Related papers: Circular plate capacitor with different disks
We study the classic problem of the capacitance of a circular parallel plate capacitor. At small separations between the plates, it is initially considered in 19th century by Kirchhoff who found the leading and the subleading term in the…
In this paper we study the two disks capacitor, for equal and different radii. The new results obtained allow a complete characterization of capacity coefficients and forces at short distances. An extensive numerical calculation confirms…
The electrostatic problem of two coaxial parallel charged disks of different radii in infinite space is solved by expansion in terms of complex potentials. For perfectly conducting disks a pair of coupled integral equations is derived for…
A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled…
This note is about uniform, plane, singly connected, regular Hall-plates with an arbitrary number of contacts exposed to a uniform magnetic field of arbitrary strength. In practice, the regular symmetry is the most common one. If the…
We consider the two-dimensional Kirchhoff-Love plate equation in the context of elasticity modeling the stresses and deformations in thin plates subjected to forces and moments. We establish global recovery of the material parameters like…
In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…
We introduce a Nitsche's method for the numerical approximation of the Kirchhoff-Love plate equation under general Robin-type boundary conditions. We analyze the method by presenting a priori and a posteriori error estimates in…
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham…
In the present article, using a non-commutative integration method of linear differential equations, we, considering the Klein-Gordon equation with the $L$-constant electric field with large $L$ and using the light cone variables, find new…
I discuss uniform, isotropic, plane, singly connected, electrically linear, regular symmetric Hall-plates with an arbitrary number of N peripheral contacts exposed to a uniform perpendicular magnetic field of arbitrary strength. In…
We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly…
A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary…
We find a system of two polynomial equations in two unknowns, whose solution allows to give an explicit expression of the conformal representation of a simply connected three sheeted compact Riemann surface onto the extended complex plane.…
The capacitance of an arbitrarily shaped object is calculated with the same second-kind integral equation method used for computing static and dynamic polarizabilities. The capacitance is simply the dielectric permittivity multiplied by the…
We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the…
We derive a residual a posteriori estimator for the Kirchhoff plate bending problem. We consider the problem with a combination of clamped, simply supported and free boundary conditions subject to both distributed and concentrated (point…
For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for the inverse problem of determining smooth cavities inside a thin isotropic cylinder {}from a single…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
The capacitance matrix relates potentials and charges on a system of conductors. We review and rigorously generalize its properties, block-diagonal structure and inequalities, deduced from the geometry of system of conductors and analytic…