Publications
Most recent papers
2021

(2021) Physical review. B.. 104, 144414. Abstract
The alternating current (ac) Josephson effect in a timeindependent spatially inhomogeneous setting is manifested by the occurrence of Josephson oscillations—periodic macroscopic phaseinduced collective motions of the quantum condensate. So far, this phenomenon was observed at cryogenic temperatures in superconductors, in superfluid helium, and in BoseEinstein condensates (BECs) of trapped atoms. Here, we report on the discovery of the ac Josephson effect in a magnon BEC carried by a roomtemperature ferrimagnetic film. The BEC is formed in a parametrically populated magnon gas in the spatial vicinity of a magnetic trench created by a dc electric current. The appearance of the Josephson effect is manifested by oscillations of the magnon BEC density in the trench, caused by a coherent phase shift between this BEC and the BEC in the nearby regions. Our findings advance the physics of roomtemperature macroscopic quantum phenomena and will allow for their application for data processing in magnon spintronics devices.

(2021) Physical Review B. 104, 10, L100410. Abstract
The appearance of spontaneous coherence is a fundamental feature of a BoseEinstein condensate and an essential requirement for possible applications of the condensates for data processing and quantum computing. In the case of a magnon condensate in a magnetic crystal, such computing can be performed even at room temperature. So far, the process of coherence formation in a magnon condensate was inaccessible. We study the evolution of magnon radiation spectra by direct detection of microwave radiation emitted by magnons in a parametrically driven yttrium iron garnet crystal. By using specially shaped bulk samples, we show that the parametrically overpopulated magnon gas evolves to a state, whose coherence is only limited by the natural magnon relaxation into the crystal lattice.

(2021) Phys. Rev. E. 104, 044903. Abstract
``Remote triggering" refers to the inducement of earthquakes by weak perturbations that emanate from far away sources, typically intense earthquakes that happen at much larger distances than their nearby aftershocks, sometimes even around the globe. Here, we propose a mechanism for this phenomenon; the proposed mechanism is generic, resulting from the breaking of Hamiltonian symmetry due to the existence of friction. We allow a transition from static to dynamic friction. {\em Linearly stable} stressed systems display giant sensitivity to small perturbations of arbitrary frequency (without a need for resonance), which trigger an instability with exponential oscillatory growth. Once nonlinear effects kick in, the blow up in meansquare displacements can reach 1520 orders of magnitude. Analytic and numerical results of the proposed model are presented and discussed.

Theory of anisotropic superfluid He4 counterflow turbulence(2021) arXiv.org. 2106.07014. Abstract
We develop an analytic theory of strong anisotropy of the energy spectra in the thermallydriven turbulent counterflow of superfluid He4. The key ingredients of the theory are the threedimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energyrate equation, which is fully supported by the numerical solution. The twodimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiment, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a nearclassical nonuniversal cascadedominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters.This article is a part of the theme issue 'Scaling the turbulence edifice'.

(2021) Physical review B.. 103, 14, 144506. Abstract
We use particle tracking velocimetry to study Eulerian and Lagrangian secondorder statistics of superfluid He4 grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov1941 scaling and are almost isotropic. The Lagrangian secondorder structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearlyclassical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various secondorder statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the twoway bridge relations between Eulerian energy spectra and secondorder structure functions to reconstruct the energy spectrum from the known velocity secondorder structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the EulerianLagrangian bridge differs from the measured Lagrangian spectrum in the quasiclassical range which calls for further investigation.
2020

(2020) Physical Review B. 101, 13, 134515. Abstract
Quantum turbulence in superfluid He4 in narrow channels often takes the form of moving localized vortex tangles. Such tangles, called turbulent plugs, also serve as building blocks of quantum turbulence in wider channels. We report on a numerical study of various aspects of the dynamics and structure of turbulent plugs in a wide range of governing parameters. The unrestricted growth of the tangle in a long channel provides a unique view on a natural tangle structure including superfluid motion at many scales. We argue that the edges of the plugs propagate as turbulent fronts, following the advectiondiffusionreaction dynamics. This analysis shows that the dynamics of the two edges of the tangle have distinctly different nature. We provide an analytic solution of the equation of motion for the fronts that define their shape, velocities and effective diffusivity, and analyze these parameters for various flow conditions.
2019

(2019) Nature Communications. 10, 2460. Abstract
A macroscopic collective motion of a BoseEinstein condensate (BEC) is commonly associated with phenomena such as superconductivity and superfluidity, often generalised by the term supercurrent. Another type of motion of a quantum condensate is second sounda wave of condensate's parameters. Recently, we reported on the decay of a BEC of magnons caused by a supercurrent outflow of the BEC from the locally heated area of a room temperature magnetic film. Here, we present the observation of a macroscopic BEC transport mechanism related to the excitation of second sound. The condensed magnons, being propelled out of the heated area, form compact humps of BEC density, which propagate many hundreds of micrometers in the form of distinct second soundBogoliubov waves. This discovery advances the physics of quasiparticles and allows for the application of related transport phenomena for lowloss data transfer in magnon spintronics devices.

(2019) Ukrainian Journal of Physics. 64, 10, p. 927932 Abstract
Magnon Bose–Einstein Condensates (BECs) and supercurrents are coherent quantum phenomena, which appear on a macroscopic scale in parametrically populated solid state spin systems. One of the most fascinating and attractive features of these processes is the possibility of magnon condensation and supercurrent excitation even at room temperature. At the same time, valuable information about a magnon BEC state, such as its lifetime, its formation threshold, and coherence, is provided by experiments at various temperatures. Here, we use Brillouin Light Scattering (BLS) spectroscopy for the investigation of the magnon BEC dynamics in a singlecrystal film of yttrium iron garnet in a wide temperature range from 30 K to 380K. By comparing the BLS results with previous microwave measurements, we revealed the direct relation between the damping of the condensed and the parametrically injected magnons. The enhanced supercurrent dynamics was detected at 180 K near the minimum of BEC damping.

(2019) Physical Review B. 100, 13, 134515. Abstract
We report on a combined theoretical and numerical study of counterflow turbulence in superfluid He4 in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normalfluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity.

(2019) Physical Review B. 100, 2, 020406. Abstract
We report the experimental realization of a spacetime crystal with tunable periodicity in time and space in a magnon BoseEinstein condensate (BEC), formed in a roomtemperature yttrium iron garnet (YIG) film by a microwave spacehomogeneous magnetic field. The magnon BEC is prepared to have a welldefined frequency and nonzero wave vector. We demonstrate how the crystalline "density" as well as the time and space textures of the resulting crystal may be tuned by varying the experimental parameters: External static magnetic field, temperature, thickness of the YIG film, and power of the microwave field. The proposed spacetime crystals provide an additional dimension for exploring dynamical phases of matter and can serve as a model nonlinear Floquet system, that brings in touch the rich fields of classical nonlinear waves, magnonics, and periodically driven systems.

(2019) Physical Review Letters. 122, 14, 144501. Abstract
Threedimensional anisotropic turbulence in classical fluids tends towards isotropy and homogeneity with decreasing scales, allowingeventuallythe abstract model of homogeneous and isotropic turbulence to be relevant. We show here that the opposite is true for superfluid He4 turbulence in threedimensional counterflow channel geometry. This flow becomes less isotropic upon decreasing scales, becoming eventually quasitwodimensional. The physical reason for this unusual phenomenon is elucidated and supported by theory and simulations.
2018

(2018) Physical Review B. 98, 17, 174509. Abstract
We report a detailed analysis of the energy spectra, second and highorder structure functions of velocity differences in superfluid He4 counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the onedimensional energy spectrum Exz(ky) (averaged over the xz plane, parallel to the channel wall), directly measured as a function of the wallnormal wave vector ky, gives more detailed information on the energy distribution over scales than the corresponding secondorder structure function S2(δy). In particular, we discover two intervals of ky with different apparent exponents: Exz(ky)kymC for kk× and Exz(ky)kymF for kk×. Here k× denotes the wave number that separates scales with relatively strong (for kk×) and relatively weak (for kk×) coupling between the normalfluid and superfluid velocity components. We interpret these k ranges as cascadedominated and mutualfrictiondominated intervals, respectively. The general behavior of the experimental spectra Exz(ky) agrees well with the predicted spectra [L'vov and Pomyalov, Phys. Rev. B 97, 214513 (2018)2469995010.1103/PhysRevB.97.214513]. Analysis of the nthorder structure functions statistics shows that in the energycontaining interval, the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade and mutualfrictiondominated intervals, we found some modest enhancement of intermittency with respect to its level in classical turbulence. However, at small scales, the intermittency becomes much stronger than in the classical turbulence.

(2018) Physical Review Letters. 121, 7, 077203. Abstract
Evolution of an overpopulated gas of magnons to a BoseEinstein condensate and excitation of a magnon supercurrent, propelled by a phase gradient in the condensate wave function, can be observed at room temperature by means of the Brillouin light scattering spectroscopy in an yttrium iron garnet material. We study these phenomena in a wide range of external magnetic fields in order to understand their properties when externally pumped magnons are transferred towards the condensed state via two distinct channels: a multistage KolmogorovZakharov cascade of the weakwave turbulence or a onestep kinetic instability process. Our main result is that opening the kinetic instability channel leads to the formation of a much denser magnon condensate and to a stronger magnon supercurrent compared to the cascade mechanism alone.

(2018) Journal Physics D: Applied Physics. 51, 23, 234003 . Abstract[All authors]
We studied the transient behavior of the spin current generated by the longitudinal spin Seebeck effect (LSSE) in a set of platinumcoated yttrium iron garnet (YIG) films of different thicknesses. The LSSE was induced by means of pulsed microwave heating of the Pt layer and the spin currents were measured electrically using the inverse spin Hall effect in the same layer. We demonstrate that the time evolution of the LSSE is determined by the evolution of the thermal gradient triggering the flux of thermal magnons in the vicinity of the YIG/Pt interface. These magnons move ballistically within the YIG film with a constant group velocity, while their number decays exponentially within an effective propagation length. The ballistic flight of the magnons with energies above 20K is a result of their almost linear dispersion law, similar to that of acoustic phonons. By fitting the timedependent LSSE signal for different film thicknesses varying by almost an order of magnitude, we found that the effective propagation length is practically independent of the YIG film thickness. We consider this fact as strong support of a ballistic transport scenario  the ballistic propagation of quasiacoustic magnons in room temperature YIG.

(2018) Physical Review B. 97, 21, 214513. Abstract
In the thermally driven superfluid He4 turbulence, the counterflow velocity Uns partially decouples normal and superfluid turbulent velocities. Recently, we suggested [J. Low. Temp. Phys. 187, 497 (2017)] that this decoupling should tremendously increase the turbulent energy dissipation by mutual friction and significantly suppress the energy spectra. Comprehensive measurements of the apparent scaling exponent nexp of the secondorder normalfluid velocity structure function S2(r) ∝ rnexp in the counterflow turbulence [J. Gao et al., Phys. Rev. B 96, 094511 (2017)] confirmed our scenario of gradual dependence of the turbulence statistics on flow parameters. We develop an analytical theory of the counterflow turbulence, accounting for a twofold mechanism of thisphenomenon: (i) a scaledependent competition between the turbulent velocity coupling by mutual friction and the Unsinduced turbulent velocity decoupling and (ii) the turbulent energy dissipation by mutual friction enhanced by the velocity decoupling. The suggested theory predicts the energy spectra for a wide range of flow parameters. The mean exponents of the normalfluid energy spectra m10, found without fitting parameters, qualitatively agree with the observed nexp+ 1 for T 1.85 K.

(2018) Physical Review Fluids. 3, 2, 024605. Abstract
The largescale turbulent statistics of mechanically driven superfluid He4 was shown experimentally to follow the classical counterpart. In this paper, we use direct numerical simulations to study the whole range of scales in a range of temperatures T [1.3,2.1] K. The numerics employ selfconsistent and nonlinearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particulary efficient in the temperature range between 1.8 and 2 K, leading to enhancement of smallscale intermittency for these temperatures. (iii) At low T and close to Tλ, the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

(2018) Physical Review B. 97, 1, 014508 . Abstract
Describing superfluid turbulence at intermediate scales between the intervortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines L. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides L and the normal and superfluid velocity fields. In this paper, we offer a minimal closure using one additional anisotropy parameter Il0. Using the example of counterflow superfluid turbulence, we derive two coupled closure equations for the vortex line density and the anisotropy parameter Il0 with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.
2017

(2017) Physical Review Letters. 118, 23, 237201. Abstract
An ensemble of magnons, quanta of spin waves, can be prepared as a Bose gas of weakly interacting quasiparticles. Furthermore, the thermalization of the overpopulated magnon gas through magnonmagnon scattering processes, which conserve the number of particles, can lead to the formation of a BoseEinstein condensate at the bottom of a spinwave spectrum. However, magnonphonon scattering can significantly modify this scenario and new quasiparticles are formedmagnetoelastic bosons. Our observations of a parametrically populated magnon gas in a singlecrystal film of yttrium iron garnet by means of wavevectorresolved Brillouin light scattering spectroscopy evidence a novel condensation phenomenon: A spontaneous accumulation of hybrid magnetoelastic bosonic quasiparticles at the intersection of the lowest magnon mode and a transversal acoustic wave.

(2017) Journal of Low Temperature Physics. 187, 56, p. 405412 Abstract
We study the coupled dynamics of normal and superfluid components of superfluid He4 in a channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case where the dynamic of the normal component is "frozen." We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore, coupling becomes stronger. The commonly measured flow properties also change when the coupling between the two components is taken into account.

(2017) Journal of Low Temperature Physics. 187, 56, p. 531537 Abstract
We report preliminary results of the complementary experimental and numerical studies on spatiotemporal tangle development and streamwise vortex line density (VLD) distribution in counterflowing He4. The experiment is set up in a long square channel with VLD and local temperature measured in three streamwise locations. In the steady state, we observe nearly streamwisehomogeneous VLD. Experimental secondsound data as well as numerical data (vortex filament method in a long planar channel starting with seeding vortices localized in multiple locations) show that the initial buildup pattern of VLD displays complex features depending on the position in the channel, but some tangle properties appear uniform along its length.

(2017) Journal of Low Temperature Physics. 187, 56, p. 497514 Abstract
Based on our current understanding of statistics of quantum turbulence as well as on results of intensive ongoing analytical, numerical and experimental studies, we overview here the following problems in the largescale, spacehomogeneous, steadystate turbulence of superfluid He4 and He3: (1) energy spectra of normal and superfluid velocity components; (2) crosscorrelation function of normal and superfluid velocities; (3) energy dissipation by mutual friction and viscosity; (4) energy exchange between normal and superfluid components; (5) highorder statistics and intermittency effects. The statistical properties are discussed for turbulence in different types of flows: coflow of He4; turbulent He3 with the laminar normal fluid; pure superflow and counterflow in He4.

(2017) Physical Review B. 95, 18, 184510. Abstract
Below the phase transition temperature Tc≃103K He3B has a mixture of normal and superfluid components. Turbulence in this material is carried predominantly by the superfluid component. We explore the statistical properties of this quantum turbulence, stressing the differences from the better known classical counterpart. To this aim we study the timehonored HallVinenBekarevichKhalatnikov coarsegrained equations of superfluid turbulence. We combine pseudospectral direct numerical simulations with analytic considerations based on an integral closure for the energy flux. We avoid the assumption of locality of the energy transfer which was used previously in both analytic and numerical studies of the superfluid He3B turbulence. For T<0.37Tc, with relatively weak mutual friction, we confirm the previously found "subcritical" energy spectrum E(k), given by a superposition of two power laws that can be approximated as E(k)kx with an apparent scaling exponent 53<x(k)<3. For T>0.37Tc and with strong mutual friction, we observed numerically and confirmed analytically the scaleinvariant spectrum E(k)kx with a (kindependent) exponent x>3 that gradually increases with the temperature and reaches a value x∼9 for T≈0.72Tc. In the nearcritical regimes we discover a strong enhancement of intermittency which exceeds by an order of magnitude the corresponding level in classical hydrodynamic turbulence.
2016

(2016) Physical Review B. 94, 17, 174504. Abstract
We report complementary experimental, numerical, and theoretical study of turbulent coflow, counterflow, and pure superflow of superfluid He4 in a channel, resulting in a physically transparent and relatively simple model of decaying quantum turbulence that accounts for interactions of coexisting quantum and classical components of turbulent superfluid He4. We further offer an analytical theory of the energy spectra of steadystate quantum turbulence in the counterflow and pure superflow, based on algebraic approximation for the energy fluxes over scales. The resulting spectra are not of the classic Kolmogorov form, but strongly suppressed by the mutual friction, leading to the energy dissipation at all scales, enhanced by the counterflowinduced decoupling of the normal and superfluid velocity fluctuations.

(2016) Nature Physics. 12, 11, p. 10571062 Abstract
A supercurrent is a macroscopic effect of a phaseinduced collective motion of a quantum condensate. So far, experimentally observed supercurrent phenomena such as superconductivity and superfluidity have been restricted to cryogenic temperatures. Here, we report on the discovery of a supercurrent in a BoseEinstein magnon condensate prepared in a roomtemperature ferrimagnetic film. The magnon condensate is formed in a parametrically pumped magnon gas and is subject to a thermal gradient created by local laser heating of the film. The appearance of the supercurrent, which is driven by a thermally induced phase shift in the condensate wavefunction, is evidenced by analysis of the temporal evolution of the magnon density measured by means of Brillouin light scattering spectroscopy. Our findings offer opportunities for the investigation of roomtemperature macroscopic quantum phenomena and their potential applications at ambient conditions.

(2016) Physical Review B. 94, 14, 146502. Abstract
This is a Reply to Nemirovskii's Comment [Phys. Rev. B 94, 146501 (2016)] on Khomenko et al. [Phys. Rev. B 91, 180504 (2015)] in which a new form of the production term in Vinen's equation for the evolution of the vortexline density L in the thermal counterflow of superfluid He4 in a channel was suggested. To further substantiate the suggested form which was questioned in the Comment, we present a physical explanation for the improvement of the closure suggested in Khomenko et al. [Phys. Rev. B 91, 180504 (2015)] in comparison to the form proposed by Vinen. We also discuss the closure for the flux term, which agrees well with the numerical results without any fitting parameters.

(2016) JETP Letters. 103, 10, p. 648652 Abstract
We summarize recent experiments on thermal counterflow turbulence in superfluid He4, emphasizing the observation of turbulence in the normal fluid and its effect on the decay process when the heat flux is turned off. We argue that what is observed as turbulence in the normal fluid is a novel form of coupled turbulence in the superfluid and normal components, with injection of energy on the scales of both the (large) channel width and the (small) spacing between quantized vortices. Although an understanding of this coupled turbulence remains challenging, a theory of its decay is developed which accounts for the experimental observations.

(2016) Physical Review B. 93, 13, 134504. Abstract
In classical turbulence the kinematic viscosity. is involved in two phenomena. The first is the energy dissipation and the second is the mechanical momentum flux toward the wall. In superfluid turbulence the mechanism of energy dissipation is different, and it is determined by an effective viscosity which was introduced by Vinen and is denoted as nu'. In this paper we show that in superfluid turbulence the transfer of mechanical momentum to the wall is caused by the presence of a quantum vortex tangle, giving rise to another effective "momentum" viscosity that we denote as nu(m)(T). The temperature dependence of the second effective viscosity is markedly different from Vinen's effective viscosity nu' (T). We show that the notion of vortextension force, playing an important role in the theory of quantum turbulence, can be understood as the gradient of the Reynoldsstress tensor, which is, in fact, determined by the second newly defined kinematic viscosity nu(m)(T).

(2016) Physical Review B. 93, 1, 014516 . Abstract
In mechanically driven superfluid turbulence, the mean velocities of the normal and superfluid components are known to coincide: U n=U s. Numerous laboratory, numerical, and analytical studies showed that under these conditions, the mutual friction between the normal and superfluid velocity components also couples their fluctuations: u n'(r,t)apu s'(r,t), almost at all scales. We show that this is not the case in thermally driven superfluid turbulence; here the counterflow velocity U nsequivU nU sne0. We suggest a simple analytic model for the crosscorrelation function u n'(r,t).u s'(r',t) and its dependence on U ns. We demonstrate that u n'(r,t) and u s'(r,t) are decoupled almost in the entire range of separations rr' between the energycontaining scale and intervortex distance.
2015

(2015) Physical Review B. 91, 18, 180504. Abstract
The quantization of vortex lines in superfluids requires the introduction of their density L(r,t) in the description of quantum turbulence. The space homogeneous balance equation for L(t), proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term P. Attempts to choose the correct one on the basis of timedependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is very suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new form of an inhomogeneous equation for L(r,t) that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.

(2015) Physical Review B. 91, 14, 144501. Abstract
We discuss the energy and vorticity spectra of turbulent superfluid He4 in the entire temperature range from T = 0 up to the phase transition "gimel point," T gimel similar or equal to 2.17 K. Contrary to classical developed turbulence in which there are only two typical scales, i.e., the energy injection L and the dissipation scales eta, here, the quantization of vorticity introduces two additional scales, the vortex core radius a(0) and the mean vortex spacing l. We present these spectra for the superand the normalfluid components in the entire range of scales from L to a(0) including the crossover scale l where the hydrodynamic eddy cascade is replaced by the cascade of Kelvin waves on individual vortices. At this scale, a bottleneck accumulation of the energy was found earlier at T = 0. We show that even very small mutual friction dramatically suppresses the bottleneck effect due to the dissipation of the Kelvin waves. Using our results for the spectra we estimate the Vinen "effective viscosity" nu' in the entire temperature range and show agreement with numerous experimental observations for. nu' (T).
2014

(2014) Physical Review B. 90, 9, 094501. Abstract
We present a comprehensive statistical study of free decay of the quantized vortex tangle in superfluid He4 at low and ultralow temperatures 0

(2014) Physical Review B. 90, 2, 024508. Abstract
A nuclear capture reaction of a single neutron by ultracold superfluid He3 results in a rapid overheating followed by the expansion and subsequent cooling of the hot subregion, in a certain analogy with the big bang of the early universe. It was shown in a Grenoble experiment that a significant part of the energy released during the nuclear reaction was not converted into heat even after several seconds. It was thought that the missing energy was stored in a tangle of quantized vortex lines. This explanation, however, contradicts the expected lifetime of a bulk vortex tangle, 10(5)10(4) s, which is much shorter than the observed time delay of seconds. In this paper we propose a scenario that resolves the contradiction: the vortex tangle, created by the hot spot, emits isolated vortex loops that take with them a significant part of the tangle's energy. These loops quickly reach the container walls. The dilute ensemble of vortex loops attached to the walls can survive for a long time, while the remaining bulk vortex tangle decays quickly.

(2014) Physical Review B. 89, 1, 014502. Abstract
The paper presents a comprehensive characterization of welldeveloped vortex tangles in a turbulent counterflow in quantum fluids (with a laminar normal fluid component). We perform and analyze extensive numerical simulations using the vortex filament method, solving the full BiotSavart equations for the vortex dynamics in a wide range of temperatures and counterflow velocities. We start with the analysis of the macroscopic characteristics of the quantum vortex tangle such as vortex line density, its mean anisotropic and curvature parameters, the mean friction force between normal and superfluid components, the drift velocity of the vortex tangle, etc. Next we proceed to the main goal of the paper and move from the traditional macroscopic approach in terms of mean characteristics of the vortex tangle to the microscopic statistical and kinetic levels of description of quantum turbulence. These include objects that are much less studied or even totally neglected such as the vortex reconnection rates, the correlations and probability distribution functions (PDFs) of the vortex loop lengths, of the line curvature, of the mean curvatures of individual loops, the crosscorrelation function between the loop length and its mean curvature, and the autocorrelation function of the vortexline orientations. This detailed statistical information is required for a deeper understanding of quantum turbulence and for the development of its advanced theoretical description. In addition, we identify which of the studied properties are strongly affected by the choice of the reconnection criteria that are traditionally used in the vortex filament method and which of them are practically insensitive to the reconnection procedure. We conclude that the vortex filament method is sufficiently robust and wellsuited for the description of the steadystate vortex tangle in the quantum counterflow.
2013

(2013) Physical Review Letters. 110, 1, 014502. Abstract
We consider the intermittent behavior of superfluid turbulence in He4. Because of the similarity in the nonlinear structure of the twofluid model of superfluidity and the Euler and NavierStokes equations, one expects the scaling exponents of the structure functions to be the same as in classical turbulence for temperatures close to the superfluid transition Tlambda and also for T
2012

(2012) Physical Review B. 85, 10, 104502. Abstract
In superfluid He3B, turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart, we adopt the timehonored approach of shell models. Using this approach, we provide numerical simulations of a Sabra shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux.

(2012) Physical Review Letters. 108, 6, 074501. Abstract
Fractal decimation reduces the effective dimensionality D of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius k is proportional to k(D) for large k. At the critical dimension Dc = 4/3 there is an equilibrium Gibbs state with a k(5/3) spectrum, as in V. L'vov et al., Phys. Rev. Lett. 89, 064501 (2002). Spectral simulations of fractally decimated twodimensional turbulence show that the inverse cascade persists below D = 2 with a rapidly rising Kolmogorov constant, likely to diverge as (D  4/3)(2/3).
2010

(2010) Chemical Physics. 370, 13, p. 98108 Abstract
The nonMarkovian master equation is applied to the calculation of reaction rates. Starting from the fluxside correlation function form, we treat both the thermal and real time evolution consistently within second order perturbation theory in the systembath coupling. It is shown that the nonMarkovian dynamics enter formally not only in the time propagation but also in the expressions for the initial systembath correlations. We show that these initial correlations can have a significant effect on the reaction rate. The method presented, although approximate, is an effective way to calculate reaction rates for weakly coupled systems over a wide range of temperatures. As such it provides a complementary approach to the exact treatment based on the MLMCTDH method of Craig et al. [1], which serves as reference in this work. (C) 2010 Elsevier B.V. All rights reserved.

(2010) NeuroImage. 50, 3, p. 12581270 Abstract
Evidence suggests that theta oscillations recruit distributed cortical representations to improve associative encoding under semantically congruent conditions. Here we show that positive effects of semantic context on encoding and retrieval of associations are mediated by changes in the coupling pattern between EEG theta sources. During successful encoding of semantically congruent facelocation associations, the right superior parietal lobe showed enhanced theta phase synchronization with other regions within the lateral posterior parietal lobe (PPL) and left medial temporal lobe (MTL). However, functional coordination involving the inferior parietal lobe was higher in the incongruent condition. These results suggest a differential engagement of topdown and bottomup mechanisms during encoding of semantically congruent and incongruent episodic associations, respectively. Although retrieval processes operated on a similar neural network, the main difference with the study phase was the larger amount of functional links shown by the lateral prefrontal cortex with regions of the MTL and PPL. All together, these results suggest that theta oscillations mediate, at least partially, the positive effect of semantic congruence on associative memory by (i) optimizing topdown attentional mechanisms through enhanced theta phase synchronization between dorsal regions of the PPL and MTL and (ii) by adjusting the control of automatic attention to sensory and contextual information reactivated in the MTL through functional connections with the inferior parietal lobe during both encoding and retrieval processes. (C) 2010 Elsevier Inc. All rights reserved.
2009

(2009) Physical Review E. 80, 6, 066319. Abstract
Finitedimensional wave turbulence refers to the chaotic dynamics of interacting wave "clusters" consisting of finite number of connected wave triads with exact threewave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finitedimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wavekinetic equations that account for interactions with overlapping quasiresonances of finite amplitude waves. The present results are directly applicable to finitedimensional wave turbulence in any wave system in finite domains with threemode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.
2008

(2008) Physical Review Letters. 101, 9, 094503. Abstract
We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortexstreet model representing the largescale structure in a selfsimilar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the largescale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless, the exact selfsimilar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.

(2008) Physical Review E. 78, 2, 027101. Abstract
A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finitetime cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.
2007

(2007) Chaos. 17, 4, 043113. Abstract
We consider the electrical signals recorded from a subdural array of electrodes placed on the pial surface of the brain for chronic evaluation of epileptic patients before surgical resection. A simple and computationally fast method to analyze the interictal phase synchrony between such electrodes is introduced and developed with the aim of detecting and localizing the foci of the epileptic seizures. We evaluate the method by comparing the results of surgery to the localization predicted here. We find an indication of good correspondence between the success or failure in the surgery and the agreement between our identification and the regions actually operated on. (c) 2007 American Institute of Physics.

(2007) JETP Letters. 86, 2, p. 102107 Abstract
An analytical model for the timedeveloping turbulent boundary layer (TD TBL) over a flat plate is presented. The model provides explicit formulae for the temporal behavior of the wallshear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatiallydeveloping turbulent boundary layers at momentum thickness Reynolds numbers equal to 1430 and 2900 [57]. Our analytical model is, to the best of our knowledge, the first of its kind for TD TBL.
2006

(2006) Physical Review Letters. 97, 13, 134301. Abstract
Dynamic fracture in a wide class of materials reveals a "fracture energy" Gamma much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, Gamma=Gamma(v). We show that a simple dynamical theory of viscoplasticity coupled to asymptotic pure linear elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixedgrip strip geometry accompanied by the identification of Gamma and its velocity dependence.

(2006) Physical Review E. 73, 1, 016303. Abstract
We construct a simple analytic model for wallbounded turbulence, containing only four adjustable parameters. Two of these parameters are responsible for the viscous dissipation of the components of the Reynolds stress tensor. The other two parameters control the nonlinear relaxation of these objects. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sublayer, through the buffer layer, and further into the loglaw turbulent region. In particular, the model predicts a very simple distribution of the turbulent kinetic energy in the loglaw region between the velocity components: the streamwise component contains a half of the total energy whereas the wallnormal and crossstream components contain a quarter each. In addition, the model predicts a very simple relation between the von Karman slope kappa and the turbulent velocity in the loglaw region v(+) (in wall units): v(+)=6 kappa. These predictions are in excellent agreement with direct numerical simulation data and with recent laboratory experiments.
2005

(2005) Journal of Chemical Physics. 123, 20, 204111 . Abstract
The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantummechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a nonMarkovian quantum master equation (NMQME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NMQME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the nonMarkovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensedphase rate constants. (c) 2005 American Institute of Physics.

(2005) Europhysics Letters. 72, 6, p. 943949 Abstract
A celebrated universal aspect of wallbounded turbulent flows is the von Karman loglawofthewall, describing how the mean velocity in the streamwise direction depends on the distance from the wall. Although the loglaw is known for more than 75 years, the von Karman constant governing the slope of the loglaw was not determined theoretically. In this letter we show that the von Karman constant can be estimated from homogeneous turbulent data, i.e. without information from wallbounded flows.

(2005) Environmental Fluid Mechanics. 5, 4, p. 373386 Abstract
We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the entire boundary region, from the viscous sublayer, through the buffer layer further into the loglaw turbulent region. In contrast to various existing interpolation formulas the model allows one to generalize the description of simple TBL of a Newtonian fluid for more complicated flows of turbulent suspensions laden with heavy particles, bubbles, longchain polymers, to include the gravity acceleration, etc.

(2005) Physical Review Letters. 94, 17, 174502. Abstract
Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking, however, making actual design quite haphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.

(2005) Physical Review E. 71, 1, 016305. Abstract
The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. Ale examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence, and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number Demuch greater than 1. We present analytic results for the suppression of the coilstretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear highquality "hydroelastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to the crossstream component of the elastic stress tensor. This component is smaller than the streamwise component by a factor proportional to De(2). Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.
2004

(2004) Physical Review E. 70, 5, 055301(R). Abstract
Drag reduction by polymers in turbulent flows raises an apparent contradiction: the stretching of the polymers must increase the viscosity, so why is the drag reduced? A recent theory proposed that drag reduction. in agreement with experiments. is consistent with the effective viscosity growing linearly with the distance from the wall. With this selfconsistent solution the reduction in the Reynolds stress overwhelms the increase in viscous drag. In this Rapid Communication we show, using direct numerical simulations. that a linear viscosity profile indeed reduces the drag in agreement with the theory and in close correspondence with direct simulations of the FENEP model at the same flow conditions.

(2004) Physical Review Letters. 92, 24, 244503. Abstract
We elucidate the mechanism of drag reduction by polymers in turbulent wallbounded flows: while momentum is produced at a fixed rate by the forcing, polymer stretching results in the suppression of momentum flux to the wall. On the basis of the equations of fluid mechanics we develop the phenomenology of the "maximum drag reduction asymptote" which is the maximum drag reduction attained by polymers. Based on Newtonian information only we demonstrate the existence of drag reduction, and with one experimental parameter we reach agreement with the experimental measurements.
2003

(2003) Physical Review E. 68, 4, 046308. Abstract
We suggested a multizone shell (MZS) model for wallbounded flows accounting for the space inhomogeneity in a piecewise approximation, in which the crosssectional area of the flow, S, is subdivided into j zones. The area of the first zone, responsible for the core of the flow, S(1)similar or equal toS/2, and the areas of the next j zones, Sj, decrease toward the wall like S(j)proportional to2(j). In each j zone the statistics of turbulence is assumed to be space homogeneous and is described by the set of shell velocities u(nj)(t) for turbulent fluctuations of the scale proportional to 2(n). The MZS model includes a set of complex variables Vj(t), j=1,2,...,infinity, describing the amplitudes of the nearwall coherent structures of the scale s(j)similar to2(j) and responsible for the mean velocity profile. The suggested MZS equations of motion for u(nj)(t) and Vj(t) preserve the actual conservation laws (energy, mechanical, and angular momenta), respect the existing symmetries (including Galilean and scale invariance), and account for the type of nonlinearity in the NavierStokes equation, dimensional reasoning, etc. The MZS model qualitatively describes important characteristics of the wallbounded turbulence, e.g., evolution of the mean velocity profile with increasing Reynolds number Re from the laminar profile toward the universal logarithmic profile near the flatplane boundary layer as Re>infinity.

(2003) Physical Review E. 68, 3, 036303. Abstract
We analyze numerically the timedependent linear operators that govern the dynamics of Eulerian correlation functions of a decaying passive scalar advected by a stationary, forced twodimensional NavierStokes turbulence. We show how to naturally discuss the dynamics in terms of effective compact operators that display Eulerian statistically preserved structures which determine the anomalous scaling of the correlation functions. In passing we point out a bonus of the present approach, in providing analytic predictions for the timedependent correlation functions in decaying turbulent transport.

(2003) Physical Review E. 67, 6, 066310. Abstract
The weak version of universality in turbulence refers to the independence of the scaling exponents of the nth order structure functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents and the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for NavierStokes turbulence.

(2003) Physical Review E. 67, 4, 046314. Abstract
We propose a onefluid analytical model for a turbulently flowing dilute suspension, based on a modified NavierStokes equation with a kdependent effective density of suspension rho(eff)(k) and an additional damping term proportional to gamma(p)(k), representing the fluidparticle friction (described by Stokes law). The statistical description of turbulence within the model is simplified by a modification of the usual closure procedure based on the RichardsonKolmogorov picture of turbulence with a differential approximation for the energy transfer term. The resulting ordinary differential equation for the energy budget is solved analytically for various important limiting cases and numerically in the general case. In the inertial interval of scales, we describe analytically two competing effects: the energy suppression due to the fluidparticle friction and the energy enhancement during the cascade process due to decrease of the effective density of the smallscale motions. An additional suppression or enhancement of the energy density may occur in the viscous subrange, caused by the variation of the extent of the inertial interval due to the combined effect of the fluidparticle friction and the decrease of the kinematic viscosity of the suspensions. The analytical description of the complicated interplay of these effects supported by numerical calculations is presented. Our findings allow one to rationalize the qualitative picture of the isotropic homogeneous turbulence of dilute suspensions as observed in direct numerical simulations.
2002

(2002) FractalsComplex Geometry Patterns And Scaling In Nature And Society. 10, 3, p. 291296 Abstract
We introduce a model of hydrodynamic turbulence with a tunable parameter epsilon, which represents the ratio between deterministic and random components in the coupling between N identical copies of the turbulent field. To compute the anomalous scaling exponents zeta(n) (of the nth order structure functions) for chosen values of epsilon, we consider a systematic closure procedure for the hierarchy of equations for the norder correlation functions, in the limit N >infinity. The parameter epsilon regularizes the closure procedure, in the sense that discarded terms are of higher order in epsilon compared to those retained. It turns out that after the terms of O(1), the first nonzero terms are O(epsilon(4)). Within this epsiloncontrolled procedure, we have a finite and closed set of scaleinvariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations retains all terms of O(1) and O(epsilon(4)) and neglects terms of O(epsilon(6)). On this basis, we expect anomalous corrections deltazeta(n) in the scaling exponents zeta(n) to increase with epsilon(n). This expectation is confirmed by extensive numerical simulations using up to 25 copies and 28 shells for various values of epsilon(n). The simulations demonstrate that in the limit N > infinity, the scaling is normal for epsilon <ε(cr) with ε(cr) &AP; 0.6. We observed the birth of anomalous scaling at ε = ε(cr) with δζ(n) &PROP; ε(4)  ε(4)(cr) according to our expectation.

(2002) Physical Review Letters. 89, 6, 064501. Abstract
The statistics of twodimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussianlike in equilibrium. The skewness Sequivalent toS(3)(R)/S2(3/2)(R) was measured as S(exp)approximate to0.03. This contradiction is lifted by understanding that twodimensional turbulence is not far from a situation with equipartition of enstrophy, which exists as true thermodynamic equilibrium with K41 exponents in space dimension of d=4/3. We evaluate the skewness S(d) for 4/3 less than or equal todless than or equal to2, showing that S(d)=0 at d=4/3, and that it remains as small as Sexp in two dimensions.

(2002) Physical Review Letters. 89, 7, 074501 . Abstract
We consider shell models that display an inverse energy cascade similar to twodimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.

Onefluid description of turbulently flowing suspension(2002) arXiv. Abstract
We suggested a onefluid model of a turbulent dilute suspension which accounts for the "twoway'' fluidparticle interactions by kdependent effective density of suspension and additional damping term in the NavierStokes equation. We presented analytical description of the particle modification of turbulence including scale invariant suppression of a small k part of turbulent spectrum (independent of the particle response time) and possible enhancement of large k region [up to the factor (1+ϕ)2/3]. Our results are in agreement with qualitative picture of isotropic homogeneous turbulence of dilute suspensions previously observed in laboratory and numerical experiments.
2001

(2001) Physical Review E. 63, 5, 056118. Abstract
Extreme events have an important role which is sometimes catastrophic in a variety of natural phenomena, including climate, earthquakes, and turbulence, as well as in manmade environments such as financial markets. Statistical analysis and predictions in such systems are complicated by the fact that on the one hand extreme events may appear as "outliers" whose statistical properties do not seem to conform with the bulk of the data, and on the other hand they dominate the tails of the probability distributions and the scaling of high moments, leading to "abnormal" or "multiscaling." We employ a shell model of turbulence to show that it is very useful to examine in detail the dynamics of onset and demise of extreme events. Doing so may reveal dynamical scaling properties of the extreme events that are characteristic to them, and not shared by the bulk of the fluctuations. As the extreme events dominate the tails of the distribution functions, knowledge of their dynamical scaling properties can be turned into a prediction of the functional form of the tails. We show that from the analysis of relatively shorttime horizons (in which the extreme events appear as outliers) we can predict the tails of the probability distribution functions, in agreement with data collected in very much longer time horizons. The conclusion is that events that may appear unpredictable on relatively short time horizons are actually a consistent part of a multiscaling statistics on longer time horizons.
2000

(2000) Europhysics Letters. 50, 4, p. 473479 Abstract
The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable parameter epsilon, 0 less than or equal to epsilon less than or equal to 1, representing the ratio between deterministic and random components in the coupling between N identical copies of the turbulent field. Our numerical experiments give strong evidence that in the limit N > infinity anomalous scaling sets in proportional to epsilon(4) This result shows consistency with the nonperturbative closure proposed by the authors in Phys. Fluids, 12 (2000) 803. In this procedure closed equations of motion for the loworder correlation and response functions are obtained, keeping terms proportional to epsilon(0) and epsilon(4), discarding terms of orders epsilon(6) and higher. Moreover we give strong evidences that the birth of anomalous scaling appears at a finite critical epsilon, being epsilon(c) approximate to 0.6.

(2000) Physics of Fluids. 12, 4, p. 803821 Abstract
We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of N suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called epsilon. It is demonstrated, using numerical simulations of up to 25 copies and 28 shells that in the N >infinity limit but for 0 infinity limit the parameter epsilon can be used to regularize the closure procedure. The main result of this paper is a finite and closed set of scaleinvariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations takes into account terms up to order epsilon(4) and neglects terms of order epsilon(6). Preliminary analysis of this set of equations indicates a K41 normal scaling at epsilon=0, with a birth of anomalous exponents at larger values of epsilon, in agreement with the numerical simulations. (C) 2000 American Institute of Physics. [S10706631(00)00204X].

(2000) Physical Review E. 61, 3, p. 25862594 Abstract
We found universal anizopropic spectra of acoustic turbulence with the linear dispersion law omega(k)=ck within the framework of generalized kinetic equation which takes into account the finite time of threewave interactions. This anisotropic spectra can assume both scaleinvariant and nonscaleinvariant form. The implications for the evolution of the acoustic turbulence with nonisotropic pumping are discussed. The main result of the article is that the spectra of acoustic turbulence tend to become more isotropic.
1999

(1999) Physical Review E. 60, 4, p. 41754184 Abstract
The Taylor hypothesis, which allows surrogating spatial measurements requiring many experimental probes : by rime series from one or two probes, is examined on the basis of a simple analytic model of turbulent statistics. The main points are as follows: (i) The Taylor hypothesis introduces systematic errors in the evaluation of scaling exponents. (ii) When the mean wind (V) over bar(0) is not infinitely larger than the rootmeansquare longitudinal turbulent fluctuations upsilon(T), the effective Taylor advection velocity Vad Should take the latter into account. (iii) When two or more probes are employed the application of the Taylor hypothesis and the optimal choice of the effective advecting wind Vad need extra care. We present practical considerations for minimizing the errors incurred in experiments using one or two probes. (iv) Analysis of the Taylor hypothesis when different probes experience different mean winds is offered. [S1063651X(99)140108].
1998

(1998) Journal of Statistical Physics. 93, 34, p. 797832 Abstract
We develop a consistent closure procedure fbr the calculation of the scaling exponents zeta(n) of the nthorder correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents zeta(n). This hierarchy was discussed in detail in a recent publication by V. S. L'vov and I. Procaccia. The scaling exponents in this set of equations cannot be found from power counting. In this paper we present in detail the lowest nontrivial closure of this infinite set of equations, and prove that this closure leads to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integrodifferential equations, reflecting the nonlinearity of the original NavierStokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Holder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L. We demonstrate that the solvability condition of our equations leads to nonKolmogorov values of the scaling exponents zeta(n). Finally, we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence.

(1998) Physical Review E. 58, 2, p. 18111822 Abstract
We introduce a shell model of turbulence that exhibits improved properties in comparison to the standard (and very popular) Gledzer, Ohkitani, and Yamada (GOY) model. The nonlinear coupling is chosen to minimize correlations between different shells. In particular, the secondorder correlation function is diagonal in the shell index and the thirdorder correlation exists only between three consecutive shells. Spurious oscillations in the scaling regime, which are an annoying feature of the GOY model, are eliminated by our choice of nonlinear coupling. We demonstrate that the model exhibits multiscaling similar to the GOY model. The scaling exponents are shown to be independent of the viscous mechanism as is expected for NavierStokes turbulence and other shell models. These properties of the model make it optimal for further attempts to achieve understanding of multiscaling in nonlinear dynamics.

(1998) Physical Review B. 58, 4, p. 20382044 Abstract
In this paper we suggest a quantitative approach for description of the bonding behavior of the individual metal atoms on Si surfaces. It is proposed to use the relative contribution of electronic and ionic components of the effective polarizability of the metal atom to characterize the type of bond. Individual As, Sb, Na atoms adsorbed on Si(001)2 x 1 surface and K atoms adsorbed on both Si(001)2 x 1 and Si(111)7 x 7 surfaces were studied. It was found that the bonding behavior of the potassium on these two surfaces is completely different. The covalency parameters calculated according to this approach allow one to define the AsSi and SbSi bonds as almost pure covalent, NaSi bond as polarized covalent, KSI bond in the Si(001)2 x 1 surface as largely ionic, while in the Si(111)7 x 7 surface it is predominantly covalent.

(1998) Physical Review B. 57, 15, p. 89898996 Abstract
The electric fieldinduced relaxation of the adsorption geometry of Sb and K atoms on Si(001)2 x 1 surface was studied using ab initio cluster calculations. We have found that the adsorption geometry changes considerably due to field. The difference in the response to the applied field of the different adatoms and the underlying Si layer is remarkable. The relaxation of the Sb dimer is less than that of the clean surface dimers, whereas the changes in K atom positions are an order of magnitude larger than those of the clean surface. In addition, there are drastic changes in the geometry of the Si dimers on the Kcovered surface. The buckling of the dimers increases greatly for a positive field; for a negative field the increase in buckling is smaller. In both surfaces the relaxation of the Si dimers, to which the adsorbed atom is bonded, is defined by the elastic interactions with the adsorbed atom and differs from that of clean surface. The distribution of the field does not affect significantly the changes in adsorption geometry. However, for the fieldsensitive surfaces, an extremely sharp tip may cause a selective desorption of the adsorbed atoms. [S01631829(98)012156].
1997

(1997) Surface Science. 382, 13, p. 275287 Abstract
The effect of the tipinduced electric field on STM images and spectra from a Si(001) surface on which Sb, Na and K atoms were adsorbed at low coverage was studied by totalenergy LDF calculations. The adsorption geometry of Na and K atoms on the Si(001) surface was found to be strongly fielddependent. In contrast, the adsorption geometry of Sb on the Si(001) surface was almost insensitive to the field. The different topographic and electronic responses of different atoms in the surface resulted in changes in the relative contrast of the adsorbed atoms and the substrate in STM images. The calculated filledstate images were found to be similar to reported experimental images [Y.W. Mo, Phys. Rev. Lett. 65 (1990) 3417; A. Brodde, Th. Bertrams, H. Neddermeyer, Phys. Rev. B 47 (1993) 4508]. We found that the electric field inhibits emptystates imaging of alkali metals on Si(001) surface. Possible distortions of the tunneling spectra are discussed. Our results demonstrate that the ripinduced electric field is an important factor in forming STM data, and cannot be neglected in the interpretation of STM images and spectra. (C) 1997 Elsevier Science B.V.