15,252 research outputs found
Truncation effects in superdiffusive front propagation with L\'evy flights
A numerical and analytical study of the role of exponentially truncated
L\'evy flights in the superdiffusive propagation of fronts in
reaction-diffusion systems is presented. The study is based on a variation of
the Fisher-Kolmogorov equation where the diffusion operator is replaced by a
-truncated fractional derivative of order where
is the characteristic truncation length scale. For there is no
truncation and fronts exhibit exponential acceleration and algebraic decaying
tails. It is shown that for this phenomenology prevails in the
intermediate asymptotic regime where
is the diffusion constant. Outside the intermediate asymptotic regime,
i.e. for , the tail of the front exhibits the tempered decay
, the acceleration is transient, and
the front velocity, , approaches the terminal speed as , where it is assumed that
with denoting the growth rate of the
reaction kinetics. However, the convergence of this process is algebraic, , which is very slow compared to the exponential
convergence observed in the diffusive (Gaussian) case. An over-truncated regime
in which the characteristic truncation length scale is shorter than the length
scale of the decay of the initial condition, , is also identified. In
this extreme regime, fronts exhibit exponential tails, ,
and move at the constant velocity, .Comment: Accepted for publication in Phys. Rev. E (Feb. 2009
Non-diffusive transport in plasma turbulence: a fractional diffusion approach
Numerical evidence of non-diffusive transport in three-dimensional, resistive
pressure-gradient-driven plasma turbulence is presented. It is shown that the
probability density function (pdf) of test particles' radial displacements is
strongly non-Gaussian and exhibits algebraic decaying tails. To model these
results we propose a macroscopic transport model for the pdf based on the use
of fractional derivatives in space and time, that incorporate in a unified way
space-time non-locality (non-Fickian transport), non-Gaussianity, and
non-diffusive scaling. The fractional diffusion model reproduces the shape, and
space-time scaling of the non-Gaussian pdf of turbulent transport calculations.
The model also reproduces the observed super-diffusive scaling
Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow
Finite Larmor radius (FLR) effects on non-diffusive transport in a
prototypical zonal flow with drift waves are studied in the context of a
simplified chaotic transport model. The model consists of a superposition of
drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow
perpendicular to the density gradient. High frequency FLR effects are
incorporated by gyroaveraging the ExB velocity. Transport in the direction of
the density gradient is negligible and we therefore focus on transport parallel
to the zonal flows. A prescribed asymmetry produces strongly asymmetric non-
Gaussian PDFs of particle displacements, with L\'evy flights in one direction
but not the other. For zero Larmor radius, a transition is observed in the
scaling of the second moment of particle displacements. However, FLR effects
seem to eliminate this transition. The PDFs of trapping and flight events show
clear evidence of algebraic scaling with decay exponents depending on the value
of the Larmor radii. The shape and spatio-temporal self-similar anomalous
scaling of the PDFs of particle displacements are reproduced accurately with a
neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma
Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics
We explore the existence of time reparametrization symmetry in p-spin models.
Using the Martin-Siggia-Rose generating functional, we analytically probe the
long-time dynamics. We perform a renormalization group analysis where we
systematically integrate over short timescale fluctuations. We find three
families of stable fixed points and study the symmetry of those fixed points
with respect to time reparametrizations. One of those families is composed
entirely of symmetric fixed points, which are associated with the low
temperature dynamics. The other two families are composed entirely of
non-symmetric fixed points. One of these two non-symmetric families corresponds
to the high temperature dynamics.
Time reparametrization symmetry is a continuous symmetry that is
spontaneously broken in the glass state and we argue that this gives rise to
the presence of Goldstone modes. We expect the Goldstone modes to determine the
properties of fluctuations in the glass state, in particular predicting the
presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature
(non-symmetric) and low temperature (symmetric) renormalization group fixed
points. Now 16 pages with 1 figure. v1: 13 page
Effect of Roughness in the Development of an Adverse Pressure Gradient Turbulent Boundary Layer
An experimental study was conducted to examine the effect of surface roughness on the development of an adverse pressure gradient turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and x-wire probes in the APG region of an open return type wind tunnel test section. The same experimental conditions (i.e. T∞, Uref, and Cp) are maintained between the smooth, k+= 0, and rough, k+= 41-60, cases. Results indicate that the mean velocity deficit and Reynolds stress profiles tend to increase with surface roughness. These effects of roughness were successfully removed from the outer mean velocity profiles using the Zagarola and Smits scaling, U∞δ*/δ. Using the integrated boundary layer equation, the skin friction was computed and showed a 58% increase due to the surface roughness effect. The effects of pressure gradient were found to be significant, of which, different profile trends with similar magnitudes were found for outer Reynolds normal stresses scaled with U∞
Separatrix Reconnections in Chaotic Regimes
In this paper we extend the concept of separatrix reconnection into chaotic
regimes. We show that even under chaotic conditions one can still understand
abrupt jumps of diffusive-like processes in the relevant phase-space in terms
of relatively smooth realignments of stable and unstable manifolds of unstable
fixed points.Comment: 4 pages, 5 figures, submitted do Phys. Rev. E (1998
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