相关论文: Approximate solutions to Mathieu's equation
Establishment of phase-coherence and a non-dissipative (super)current between two weakly coupled superconductors, known as the Josephson effect, plays a foundational role in basic physics and applications to metrology, precision sensing,…
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a second moment, it is…
We study the following ultraparabolic equation \[ \frac{\partial}{\partial t}u\left(t,s\right)+\frac{\partial}{\partial…
This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in L^2\_{loc} of a parabolic-relaxed approximation towards the unique constrained…
We give examples where the Heun function exists in general relativity. It turns out that while a wave equation written in the background of certain metric yields Mathieu functions as its solutions in four space-time dimensions, the trivial…
This paper discusses some regularity of almost periodic solutions of the Poisson's equation $-\Delta u = f$ in $\mathbb{R}^n$, where $f$ is an almost periodic function. It has been proved by Sibuya [Almost periodic solutions of Poisson's…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
The spinless Salpeter equation represents the simplest and most straightforward generalization of the Schroedinger equation of standard nonrelativistic quantum theory towards the inclusion of relativistic kinematics. Moreover, it can be…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
Maxwell's equations resemble Schr\"odinger's equation in that an exact solution for a well-defined model delivers all physically relevant details. Solvable microscopic electrodynamic models, however, are rare. An exception is the discrete…
Adjoint field methods are both elegant and efficient for calculating sensitivity information required across a wide range of physics-based inverse problems. Here we provide a unified approach to the derivation of such methods for problems…
The theory of ferromagnetic Pi-junction near the critical temperature is presented. It is demonstrated that in the dirty limit the modified Usadel equation adequately describes the proximity effect in ferromagnets. To provide the…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
The Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of…
The idea of equivalence of the free electromagnetic phase and quantum-mechanical one is investigated in an attempt to seek modifications of Schr\"{o}dinger's equation that could realize it. It is assumed that physically valid realizations…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
We show that recent experiments based on Josephson junctions, SQUIDS, and coupled Josephson qubits have a cosmological interpretation in terms of axionic dark matter physics, in the sense that they allow for analogue simulation of…
We discuss the equivalence relation between the Euclidean bipartite matching problem on the line and on the circumference and the Brownian bridge process on the same domains. The equivalence allows us to compute the correlation function and…
This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference…