On the initial layer solution of the Boltzmann equation with small Knudsen number

We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.     

The maximum entropy principle as a consequence of the principle of Laplace

The maximum entropy principle states that the probability distribution which best represents our information is the one which maximizes the entropy with the given evidence as constraints. We prove that this principle is implied from the Laplace principle of equiprobabilities applied to the setS of allN-term sequences of results which are compatible with the given evidence. We generalize to the information gain method of Kullback.     

The Quantum Evolution of the Closed Friedman Universe with “Bouncing Off”

The homogeneous and isotropic closed Friedmanuniverse evolution in higher-order gravity theories isconsidered. The model takes into account vacuumpolarisation of conformal and nonconformal fields. That leads to the following addition in the Einsteinlagrangian: R² ln |R/R₀|. Near theregular minimum of the scale factor the model has ananalytical solution depending on an integration constantC. If |R/R₀| > 1, the solution passes through the regularminimum, experiences inflation with a decreasing valueof R and approaches to the critical value R =R₀. In the interval |R/R₀| < 1,the solutions have non-linear oscillations (i.e. the scalaronstage). On this stage of the evolution the universe isfilled with relativistic plasma. The continuoustransition through the critical point R = R₀is possible in only one type of solution, the separatrix.Though other solutions have no features in this point,they experience the discontinuity in derivatives of R.It is unsuitable since higher-order gravity theories are considered. Thus the measure of continuoussolutions giving a hot universe is negligible. Howeversolutions of the model can be continued in the imaginarytime. In such a case the Euclidean action will have a non-zero value because of the spaceclosed boundedness of the universe and the finiteness ofthe imaginary time interval (instanton). The last allowsus to calculate the probability of the quantum tunnelling of the Friedman universe from theinflation region into the scalaron region.     

Linear Theory of the Beam-Wave Interaction in the Arbitrary Cylindrical Cerenkov Device

The hot dispersion equation in Cerenkov devices has been derived and analyzed numerically using the self-consistent linear theory. In principle, the linear analysis can be applied to efficiently calculating all kinds of beam-wave interaction in various Cerenkov devices composed of axisymmetric slow-wave structures (SWS) with arbitrary periodic profile. Then the results for Cerenkov devices with three typical SWS profiles are presented.     

Gravitational Waves in Matter

The theory of gravitational waves in matter is given. This covers the questions of constitutive relation, number of independent polarizations, index of refraction, reflection and refraction at an interface, etc. The theory parallels the familiar optics of electromagnetic waves in material media, but there are some striking differences. The use of the Campbell-Morgan formalism in which the gauge-invariant tidal force dyads E and B rather than the gauge-dependent metric perturbations are the unknowns is essential. The main justification of the theory at the moment is as a theoretical exercise worth doing. The assumption: size L of the medium gravitational wave length (infinite medium) rules out application to the already well-understood detection problem, but there may be an application to gravitational wave propagation through molecular gas clouds of galactic or inter-galactic size.     

Interactions between dislocations and γ/γ' interfaces in superalloys

In situ transmission electron microscopy observations of the dislocation motion at vicinity of the /' interfaces in a Ni-base superalloy have been performed. They allow to identify the elemental mechanisms, under stress and at different temperatures, of the deformation propagation across the interfaces. It is shown that some of the mechanisms already analyzed in the literature occur. Moreover, new processes are revealed such as the formation of small dislocation pile-ups on the /' interfaces. Such a configuration, which increases the local stress, favors the overcoming of the interface.These observations together with new considerations on stresses are taken into account for proposing a new equilibrium equation for a dislocation abutting on a /' interface. This equation involves all the stress components acting on a dislocation: the applied stress, the misfit stress, the friction stress, the stress concentration due to the dislocation pile-up and the image stress.     

Comment on the calculation of thermal averages by long-time Monte Carlo simulations

It is shown that the effect of turnovers of the whole spin lattice for temperatures below the ordering temperature during a long-time computer simulation is not always satisfactorily reduced by considering the absolute value of the order parameter. A simple method to overcome this problem is suggested.     

