Related papers: Experimental determination of circuit equations
The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a…
The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general…
Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we…
We give integral formulas to approximate solutions of Dirichlet and Neumann problems for Helmholtz equation at high frequencies. These approximations are valid in the complementary of a union of convex compact obstacles. The first step of…
In a recent article, we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance, inductive…
We introduce a new motif for constructing robust digital logic circuits using input/output chemical reaction networks. These chemical circuits robustly handle perturbations in input signals, initial concentrations, rate constants, and…
Let $\log^Cn\le d\le n/2$ for a sufficiently large constant $C>0$ and let $A_n$ denote the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices. We prove that as $n$ tends to infinity, the empirical spectral…
The regular solutions to the Sch\"ordinger equation in the case of an electron experiencing a Coulomb force are well known. Being that the radial part of the differential equation to be solved is second order in derivatives, it will have…
We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of…
A short review is given of the simplified differential equations approach to Master Integrals, which was recently proposed by one of the authors. We show its applicability by calculating some non-trivial two-loop planar Master Integrals,…
In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is…
This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight,…
An equational logic program is a set of directed equations or rules, which are used to compute in the obvious way (by replacing equals with ``simpler'' equals). We present static analysis techniques for efficient equational logic…
This paper is an electronic application to my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a very…
This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in $\R^2$. It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form…
Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov…
The conductivity of an electron gas can be alternatively calculated either from the current--current or from the density--density correlation function. Here, we compare these two frequently used formulations of the Kubo formula for the…
Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparametrization invariance of the free…