38 research outputs found
On the dynamics of a self-gravitating medium with random and non-random initial conditions
The dynamics of a one-dimensional self-gravitating medium, with initial
density almost uniform is studied. Numerical experiments are performed with
ordered and with Gaussian random initial conditions. The phase space portraits
are shown to be qualitatively similar to shock waves, in particular with
initial conditions of Brownian type. The PDF of the mass distribution is
investigated.Comment: Latex, figures in eps, 23 pages, 11 figures. Revised versio
A non-perturbative renormalization group study of the stochastic Navier--Stokes equation
We study the renormalization group flow of the average action of the
stochastic Navier--Stokes equation with power-law forcing. Using Galilean
invariance we introduce a non-perturbative approximation adapted to the zero
frequency sector of the theory in the parametric range of the H\"older exponent
of the forcing where real-space local interactions are
relevant. In any spatial dimension , we observe the convergence of the
resulting renormalization group flow to a unique fixed point which yields a
kinetic energy spectrum scaling in agreement with canonical dimension analysis.
Kolmogorov's -5/3 law is, thus, recovered for as also predicted
by perturbative renormalization. At variance with the perturbative prediction,
the -5/3 law emerges in the presence of a \emph{saturation} in the
-dependence of the scaling dimension of the eddy diffusivity at
when, according to perturbative renormalization, the velocity
field becomes infra-red relevant.Comment: RevTeX, 18 pages, 5 figures. Minor changes and new discussion
Pressure and intermittency in passive vector turbulence
We investigate the scaling properties a model of passive vector turbulence
with pressure and in the presence of a large-scale anisotropy. The leading
scaling exponents of the structure functions are proven to be anomalous. The
anisotropic exponents are organized in hierarchical families growing without
bound with the degree of anisotropy. Nonlocality produces poles in the
inertial-range dynamics corresponding to the dimensional scaling solution. The
increase with the P\'{e}clet number of hyperskewness and higher odd-dimensional
ratios signals the persistence of anisotropy effects also in the inertial
range.Comment: 4 pages, 1 figur
On the canonically invariant calculation of Maslov indices
After a short review of various ways to calculate the Maslov index appearing
in semiclassical Gutzwiller type trace formulae, we discuss a
coordinate-independent and canonically invariant formulation recently proposed
by A Sugita (2000, 2001). We give explicit formulae for its ingredients and
test them numerically for periodic orbits in several Hamiltonian systems with
mixed dynamics. We demonstrate how the Maslov indices and their ingredients can
be useful in the classification of periodic orbits in complicated bifurcation
scenarios, for instance in a novel sequence of seven orbits born out of a
tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.
Generally covariant state-dependent diffusion
Statistical invariance of Wiener increments under SO(n) rotations provides a
notion of gauge transformation of state-dependent Brownian motion. We show that
the stochastic dynamics of non gauge-invariant systems is not unambiguously
defined. They typically do not relax to equilibrium steady states even in the
absence of extenal forces. Assuming both coordinate covariance and gauge
invariance, we derive a second-order Langevin equation with state-dependent
diffusion matrix and vanishing environmental forces. It differs from previous
proposals but nevertheless entails the Einstein relation, a Maxwellian
conditional steady state for the velocities, and the equipartition theorem. The
over-damping limit leads to a stochastic differential equation in state space
that cannot be interpreted as a pure differential (Ito, Stratonovich or else).
At odds with the latter interpretations, the corresponding Fokker-Planck
equation admits an equilibrium steady state; a detailed comparison with other
theories of state-dependent diffusion is carried out. We propose this as a
theory of diffusion in a heat bath with varying temperature. Besides
equilibrium, a crucial experimental signature is the non-uniform steady spatial
distribution.Comment: 24 page
On the strong anomalous diffusion
The superdiffusion behavior, i.e. , with , in general is not completely characherized by a unique exponent. We study
some systems exhibiting strong anomalous diffusion, i.e. where and is not a linear function of .
This feature is different from the weak superdiffusion regime, i.e.
, as in random shear flows. The strong anomalous diffusion
can be generated by nontrivial chaotic dynamics, e.g. Lagrangian motion in
time-dependent incompressible velocity fields, symplectic maps and
intermittent maps. Typically the function is piecewise linear. This
corresponds to two mechanisms: a weak anomalous diffusion for the typical
events and a ballistic transport for the rare excursions. In order to have
strong anomalous diffusion one needs a violation of the hypothesis of the
central limit theorem, this happens only in a very narrow region of the control
parameters space.Comment: 27 pages, 14 figure
Shell Model for Time-correlated Random Advection of Passive Scalars
We study a minimal shell model for the advection of a passive scalar by a
Gaussian time correlated velocity field. The anomalous scaling properties of
the white noise limit are studied analytically. The effect of the time
correlations are investigated using perturbation theory around the white noise
limit and non-perturbatively by numerical integration. The time correlation of
the velocity field is seen to enhance the intermittency of the passive scalar.Comment: Replaced with final version + updated figure
Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
The first example of a turbulent system where the failure of the hypothesis
of small-scale isotropy restoration is detectable both in the `flattening' of
the inertial-range scaling exponent hierarchy, and in the behavior of odd-order
dimensionless ratios, e.g., skewness and hyperskewness, is presented.
Specifically, within the kinematic approximation in magnetohydrodynamical
turbulence, we show that for compressible flows, the isotropic contribution to
the scaling of magnetic correlation functions and the first anisotropic ones
may become practically indistinguishable. Moreover, skewness factor now
diverges as the P\'eclet number goes to infinity, a further indication of
small-scale anisotropy.Comment: 4 pages Latex, 1 figur