We study the universal nonstationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the system or to a finite-time blowup. We identify self-similar regimes in BECs by numerically simulating the forced and unforced Gross-Pitaevskii equation (GPE) and the associated wave kinetic equation (WKE) for the direct and inverse cascades, respectively.
View Article and Find Full Text PDFWhen a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact nonlinearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred toward small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs.
View Article and Find Full Text PDFWe present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schrödinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic vortices on the background of a spatially infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex.
View Article and Find Full Text PDFWe test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both the wave-action spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of the GPE data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times.
View Article and Find Full Text PDFWe report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for the turbulent energy spectrum, E(k)=C_{1}sqrt[ϵac_{s}]/k, of acoustic waves in 2D with almost linear dispersion law, ω_{k}=c_{s}k[1+(ak)^{2}], ak≪1. Here, ϵ is the energy flux over scales, and C_{1} is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates.
View Article and Find Full Text PDFIn a recent paper, Tanogami [Phys. Rev. E 103, 023106 (2021)2470-004510.
View Article and Find Full Text PDFPhilos Trans A Math Phys Eng Sci
March 2022
We develop a theory of strong anisotropy of the energy spectra in the thermally driven turbulent counterflow of superfluid He. The key ingredients of the theory are the three-dimensional 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 energy-rate equation, which is fully supported by our numerical solution.
View Article and Find Full Text PDFWe present the first direct numerical simulation of gravitational wave turbulence. General relativity equations are solved numerically in a periodic box with a diagonal metric tensor depending on two space coordinates only, g_{ij}≡g_{ii}(x,y,t)δ_{ij}, and with an additional small-scale dissipative term. We limit ourselves to weak gravitational waves and to a freely decaying turbulence.
View Article and Find Full Text PDFWe present a comprehensive study of the statistical features of a three-dimensional (3D) time-reversible truncated Navier-Stokes (RNS) system, wherein the standard viscosity ν is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the statistical features of the RNS steady states in terms of a non-negative dimensionless control parameter R_{r}, which quantifies the balance between the fluctuations of kinetic energy at the forcing length scale ℓ_{f} and the total energy E_{0}. For small R_{r}, the RNS equations are found to produce "warm" stationary statistics, e.
View Article and Find Full Text PDFWe study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in the reduced case of a 2.5+1 diagonal metric tensor.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
November 2015
We present a systematic derivation of the Biot-Savart equation from the nonlinear Schrödinger equation, in the limit when the curvature radius of vortex lines and the intervortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines,H=κ(2)/8π∫(|s-s'|>ξ(*))(ds·ds')/|s-s'|,with cutoff length ξ(*)≈0.3416293/√(ρ(0)), where ρ(0) is the background condensate density far from the vortex lines and κ is the quantum of circulation.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
July 2015
In field theory, particles are waves or excitations that propagate on the fundamental state. In experiments or cosmological models, one typically wants to compute the out-of-equilibrium evolution of a given initial distribution of such waves. Wave turbulence deals with out-of-equilibrium ensembles of weakly nonlinear waves, and is therefore well suited to address this problem.
View Article and Find Full Text PDFWave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence.
View Article and Find Full Text PDFWeak Alfvénic turbulence in a periodic domain is considered as a mixed state of Alfvén waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed, and, indeed, none is found. If the 2D modes are not directly forced, k(-2) and k(-1) spectra are found for the Alfvén waves and the 2D modes, respectively, with the latter less energetic than the former.
View Article and Find Full Text PDFWe study quasigeostrophic (QG) and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus on the zonostrophy, an extra invariant in the CHM model, and on its role in the formation of zonal jets. We use a generalized Fjørtoft argument for the energy, enstrophy, and zonostrophy and show that they cascade anisotropically into nonintersecting sectors in k space with the energy cascading towards large zonal scales.
View Article and Find Full Text PDFWe present the first simultaneous space-time measurements for gravity wave turbulence in a large laboratory flume. We found that the slopes of k and omega wave spectra depend on wave intensity. This cannot be explained by any existing theory considering wave turbulence as the result of either breaking events or weakly nonlinear wave interactions.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
July 2008
We study exact four-wave resonances among gravity water waves in a square box with periodic boundary conditions. We show that these resonant quartets are linked with each other by shared Fourier modes in such a way that they form independent clusters. These clusters can be formed by two types of quartets: (1) Angle resonances which cannot directly cascade energy but which can redistribute it among the initially excited modes and (2) scale resonances which are much more rare but which are the only ones that can transfer energy between different scales.
View Article and Find Full Text PDFWe present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size 12 x 6 m. For a wide range of amplitudes the wave energy spectrum was found to scale as Eomega approximately omega(-nu) in a frequency range of up to one decade. However, nu appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4.
View Article and Find Full Text PDFObjective: To develop a mathematical model for more precise estimation of the incidence of chromosomal abnormalities and the sex ratio among spontaneous abortions masked by maternal cell contamination.
Design: Retrospective analysis.
Setting: Academic medical center.
Phys Rev E Stat Nonlin Soft Matter Phys
June 2004
We study the k-space fluctuations of the wave action about its mean spectrum in the turbulence of dispersive waves. We use a minimal model based on the random phase approximation (RPA) and derive evolution equations for the arbitrary-order one-point moments of the wave intensity in the wave-number space. The first equation in this series is the familiar kinetic equation for the mean wave-action spectrum, whereas the second and higher equations describe the fluctuations about this mean spectrum.
View Article and Find Full Text PDFCytogenetic analysis of reproductive wastage is an important stage in understanding the genetic background of early embryogenesis. The results of conventional cytogenetic studies of spontaneous abortions depend on tissue culturing and are associated with a significant cell culture failure rate. We performed interphase dual-colour FISH analysis to detect chromosomal abnormalities in noncultured cells from two different tissues-cytotrophoblast and extraembryonic mesoderm-of 60 first-trimester spontaneous abortions from which cells had failed to grow in culture.
View Article and Find Full Text PDFA phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is analyzed. The general steady state contains a nonlinear mixture of the constant-flux Kolmogorov and fluxless thermodynamic components. Such "warm cascade" solutions describe a bottleneck phenomenon of spectrum stagnation near the dissipative scale.
View Article and Find Full Text PDFUniparental disomy (UPD) 15, detected in patients with Prader-Willi (PWS) and Angelman syndromes, has to date always involved the entire chromosome 15. We report the first case of segmental maternal uniparental heterodisomy confined to a proximal part of chromosome 15 in a child with clinical features of PWS. This unusual finding can be explained by the rare combination of three consecutive events: a trisomy 15 zygote caused by a maternal meiosis I error, early postzygotic mitotic recombination between maternal and paternal chromatids, and, finally, trisomy rescue by the loss of the rearranged chromosome 15 containing the paternal 15q11-q13 segment.
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