Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay

To obtain sufficient conditions for the asymptotic stability of linear periodic systems with fixed delay commensurable with the period of coefficients, singular numbers of the monodromy operator are used. To find these numbers, a self-adjoint boundary value problem for ordinary differential equations is applied. We study the motion of eigenvalues of this boundary value problem under a variation of a parameter. Obtaining sufficient conditions for the asymptotic stability is reduced to finding the bifurcation value of the parameter for the boundary value problem.     

Complex Calculation of Solution Pulsed Nuclear Reactor VIR-2M

Physics of Atomic Nuclei - The results of complex calculation of the solution pulsed nuclear reactor (PNR) VIR-2M are presented. The simulation of the fuel solution dynamics is described, and...     

Interaction of solitary waves for the generalized KdV equation

We consider a class of generalized KdV equations with a small parameter and nonlinearities of the type u^m. We create a finite differences scheme to simulate the solution of the Cauchy problem and present some numerical results for the problem of the solitary waves interaction. In particular, we consider sufficient condition under which pairs of solitary waves interact, in the asymptotic sense, in accordance with the soliton scenario.     

Mathematical simulation of the shock compression of porous molybdenum using a heterogeneous model

The shock compression of a heterogeneous material is numerically simulated. The physical model used for the simulation is based on a layered model of a porous material and consists of a set of thin matrix plates with a known equation of state that are separated by filler layers also with a known equation of state. The model is intended to calculate the parameters (pressure, temperature, mass velocity) of shock compression of the matrix and the filler of heterogeneous materials during their one-dimensional shock compression in terms of a developed hydrodynamic code. The adequacy of the proposed model is tested on porous molybdenum during shock-wave loading to a pressure of 15–70 GPa and a temperature of 4000 K.     

Long-wavelength optical phonons in the ZnTe/Zn<Subscript>0.8</Subscript>Cd<Subscript>0.2</Subscript>Te superlattice

The lattice IR reflection spectra of a ZnTe/Zn_0.8Cd_0.2Te superlattice measured at temperatures of 300 and 10 K are analyzed. The ZnTe/Zn_0.8Cd_0.2Te superlattice is grown by molecular-beam epitaxy on a GaAs substrate with a ZnTe buffer layer. It is found that the lattice IR reflection spectra of the studied structure exhibit only one reflection band. Dispersion analysis of the experimental spectrum has revealed the presence of one lattice TO mode close in frequency to the mode of pure ZnTe. This result is explained by a shift in the frequency of the lattice modes of the ZnTe and Zn_0.8Cd_0.2Te layers of the superlattice toward each other. In turn, this shift is caused by internal elastic stresses in the superlattice due to a mismatch between the lattice parameters of the materials of these layers.     

The Kuramoto-Sivashinsky equation for the defect-deformation instability of a surface-stressed nanolayer

It is demonstrated that the evolution of the surface relief of the stressed elastic nanolayer that interacts with mobile point defects can be described using a nonlinear equation similar to the Kuramoto-Sivashinsky equation. The solution to the equation describes the threshold (with respect to the defect concentration or the mechanical stress) transition to the periodic spatially bent state of the layer with the simultaneous generation of spatially periodic defect clusters at the extrema of the spontaneously emerging surface relief. In this case, the layer deformation corresponds to the displacements in the static bending Lamb wave. The self-organizing periodic cellular deformation-defect surface structure can serve as a universal seed for the subsequent growth of nanoparticles in the processes of laser, ion, or electrochemical etching and in molecular beam epitaxy of nanostructures. Original Text ? Astro, Ltd., 2009.     

Determination of the saturation vapor pressure of silicon by Knudsen cell mass spectrometry

Silicon evaporation has been investigated by high-temperature mass spectrometry, and the saturation vapor pressure of silicon over its melt has been determined over the temperature range from 1739 and 2326 K. The saturation vapor pressure data obtained via silicon evaporation from Knudsen cells made of molybdenum, tungsten, molybdenum disilicide-lined molybdenum, and graphite silicided by the gas-phase method are compared. Among these materials, silicided graphite is the most inert toward silicon vapor. The silicon partial pressures measured in the silicided graphite cell are close to the recommended values.     

Plasmochemical modification of fluorocarbon polymers for creation of new hemocompatible materials

The various plasmochemical technique for the surface functionalization and regulation of the biological characteristics of fluorocarbon polymers aimed at the enhance their blood compatibility are described. The plasmochemical treatment in oxygen and nitrogen containing gases has been used to increase of surface energy and hydrophoby of fluorocarbon polymers. Modification of the surface morphology and chemical structure to improve thromboresistive properties of polymers by plasma etching and deposition of biocompatible materials was demonstrated and discussed. Plasma-assisted immobilization of proteins in combination with other plasma modification methods provides a promising technique for engineering of a new generation of hemocompatible materials.     

The thermodynamic parameters of the step dissociation of L-phenylalanyl in aqueous solution

The heats of interaction of L-phenylalanine with solutions of nitric acid and potassium and lithium hydroxides were determined calorimetrically at 288.15, 298.15, and 308.15 K and solution ionic strengths of 0.5, 0.75, and 1.0 in the presence of LiNO₃ and KNO₃. The standard thermodynamic characteristics (Δ_r H°, Δ_r G°, Δ_r S°, and ΔC _p ^° of acid-base interactions in aqueous solutions of L-phenylalanine were calculated. The influence of the concentration of background electrolytes and temperature on the heats of dissociation of L-phenylalanine was considered. A comparative analysis of the standard thermodynamic characteristics of step dissociation of L-phenylalanine and alanine was performed in terms of the modern concepts of the structure and physicochemical properties of these compounds and their solutions.     

Thermal resistance of composites based on nanodispersed aluminum

Thermolysis of low and high molecular aliphatic carboxylated compounds in composite systems based on nanosized aluminum were studied by the thermal desorption mass spectrometry. The conditions for maximal separation of the thermolysis products and their composition were determined. The kinetic parameters of thermal desorption and thermal degradation of the modifiers were calculated. Differences in the thermal stabilities of the polymer composites based on nanosized aluminum and different modifiers (carboxylated divinyl and divinyl nitrile oligomers) were presented.