Combined modes of a two-layer fluid and a solid block in an infinite waveguide

It is shown that a waveguide in the form of a channel of infinite length filled by a two-layer heavy fluid with a free surface can have nonpropagating waves (trapped vibrational modes) along with traveling waves. These waves are localized in the region of a dynamic inclusion, i.e., a solid block (massive die) on the bottom of the channel. The appearance of such waves is due to the presence of a real discrete frequency spectrum of eigenmodes, which is located on the axis of the continuous spectrum corresponding to the divergent waves in the fluid. A relation between the geometric parameters of the channel and the characteristics of the fluid and the solid block for which such a spectrum exists is found for cases with fluids of similar density in the waveguide. Zh. Tekh. Fiz. 68, 15–19 (March 1998)     

Instability of a charged layer of a viscous liquid on the surface of a solid spherical core

The dispersion relation for the spectrum of capillary waves of a spherical layer of a viscous liquid coating a solid spherical core with a layer of finite thickness is introduced and analyzed. It is shown that the existence of two mechanisms for the viscous dissipation of the energy of the capillary-wave motions of the liquid, viz., damping in the bulk of the layer and on the solid core, leads to restriction of the spectrum of the realizable capillary waves of the liquid on both the high-and low-mode sides. At a fixed value of the system charge which is supercritical for the first several capillary modes, the maximum growth rates in the case of a small solid core are possessed by modes from the middle of the band of unstable modes, while in thin liquid layers the highest of the unstable modes have the largest growth rates. This points out differences in the realization of the instability of the charged surface of the spherical layer for small and large relative sizes of the solid core. Zh. Tekh. Fiz. 67, 8–13 (September 1997)     

Influence of charge relaxation on the capillary oscillations of a charged viscous spheroidal drop

A dispersion relation is derived for the spectrum of capillary modes of a charged spheroidal drop of a viscous liquid with allowance for charge relaxation. It is shown that the finite charge transport rate leads to lowering of the instability growth rates for various capillary modes of a spheroidal drop of a low-viscosity liquid. As the degree of deformation of the drop increases, the magnitude of the absolute change in the growth rate caused by the finite rate of charge redistribution decreases. Zh. Tekh. Fiz. 69, 28–36 (August 1999)     

Nonlinear oscillations and stability of a charged drop moving relative to a dielectric medium

Nonlinear calculations to within the second order of smallness with respect to the initial deformation of a liquid drop show that a stream of an ideal incompressible dielectric liquid streamlining the charged ideally conducting drop causes interaction between modes both in the first and second orders of smallness. Both the linear and nonlinear interactions of the oscillation modes result in the excitation of modes absent in the spectrum of the initial drop deformation. The relative motion of the drop and the medium leads to broadening of the spectrum of modes excited in the second order of smallness. The presence of the flow streamlining the drop and the intermode interaction result in decreasing the critical magnitudes of the drop charge and the velocity and density of the medium determining drop instability development.     

Nonlinear oscillations of a charged layer of a conducting liquid on the surface of a solid spherical core

Nonlinear oscillations of a layer of an ideal incompressible perfectly conducting liquid on the surface of a charged melting hailstone (solid core) are studied using analytical asymptotic calculations of the second order of smallness in initial deformation amplitude. Specifically, it is shown that, when the thickness of the layer is much less than the characteristic linear size (radius) of the solid core, the size of the core considerably influences the amplitudes of capillary oscillation modes arising on the surface of the charged layer via nonlinear interaction. It is found that, as the liquid layer on the surface of the solid core gets thinner, the energy in the spectrum of nonlinearly excited modes is redistributed with its maximum shifting toward higher (larger number) modes.     

Experimental Study of Flow Through a Blade Trailing Edge with a Wavy Partition

Abstract

Flow through a blade trailing edge passage has been experimentally investigated in this article. This rectangular passage is divided into two channels by either a straight or a 120° wavy partition. Fluid in the first channel was injected into the second channel via 14 openings (holes) distributed uniformly and in the crests and troughs for the wavy configuration. Particle image velocimetry and a charge coupled device camera were used in experiment, with Reynolds number varying from 1,800 to 6,700. Experimental results show that the wavy configuration produces an oscillation flow in the second channel. The cause for the oscillation may due to the 120° wavy partition causing shear-layer instabilities and the formation of spanwise eddies by the wavy board. Pictures from the charge coupled device camera revealed strong mixing in the trailing edge, and this mixing could enhance heat transfer, which was confirmed in previous research. The amplitude of oscillation depends on Reynolds number and hole positions. It was observed that the injection flow was not symmetric to the openings, and it was skewed to the direction of the first channel main flow. The ratio of flow rate through the outlet and the bleeding holes was from 1:1 to 1:3.     

