On Coercive Estimates for Solutions of Linear Systems of Hydrodynamic Type

Local and nonlocal coercive estimates in Lebesgue, Hölder, and Morrey–Campanato spaces are proved for solutions of linear stationary systems of hydrodynamic type. For this purpose, the technique proposed by Italian mathematicians for the study of solutions to equations and systems of elliptic and parabolic types is developed. Bibliography: 14 titles.     

Absorption and propagation of light in quaterthiophene crystals

We examine absorption of light in quaterthiophene crystals for different directions of the ray and wave-normal vector after refraction on the vacuum/crystal interface. Experimental non-normal incidence spectra are reported where different absorption bands show different behaviour as a function of the angle of incidence. This allows to identify those originating from the b_u Frenkel exciton state.     

Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry

A method for increasing measurement sensitivity in the visualization of dynamics of changes in wavefront shape with the use of holographic lateral-shearing interferometry is considered. At the first stage of this method, a photograph of a reference shear interferogram obtained with tuning to closely spaced fringes is recorded under linear conditions. After chemical treatment, the photograph of the reference shear interferogram is installed in exactly its initial position. At the second stage, a series of photographs of lateral-shear interferograms of the wavefront under study is recorded under nonlinear conditions using the photograph of the reference interferogram. The photographs of the lateral-shear interferograms are optically processed by two coherent beams with selection of the highest diffraction orders, which makes it possible to visualize the dynamic component of the wavefront deformation with an increase in the measurement sensitivity (the static component is excluded in this case). The effect of the degree of nonlinearity of photograph recording on the range in which the measurement sensitivity can be controlled during the optical processing of a pair of matched photographs or one double-exposure photograph of interferograms recorded at different values of a lateral shift is analyzed.     

Condensate formation and vortex generation in Bose gas upon cooling

The mechanism of transition of a Bose gas to the superfluid state via thermal fluctuations under the condition of external cooling at a temperature above the transition point is considered. The probability of formation of such critical fluctuations (instantons) is calculated; it is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.     

Study of the dynamic structure factor of strong glasses

The dynamic structure factors (DSFs) of several strong glasses (SF6, SF10, BK7, SUPRASIL) measured by Brillouin light scattering spectroscopy are reported. Spectra have been collected, at and above room temperature, at two scattering angles, θ=90° and θ=180° corresponding to exchanged wavevector q values ranging from 0.0256 to 0.0448 nm⁻¹. In particular we find that the isotropic spectral lineshapes are in all cases well described by the simple hydrodynamic theory of an amorphous solid. The width of the Brillouin peaks are found to be consistent with the predicted q² dependence at both investigated temperatures. This damping is however found to account only partially for the strong asymmetry of the Brillouin line clearly visible on a logarithmic intensity scale. As a matter of fact there is an excess intensity in the very low frequency plateau underlying the central component. The height of this plateau and hence the entire lineshape is well reproduced if a relaxation process is taken into account in the hydrodynamic equations. Owing to the intense elastic scattering we are able to determine unambiguously only the ratio between amplitude and characteristic time of this process which quantifies the sound dispersion to be of the order of a few percent in all samples. The temperature dependence of the parameters indicates that this relaxation cannot be attributed to thermally activated relaxation phenomena. These general findings favorably compare with molecular dynamics simulation results on similar systems.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Scattering of excited atoms due to ion bombardment of metals

The spectrum and the spatial distribution of the emission of scattered particles upon bombardment of Be, Ti, Ta, and W with H and He ions were studied. The quantum yield and the velocity and angular distributions of the scattered excited particles were measured. Computer simulation of the scattering of H ions and He ions from the metals under study was performed with the use of the program TRIM-95. Agreement is observed between the calculated and experimentally measured angular distributions of the scattered particles.     

Univariate Ore Polynomial Rings in Computer Algebra

We present some algorithms related to rings of Ore polynomials (or, briefly, Ore rings) and describe a computer algebra library for basic operations in an arbitrary Ore ring. The library can be used as a basis for various algorithms in Ore rings, in particular, in differential, shift, and q-shift rings. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 13, Algebra, 2004.