Interaction Renormalization and Validity of Kinetic Equations for Turbulent States.

We consider turbulence of waves interacting weakly via four-wave scattering (sea waves, plasma waves, spin waves, etc.). In the first order in the interaction, a closed kinetic equation has stationary solutions describing turbulent cascades.

Multimode correlations and the entropy of turbulence in shell models.

We suggest a new focus for turbulence studies-multimode correlations-which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such models allows one to study turbulence close to thermal equilibrium, which happens when the interaction time weakly depends on the mode number.

Sum-of-squares bounds on correlation functions in a minimal model of turbulence.

We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of two resonantly interacting modes when one is pumped and the other dissipates.

Information theory characteristics improve the prediction of lithium response in bipolar disorder patients using a support vector machine classifier.

Aim: Bipolar disorder (BD) is a mood disorder with a high morbidity and death rate. Lithium (Li), a prominent mood stabilizer, is often used as a first-line treatment. However, clinical studies have shown that Li is fully effective in roughly 30% of BD patients.

Singular Measures and Information Capacity of Turbulent Cascades.

How weak is the weak turbulence? Here, we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence. The mutual information between modes is stationary and small in thermal equilibrium, yet it is shown here to grow with time for weak turbulence in a finite box.

Light transport and vortex-supported wave-guiding in micro-structured optical fibres.

In hydrodynamics, vortex generation upon the transition from smooth laminar flows to turbulence is generally accompanied by increased dissipation. However, vortices in the plane can provide transport barriers and decrease losses, as it happens in numerous geophysical, astrophysical flows and in tokamaks. Photon interactions with matter can affect light transport in ways resembling fluid dynamics.

Confinement of surface spinners in liquid metamaterials.

We show that rotating particles at the liquid-gas interface can be efficiently manipulated using the surface-wave analogue of optical lattices. Two orthogonal standing waves generate surface flows of counter-rotating half-wavelength unit cells, the liquid interface metamaterial, whose geometry is controlled by the wave phase shift. Here we demonstrate that by placing active magnetic spinners inside such metamaterials, one makes a powerful tool which allows manipulation and self-assembly of spinners, turning them into vehicles capable of transporting matter and information between autonomous metamaterial unit cells.

Freely Flowing Currents and Electric Field Expulsion in Viscous Electronics.

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that the nonlocal relation between the current and electric field due to momentum-conserving interparticle collisions leads to a total or partial field expulsion from such flows. That results in freely flowing currents in the bulk and a boundary jump in the electric potential at current-injecting electrodes.

Particle Collisions and Negative Nonlocal Response of Ballistic Electrons.

An electric field that builds in the direction against current, known as negative nonlocal resistance, arises naturally in viscous flows and is thus often taken as a telltale of this regime. Here, we predict negative resistance for the ballistic regime, wherein the ee collision mean free path is greater than the length scale at which the system is being probed. Therefore, negative resistance alone does not provide strong evidence for the occurrence of the hydrodynamic regime; it must thus be demoted from the rank of irrefutable evidence to that of a mere forerunner.

Turbulence Appearance and Nonappearance in Thin Fluid Layers.

Flows in fluid layers are ubiquitous in industry, geophysics, and astrophysics. Large-scale flows in thin layers can be considered two dimensional with bottom friction added. Here we find that the properties of such flows depend dramatically on the way they are driven.

Fluidity onset in graphene.

Viscous electron fluids have emerged recently as a new paradigm of strongly-correlated electron transport in solids. Here we report on a direct observation of the transition to this long-sought-for state of matter in a high-mobility electron system in graphene. Unexpectedly, the electron flow is found to be interaction-dominated but non-hydrodynamic (quasiballistic) in a wide temperature range, showing signatures of viscous flows only at relatively high temperatures.

Linking Spatial Distributions of Potential and Current in Viscous Electronics.

Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons behave as a fluid. Electron viscous flows are governed by a nonlocal current-field relation which renders the spatial patterns of the current and electric field strikingly dissimilar. Notably, driven by the viscous friction force from adjacent layers, current can flow against the electric field, generating negative resistance, vorticity, and vortices.

Higher-than-ballistic conduction of viscous electron flows.

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here, we show that in viscous flows, interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit [Formula: see text] The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum mechanical ballistic transport at [Formula: see text] but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodynamic variables.

Interaction between mean flow and turbulence in two dimensions.

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios.

Time irreversibility of the statistics of a single particle in compressible turbulence.

We investigate time irreversibility from the point of view of a single particle in Burgers turbulence. Inspired by the recent work for incompressible flows [Xu et al., Proc.

Cascades in nonlocal turbulence.

We consider developed turbulence in the two-dimensional Gross-Pitaevskii model, which describes wide classes of phenomena from atomic and optical physics to condensed matter, fluids, and plasma. The well-known difficulty of the problem is that the hypothetical local spectra of both inverse and direct cascades in the weak-turbulence approximation carry fluxes that are either zero or have the wrong sign; Such spectra cannot be realized. We analytically derive the exact flux constancy laws (analogs of Kolmogorov's 4/5 law for incompressible fluid turbulence), expressed via the fourth-order moment and valid for any nonlinearity.

Universal profile of the vortex condensate in two-dimensional turbulence.

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate-a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions.

New type of anomaly in turbulence.

The turbulent energy flux through scales, ε̅, remains constant and nonvanishing in the limit of zero viscosity, which results in the fundamental anomaly of time irreversibility. It was considered straightforward to deduce from this the Lagrangian velocity anomaly, ⟨du(2)/dt⟩=-4ε̅ at t=0, where u[over →] is the velocity difference of a pair of particles, initially separated by a fixed distance. Here we demonstrate that this assumed first taking the limit t→0 and then ν→0, while a zero-friction anomaly requires taking viscosity to zero first.

Flight-crash events in turbulence.

The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence.

Oscillations in a turbulence-condensate system.

We consider developed turbulence in the Gross-Pitaevsky model, where a condensate appears due to an inverse cascade. Despite being fully turbulent, the system demonstrates nondecaying periodic oscillations around a steady state, when turbulence and condensate periodically exchange a small fraction of waves. We show that these collective oscillations are not of a predator-prey type, as was suggested earlier; rather, they are due to phase coherence and anomalous correlations imposed by the condensate.

Single flow snapshot reveals the future and the past of pairs of particles in turbulence.

We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The formalism establishes a bridge between single-time Eulerian and long-time Lagrangian pictures of turbulent flows. In particular, we derive an exact formula for a short-term counterpart of the long-time Richardson law, and we identify a conservation law of turbulent dispersion which is true even in nonstationary turbulence.

Optical turbulence and spectral condensate in long fibre lasers.

We study numerically optical turbulence using the particular example of a recently created, ultra-long fibre laser. For normal fibre dispersion, we observed an intermediate state with an extremely narrow spectrum (condensate), which experiences instability and a sharp transition to a fluctuating regime with a wider spectrum. We demonstrate that the number of modes has an impact on the condensate's lifetime.

Phase transitions in wave turbulence.

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space.

Vorticity statistics in the direct cascade of two-dimensional turbulence.

For the direct cascade of steady two-dimensional (2D) Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When ϖ is the vorticity coarse-grained over a scale R, the probability density function (PDF), P(ϖ), has a universal asymptotic behavior lnP~-ϖ/ϖ(rms) at ϖ≫ϖ(rms)=[Hln(L/R)](1/3), where H is the enstrophy flux and L is the pumping length. Therefore, the PDF has exponential tails and is self-similar, that is, it can be presented as a function of a single argument, ϖ/ϖ(rms), in distinction from other known direct cascades.

Fluid-particle separation in a random flow described by the telegraph model.

We study the statistics of the relative separation between two fluid particles in a spatially smooth and temporally random flow. The Lagrangian strain is modeled by a telegraph noise, which is a stationary random Markov process that can only take two values with known transition probabilities. The simplicity of the model enables us to write closed equations for the interparticle distance in the presence of a finite-correlated noise.