Extended characteristics method in nonlinear geometric acoustics

An asymptotic “extended characteristics method” is developed for solving nonlinear Riemann-type wave equations as applied to calculating the ray pattern of intense spatially modulated waves in weakly inhomogeneous media. The method makes it possible to avoid the singularity related to the foci of the initial wavefront, calculate the displacement in foci caused by the inhomogeneity of the medium, and thus calculate the ray pattern and intensity of the acoustic field. The beauty of the method is an exact nonlinear transfer equation for the field along the ray and the construction of its general solution for an arbitrary form of inhomogeneity. It is shown that the method is applicable to calculating the spatial structure of intense focused waves and wave beams outside the focal region in a nonlinear geometric acoustics approximation.     

Estimation of the density particle fluxes in the weakly dissipative Kolmogorov-Arnol’d-Mozer theory

New calculated data on estimation of the density of particle fluxes are presented. These particles move freely in a surrounding medium during the constant transit time and are then rescattered under the potential force field weakly perturbed by generalized viscosity forces. An anharmonic potential on a phase straight line is taken as a potential, and the generalized viscosity force corresponds to a small viscosity coefficient affinely dependent on the phase coordinate. The word “small’ here means that the order of the generalized viscosity forces is less than two. The particle fluxes correspond to the periodic motion of particles, asymptotically stable (unstable) states (“in” and “out” states) as t → (−) + ∞ that have basins of attraction (repulsion) with a positive measure.     

Spatial Divergence of Multimode Acoustic Beams Formed by a Vertical Array in a Refracting Oceanic Waveguide

We consider the patterns manifested during the formation of the spatial intensity distribution of an acoustic field excited by a vertical array in a deep-water oceanic waveguide with an underwater sound channel open to the surface and an acoustically transparent bottom. The study focuses on the dependence of the spatial divergence of multimode beams on the angle of compensation of an array emitting a tone signal. It is established that if the size of the array aperture significantly exceeds the optimal size, then at a certain angle of compensation appreciably differing from zero, a multimode beam forms with minimal diffraction divergence even in the absence of bending points and smooth extrema of the dependence of the length of the ray cycle on the ray parameter.     

Optical vortices in the scattering field of magnetic domain holograms

Experimental investigations and theoretical-model analyses have been made of the magnetooptic diffraction of light at ferrite garnet magnetic films with a banded domain structure which includes isolated magnetic grating defects in the form of “forks” and “breaks.” An analysis of the magnetic grating structure and the light diffraction field shows that in terms of its action on laser radiation, a banded domain grating is similar to a computer-synthesized phase hologram of an isolated pure screw-wavefront dislocation. It is shown that as a result of magnetooptic diffraction at a magnetic hologram, optical vortices may be reconstructed with a helicoidal wavefront carrying the topological charge l=±1,±2. Zh. Tekh. Fiz. 68, 54–58 (December 1998)     

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

We elaborate on a general method that we recently introduced for characterizing the “natural” structures in complex physical systems via multi-scale network analysis. The method is based on “community detection” wherein interacting particles are partitioned into an “ideal gas” of optimally decoupled groups of particles. Specifically, we construct a set of network representations (“replicas”) of the physical system based on interatomic potentials and apply a multiscale clustering (“multiresolution community detection”) analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A₈₀B₂₀ , a ternary model system with components “A”, “B”, and “C” in ratios of A₈₈B₇C₅ (as in Al₈₈Y₇Fe₅ , and to atomic coordinates in a Zr₈₀Pt₂₀ system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Holography with guided optical waves

This paper deals with “waveguide holograms” recorded in a layer of storage material covering a planar dielectric waveguide. Reference and read-out waves are guided modes of the waveguide. Their field in the storage medium is evanescent. A theory of the diffraction efficiencies of these waveguide holograms is presented fors-polarized wavefields. To calculate the hologram structure the attenuation of the reference wave caused by absorption in the light-sensitive storage material is taken into account. Analytical expressions for the local and the overall diffraction efficiencies and for the intensity profiles of the diffracted fields are derived. The dependence of these quantities on experimental parameters (the waveguide thickness, the mode numbers of the reference and read-out waves, and the angle of incidence of the plane object wave) is presented graphically, i.e., by computer plots. Grating couplers for integrated optics can be made by waveguide holography. We consider this application to be interesting because incoupling efficiencies for Gaussian beams of up to 96% can be achieved theoretically.     

The impact of collisions on platelet distribution in the blood flow

The impact of platelet collisions on their distribution in a viscous liquid flow has been analyzed. It has been shown that platelet distribution in the flow perpendicular to current lines resulting from their collisions can be described as “shear” diffusion. In the wide physiological range of shear velocities specific for blood, the coefficient of “shear” diffusion is much larger than the coefficient of “Brownian” diffusion. For a parabolic fluid velocity profile (Poiseuille flow) in cylindrical vessel “shear” diffusion causes uneven radial distribution of platelets over the vessel radius. “Shear” diffusion causes platelet concentration to grow from the wall toward the center (vessel axis). This effect appears to be a consequence of the specific distribution of platelet collision frequency reaching its maximum at the vessel wall.     

