5,019 research outputs found
Studies for Type-I, type-II and Type-III Intermittencies.
There are several topics in fluid mechanics where the intermittency phenomenon appears, such as in Lorenz systems, Rayleigh-Bénard convection, DNLS equation and turbulence. The correct evaluation of the intermittency phenomenon contributes to a better prediction and a proper description of these topics. We summarized here a new method we have recently proposed to evaluate the reinjection probability function for type-II and type-III intermittencies. The new reinjection probability density (RPD) has been observed in the broad class of maps, as we have checked by both numerical simulations and analytical studies. For type-II and type-III intermittencies, we presented a new one-parameter family of functions describing the reinjection probability, being the usual type-II uniform reinjection probability a particular case of our RPD. For the type-III case, a new two-parameter family of RPD has been found from which one can derive the lower bound of reinjection (LBR). By extending the preceding analysis of type-II and type-III intermittencies, we give here a new RPD for the type-I case, from which we also derive the densities of the laminar phase lengths and the new characteristic relations
Intermittency reinjection probability density function with and without noise effects.
Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations
Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map : Mechanisms and their characterizations
A simple quasiperiodically forced one-dimensional cubic map is shown to
exhibit very many types of routes to chaos via strange nonchaotic attractors
(SNAs) with reference to a two-parameter space. The routes include
transitions to chaos via SNAs from both one frequency torus and period doubled
torus. In the former case, we identify the fractalization and type I
intermittency routes. In the latter case, we point out that atleast four
distinct routes through which the truncation of torus doubling bifurcation and
the birth of SNAs take place in this model. In particular, the formation of
SNAs through Heagy-Hammel, fractalization and type--III intermittent mechanisms
are described. In addition, it has been found that in this system there are
some regions in the parameter space where a novel dynamics involving a sudden
expansion of the attractor which tames the growth of period-doubling
bifurcation takes place, giving birth to SNA. The SNAs created through
different mechanisms are characterized by the behaviour of the Lyapunov
exponents and their variance, by the estimation of phase sensitivity exponent
as well as through the distribution of finite-time Lyapunov exponents.Comment: 27 pages, RevTeX 4, 16 EPS figures. Phys. Rev. E (2001) to appea
Aspects of the stochastic Burgers equation and their connection with turbulence
We present results for the 1 dimensional stochastically forced Burgers
equation when the spatial range of the forcing varies. As the range of forcing
moves from small scales to large scales, the system goes from a chaotic,
structureless state to a structured state dominated by shocks. This transition
takes place through an intermediate region where the system exhibits rich
multifractal behavior. This is mainly the region of interest to us. We only
mention in passing the hydrodynamic limit of forcing confined to large scales,
where much work has taken place since that of Polyakov.
In order to make the general framework clear, we give an introduction to
aspects of isotropic, homogeneous turbulence, a description of Kolmogorov
scaling, and, with the help of a simple model, an introduction to the language
of multifractality which is used to discuss intermittency corrections to
scaling.
We continue with a general discussion of the Burgers equation and forcing,
and some aspects of three dimensional turbulence where - because of the
mathematical analogy between equations derived from the Navier-Stokes and
Burgers equations - one can gain insight from the study of the simpler
stochastic Burgers equation. These aspects concern the connection of
dissipation rate intermittency exponents with those characterizing the
structure functions of the velocity field, and the dynamical behavior,
characterized by different time constants, of velocity structure functions. We
also show how the exponents characterizing the multifractal behavior of
velocity structure functions in the above mentioned transition region can
effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure
Current reversal with type-I intermittency in deterministic inertia ratchets
The intermittency is investigated when the current reversal occurs in a
deterministic inertia ratchet system. To determine which type the intermittency
belongs to, we obtain the return map of velocities of particle using
stroboscopic recording, and numerically calculate the distribution of average
laminar length . The distribution follows the scaling law of , the characteristic relation of type-I
intermittency.Comment: 4 pages, 7 figure
Spatiotemporal intermittency and scaling laws in the coupled sine circle map lattice
We study spatio-temporal intermittency (STI) in a system of coupled sine
circle maps. The phase diagram of the system shows parameter regimes with STI
of both the directed percolation (DP) and non-DP class. STI with synchronized
laminar behaviour belongs to the DP class. The regimes of non-DP behaviour show
spatial intermittency (SI), where the temporal behaviour of both the laminar
and burst regions is regular, and the distribution of laminar lengths scales as
a power law. The regular temporal behaviour for the bursts seen in these
regimes of spatial intermittency can be periodic or quasi-periodic, but the
laminar length distributions scale with the same power-law, which is distinct
from the DP case. STI with traveling wave (TW) laminar states also appears in
the phase diagram. Soliton-like structures appear in this regime. These are
responsible for cross-overs with accompanying non-universal exponents. The
soliton lifetime distributions show power law scaling in regimes of long
average soliton life-times, but peak at characteristic scales with a power-law
tail in regimes of short average soliton life-times. The signatures of each
type of intermittent behaviour can be found in the dynamical characterisers of
the system viz. the eigenvalues of the stability matrix. We discuss the
implications of our results for behaviour seen in other systems which exhibit
spatio-temporal intermittency.Comment: 25 pages, 11 figures. Submitted to Phys. Rev.
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