232 research outputs found
Statistical geometry in scalar turbulence
A general link between geometry and intermittency in passive scalar
turbulence is established. Intermittency is qualitatively traced back to events
where tracer particles stay for anomalousy long times in degenerate geometries
characterized by strong clustering. The quantitative counterpart is the
existence of special functions of particle configurations which are
statistically invariant under the flow. These are the statistical integrals of
motion controlling the scalar statistics at small scales and responsible for
the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure
Dynamics of Fluctuation Dominated Phase Ordering: Hard-core Passive Sliders on a Fluctuating Surface
We study the dynamics of a system of hard-core particles sliding downwards on
a one dimensional fluctuating interface, which in a special case can be mapped
to the problem of a passive scalar advected by a Burgers fluid. Driven by the
surface fluctuations, the particles show a tendency to cluster, but the
hard-core interaction prevents collapse. We use numerical simulations to
measure the auto-correlation function in steady state and in the aging regime,
and space-time correlation functions in steady state. We have also calculated
these quantities analytically in a related surface model. The steady state
auto-correlation is a scaling function of t/L^z, where L is the system size and
z the dynamic exponent. Starting from a finite intercept, the scaling function
decays with a cusp, in the small argument limit. The finite value of the
intercept indicates the existence of long range order in the system. The
space-time correlation, which is a function of r/L and t/L^z, is non-monotonic
in t for fixed r. The aging auto-correlation is a scaling function of t_1 and
t_2 where t_1 is the waiting time and t_2 the time difference. This scaling
function decays as a power law for t_2 \gg t_1; for t_1 \gg t_2, it decays with
a cusp as in steady state. To reconcile the occurrence of strong fluctuations
in the steady state with the fact of an ordered state, we measured the
distribution function of the length of the largest cluster. This shows that
fluctuations never destroy ordering, but rather the system meanders from one
ordered configuration to another on a relatively rapid time scale
Statistical conservation laws in turbulent transport
We address the statistical theory of fields that are transported by a
turbulent velocity field, both in forced and in unforced (decaying)
experiments. We propose that with very few provisos on the transporting
velocity field, correlation functions of the transported field in the forced
case are dominated by statistically preserved structures. In decaying
experiments (without forcing the transported fields) we identify infinitely
many statistical constants of the motion, which are obtained by projecting the
decaying correlation functions on the statistically preserved functions. We
exemplify these ideas and provide numerical evidence using a simple model of
turbulent transport. This example is chosen for its lack of Lagrangian
structure, to stress the generality of the ideas
Raman scattering in Mott-Hubbard systems
We present a theory of Raman scattering in the Hubbard model. The scattering of light has two contributions. One gives rise to scattering by spin degrees of freedom in the insulating case where the general form of the scattering Hamiltonian is derived. The fluctuations of the "chiral" spin operator ∑ Si·(Sj×Sk) are shown to contribute in the B2g scattering geometry. The other contributes in the doped case and is shown to probe the fluctuations of the "stress tensor." This quantity is not conserved, and hence its fluctuations at small q inherent in optical experiments need not be small, in striking contrast to density fluctuations in usual metals
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
The intermittent behavior and hierarchical clustering of the cosmic mass field
The hierarchical clustering model of the cosmic mass field is examined in the
context of intermittency. We show that the mass field satisfying the
correlation hierarchy is intermittent if , where is the dimension of the field, and is the power-law
index of the non-linear power spectrum in the discrete wavelet transform (DWT)
representation. We also find that a field with singular clustering can be
described by hierarchical clustering models with scale-dependent coefficients
and that this scale-dependence is completely determined by the
intermittent exponent and . Moreover, the singular exponents of a field
can be calculated by the asymptotic behavior of when is large.
Applying this result to the transmitted flux of HS1700 Ly forests, we
find that the underlying mass field of the Ly forests is significantly
intermittent. On physical scales less than about 2.0 h Mpc, the observed
intermittent behavior is qualitatively different from the prediction of the
hierarchical clustering with constant . The observations, however, do show
the existence of an asymptotic value for the singular exponents. Therefore, the
mass field can be described by the hierarchical clustering model with
scale-dependent . The singular exponent indicates that the cosmic mass
field at redshift is weakly singular at least on physical scales as
small as 10 h kpc.Comment: AAS Latex file, 33 pages,5 figures included, accepted for publication
in Ap
Fronts in passive scalar turbulence
The evolution of scalar fields transported by turbulent flow is characterized
by the presence of fronts, which rule the small-scale statistics of scalar
fluctuations. With the aid of numerical simulations, it is shown that: isotropy
is not recovered, in the classical sense, at small scales; scaling exponents
are universal with respect to the scalar injection mechanisms; high-order
exponents saturate to a constant value; non-mature fronts dominate the
statistics of intense fluctuations. Results on the statistics inside the
plateaux, where fluctuations are weak, are also presented. Finally, we analyze
the statistics of scalar dissipation and scalar fluxes.Comment: 18 pages, 27 figure
Universal decay of scalar turbulence
The asymptotic decay of passive scalar fields is solved analytically for the
Kraichnan model, where the velocity has a short correlation time. At long
times, two universality classes are found, both characterized by a distribution
of the scalar -- generally non-Gaussian -- with global self-similar evolution
in time. Analogous behavior is found numerically with a more realistic flow
resulting from an inverse energy cascade.Comment: 4 pages, 3 Postscript figures, submitted to PR
Spatiotemporal Chaos, Localized Structures and Synchronization in the Vector Complex Ginzburg-Landau Equation
We study the spatiotemporal dynamics, in one and two spatial dimensions, of
two complex fields which are the two components of a vector field satisfying a
vector form of the complex Ginzburg-Landau equation. We find synchronization
and generalized synchronization of the spatiotemporally chaotic dynamics. The
two kinds of synchronization can coexist simultaneously in different regions of
the space, and they are mediated by localized structures. A quantitative
characterization of the degree of synchronization is given in terms of mutual
information measures.Comment: 6 pages, using bifchaos.sty (included). 7 figures. Related material,
including higher quality figures, could be found at
http://www.imedea.uib.es/PhysDept/publicationsDB/date.html . To appear in
International Journal of Bifurcation and Chaos (1999
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