Propagation of acoustic waves in a fibrous fluid-filled material

The homogenization method is used for the analysis of acoustic wave propagation in a unidirectional fibrous material for the acoustic control of the fiber arrangement in manufacturing composites. Acoustic equations for a rigid periodic structure filled by a nonviscous fluid are obtained by two-dimensional asymptotic expansions. A regular square and triangular arrangement of the fibers with a round cross-section are considered. The analysis reveals that the velocity of acoustic waves is significantly affected by both the volume content and the fiber arrangement.Moscow State Academy of Chemical Engineering, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 651–655 September–October, 1997.     

Remote acoustic diagnostics of a wake behind a heated cylinder

The possibilities of remote acoustic diagnostics of flows are experimentally and theoretically studied. A Karman vortex street behind a cylinder is used as a model. The vortex temperature exceeded that of the surrounding medium. A laboratory experiment carried out in a low-turbulence wind tunnel at Re100 has shown that vorticity, stall rate, spatial period, and vortex temperature can be found from the characteristics of sound scattered by the flow.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 8, pp. 832–840, August, 1995.     

Parallelization of matrix algorithms for Gröbner basis computation

Sequential and parallel implementations of the F4 algorithm for computing Gröbner bases of polynomial ideals are discussed.     

Experimental determination of dust-particle charge in a discharge plasma at elevated pressures

The charge of dust particles is determined experimentally in a bulk dc discharge plasma in the pressure range 20-100 Pa. The charge is obtained by two independent methods: one based on an analysis of the particle motion in a stable particle flow and another on an analysis of the transition of the flow to an unstable regime. Molecular-dynamics simulations of the particle charging for conditions similar to those of the experiment are also performed. The results of both experimental methods and the simulations demonstrate good agreement. The charge obtained is several times smaller than predicted by the collisionless orbital motion theory, and thus the results serve as an experimental indication that ion-neutral collisions significantly affect particle charging.     

Physical aspects of dust–plasma interactions

Low-pressure gas discharge plasmas are known to be strongly affected by the presence of small dust particles. This issue plays a role in the investigations of dust particle-forming plasmas, where the dust-induced instabilities may affect the properties of synthesized dust particles. Also, gas discharges with large amounts of microparticles are used in microgravity experiments, where strongly coupled subsystems of charged microparticles represent particle-resolved models of liquids and solids. In this field, deep understanding of dust–plasma interactions is required to construct the discharge configurations which would be able to model the desired generic condensed matter physics as well as, in the interpretation of experiments, to distinguish the plasma phenomena from the generic condensed matter physics phenomena. In this review, we address only physical aspects of dust–plasma interactions, that is, we always imply constant chemical composition of the plasma as well as constant size of the dust particles. We also restrict the review to two discharge types: dc discharge and capacitively coupled rf discharge. We describe the experimental methods used in the investigations of dust–plasma interactions and show the approaches to numerical modelling of the gas discharge plasmas with large amounts of dust. Starting from the basic physical principles governing the dust–plasma interactions, we discuss the state-of-the-art understanding of such complicated, discharge-type-specific phenomena as dust-induced stratification and transverse instability in a dc discharge or void formation and heartbeat instability in an rf discharge.     

Differential standard bases under composition

We generalize Hoon Hong’s theorem on Gröbner bases under composition to the case of differential standard bases in the ordinary ring of differential polynomials {ie4152-01}. In particular, we prove that some ideals have finite differential standard bases. We construct special orderings on differential monomials such that ideals generated by some power of a quasi-linear polynomial acquire finite differential standard bases.     

Electronic absorption spectra determination of C60 content in soot produced in hydrocarbon flames

We analyze the possibilities of eliminating hydrocarbon compounds from soot produced in hydrocarbon flames for the purpose of using the method of electronic absorption spectra to measure the content of fullerenes. The sensitivity limit of the spectral-absorption method has been determined. The solubility of C₆₀ in ether has been measured. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 253–256, March–April, 2000.     

One-element differential standard bases with respect to inverse lexicographical orderings

We give a simplified proof of the following fact: for all nonnegative integers n and d the monomial y _n ^d forms a differential standard basis of the ideal [y _n ^d ]. In contrast to Levi’s combinatorial proof, in this proof we use the Gröbner bases technique. Under some assumptions we prove the converse result: if an isobaric polynomial f forms a differential standard basis of [f], then f = y _n ^d .     

Asymptotic Method of Homogenization in Problems of Heating Composite Plates of Periodic Structure in a High-Frequency Electromagnetic Field

In this paper, we examine the influence of electromagnetic and thermal fields on an inhomogeneous medium of periodic structure and heating of a laminated composite of periodic structure in a high-frequency electromagnetic field.     

Dust-acoustic instability in an inductive gas-discharge plasma

Spontaneous excitation of a dust-particle density wave is observed in a dust cloud levitating in the region of the diffused edge of an rf inductive low-pressure gas-discharge plasma. The main physical parameters of this wave and of the background plasma are measured. The analytic model proposed for the observed phenomenon is based on the theory of dust sound and successfully correlates with experimental data in a wide range of experimental conditions. The effect of variable charge of dust particles on the evolution of the observed dust-plasma instability is studied analytically. It is shown that the necessary condition for the development of the dust-acoustic instability is the presence of a dc electric field in the dust cloud region.