Related papers: A Conducting Checkerboard
We examine several conducting spheres moving through a magnetic field gradient. An analytical approximation is derived and an experiment is conducted to verify the analytical solution. The experiment is simulated as well to produce a…
Let $X$ be a quadratic vector field with a center whose generic orbits are algebraic curves of genus one. To each $X$ we associate an elliptic surface (a smooth complex compact surface which is a genus one fibration). We give the list of…
Ellipses, parabolas and hyperbolas all have beautiful reflective properties. However, an intuitive explanation for why they have those properties has been lacking. There exist many mathematical proofs, but they tend to involve several…
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…
We investigate the transport of active matter system in the presence of a disordered square lattice of half-circles, which is built by removing a fraction of them from the initial full lattice. We consider no external field. We observe a…
In this paper Tricomi-Gellerstedt-Keldysh-type fractional elliptic equations are studied. The results on the well-posedness of fractional elliptic boundary value problems are obtained for general positive operators with discrete spectrum…
A composite conductive material, which consists of fibers of a high conductivity in a matrix of low conductivity, is discussed. The effective conductivity of the system considered is calculated in Clausius-Mossotti approximation. Obtained…
The conductance of one-dimensional nano-wires of interacting electrons connected to non-interacting leads is calculated in the linear response regime. Two different approaches are used: a many-body Green function technique and a relation to…
The complexity of the elliptic curve method of factorization (ECM) is proven under the celebrated conjecture of existence of smooth numbers in short intervals. In this work we tackle a different version of ECM which is actually much more…
We take account of normal currents that emerge when vortices move. Moving Abrikosov vortices in the bulk and Pearl vortices in thin films are considered. Velocity dependent distributions of both normal and persistent currents are studied in…
In this article, we investigate certain theoretical aspects of the hierarchical controllability problem in one-dimensional wave equations within a moving domain using Stackelberg strategy. The controls are applied along a portion of the…
We calculate the correlation functions and the DC conductivity of Luttinger liquid superlattices, modeled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a…
We determine the distribution of the conductors $N$ of rational elliptic curves when ordered by naive height $H$, in the form of an explicit density function for the ratios $N/H$. Our work is essentially an effective version of the…
Consider a three dimensional system which looks like a cross-connected pipe system, i.e. a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we…
We develop a detailed analysis of electron transport in normal diffusive conductors in the presence of proximity induced superconducting correlation. We calculated the linear conductance of the system and the profile of the electric field.…
When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exceeds the percolation threshold. Such a behavior is well known…
This paper presents the basic ideas and properties of elliptic functions and elliptic integrals as an expository essay. It explores some of their numerous consequences and includes applications to some problems such as the simple pendulum,…
We propose an approach allowing the computation of currents and their correlations in interacting multiterminal mesoscopic systems involving quantum dots coupled to normal and/or superconducting leads. The formalism relies on the expression…
We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more efficient than current implementation as the conductor of…
We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the…