4,696 research outputs found
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
On a new fixed point of the renormalization group operator for area-preserving maps
The breakup of the shearless invariant torus with winding number
is studied numerically using Greene's residue criterion in
the standard nontwist map. The residue behavior and parameter scaling at the
breakup suggests the existence of a new fixed point of the renormalization
group operator (RGO) for area-preserving maps. The unstable eigenvalues of the
RGO at this fixed point and the critical scaling exponents of the torus at
breakup are computed.Comment: 4 pages, 5 figure
Chaotic dynamics and superdiffusion in a Hamiltonian system with many degrees of freedom
We discuss recent results obtained for the Hamiltonian Mean Field model. The
model describes a system of N fully-coupled particles in one dimension and
shows a second-order phase transition from a clustered phase to a homogeneous
one when the energy is increased. Strong chaos is found in correspondence to
the critical point on top of a weak chaotic regime which characterizes the
motion at low energies. For a small region around the critical point, we find
anomalous (enhanced) diffusion and L\'evy walks in a transient temporal regime
before the system relaxes to equilibrium.Comment: 7 pages, Latex, 6 figures included, Contributed paper to the Int.
Conf. on "Statistical Mechanics and Strongly Correlated System", 2nd Giovanni
Paladin Memorial, Rome 27-29 September 1999, submitted to Physica
Diffusive transport and self-consistent dynamics in coupled maps
The study of diffusion in Hamiltonian systems has been a problem of interest
for a number of years.
In this paper we explore the influence of self-consistency on the diffusion
properties of systems described by coupled symplectic maps. Self-consistency,
i.e. the back-influence of the transported quantity on the velocity field of
the driving flow, despite of its critical importance, is usually overlooked in
the description of realistic systems, for example in plasma physics. We propose
a class of self-consistent models consisting of an ensemble of maps globally
coupled through a mean field. Depending on the kind of coupling, two different
general types of self-consistent maps are considered: maps coupled to the field
only through the phase, and fully coupled maps, i.e. through the phase and the
amplitude of the external field. The analogies and differences of the diffusion
properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure
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