On the properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e. a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent flow.Comment: latex prl-stationary-051215arxiv.tex, 9 files, 6 figures, 4 pages (http://www-drecam.cea.fr/spec/articles/S06/008/

An inertial range length scale in structure functions

It is shown using experimental and numerical data that within the traditional inertial subrange defined by where the third order structure function is linear that the higher order structure function scaling exponents for longitudinal and transverse structure functions converge only over larger scales, $r>r_S$, where $r_S$ has scaling intermediate between $\eta$ and $\lambda$ as a function of $R_\lambda$. Below these scales, scaling exponents cannot be determined for any of the structure functions without resorting to procedures such as extended self-similarity (ESS). With ESS, different longitudinal and transverse higher order exponents are obtained that are consistent with earlier results. The relationship of these statistics to derivative and pressure statistics, to turbulent structures and to length scales is discussed.Comment: 25 pages, 9 figure

Magnetic Properties of a Bose-Einstein Condensate

Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behaviour of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation $T_{BEC}$ increases with magnetic field. In particular the system is ferromagnetic below $T_{BEC}$ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetisation with regard to temperature or magnetic field are discontinuous along the phase boundary.Comment: 5 pages, 5 figures included, to appear in Phys. Rev.

Probabilistic Clustering of Sequences: Inferring new bacterial regulons by comparative genomics

Genome wide comparisons between enteric bacteria yield large sets of conserved putative regulatory sites on a gene by gene basis that need to be clustered into regulons. Using the assumption that regulatory sites can be represented as samples from weight matrices we derive a unique probability distribution for assignments of sites into clusters. Our algorithm, 'PROCSE' (probabilistic clustering of sequences), uses Monte-Carlo sampling of this distribution to partition and align thousands of short DNA sequences into clusters. The algorithm internally determines the number of clusters from the data, and assigns significance to the resulting clusters. We place theoretical limits on the ability of any algorithm to correctly cluster sequences drawn from weight matrices (WMs) when these WMs are unknown. Our analysis suggests that the set of all putative sites for a single genome (e.g. E. coli) is largely inadequate for clustering. When sites from different genomes are combined and all the homologous sites from the various species are used as a block, clustering becomes feasible. We predict 50-100 new regulons as well as many new members of existing regulons, potentially doubling the number of known regulatory sites in E. coli.Comment: 27 pages including 9 figures and 3 table

Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Frequency Dependent Viscosity Near the Critical Point: The Scale to Two Loop Order

The recent accurate measurements of Berg, Moldover and Zimmerli of the viscoelastic effect near the critical point of xenon has shown that the scale factor involved in the frequency scaling is about twice the scale factor obtained theoretically. We show that this discrepancy is a consequence of using first order perturbation theory. Including two loop contribution goes a long way towards removing the discrepancy.Comment: No of pages:7,Submitted to PR-E(Rapid Communication),No of EPS files:

Bose-Einstein condensation with internal degrees of freedom in alkali atom gases

The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian constructed from general gauge and spin rotation symmetry principles fundamental equations for condensate are derived. The ground state where time reversal symmetry is broken in some case and low-lying collective modes, e.g. spin and density wave modes, are discussed. Novel vortex as a topological defect can be created experimentally.Comment: 4 pages, 1 eps figur

Domain Coarsening in Systems Far from Equilibrium

The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from the inverse width of the Fourier spectrum is studied for both potential and nonpotential models. The morphology of the domains and the defect structures are however quite different in the two cases, and evidence is presented for a second length scale in the nonpotential case.Comment: 11 pages, RevTeX; 3 uufiles encoded postscript figures appende

The signal-to-noise analysis of the Little-Hopfield model revisited

Using the generating functional analysis an exact recursion relation is derived for the time evolution of the effective local field of the fully connected Little-Hopfield model. It is shown that, by leaving out the feedback correlations arising from earlier times in this effective dynamics, one precisely finds the recursion relations usually employed in the signal-to-noise approach. The consequences of this approximation as well as the physics behind it are discussed. In particular, it is pointed out why it is hard to notice the effects, especially for model parameters corresponding to retrieval. Numerical simulations confirm these findings. The signal-to-noise analysis is then extended to include all correlations, making it a full theory for dynamics at the level of the generating functional analysis. The results are applied to the frequently employed extremely diluted (a)symmetric architectures and to sequence processing networks.Comment: 26 pages, 3 figure

Scaling and universality in turbulent convection

Anomalous correlation functions of the temperature field in two-dimensional turbulent convection are shown to be universal with respect to the choice of external sources. Moreover, they are equal to the anomalous correlations of the concentration field of a passive tracer advected by the convective flow itself. The statistics of velocity differences is found to be universal, self-similar and close to Gaussian. These results point to the conclusion that temperature intermittency in two-dimensional turbulent convection may be traced back to the existence of statistically preserved structures, as it is in passive scalar turbulence.Comment: 4 pages, 6 figure