Space Videophotometric System for Recording Optical Radiations in the Earth Atmosphere

This paper describes the VFS-3M videophotometric system designed for automatic remote recording of images and parameters of optical radiations following lightning discharges from aboard the Russian segment of the International space station. The characteristics of the system and the possibilities of recording such types of radiation as Red Sprites and Blue Jets are given.     

Synthesis of peptidomimetics using a polymer-bound Boc-linker

Boc-resin-bound -hydroxy--amino-aldehydes are accessible starting from N-terminally bound amino acidesters by using Dondoni's C₁-homologationreaction sequence. The conversion of these synthons totwo different peptide mimetics – 2-hydroxy-1,3-ethyl-diamines and -hydroxy--amino-vinyl sulfones – hasbeen investigated. The successful transfer of thecomplex -amino acid homologation reactionsequence into solid-phase chemistry demonstrates thepotentials of the Boc-resin for synthesis of peptidomimetics.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Analysis of the Tautomeric Properties of 2-Formylcyclopentane-1,3-Dione Using the Data of IR Spectroscopy and Nonempirical (ab initio and DFT) Quantum-Chemical Calculations

The tautomerism, spectral properties, and properties of intramolecular hydrogen bonds in 2-formylcyclopentane-1,3-dione (FCPD) have been investigated by the methods of nonempirical quantum chemistry (calculations by the ab initio and DFT methods) and IR and ¹³C NMR spectroscopy. It is shown that FCPD in a crystalline form, as also does malonic dialdehyde, exists as self-associated enolized molecules with an open chelate ring. It is found that in solutions in CCl₄ the compound investigated exists as an equilibrium mixture of its exo- and endoenolic forms, with predominance of the former. The IR spectra of the solutions of FCPD in CCl₄ fix the presence of small amounts of the associate formed from the anionic and protonated forms of the substance. For the first time, the energies of the intramolecular H bonds of the endo- and exoenolic tautomeric forms in FCPD have been estimated theoretically. They appeared to be equal to 3.69 and 4.91 kcal·mole^–1, respectively. The possible mechanisms of enol-enolic interconversions of FCPD have been discussed.     

Preparation, Luminescence Properties, and Application of Scintillators Based on Lu3Al5O12:Ce Single‐Crystal Films

The possibility of obtaining scintillators with a high effective atomic number of the element Z _ef based on Lu₃Al₅O₁₂:Ce³⁺ singlecrystal films (SCF) on doping with La³⁺ and Sc³⁺ ions on Y₃Al₅O₁₂ substrates has been investigated. It is established that the SCF of (LuLaY)₃Al₅O₁₂:Ce³⁺ (Z _ef = 58.9 and = 6.67 g/cm²) does not rank below those of Y₃Al₅O₁₂:Ce³⁺ (Z _ef = 29 and = 4.52 g/cm²) in the conversion efficiency of radiation at the band with _max = 515 nm. This allows their use as screens of xray images with a space resolution of 0.75–1.00 m. It is suggested that in the SCF of Lu₃Al₅O₁₂ the isoelectronic impurities of lanthanum and scandium form radiative recombination centers of the type La_Lu, Sc_Lu, and ScAl as well as the centers Lu as a consequence of the effect of replacement of some Lu³⁺ ions by the La³⁺ ions to octanodes of the garnet lattice. The low efficiency of Ce³⁺ radiation in the SCF of (LuSc)₃(AlSc)₅O₁₂:Ce is explained by substantial losses due to excitation of the recombination luminescence in the UV region of the centers formed by the isoelectronic impurities of scandium and to the possible existence of the channel of energy excitation dissipation related to the transitions between extrema of the allowed energy bands and activator levels.     

“Quantal” Behavior in Classical Probability

A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic—the incompatibility and value-indeterminateness of variables, the non-existence of dispersion-free states, the failure of the standard marginal-probability formula, the failure of the distributive law of disjunction and interference—are exemplified in an emphatically non-quantal system: a deck of playing cards. Thus the appearance in quantum mechanics of incompatibility and these associated phenomena requires neither explanation nor interpretation.     

