Stability estimates for linear stochastic systems with deviating argument of neutral type

We study linear stochastic differential equations with deviating argument of neutral type and establish sufficient conditions of stability. The functions determining the initial perturbations of solutions are found.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 834–842, June, 1993.     

Reflection of electromagnetic waves from the surface of a cubic ferrite

The reflectivity of electromagnetic waves incident on the surface of a semi-infinite nonconducting cubic ferrite was found both analytically and numerically with inclusion of spin-wave damping. The frequency and field dependences of the reflectivity were found for various values of the damping parameter and the anisotropy and magnetostriction constants in a region far from the point of the orientational phase transition and at this point. It is shown that the reflectivity has peaks near the frequencies of ferromagnetic, magnetoacoustic, and magnetostatic resonances. The peak amplitude decreases with increasing spin-wave damping. At frequencies below the magnetoelastic gap, the reflectivity can take on anomalously small (down to zero) and anomalously large (up to unity) values. These frequencies can lie in the microwave range.     

VUV photon induced fluorescence study of SF5CF3

The interaction of SF(5)CF(3) with vacuum-UV radiation has been investigated by photon induced fluorescence spectroscopy. Total fluorescence yield and dispersed fluorescence spectra of SF(5)CF(3) were recorded in the 200-1000 nm fluorescence window. In all cases, the fluorescence spectra resemble those of CF(3)X (X = H, F, Cl, and Br) molecules. At photon energies below 20 eV, the emission is attributed to the excited CF(3) and CF(2) fragments. The threshold for the CF(3) emission is 10.2 +/- 0.2 eV, giving an upper limit estimate for the SF(5)-CF(3) bond dissociation energy of 3.9 +/- 0.3 eV. The excitation functions of the CF(3) and CF(2) emissions were measured in the photon energy range 13.6-27.0 eV. The resonant structures observed in SF(5)CF(3) are attributed to electronic transitions from valence to Rydberg orbitals, following similar assignments in CF(3)X molecules. The photoabsorption spectrum of SF(5)CF(3) shows features at the same energies, indicating a strong contribution from Rydberg excitations.     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.     

Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Asymptotics of the solution of an initial-boundary value problem for a singularly perturbed parabolic equation in the case of double root of the degenerate equation

For a singularly perturbed parabolic equation, we construct and justify the asymptotics of the classical solution of an initial-boundary value problem in the case of a double root of the degenerate equation. This case substantially differs from the case of a simple root in that the scales of the boundary layer variables are different.     

Stabilization of polystyrene by styrylquinoline containing methacrylates

Abstract

The thermostability of polysterene with/without new styrylquinoline containing methacrylic fragments has been described in the present work. Polystyrene and copolymers based on styrene and new methacrylic styrylquinoline containing monomers were synthesized by free radical thermoinitiated polymerization in the presence of 2,2′-azobisisobutyronitrile (1?wt%) as initiator at inert atmosphere. The impact of 2-[2-(4-methoxyphenyl)ethenyl]quinolin-8-yl 2-methylpropyl-2-enoate (М1), 2-(2-phenylethenyl)quinolin-8-yl 2-methylpropyl-2-enoate (М2), 2-[2-(4-nitrophenyl)ethenyl]quinolin-8-yl 2-methylpropyl-2-enoate (М3) on thermal stability of polystyrene was investigated. The thermostability of polystyrene and copolymers ST:M1, ST:M2, ST:M3 were studied by dynamic thermograviametric analysis. It was shown that destruction of polystyrene with corresponding units M1-M2 starts at 41–42°С higher, than reference polystyrene.