Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation

The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. We introduce the dissipation term which works only in the scale smaller than the healing length, to remove short wavelength excitations which may hinder the cascade process of quantized vortices in the inertial range. The obtained energy spectrum is consistent with the Kolmogorov law.Comment: 4 pages, 4 figures and 1 table. Submitted to American Journal of Physic

Rapid turnover of T cells in acute infectious mononucleosis.

During acute infectious mononucleosis (AIM), large clones of Epstein-Barr virus-specific T lymphocytes are produced. To investigate the dynamics of clonal expansion, we measured cell proliferation during AIM using deuterated glucose to label DNA of dividing cells in vivo, analyzing cells according to CD4, CD8 and CD45 phenotype. The proportion of labeled CD8(+)CD45R0(+) T lymphocytes was dramatically increased in AIM subjects compared to controls (mean 17.5 versus 2.8%/day; p<0.005), indicating very rapid proliferation. Labeling was also increased in CD4(+)CD45R0(+) cells (7.1 versus 2.1%/day; p<0.01), but less so in CD45RA(+) cells. Mathematical modeling, accounting for death of labeled cells and changing pool sizes, gave estimated proliferation rates in CD8(+)CD45R0(+) cells of 11-130% of cells proliferating per day (mean 47%/day), equivalent to a doubling time of 1.5 days and an appearance rate in blood of about 5 x 10(9) cells/day (versus 7 x 10(7) cells/day in controls). Very rapid death rates were also observed amongst labeled cells (range 28-124, mean 57%/day),indicating very short survival times in the circulation. Thus, we have shown direct evidence for massive proliferation of CD8(+)CD45R0(+) T lymphocytes in AIM and demonstrated that rapid cell division continues concurrently with greatly accelerated rates of cell disappearance

Thermal dissipation in quantum turbulence

The microscopic mechanism of thermal dissipation in quantum turbulence has been numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtained the mutual friction coefficients of the vortex dynamics as functions of temperature, which can be applied to the vortex dynamics in dilute Bose-Einstein condensates.Comment: 4 pages, 6 figures, submitted to AP

Spectrum of turbulent Kelvin-waves cascade in superfluid helium

To explain the observed decay of superfluid turbulence at very low temperature, it has been proposed that a cascade of Kelvin waves (analogous to the classical Kolmogorov cascade) transfers kinetic energy to length scales which are small enough that sound can be radiated away. We report results of numerical simulations of the interaction of quantized vortex filaments. We observe the development of the Kelvin-waves cascade, and compute the statistics of the curvature, the amplitude spectrum (which we compare with competing theories) and the fractal dimension.Comment: 32 pages, 22 figure

Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature

By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. Finally, for the sake of more concrete illustration, we relate the fractal dimension of the tangle to the scaling exponents of amplitude and wavelength of a cascade of Kelvin waves.Comment: 12 pages, 1 figur

Turbulent superfluid profiles in a counterflow channel

We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.Comment: 3 double figures, 9 page

Rotating Superfluid Turbulence

Almost all studies of vortex states in helium II have been concerned with either ordered vortex lattices or disordered vortex tangles. This work studies numerically what happens in the presence of both rotation (which induces order) and thermal counterflow (which induces disorder). We find a new statistically steady state in which the vortex tangle is polarized along the rotational axis. Our results are used to interpret an instability which was discovered experimentally by Swanson et al. years ago but has been unexplained until now

Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure