No 4 (2015)

In this paper the solvability of a functional-differential equation is studied in the scale of Kondrat’ev weighted spaces. The equation is considered in the real plane, it has constant coefficients and transformations of arguments of required function, and this transformation consists in the contraction of one argument and the expansion of another. These transformations are called by orthotropic contractions here. The considered problem boils down to an invertibility of a difference operator on the real line with variable smooth coefficients stabilized in the infinity. Sufficient conditions of the invertibility of the difference operator and the initial functional differential operator were obtained in algebraic form. It is well-known that the properties of functional differential equations are largely defined by the structure of point orbits under the action of a group generated by transformations attended in the equation. The orbits of isotropic contractions are situated on the rays passing through the origin and condense near the origin”- a fixed point of the operator. In case of contraction of one argument and expansion of another the orbits are situated on curves having a form of hyperbolas. Herewith the origin is a fixed point of the operator as before. Therefore it is natural to assume that problems with orthotropic contractions differ in their properties and analysis methods from problems with isotropic contractions.

The paper presents some test results of the heterogeneous computing cluster HybriLIT put into operation at the Laboratory information technologies of the Joint Institute for Nuclear Research. The structure of the cluster includes computational nodes with NVIDIA graphical accelerators and Intel Xeon Phi coprocessors. The necessity of integration of such a computational platform in the JINR Multifunctional Information and Computing Complex is determined by a global tendency to use hybrid computing architectures for carrying out massive-parallel computations in applied scientific problems solution. Test of the cluster aimed at: first of all, test of the efficiency of hardware and software settings that include operational system, resource manager, file system, compilers, and, secondly, test of the efficiency of using different architectures for the solution of particular applied problems in order to provide user guides on specialized libraries. For realization of the cluster test, an approach that includes test computations by means of standard program packages such as Linpack and program complexes established in LIT has been developed. The presented results show that the use of hybrid computing architectures allow accelerate the solution of applied scientific problems, and heterogeneous computing cluster HybriLIT is an effective means of accomplishing this aim.

Optical waveguide devices - modulators and switches are one of the most demanded photon devices on whom further possibility of increase of keyword parameters of integrated optical circuits and telecommunication systems depends. Search of new development approaches of necessary element basis on the basis of combination of planar technology of integrated optics and the thin-film technology “silicon on an insulator” is necessary for increase of their competitiveness. For silicon devices methods of electrooptical modulation are based on effect of dispersion of the free carriers which density depends on the level of applied voltage. In operation the perspectives of application of p-i-n of electrooptical modulators executed on the basis of the “silicon on an insulator” technology are discussed. In comparison with other class of modulators on the basis of lithium niobate, the researched devices potentially have a row of advantages, such as the low level of power consumption (within 1 W), nanosized miniaturization, high throughput (modulation frequency band over 100 GHz). The researched nanophoton devices are hi-tech and expensive. Their simulation at the physical layer is important and as for understanding of the physical processes proceeding in them and for optimization of their parameters for the purpose of achievement of optimum characteristics. On the basis of computer simulation in this operation possibility of optimization of parameters of nanosized electrooptical p-i-n of the waveguide modulators which potentially will allow to realize highly effective optical modulation is researched.

Results of the study of charged particle trajectories in a toroidal magnetic configuration like tokamak with “magnetic islands” are presented. Particle trajectories are calculated using the three-dimensional numerical code based on numerical integration of exact equations of motion. Magnetic configuration is described analytically with use of an universal approach in terms of Hamiltonian function. This approach generalizes the traditional streaming presentation of magnetic field and guaranties the solenoidality condition being satisfied exactly. To describe magnetic configuration with islands, iterative procedure is used; the initial (basic) magnetic configuration is chosen to have nested magnetic surfaces. Small helical perturbation splits the rational surface resonant with the perturbation helicity. In the vicinity of such surface the chain of magnetic islands is formed. Our study of the motion of charged particles showed that the existence of the magnetic island has no qualitative impact on the Poincare cross-section of the trapped particle trajectory for having a standard “banana” form, typical for basic tokamak configuration. As for passing particle, which moves predominantly along the magnetic field line, its trace of the trajectory has an island structure in the poloidal cross-section. It is shown that both trapped and passing particles in their motion can cross the separatrix between magnetic island and nested magnetic surfaces; the crossing can happen in any point of separatrix. Thus, it is shown that the magnetic island has no “barrier” properties and isn’t capable to provide the improved confinement of charged particles.