Configuration of a chiral smectic-C film with a circular inclusion

It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing tangential anchoring. We find how the angle α between two surface defects seen from the center of the inclusion depends on the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity; it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the c -director and the position of the surface defects.     

Weak localization with a specific role of t symmetry (2D and 3D holes in tellurium)

The anomalous magnetoresistance in crystalline tellurium is analyzed for different p-type carrier dimensions: a bulk sample, size-quantized accumulation layers on different tellurium crystallographic surfaces, and tellurium clusters (tellurium embedded in a dielectric opal matrix). It is shown that the effect can be interpreted in all cases in terms of the theory of weak localization of noninteracting particles with inclusion of the specific features of the tellurium band spectrum, namely, fully lifted spin degeneracy, trigonal spectrum distortion, and a specific role played by the t symmetry in inter-valley scattering. The differences observed among the various manifestations of the weak localization effect are determined by the hole wave function phase-relaxation channel which is dominant in a particular case. A case is discussed where the time characterizing the inter-valley transition probability becomes comparable to the momentum relaxation time. Fiz. Tverd. Tela (St. Petersburg) 41, 879–881 (May 1999)     

Capillary oscillations of a charged viscous spheroidal droplet

Dispersion relations are derived for the capillary oscillations of a charged viscous spheroidal droplet by scalarization within perturbation theory using an expansion in two small parameters, viz., the magnitude of the perturbation of the spheroidal surface as a result of thermal fluctuations and the magnitude of the deviation of the equilibrium spheroidal droplet shape from a spherical shape. It is shown analytically that the motion spectrum of the liquid consists of two components that interact in the linear theory: toroidal vortex motion and poloidal potential motions. A numerical analysis reveals that the instability growth rates of the higher modes of a highly charged droplet increase with enhancement of the degree of spheroidal strain and decrease rapidly as the viscosity of the liquid increases. Zh. Tekh. Fiz. 68, 20–27 (April 1998)     

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.     

Orientation phenomena in nematic liquid crystals under a periodic compressional deformation

The orientation behavior of homogeneous planar layers of nematic liquid crystals with open and closed ends in the field of compressional deformations caused by an acoustic effect is studied. The mechanisms determining the connection of the optical response of a nematic liquid crystal (the variable component of an optical signal and its spectrum) with the acoustic parameters (the oscillation amplitude and frequency, and the amplitude of sound pressure) and the layer thickness are revealed. The factors responsible for the mechanism and modes of acoustooptic conversion are considered. It is demonstrated that, by varying the layer thickness, it is possible to implement different modes of signal conversion. The possibility of designing a new modification of a sound receiver based on a nematic liquid crystal and the specific features of this design are discussed. Its advantages over conventional sound pressure receivers based on nematic liquid crystals are indicated, in particular, the absence of limitation of the frequency of the received signal in the low-frequency range.     

Analysis of photonic crystal fibers infiltrated with nematic liquid crystal

The spectral characteristic of a nematic liquid crystal photonic crystal fiber is analyzed. The locations of the transmission minima in the transmission spectrum can be evaluated by examining the modal cutoffs of specific modes in the liquid crystal inclusion. The selection criteria for these specific modes are based on the fraction of power residing in the core. Explicit expressions for these modal cutoffs are also derived.     

Experimental investigation of the dielectric strength of the H 011 and E 111 oscillation modes in a cylindrical resonator using compressed gas

It is shown experimentally that in order to increase the stored energy in storage resonators using compressed gas, it is preferable to have oscillation modes in which the electrical components of the fields do not interact with the inner surfaces of the resonator. Zh. Tekh. Fiz. 68, 98–100 (December 1998)     

Linear electromechanical effect in free-standing ferroelectric liquid-crystalline films

Mechanical oscillations of free-standing films based on ferroelectric liquid crystals were studied by optical methods. The intrinsic oscillation modes in the samples were excited by applying an alternating electric field parallel to the film surface. The surface viscosity of the films determined using the electromechanical effect was η_s=8.8×10^?3 g/s under normal pressure and η_s=1.5×10^?3 g/s in vacuum. The surface tension measured in a special experiment was σ=35.3 din/cm. It was established that the spectrum of mechanical oscillations in the system studied is affected by the vapors of volatile organic solvents such as kerosene, toluene, and ethyl alcohol. The linear electromechanical effect in the free-standing films was used to observe inversion of the sign of spontaneous polarization in a ferroelectric liquid crystal.     

Resonance fluorescence in an atom + dielectric microsphere system excited by a single photon

The resonance interaction of a two-level atom with a continuum of free-space modes modified by the presence of a dielectric microsphere (modified free-space modes — MFSMs) is studied. In the case that quantized MFSMs are initially excited within the contour of one of the resonance modes of the microsphere, the spectrum of emitted photons depends strongly on the excitation method. Under optimal excitation conditions efficient excitation of the atom accompanied by the formation of a Rabi doublet in the fluorescence spectrum occur. As the excitation conditions depart from optimality, the spectrum becomes a triplet. If the departure from optimality of excitation is large, the atom remains essentially unexcited, and the fluorescence spectrum has a singlet character. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 2, 115–120 (25 July 1998)     

Electron-LO-phonon interaction in wurtzite GaN quantum wells under a magnetic field

We calculate the electron-LO-phonon relaxation rates in wurtzite GaN quantum wells in the presence of a magnetic field parallel to the growth direction. Using the dielectric continuum model (DCM), we are able to include contributions from both the interface and the quasi-confined phonon modes. The relaxation rate expression takes the phonon dispersion into account, and is applicable to all phonon modes. We find that the relaxation rates show strong oscillations as a function of the applied magnetic field. In relatively wide (8 nm) quantum wells, the inclusion of interface phonon mode decreases this oscillation amplitude. But in thin wells (5 nm), the interface phonon mode is of the same importance as the quasi-confined mode, and it strongly modifies the oscillation behavior.     

Experimental study of neutrino oscillations at a fission reactor

The electron-antineutrino spectrum has been measured at a position 8.75 m from the “point-like” core of the ILL ²³⁵U fission reactor, using the reaction $\text{ν}$_e + p → e⁺ + n. Positrons and neutrons were detected in coincidence by means of a low-background liquid scintillator and a ³He detector system. The observed neutron correlated positron spectrum is consistent with theoretical predictions assuming no neutrino oscillations. Upper limits for the oscillation parameter are presented.     

Fractional-harmonic components in an acoustical wave in a liquid

The amplitudes and frequencies of the components of the acoustical spectrum of an acoustical wave, generated in a non-viscous liquid filling a cavity, are calculated by solving a boundary value problem. Apart from forced oscillations, the frequencies of the acoustical spectrum are equal to the frequency of the fundamsntal oscillation of the liquid in the cavity and its higher harmonics. If the frequency of the driving acoustical wave coincides with one of these (proper) frequencies, thefractional harmonic components appear. The amplitudes of the component oscillations decrease monotonically as the absolute value of the difference between the frequency of the driving acoustical wave and the frequency of the respective oscillation is increased. The derived relations are compared with the results of some published measurements.     

Capillary oscillations and Tonks-Frenkel instability of a liquid layer of finite thickness

A dispersion relation is derived and analyzed for the spectrum of capillary motion at a charged flat surface of viscous liquid covering a solid substrate with a layer of finite thickness. It is shown that for waves whose wavelengths are comparable with the layer thickness, viscous damping at the solid bottom begins to play an important role. The spectrum of capillary liquid motion established in this system has high and low wave number limits. The damping rates of the capillary liquid motion with wave lengths comparable with the layer thickness are increased considerably and the Tonks-Frenkel instability growth rates are reduced compared with those for a liquid of infinite depth. Zh. Tekh. Fiz. 67, 27–33 (August 1997)     

Electronic resonances in a quantum well having a periodically uneven boundary

The spectrum of the electronic states in an infinitely deep two-dimensional potential well, where one wall is periodically uneven, is investigated theoretically. It is shown that in non-Bragg type resonances — standing electron wave resonances, which are modes of different spatial harmonics of the electron wave function — arise in such a well. The resonances occur in a wide range of energies, starting at values close to the bottom in each 2D subband. The resonance interaction splits the energy spectrum and results in the appearance of gaps, giving the electron spectrum a miniband character. The properties of the electron gas vary substantially in accordance with the new characteristics of the spectrum. Fiz. Tverd. Tela (St. Petersburg) 41, 1867–1870 (October 1999)