We consider the problem of domain approximation in finite element methods for Maxwell equations on curved domains, i.e., when affine or polynomial meshes fail to exactly cover the domain of interest. In such cases, one is forced to…
We give a new, simpler proof of the fractional Korn's inequality for subsets of $\mathbb{R}^d$. We also show a framework for obtaining Korn's inequality directly from the appropriate Hardy-type inequality.
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on…
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the…
A translational surface is a tensor product surface constructed from two space curves by translating one along the other. These surfaces are common within geometric modeling and, since their description is parametric, it is desirable to…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Motivated by the problem of optimization of force-field systems in physics using large-scale computer simulations, we consider exploration of a deterministic complex multivariate response surface. The objective is to find input combinations…