Boundary Problems for the Quantum Bose Gas

A relaxation kinetic equation that describes the behavior of a Bose gas is derived. The Kramers half-space problem on isothermal slip is treated. An analytical solution and the number-of-particle distribution function for particles flying toward a wall, in explicit form, are obtained. The dependence of the slip velocity on the parameter that is the ratio of the chemical potential to the product of Boltzmann's constant by the absolute temperature is analyzed. The influence of the quantum effects on the isothermal slip coefficient is evaluated for He⁴.     

The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method

Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.Partially supported by the Office of Naval Research under Grant N-00014-85-K-0169Research partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0322     

The effect of geoacoustic characteristics of the bottom on the long-range sound propagation in an inhomogeneous ocean

The long-range sound propagation from a deep ocean to a receiving system located on the shelf is modeled. The waveguide model is constructed on the basis of the data of an acoustic-oceanographic experiment carried out in the northwestern Pacific. The sensitivity and the frequency dependence of the difference in the sound field levels at the crossing of the frontal zone on the geoacoustic characteristics of the bottom of the shelf and the continental slope are investigated. It is shown that the level difference decreases by 8.2 dB as the velocity of longitudinal waves increases by 100 m/s in the range within 1490–1820 m/s.     

Wave biomechanics of the skeletal muscle

Results of acoustic measurements in skeletal muscle are generalized. It is shown that assessment of the pathologies and functional condition of the muscular system is possible with the use of shear waves. The velocity of these waves in muscles is much smaller than the velocity of sound; therefore, a higher symmetry type is formed for them. In the presence of a preferential direction (along muscle fibers), it is characterized by only two rather than five (as in usual media with the same anisotropy) moduli of elasticity. A covariant form of the corresponding wave equation is presented. It is shown that dissipation properties of skeletal muscles can be controlled by contracting them isometrically. Pulsed loads (shocks) and vibrations are damped differently, depending on their frequency spectrum. Characteristic frequencies on the order of tens and hundreds of hertz are attenuated due to actin-myosin bridges association/dissociation dynamics in the contracted muscle. At higher (kilohertz) frequencies, when the muscle is tensed, viscosity of the tissue increases by a factor of several tens because of the increase in friction experienced by fibrillar structures as they move relative to the surrounding liquid; the tension of the fibers changes the hydrodynamic conditions of the flow around them. Finally, at higher frequencies, the attenuation is associated with the rheological properties of biological molecules, in particular, with their conformational dynamics in the wave field. Models that describe the controlled shock dissipation mechanisms are proposed. Corresponding solutions are found, including those that allow for nonlinear effects.     

The application of the construction of Kolmogorov complexity and of a theorem by Maslov to semiotic systems

The results obtained in V. P. Maslov’s article [1] can automatically be carried over to arbitrary semiotic systems if the string of signs is sufficiently long. We shall show in this article, by using arguments based on the ideas of Kolmogorov complexity and by applying the theorem of V. P. Maslov from [2], that one can obtain similar formulas for the distribution of various semiotic objects. In order to do this, we must introduce notions generalizing the occurrence frequency of words in corpora of texts. We also interpret a formula due to Maslov (appearing in [3]) from the point of view of the general semiotic notions introduced here.