The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of real and imaginary parts of second difference, as well as of its radius and of its argument (angle). For the generic N-dimensional Ginibre ensemble an exact ...

Abstract. In the case of the heat equation ut = uxx + V u on the real line there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a similar phenomenon holds when one replaces the real line by the integers. In this case the second derivative is replaced by the second difference operator L...

This paper is devoted for a rigorous investigation of Hahn’s difference operator and the associated calculus. Hahn’s difference operator generalizes both the difference operator and Jackson’s q-difference operator. Unlike these two operators, the calculus associated with Hahn’s difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to...

The Ginibre ensemble of complex random matrices is studied. The complex-valued random variable of the second difference of complex energy levels is defined. For the N = 3 dimensional ensemble, we calculate distributions of the second difference real and imaginary parts, as well as its radius and of its argument (angle). For the generic N -dimensional Ginibre ensemble an exact analytical formula...

This article shows the interfacial relation in electrodynamics shall be corrected in discrete grid form which can be seen as certain numerical dispersion beyond the usual bulk type. Furthermore we construct a lossy conductor model to illustrate how to simulate more general materials other than traditional PEC or simple dielectrics, by a new conformal FDTD method which main considers the effects...

Calculus on time scales was established in 1988 by Stefan Hilger. It includes both the classical derivative and the forward difference operator as special cases. It also includes Riemann integrals and finite sums as inverse operations. However, it does not include the Jackson q-difference operator on R and the Jackson q-integral on R. Also, it does not include neither the difference operator on...

The combination of classical time reversal techniques and nonlinear elastic wave response, induced by the presence of a localized area of damage, brings about a significant enhancement of nonlinear imaging. In this paper, this concept is discussed from a numerical point of view, using multiscale Finite Difference Time Domain and PseudoSpectral Time Domain elastic wave solvers.

In this paper, the parallel implementation of the Wave-Equation Finite Difference Time Domain (WE-FDTD) method, using the Message Passing Interface (MPI) system, is presented. The WE-FDTD computational domain is divided into subdomains using onedimensional topology. Numerical simulations have been carried out for a line current source radiating in two-dimensional domains of different sizes and ...

The Quantum Finite-Difference Time-Domain (FDTD-Q) method is a numerical method for solving the time evolution of the Schrödinger equation. It can be applied to systems of interacting particles, allowing for realistic simulations of quantum mechanics of various experimental systems. One of the drawbacks of the method is that divergences in the numerical evolution occur rather easily in the pres...