Thickness dependence of temperature coefficient of resistance of MnBi films

In-situ measurements of the temperature coefficient of resistance of electron-beam evaporated MnBi films are reported for the thickness range 30–180 nm. The thickness dependence of the temperature coefficient of resistance curves are plotted for different weight ratios, annealing times and substrate temperatures. The temperature coefficient of resistance shows marked size effect, and is negative for lower thicknesses (<100nm) and positive for higher thicknesses. The experimental data is in good agreement with the Mayadas-Shatzkes theory. The thickness dependence of the Curie temperature also indicates marked size effect.     

Two-dimensional commensurate soliton structures

A phase diagram of pinned soliton structures in two dimensions has been found for a repulsive interactionU(x) between solitons withU(x)>0. The critical fugacity of the commensurate soliton structure is shown to be proportional toU(l), wherel is the period of this structure.     

Specific Features of Light Scattering in [N(CH3)4]2CuCl4 Crystals with an Incommensurable Phase

We present the results of investigation of the optical birefringence and intensity of the main light beam that passed through an [N(CH₃)₄]₂CuCl₄ crystal under the conditions of viscous interaction of the incommensurable structure with defects. A nonmonotonic temperature dependence of the basic signal is revealed. The observed temperature dependence of the intensity (in the form of irregular steps) is related to different periods of the incommensurable structure. In transitions between adjacent metastable states the periodicity of the incommensurable structure changes. It is shown that in transition regions for the central beam one observes an anomalous decrease in the light intensity due to the appearance of a perturbation lattice with the wave vector q.     

Diffusion of interacting particles on a percolating lattice

The diffusion has been simulated by the Monte Carlo method on a random lattice. As in the ant in the labyrinth problem the particles move by stepping to allowed, randomly chosen neighboring fields. The particle interaction has been defined by the constraint that only one particle can occupy a site at a time. Biased diffusion means that one of the directions will be chosen with a greater probability than the others. It was shown that, with an increasing number of walkers, the displacement of the particles first of all increases to a maximum value and then decreases. This filling-up effect will not occur with small bias fields and on lattices with a high concentration of allowed sites.     

Raman scattering of light in doped cubic boron nitride

The Raman spectra of single crystals of cubic boron nitride (cBN) doped with beryllium and also synthesized in the absence of dopants are investigated. It is shown that the wide bands at 215 and 535 cm^–1 can be registered in the Raman spectra of the ( ) faces of undoped cBN crystals and that the Be impurity penetrates into the cBN crystals predominantly in the direction of these faces. In the spectra of the investigated cBN samples doped with Be, the contour of the TO and LO phonon lines does not take the Fano shape, in contrast to diamond, which can point to an insufficient concentration of the dopant for attaining the Fano interference or to the absence of it in cBN. The wide bands have been investigated on the assumption that they are boson-like and result from small-size disorders in both undoped and doped cBN samples with the sp ³ bond deformed by Be.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 803–809, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Optical Ray Movement Inside Dielectric Sphere

The paper presents results of numerical investigations of electromagnetic (optical) ray propagation inside a sphere, made of optically uniaxial crystal. The types of caustics formed by the ray trajectory inside the sphere are cleared up. It has been demonstrated the difference between types of caustics formed by the extraordinary ray trajectory inside the sphere made of optically positive and negative crystals. Results are discussed on the basis of one-to-one mapping of 2D billiard problem inside isotropic region bounded by ellipse onto anisotropic one.     

Anti‐Stokes Luminescence of Cadmium Telluride Nanocrystals

For the first time, the antiStokes luminescence in colloidal solutions of CdTe nanocrystals on excitation below the absorption edge has been discovered. The maximum spectral shift to the shortwave region relative to the excitation energy E _con ^max = 319 meV is obtained for meansized nanocrystals (2.5 nm). The conversion efficiency of the absorbed radiant energy is 1.3·10^–2%. The rise in the antiStokes photoluminescence intensity with increasing temperature and the linear dependence on the exciting radiation intensity have been established. It is shown that the effect observed cannot be caused by twophoton excitation or by Auger recombination. It is assumed that the basic mechanism of the luminescence observed is the radiative recombination through the energy levels of the states attributable to the disturbance of the crystal structure in the nanocrystals.