A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complexvalued eigenenergies Zi are random variables. The second differences ∆ Zi are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). ForN=3 dimensional Ginibre ens...

Currently, there is much interest in the development of geometric integrators, which retain analogues of geometric properties of an approximated system. This paper provides a means of ensuring that finite difference schemes accurately mirror global properties of approximated systems. To this end, we introduce a cohomology theory for lattice varieties, on which finite difference schemes and othe...

Modeling complex networks of cables inside structures and modeling disjoint objects connected by cables inside large computational domains with respect to the wavelength are two problems that currently present many difficulties. In this paper, we propose a 1D/3D hybrid method in time domain to solve efficiently these two kinds of problems. The method, based upon finite difference schemes, coupl...

We present a well-posed and discretely stable perfectly matched layer for the anisotropic (and isotropic) elastic wave equations without first re-writing the governing equations as a first order system. The new model is derived by the complex coordinate stretching technique. Using standard perturbation methods we show that complex frequency shift together with a chosen real scaling factor ensur...

The authors address the Matched Phase Velocity method for bounding an electromagnetic (EM) domain in the MAGIC finite difference-time domain (FDTD) particle-in-cell (PIC) EM code. Reflected power is shown to be reduced 18 dB compared to the conventional port treatment. Boundary quality is preserved under penetration by charged particles.

A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the lin...

We develop a local flux mimetic finite difference method for second order elliptic equations with full tensor coefficients on polyhedral meshes. To approximate the velocity (vector variable), the method uses two degrees of freedom per element edge in two dimensions and n degrees of freedom per n-gonal mesh face in three dimensions. To approximate the pressure (scalar variable), the method uses ...

In the present note we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon depending on the value of a free parameter. To this equation we apply an adaptive numerical method on redistributed grids. We show that usual central finite differences, which are second order accurate on a uniform grid, c...