Numerical analysis of time-dependent Boussinesq models

In this paper we analyse numerical models for time-dependent Boussinesq equations. These equations arise when so-called Boussinesq terms are introduced into the shallow water equations. We use the Boussinesq terms proposed by Katapodes and Dingemans. These terms generalize the constant depth terms given by Broer. The shallow water equations are discretized by using fourth-order finite difference formulae for the space derivatives and a fourth-order explicit time integrator. The effect on the stability and accuracy of various discrete Boussinesq terms is investigated. Numerical experiments are presented in the case of a fourth-order Runge-Kutta time integrator.     

Front roughening in three-dimensional imbibition

We investigate the structure and dynamics of the interface between two immiscible liquids in a three-dimensional disordered porous medium. We apply a phase-field model that includes explicitly disorder and discuss both spontaneous and forced imbibition. The structure of the interface is dominated by a length scale ξ_× which arises from liquid conservation. We further show that disorder in the capillary and permeability act on different length scales and give rise to different scalings and structures of the interface properties. We conclude with a range of applications.     

A manifestation of magnetism of bismuth in iron garnet films

Bismuth iron garnet films prepared through electron-beam and laser-induced evaporation on (001)-oriented substrates of scandium gallium gadolinium garnet are investigated using ferromagnetic resonance. It is assumed that the additional minima observed in the angular dependence of the resonance field can be associated with the magnetic moment of bismuth ions.     

Domain wall dynamics in a two-layer uniaxial film

Numerical solution of the Slonczewski equations were used to study the motion of an individual domain wall in a two-layer uniaxial film in which the damping parameter and the gyromagnetic ratio depend on the specific layer.     

Recording and reading of three-dimensional optical memory in glasses

We report on three-dimensional (3D) optical memory recording and reading in glass by femtosecond pulses. Optically induced dielectric breakdown of glass is a mechanism of recording. The formulae of dielectric breakdown presented are applicable, in principle, for any crystalline or amorphous dielectric material. Scaling dependences of the probabilities of multi-photon and impact ionization are given. The measured threshold of an in-bulk dielectric breakdown of silica was reproduced numerically by implementing the ionization potential of Si (8.15 eV) for calculations. Exact measures of focal spot size and pulse duration at the focus allowed us to evaluate the intensity of a pulse during recording of 3D optical memory bits with high accuracy. The readout of the 3D optical memory was carried out by the white-light continuum generated from the previously damaged sites (recorded memory bits). The mechanism of the readout was a four-photon parametric interaction. PACS 42.65.Jx; 42.65.Ky; 42.70.Ce; 42.79.Vb     

Fano direct products as rationally connected fibrations

Combining the connectedness principle of Shokurov and Kollár, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational self-maps of Fano direct products coincide. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 183–206, 2004.