364 research outputs found
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, , where
has scaling intermediate between and as a function of
. 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 increases with magnetic field.
In particular the system is ferromagnetic below 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
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:
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
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 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
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