Diffusion of Phonons in Polycrystalline YAG Ceramic Samples at Liquid-Helium Temperatures,According to the Stationary and Non-Stationary Measurement Data

Crystallography Reports - The specific features of the transport of thermal-frequency phonons at liquid-helium (He) temperatures under the conditions of non-stationary measurements and thermal...     

Generation of large-amplitude solitons in the extended Korteweg-de Vries equation

We study the extended Korteweg-de Vries equation, that is, the usual Korteweg-de Vries equation but with the inclusion of an extra cubic nonlinear term, for the case when the coefficient of the cubic nonlinear term has an opposite polarity to that of the coefficient of the linear dispersive term. As this equation is integrable, the number and type of solitons formed can be determined from an appropriate spectral problem. For initial disturbances of small amplitude, the number and type of solitons generated is similar to the well-known situation for the Korteweg-de Vries equation. However, our interest here is in initial disturbances of larger amplitude, for which there is the possibility of the generation of large-amplitude "table-top" solitons as well as small-amplitude solitons similar to the solitons of the Korteweg-de Vries equation. For this case, and in contrast to some earlier results which assumed that an initial disturbance in the shape of a rectangular box would be typical, we show that the number and type of solitons formed depend crucially on the disturbance shape, and change drastically when the initial disturbance is changed from a rectangular box to a "sech"-profile. (c) 2002 American Institute of Physics.     

Exawatt-Zettawatt pulse generation and applications

A new amplification method, weaving the three basic compression techniques, Chirped Pulse Amplification (CPA), Optical Parametric Chirped Pulse Amplification (OPCPA) and Plasma Compression by Backward Raman Amplification (BRA) in plasma, is proposed. It is called C³ for Cascaded Conversion Compression. It has the capability to compress with good efficiency kilojoule to megajoule, nanosecond laser pulses into femtosecond pulses, to produce exawatt-and-beyond peak power. In the future, C³ could be used at large-scale facilities such as the National Ignition Facility (NIF) or the Laser Megajoule (LMJ) and open the way to zettawatt level pulses. The beam will be focused to a wavelength spot size with a f#1. The very small beam size, i.e. few centimeters, along with the low laser repetition rate laser system will make possible the use of inexpensive, precision, disposable optics. The resulting intensity will approach the Schwinger value, thus opening up new possibilities in fundamental physics.     

Effect of substitutional order on the relaxation of aluminum nuclei in Y<Subscript>3−<Emphasis Type="Italic">x</Emphasis></Subscript>Lu<Subscript>x</Subscript>Al<Subscript>5</Subscript>O<Subscript>12</Subscript> mixed garnets

The spin-lattice relaxation time of ²⁷Al nuclei residing in the octahedral and tetrahedral oxygen environment in Y_{3 ?x}Lu_xAl₅O₁₂ mixed aluminum-yttrium garnets was measured by the NMR method for 0≤x≤3. A maximum in the concentration dependence of the relaxation time was observed for both crystallographic positions at x=0.75; this maximum correlates with the minimum in the NMR linewidth, indicating the ordering obtained as the yttrium and lutetium ions occupy the dodecahedral positions in the garnet lattice.     

To the Solution of Partial Eigenproblems for Polynomial Matrices

Methods for computing scalar and vector spectral characteristics of a polynomial matrix are proposed. These methods are based on determining the so-called generating vectors (eigenvectors and principal vectors) by using the method of rank factorization of polynomial matrices. The possibility of extending the methods to the case of two-parameter polynomial matrices is indicated. Bibliography: 4 titles.     

On Some Properties of Polynomial Bases of Subspaces over the Field of Rational Functions in Several Variables

Spaces of multiparameter rational vectors, i.e., of vectors whose components are rational functions in several variables, and polynomial bases of their subspaces are considered. The conjecture that any subspace in the space of multiparameter rational vectors possesses a free polynomial basis, i.e., a basis such that the associated basis multiparameter polynomial matrix has no finite regular spectrum, is disproved by an example. Some consequences of this fact are indicated. Simpler proofs of some properties of the singular spectra of basis polynomial matrices corresponding to the null-spaces of a singular polynomial matrix are presented. Bibliography: 5 titles.     

Berkhoff approximation in a problem on surface gravity wave propagation in a basin with bottom irregularities

The problem of the propagation of small-amplitude surface gravity waves in a basin of constant mean depth with one- and two-dimensional bottom roughness is solved in the framework of the Berkhoff model by a mean-field method. In both cases the solutions obtained are compared with the solutions of sets of exact linearized equations of the hydrodynamics of an incompressible fluid. The comparison of the exact and approximate mean-field attenuation coefficients has shown that the Berkhoff approximation is appropriate for the solution of this problem in the case of shallow water for an arbitrary correlation length of bottom irregularities and in the case of arbitrary depth and large-scale irregularities. An explanation is given for the limits of applicability of the Berkhoff approximation which are connected with the weak variability of the vertical structure of the wave field in shallow water and in a basin with large-scale depth fluctuations. The mean-field attenuation coefficients reach their maximum values in the region k_oh_o≥1 (where k_o is the wavenumber of the surface gravity wave in a basin of constant depth h_o). The location of these maxima is practically independent of the correlation length of the bottom irregularities. For the case of one-dimensional irregularities the effect of bottom roughness on the surface gravity wave velocity is investigated. It is shown that the surface wave in a basin with an uneven bottom may propagate more slowly, as well as faster than the wave in a basin with an even bottom, depending on the relations between the wavelength, depth and correlation length of the bottom imperfections.     

Some spectral characteristics of λ-matrices

The investigation of spectral properties and characteristics of -matrices of general form is continued. The concept of a matrix solution is extended to the case of singular -matrices. The concept of reducing subspaces and the concepts of a block eigenvalue and a block eigenvector are generalized. Existence theorems are proved; spectral properties of matrix quantities associated with the concepts indicated and their generalizations are established.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 111–124, 1984.     

Modifications of the ΔW-q Factorization Method for Multiparameter Polynomial Matrices and Their Properties

Properties of the method of ΔW-q factorization of multiparameter polynomial matrices are analyzed. Modifications of the method, used in solving spectral and other multiparameter problems of algebra, are discussed. Bibliogrhaphy: 11 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 154–165.