Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

Expansion of monomer units in poly(ethylene terephthalate) molecules under conditions of thermal and zero-point atomic vibrations

The temperature dependence of the expansion ?_C of trans conformers of the carbon skeleton of macromolecules in crystallized and amorphous poly(ethylene terephthalate) (PET) due to zero-point and thermal atomic vibrations is investigated by IR spectroscopy. It is found that the thermal expansion coefficient β_C jumpwise increases at the characteristic temperatures T _t and T _b. This increase is associated with the crossover from the quantum to classical statistics of torsional and bending vibration modes. The quantum and classical contributions to the expansion ?_C are determined for each mode. The quantum and classical contributions of the torsional vibrational mode in the amorphous polymer are approximately 1.5 times larger than those in the crystallized polymer. This effect is caused by an increase in the anharmonicity of torsional vibrations in the amorphous polymer.     

Stoner-Wohlfarth-type behavior of a close-packed array of high-anisotropy hexaferrite nanoparticles

Magnetization and remagnetization processes in a close-packed nanodispersed barium hexaferrite powder sample in the magnetically stable state were analyzed. Reversibility effects were discussed in terms of interparticle interaction. Judging from the magnetization curve and the parameters characterizing remagnetization irreversibility, the sample under study is a model system of small Stoner-Wohlfarth particles.     

Coherence properties of the supercontinuum source

Mutual–temporal coherence of the supercontinuum (SC) generation has been experimentally investigated using a diffraction grating based interferometer. A broadband SC generation was produced in a pyrex glass plate with a 1.6-μm coherence length at 550-nm center wavelength. The degree of mutual coherence of 0.34 was measured for a wavefront shift for zero and first diffraction orders of half of the beam diameter. A design of SC source with the capability of manipulating the amplitudes and phases of optical frequency components within the SC pulse is presented for coherence applications.     

Dynamic holograms and optical limiting: Asymmetric two-wave interactions

The conditions for obtaining a high efficiency of energy exchange upon two-wave interactions in dynamic holograms are found by analysis and numerical simulation of a system of nonlinear equations. Use of an asymmetric scheme of beam interaction in a medium with two nonlinearities, one of which determines the amplitude and relaxation time of a grating and the other of which provides phase modulation of the interacting beams, is proposed. It is shown that such a scheme in combination with the specific properties of a medium makes it possible to radically reduce the requirements for the nonlinearity of a medium and the intensity of a light flux in limiting systems, as well as to significantly decrease the time of the transition process. As a result, it becomes possible to attain an efficiency of energy transfer higher than 90% and to increase the corresponding attenuation of a high-power beam by almost two orders of magnitude, which is of interest for optical limiting of intense light fluxes.     

Quantum effects in a one-dimensional magnetic gravitational trap for ultracold neutrons

JETP Letters - The problem of storing ultracold neutrons over a plane magnetic mirror in the presence of gravity is considered. For neutrons with a definite polarization, the sum of the magnetic...     

Nonequilibrium Ionization by Vibrationally Excited Molecules in Supersonic Flows

The results of experimental investigations on thermal nonequilibrium ionization in CO₂: N₂: He mixtures are presented. Measurements of electron density, n_e, in vibrationally excited nitrogen were made in a supersonic flow with different CO₂ contents as well as in a CO₂: N₂: He = 1 : 5 : 4 mixture laser gas. The mixtures were heated in a shock tube and expanded through a supersonic nozzle. Furthermore, supersonic mixing of N₂ and CO₂ + He was used in some experiments. The measured values of n_e in the plenum chamber and in the supersonic nozzle are reported, and the processes responsible for nonequilibrium ionization in a laser-active medium are discussed.     

Quantum diffusion

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.