Double passage of electromagnetic waves through magnetized plasma: approximation of independent normal waves

Polarization properties of electromagnetic waves, double-passed through magnetized plasma, are studied. Analyses are performed in the case of non-interacting normal modes, propagating in homogeneous and weakly inhomogeneous plasmas, and for three kinds of reflectors: metallic plane, 2D corner retro-reflector (2D-CR), and cubic corner retro-reflector (CCR). It is shown that an electromagnetic wave, reflected from a metallic plane and from a CCR, contains only “velocity-preserving” channels, whose phases are doubled in comparison with those of a single-passage propagation. At the same time, an electromagnetic wave reflected from a 2D-CR is shown to contain both “velocity-preserving” and “velocity-converting” channels, the latter converting the fast wave into the slow one and vice-versa. One characteristic feature of “velocity-converting” channels is that they reproduce the initial polarization state near the source, which might be of practical interest for plasma interferometry. In the case of circularly polarized modes, “velocity-preserving” channels completely disappear, and only “velocity-converting” channels are to be found.     

Similarity of Co-Species in Co and CoMo-sulfide catalysts supported on carbon and alumina. A Mössbauer emission spectroscopic study

It is shown that, irrespective of the application of carbon or alumina as a support, the local structure of the “Co-sulfide” phase formed during sulfidation of Co-and CoMo-catalysts is the same. A relation is found between the quadrupole splitting (Q.S. value) of the “Co-sulfide” phase and its dispersion. The higher the dispersion, the larger the Q.S. value. The so-called “Co-Mo-S” doublet is observed in all cases and it turns out to be related to a highly dispersed “Co-sulfide” phase instead of a Co, Mo and S containing phase.     

High-temperature behaviour of average structure and vibrational density of states in the ternary superionic compound AgCuSe

Results of simultaneous thermal analysis (STA), synchrotron powder diffraction (in the range 300–973 K) and inelastic neutron scattering (at 285 and 505 K) on non-superionic β- and superionic α-AgCuSe are reported. The sample is stable in argon on heating. The volume change at the superionic phase transition is about 5%. A model for the average structure of α-AgCuSe is proposed. No anomalies in the temperature dependence of the parameters of the average structure were revealed. Ionic conductivity in α-AgCuSe can originate from cation jumps in “skewed” 〈100 〉 directions between nearest-neighbour tetrahedral sites via the peripheries of the octahedral cavities. A correlation between the temperature dependence of the cation redistribution in α-AgCuSe and the temperature dependence of the ionic conductivity is supposed. Various contributions (anharmonic effects, time-average static disorder and phonon-phonon scattering) to the widths of individual phonons upon temperature increase lead to pronounced changes in the neutron-weighted densities of states of β- and α-AgCuSe and accompany the superionic phase transition as well.     

A visual study on flow pattern around the strip moving Uniformly in a continuously stratified fluid

The flow pattern around a thin strip horizontally towed at constant velocity in a continuously stratified liquid is visualized by conventional “Vertical slit-Foucault’s knife”, “Maksoutov’s slit-thread” and “horizontal slit-regular grating” methods. Using these sensitive high-resolution methods enables to reveal new kind of the streaky structure including a sequence of thin sloping interfaces both on the strip surface and inside its wake. When velocity or distance from the strip increases, the streaks may be turned into the sloping or nearly horizontal interfaces. Reconnections of outer edges of the streaks result in appearance of a set of symmetrical “butterfly-like” vortices, which are perturbed by a shear flow inside the downstream wake. Lift forces caused by a slope of the strip produce an asymmetry of the wake and lead to fast degeneration ofthe streaky structures.     

A method for determining optical constants, dimensions, and concentrations of “soft” absorbing particles in the brightening band region

We investigate the possibilities of creating a method for estimating the optical constants, dimensions, and concentrations of “soft” absorbing particles by applying a theoretical analysis of the angular dependence of the intergrated indicatrix, overall characteristics of light scattering, and absorption on the phase shift and diffraction parameter of particles in the brightening band region. We show that using the investigated optical characteristics, it is possible to determine the unknown parameters of a suspension from experimental data. Institute of Biophysics, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 807–812, November–December, 1997.     

Lorentz gas interacting with an inhomogeneous thermostat

The equilibrium distribution of a Lorentz gas (“electrons”) interacting with an inhomogenous thermostat (“atoms”) is examined with consideration of 1) the concept of volumes available and forbidden for the gas particles and 2) the solution of the kinetic equation. Analytical calculations for “electrons” and “atoms” repelling each other with the force ≈r⁻⁵ (where r is the distance between the particles) have shown that the coordinate- and velocity-dependent variables in the distribution function cannot be separated. In particular, this leads to the dependence of the average kinetic energy per “electron” on the coordinate: it is higher in the region with higher density of the “atoms”. It is assumed that the Gibbs distribution does not describe the properties of the system under consideration, because in this case the interaction between the system and thermostat cannot be considered small. Scientific-Research Physical-Technical Institute at N. I. Lobachevskii Nizhnii Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–43, June, 1999.     

Effect of plastic deformation on phase transitions in a Ti50Ni47Fe3 alloy

The results of x-ray structural studies of the effect of previous plastic deformation by rolling on the occurrence of phase transitions in a TiNi(Fe) alloy are presented in the present work. The temperature dependences of the Bragg reflection intensities and half-widths and the dependence of the rhombic angle in the R phase with various degrees of deformation were obtained. Analysis of the results found gave the following rules. Plastic deformation substantially shifts the characteristic temperatures of the martensitic transitions (MT) R-B19′ and B19′-B19″, increases the temperature range of the transformation and can result in a “stepwise” transformation. It was observed that deformation weakly affects the temperature T_R for the B2-R transformation. Tomsk State Architecture and Construction Academy. V. D. Kuznetsov Siberian Physicotechical Institute at Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 11–20, July, 1996.     

Hysteresis Phenomenon in Deterministic Traffic Flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic “particle-hopping” traffic flow model being a straightforward generalization to the well known Nagel–Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the “free-flowing” (or “gaseous”) phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the “jammed” (or “liquid”) phase. Between the two critical values each of these phases may take place, which can be interpreted as an “overcooled gas” phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles. This research has been partially supported by Russian Foundation for Fundamental Research and French Ministry of Education grants.     

Ion transport and solid state battery studies on a new silver molybdate superionic glass system: x[0.75AgI: 0.25AgCl]: (1-x)[Ag2O: MoO3]

Preparation, material characterization, ion transport and battery discharge characteristic studies are reported for a new silver molybdate glass system: x[0.75AgI: 0.25AgCl]: (1-x)[Ag₂O: MoO₃], where 0<x<1 in molar weight fraction. The traditional host AgI has been replaced by an alternate compound: “a quenched [0.75AgI: 0.25 AgCl] mixed system/solid solution”. Electrical conductivity (σ), ionic mobility (μ) and mobile ion concentration (n) measurements were carried out as a function of “x”. The composition: 0.8[0.75AgI: 0.25AgCl]: 0.2[Ag₂O: MoO₃] exhibited the highest conductivity (∼ 6×10⁻³ S·cm⁻¹) at room temperature and has been referred to as ‘optimum conducting composition (OCC)’. The compositional variation of “μ” and “n” revealed that the enhancement in the room temperature conductivity of OCC is predominantly due to the increase in mobile ion concentration. The XRD and DSC analysis on OCC indicated the formation of glassy phase with partial presence of unreacted polycrystalline phase of the host salt. The temperature dependence of various ionic transport parameters viz. “σ”, “μ”, “n” and ionic transference number (t_ion) were carried out on the OCC and the results have been discussed on the basis of theoretical models suggested for superionic glasses. In addition to this, solid state batteries were fabricated using OCC as electrolyte and discharge characteristics were studied under varying load conditions.     

On the “supercollimation” of X-ray beams in rough interfacial channels

The transmission of x rays through rough submicron narrow channels is investigated by numerical simulation with diffraction and decay of coherence taken into account. It is found that transmission is strongly increased for directions within the diffraction limit λ/d (d is the channel width). For larger angles strong roughness scattering results in rapid decay of coherence and absorption of the x-ray beams. When the coherent part is a significant portion of the transmitted beam, its divergence is also within the diffraction limit, which can be an order of magnitude smaller than the Fresnel angle of total external reflection. The effects are explained with the statistical theory of x-ray scattering in a rough transitional layer. Such “supercollimation” can be used for fine angular discrimination of x radiation and for the production of very narrow diffraction-quality x-ray beams. Zh. éksp. Teor. Fiz. 69, No. 10, 686–690 (25 May 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Paradoxes of neutrino oscillations

Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss a number of such issues, including the relevance of the “same energy” and “same momentum” assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the coherence and localization conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, and the applicability limits of the stationary-source approximation. We also develop a novel approach to calculation of the oscillation probability in the wave-packet approach, based on the summation/integration conventions different from the standard one, which allows a new insight into the “same energy” vs. “same momentum” problem. We also discuss a number of apparently paradoxical features of the theory of neutrino oscillations. The text was submitted by the authors in English.