相关论文: A Conducting Checkerboard
The effective conductivity of the infinite checkerboard (chessboard) and analogous higher-dimensional checkered structures, are considered. An algebraic expression is derived by accounting for the symmetries of the structures.
We consider the so called Calder\'on problem which corresponds to the determination of a conductivity appearing in an elliptic equation from boundary measurements. Using several known results we propose a simplified and self contained proof…
This work provides a comprehensive exploration of various methods in solving incompressible flows using a projection method, and their relation to the occurrence and management of checkerboard oscillations. It employs an algebraic…
Many practical applications exploit an external local magnetic field -- magnetic obstacle -- as an essential part of their constructions. Recently, it has been demonstrated that the flow of an electrically conducting fluid influenced by an…
The volume charge density for a conducting ellipsoid is expressed in simple geometrical terms, and then used to obtain the known surface charge density as well as the uniform charge per length along any principal axis. Corresponding results…
We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find the mean flow through an arbitrary…
Within a Green's function formalism we calculate the electronic structure around static extended magnetic and non-magnetic perturbations in a d-wave superconductor. In partucular, we discuss recent elastic neutron scattering and scanning…
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
We consider a system of multiple insulating rigid bodies moving inside of an electrically conducting compressible fluid. In this system we take into account the interaction of the fluid with the bodies as well as with the electromagnetic…
The effective action for the current and density is shown to satisfy an evolution equation, the functional generalization of Callan-Symanzik equation. The solution describes the dependence of the one-particle irreducible vertex functions on…
The present work is aimed at defining the behavior of the electromagnetic field near the edge of a resistive half-plane, taken separately, as well as in conjunction with a perfectly conducting half-plane. The efficiency of accounting for…
An algorithm is given to efficiently compute $L$-functions with large conductor in a restricted range of the critical strip. Examples are included for about 21000 dihedral Galois representations with conductor near $10^7$. The data shows…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…
In two dimensions, quenched disorder always rounds transitions involving the breaking of spatial symmetries so, in practice, it can often be difficult to infer what form the symmetry breaking would take in the ``ideal,'' zero disorder…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
We predict the existence of large electric fields near the surface of superconducting bodies of ellipsoidal shape of dimensions comparable to the penetration depth. The electric field is quadrupolar in nature with significant corrections…
Electron conductivity is an important material property that can provide a wealth of information about the underlying system. Especially, the response of the conductivity with respect to electromagnetic fields corresponds to various…
Two dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on `capacitor-like' geometries with current flowing between two…
The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse…