相关论文: Persistent currents on graphs

The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal-insulator…

Previously, the graph permanent was introduced as a single-valued invariant for graphs $G$ with $|E(G)| = k(|V(G)|-1)$ for some $k \in \mathbb{Z}_{>0}$. Herein, we construct the extended graph permanent, an infinite sequence for all graphs.…

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…

In this work, we study the propagation of influence and computation in dynamic distributed systems. We focus on broadcasting models under a worst-case dynamicity assumption which have received much attention recently. We drop for the first…

We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the current through the emergent conducting graph, representing a digital circuit. In the interior of a large network…

We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…

The two components for infinite exchangeability of a sequence of distributions $(P_n)$ are (i) consistency, and (ii) finite exchangeability for each $n$. A consequence of the Aldous-Hoover theorem is that any node-exchangeable,…

We calculate the average persistent current in a mesoscopic metal ring threaded by a magnetic flux in the diffusive regime. It is shown that the classical electromagnetic energy leads to a {\it{universal}} average current of the order of $…

We propose four different mechanisms responsible for paramagnetic or diamagnetic persistent currents in normal metal rings and determine the circumstances for change of the current from paramagnetic to diamagnetic ones and {\it vice versa}.…

In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…

The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…

We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localised initial conditions, that are unbiased with respect to the…

We present a general theory of current deviations in straight current carrying wires with random imperfections, which quantitatively explains the recent observations of organized patterns of magnetic field corrugations above micron-scale…

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…

We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobius inversion of the graded rank function, which is obtained from the rank function using the unary numeral system. Both persistence diagrams…

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the…

The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

The response function of graphene is calculated in the presence of a constant current across the sample. For small drift velocities and finite chemical potential, analytic expressions are obtained and consequences on the plasmonic…