140 research outputs found
Fractional Fourier detection of L\'evy Flights: application to Hamiltonian chaotic trajectories
A signal processing method designed for the detection of linear (coherent)
behaviors among random fluctuations is presented. It is dedicated to the study
of data recorded from nonlinear physical systems. More precisely the method is
suited for signals having chaotic variations and sporadically appearing regular
linear patterns, possibly impaired by noise. We use time-frequency techniques
and the Fractional Fourier transform in order to make it robust and easily
implementable. The method is illustrated with an example of application: the
analysis of chaotic trajectories of advected passive particles. The signal has
a chaotic behavior and encounter L\'evy flights (straight lines). The method is
able to detect and quantify these ballistic transport regions, even in noisy
situations
Reducing or enhancing chaos using periodic orbits
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of
freedom is discussed. This method is based on finding a suitable perturbation
of the system such that the stability of a set of periodic orbits changes
(local bifurcations). Depending on the values of the residues, reflecting their
linear stability properties, a set of invariant tori is destroyed or created in
the neighborhood of the chosen periodic orbits. An application on a
paradigmatic system, a forced pendulum, illustrates the method
Microscopic Deterministic Dynamics and Persistence Exponent
Numerically we solve the microscopic deterministic equations of motion with
random initial states for the two-dimensional theory. Scaling behavior
of the persistence probability at criticality is systematically investigated
and the persistence exponent is estimated.Comment: to appear in Mod. Phys. Lett.
Finite-size effects on the Hamiltonian dynamics of the XY-model
The dynamical properties of the finite-size magnetization M in the critical
region T<T_{KTB} of the planar rotor model on a L x L square lattice are
analyzed by means of microcanonical simulations . The behavior of the q=0
structure factor at high frequencies is consistent with field-theoretical
results, but new additional features occur at lower frequencies. The motion of
M determines a region of spectral lines and the presence of a central peak,
which we attribute to phase diffusion. Near T_{KTB} the diffusion constant
scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter
Passive Tracer Dynamics in 4 Point-Vortex Flow
The advection of passive tracers in a system of 4 identical point vortices is
studied when the motion of the vortices is chaotic. The phenomenon of
vortex-pairing has been observed and statistics of the pairing time is
computed. The distribution exhibits a power-law tail with exponent
implying finite average pairing time. This exponents is in agreement with its
computed analytical estimate of 3.5. Tracer motion is studied for a chosen
initial condition of the vortex system. Accessible phase space is investigated.
The size of the cores around the vortices is well approximated by the minimum
inter-vortex distance and stickiness to these cores is observed. We investigate
the origin of stickiness which we link to the phenomenon of vortex pairing and
jumps of tracers between cores. Motion within the core is considered and
fluctuations are shown to scale with tracer-vortex distance as . No
outward or inward diffusion of tracers are observed. This investigation allows
the separation of the accessible phase space in four distinct regions, each
with its own specific properties: the region within the cores, the reunion of
the periphery of all cores, the region where vortex motion is restricted and
finally the far-field region. We speculate that the stickiness to the cores
induced by vortex-pairings influences the long-time behavior of tracers and
their anomalous diffusion.Comment: 18 pages, 15 figure
Phase Ordering Dynamics of Theory with Hamiltonian Equations of Motion
Phase ordering dynamics of the (2+1)- and (3+1)-dimensional theory
with Hamiltonian equations of motion is investigated numerically. Dynamic
scaling is confirmed. The dynamic exponent is different from that of the
Ising model with dynamics of model A, while the exponent is the same.Comment: to appear in Int. J. Mod. Phys.
Sticky islands in stochastic webs and anomalous chaotic cross-field particle transport by ExB electron drift instability
The ExB electron drift instability, present in many plasma devices, is an
important agent in cross-field particle transport. In presence of a resulting
low frequency electrostatic wave, the motion of a charged particle becomes
chaotic and generates a stochastic web in phase space. We define a scaling
exponent to characterise transport in phase space and we show that the
transport is anomalous, of super-diffusive type. Given the values of the model
parameters, the trajectories stick to different kinds of islands in phase
space, and their different sticking time power-law statistics generate
successive regimes of the super-diffusive transport.Comment: This manuscript contains 13 Pages and 21 figure
Stabilizing the intensity for a Hamiltonian model of the FEL
The intensity of an electromagnetic wave interacting self-consistently with a
beam of charged particles, as in a Free Electron Laser, displays large
oscillations due to an aggregate of particles, called the macro-particle. In
this article, we propose a strategy to stabilize the intensity by destabilizing
the macro-particle. This strategy involves the study of the linear stability of
a specific periodic orbit of a mean-field model. As a control parameter - the
amplitude of an external wave - is varied, a bifurcation occur in the system
which has drastic effects on the self-consistent dynamics, and in particular,
on the macro-particle. We show how to obtain an appropriate tuning of the
control parameter which is able to strongly decrease the oscillations of the
intensity without reducing its mean-value
Emergence of a non trivial fluctuating phase in the XY model on regular networks
We study an XY-rotor model on regular one dimensional lattices by varying the
number of neighbours. The parameter is defined.
corresponds to mean field and to nearest neighbours coupling. We
find that for the system does not exhibit a phase transition,
while for the mean field second order transition is recovered.
For the critical value , the systems can be in a non
trivial fluctuating phase for whichthe magnetisation shows important
fluctuations in a given temperature range, implying an infinite susceptibility.
For all values of the magnetisation is computed analytically in the
low temperatures range and the magnetised versus non-magnetised state which
depends on the value of is recovered, confirming the critical value
Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions
Recently, there has been some vigorous interest in the out-of-equilibrium
quasistationary states (QSSs), with lifetimes diverging with the number N of
degrees of freedom, emerging from numerical simulations of the ferromagnetic XY
Hamiltonian Mean Field (HMF) starting from some special initial conditions.
Phase transitions have been reported between low-energy magnetized QSSs and
large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization.
This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is
argued that the time-asymptotic states emerging in the Vlasov limit can be
related to simple generic time-asymptotic forms for the force field. The
proposed picture unveils the nature of the out-of-equilibrium phase transitions
reported for the ferromagnetic HMF: this is a bifurcation point connecting an
effective integrable Vlasov one-particle time-asymptotic dynamics to a partly
ergodic one which means a brutal open-up of the Vlasov one-particle phase
space. Illustration is given by investigating the time-asymptotic value of the
magnetization at the phase transition, under the assumption of a sufficiently
rapid time-asymptotic decay of the transient force field
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