相关论文: A Conducting Checkerboard
We investigate equilibrium flux lattice structures in superconductors with unconventional order parameters, such as high-$T_c$ cuprates, using a generalized London model with non-local electrodynamics derived from a simple microscopic…
A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on the rank of an elliptic curve is formulated.
Study of various interesting features related to the nonlinear electrical response in composite materials through a model bond percolative system.
We rederive, using an elementary formalism, the general solution to the equations of motion for a superconducting string with a chiral (null) neutral current, earlier obtained by Carter and Peter. We apply this solution to show that the…
We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.
In this paper we study the existence of solutions of thedegererate elliptic system.
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
As a method for controlling active materials, researchers have suggested designing patterns of activity on a substrate, which should guide the motion of topological defects. To investigate this concept, we model the behavior of a single…
In this brief tutorial review, I show how phase coherent properties of disordered conductors can be described in a simple and unified way. These properties include transport properties like weak-localization correction and universal…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
We established the existence, uniqueness and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two dimensional steady compressible Euler equations. The vortex line…
A point charge between the plates of a capacitor generates an influence charge distribution on the plates that modify the electric field acting upon the point charge. This effect is described by the well-known Dirichlet Green's function for…
In this note we show that any embedded graph has a checkerboard colourable twisted dual and any Eulerian embedded graph has a checkerboard colourable partial Petrial, answering questions posed by Ellis-Monaghan and Moffatt. The proofs are…
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…
In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
The interplay between electrostatic interactions and orientational correlations is studied for a model system of charged rods positioned on a chain, using Monte Carlo simulation techniques. It is shown that the coupling brings about the…
The checkerboard lattice has been proposed to host topological flat bands as a result of destructive interference among its various electronic hopping terms. However, it has proven challenging to realize experimentally due to the difficulty…
We introduce a class of billiards with chaotic unidirectional flows (or non-chaotic unidirectional flows with "vortices") which go around a chaotic or non-chaotic "core", where orbits can change their orientation. Moreover, the…
The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux…