Publications

In recent work it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform static loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field associated with plastic responses. Here we study the dynamical responses induced by oscillatory loads. The required modification to classical elasticity is described. Exact solutions for the displacement field in circular geometry are presented, demonstrating that dipole screening results in essential departures from the expected predictions of classical elasticity theory. Numerical simulations are conducted to validate the theoretical predictions and to delineate their range of validity.

Nonlinear interactions are crucial in science and engineering. Here, we investigate wave interactions in a highly nonlinear magnetic system driven by parametric pumping leading to Bose-Einstein condensation of spin-wave quanta—magnons. Using Brillouin light scattering spectroscopy in yttrium-iron garnet films, we found and identified a set of nonlinear processes resulting in off-resonant spin-wave excitations—virtual magnons. In particular, we discovered a dynamically strong, correlation-enhanced four-wave interaction process of the magnon condensate with pairs of parametric magnons having opposite wave vectors and fully correlated phases.

"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 mean-square displacements can reach 15-20 orders of magnitude. Analytic and numerical results of the proposed model are presented and discussed.

A macroscopic collective motion of a Bose-Einstein 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 sound-a 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 sound-Bogoliubov waves. This discovery advances the physics of quasiparticles and allows for the application of related transport phenomena for low-loss data transfer in magnon spintronics devices.

We report a detailed analysis of the energy spectra, second- and high-order structure functions of velocity differences in superfluid He4 counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the one-dimensional energy spectrum Exz(ky) (averaged over the xz plane, parallel to the channel wall), directly measured as a function of the wall-normal wave vector ky, gives more detailed information on the energy distribution over scales than the corresponding second-order structure function S2(δy). In particular, we discover two intervals of ky with different apparent exponents: Exz(ky)ky-mC for kk× and Exz(ky)ky-mF for kk×. Here k× denotes the wave number that separates scales with relatively strong (for kk×) and relatively weak (for kk×) coupling between the normal-fluid and superfluid velocity components. We interpret these k ranges as cascade-dominated and mutual-friction-dominated 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)2469-995010.1103/PhysRevB.97.214513]. Analysis of the nth-order structure functions statistics shows that in the energy-containing interval, the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade- and mutual-friction-dominated 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.

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 magnon-magnon scattering processes, which conserve the number of particles, can lead to the formation of a Bose-Einstein condensate at the bottom of a spin-wave spectrum. However, magnon-phonon scattering can significantly modify this scenario and new quasiparticles are formed - magnetoelastic bosons. Our observations of a parametrically populated magnon gas in a single-crystal film of yttrium iron garnet by means of wave-vector-resolved 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.

We report complementary experimental, numerical, and theoretical study of turbulent coflow, counterflow, and pure superflow of superfluid He-4 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 He-4. We further offer an analytical theory of the energy spectra of steady-state 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 counterflow-induced decoupling of the normal and superfluid velocity fluctuations.

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 time-dependent 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.

We present a comprehensive statistical study of free decay of the quantized vortex tangle in superfluid He4 at low and ultralow temperatures 0≤T≤1.1 K. Using high-resolution vortex filament simulations with full Biot-Savart vortex dynamics, we show that for ultralow temperatures T≲0.5 K, when the mutual friction parameters α≃α′

In superfluid 3He-B, 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 time-honored 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.

The non-Markovian master equation is applied to the calculation of reaction rates. Starting from the flux-side correlation function form, we treat both the thermal and real time evolution consistently within second order perturbation theory in the system-bath coupling. It is shown that the non-Markovian dynamics enter formally not only in the time propagation but also in the expressions for the initial system-bath 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 ML-MCTDH method of Craig et al. [1], which serves as reference in this work.

We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortex-street model representing the large-scale structure in a self-similar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the large-scale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless, the exact self-similar 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.

An analytical model for the time-developing turbulent boundary layer (TD TBL) over a flat plate is presented. The model provides explicit formulae for the temporal behavior of the wall-shear 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 spatially-developing turbulent boundary layers at momentum thickness Reynolds numbers equal to 1430 and 2900 [5-7]. Our analytical model is, to the best of our knowledge, the first of its kind for TD TBL.

We construct a simple analytic model for wall-bounded 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 log-law turbulent region. In particular, the model predicts a very simple distribution of the turbulent kinetic energy in the log-law region between the velocity components: the streamwise component contains a half of the total energy whereas the wall-normal and cross-stream components contain a quarter each. In addition, the model predicts a very simple relation between the von Kármán slope κ and the turbulent velocity in the log-law region v+ (in wall units): v+ =6κ. These predictions are in excellent agreement with direct numerical simulation data and with recent laboratory experiments.

A celebrated universal aspect of wall-bounded turbulent flows is the von Kármán log-law-of-the-wall, describing how the mean velocity in the stream-wise direction depends on the distance from the wall. Although the log-law is known for more than 75 years, the von Kármán constant governing the slope of the log-law was not determined theoretically. In this letter we show that the von Kármán constant can be estimated from homogeneous turbulent data, i. e, without information from wall-bounded flows.

The drag reduction by polymers in turbulent flows was analyzed. The drag reduction, in a recent theory, was found to be consistent with the effective viscocity growing linearly with the distance from the wall. the reduction in the Reynolds stress overwhelmed the increase in the viscous drag by the self-consistent solution. By using the direct numerical simulations it was shown that a linear viscosity profile reduced the drag in agreement with the theory and in close correspondence with direct simulations of the FENE-P model at the same flow conditions.

A multizone shell (MSZ) model for wall-bounded flows, accounting for the space inhomogenity in a piecewise approximation in which the cross-sectional area of the flow was subdivided into zones, was discussed. The MSZ model includes a set of complex variables describing the amplitudes of the near-wall coherent structure. The evolution of the mean velocity profile with increasing Reynolds number from the laminar profile toward the universal logarithmic profile near the flat-plane boundary layer was also elaborated.

We introduce a model of hydrodynamic turbulence with a tunable parameter ε, 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 ζ_n (of the nth order structure functions) for chosen values of ε, we consider a systematic closure procedure for the hierarchy of equations for the n-order correlation functions, in the limit N → ∞. The parameter ε regularizes the closure procedure, in the sense that discarded terms are of higher order in ε compared to those retained. It turns out that after the terms of O(1), the first nonzero terms are O(ε⁴). Within this ε-controlled procedure, we have a finite and closed set of scale-invariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations retains all terms of O(1) and O(ε⁴) and neglects terms of O(ε⁶). On this basis, we expect anomalous corrections δζ_n in the scaling exponents ζ_n to increase with ε_n. This expectation is confirmed by extensive numerical simulations using up to 25 copies and 28 shells for various values of ε_n. The simulations demonstrate that in the limit N → ∞, the scaling is normal for ε cr with ε_cr ≈ 0.6. We observed the birth of anomalous scaling at ε = ε_cr with δζ_n ∝ ε⁴ - ε_cr⁴ according to our expectation.

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 ∈, 0 ≤ ∈ ≤ 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 → ∞ anomalous scaling sets in proportional to ∈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 low-order correlation and response functions are obtained, keeping terms proportional to ∈⁰ and ∈⁴, discarding terms of orders ∈⁶ and higher. Moreover we give strong evidences that the birth of anomalous scaling appears at a finite critical ∈, being ∈_c ≈ 0.6.

We develop a consistent closure procedure for the calculation of the scaling exponents ζ_n of the nth-order 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 ζ_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 integro-differential equations, reflecting the nonlinearity of the original Navier-Stokes 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 Hölder 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 non-Kolmogorov values of the scaling exponents ζ_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.