Related papers: Electrostatics and Riemann Surfaces
Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties…
We survey some recent developments in the ergodic theory for hyperbolic Riemann surface laminations. The emphasis is on singular holomorphic foliations. These results not only illustrate the strong similarity between the ergodic theory of…
This paper presents results for the electric field due to a uniformly charged elliptical beam in the region outside the beam.
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes.…
The problem of the surface current excitation in a conductive targets by a relativistic electron electric field as the origin of such radiation mechanisms as diffraction and transition radiation of relativistic electron was considered in…
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with…
Combining classical electrodynamics and density functional theory (DFT) calculations, we develop a general and rigorous theoretical framework that describes the energetics of metal surfaces under high electric fields. We show that the…
We look at computational physics from an electrical engineering perspective and suggest that several concepts of mathematics, not so well-established in computational physics literature, present themselves as opportunities in the field. We…
A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in. e.g., first-principles-based simulations of…
Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…
A setup for studying the influence of external electric fields on dynamic surface processes is described. Spatially-extended homogeneous electric fields are realized by applying a DC voltage in between a planar electrode and a metallic…
A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…
We introduce Explicit Neural Surfaces (ENS), an efficient smooth surface representation that directly encodes topology with a deformation field from a known base domain. We apply this representation to reconstruct explicit surfaces from…
We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
This paper is concerned with the construction of extremal elliptic K3 surfaces. It gives a complete treatment of those fibrations which can be derived from rational elliptic surfaces by easy manipulations of their Weierstrass equations. In…
We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used to study the Picard numbers, the ranks and the minimal…
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…
Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough…
We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory…