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7,800 | New mathematical models for particle flow dynamics | nlin.CD | A new class of integro-partial differential equation models is derived for
the prediction of granular flow dynamics. These models are obtained using a
novel limiting averaging method (inspired by techniques employed in the
derivation of infinite-dimensional dynamical systems models) on the Newtonian
equations of motion... | physics |
7,801 | Viewing the efficiency of chaos control | nlin.CD | This paper aims to cast some new light on controlling chaos using the OGY-
and the Zero-Spectral-Radius methods. In deriving those methods we use a
generalized procedure differing from the usual ones. This procedure allows us
to conveniently treat maps to be controlled bringing the orbit to both various
saddles and to ... | physics |
7,802 | Local estimates for entropy densities in coupled map lattices | nlin.CD | We present a method to derive an upper bound for the entropy density of
coupled map lattices with local interactions from local observations. To do
this, we use an embedding technique being a combination of time delay and
spatial embedding. This embedding allows us to identify the local character of
the equations of mo... | physics |
7,803 | Lyapunov Instability for a hard-disk fluid in equilibrium and nonequilibrium thermostated by deterministic scattering | nlin.CD | We compute the full Lyapunov spectra for a hard-disk fluid under temperature
gradient and shear. The system is thermalized by deterministic and
time-reversible scattering at the boundary. This thermostating mechanism allows
for energy fluctuations around a mean value which is reflected by only two
vanishing Lyapunov ex... | physics |
7,804 | Frobenius-Perron Resonances for Maps with a Mixed Phase Space | nlin.CD | Resonances of the time evolution (Frobenius-Perron) operator P for phase
space densities have recently been shown to play a key role for the
interrelations of classical, semiclassical and quantum dynamics. Efficient
methods to determine resonances are thus in demand, in particular for
Hamiltonian systems displaying a m... | physics |
7,805 | The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles | nlin.CD | We analyze statistical properties of the city bus transport in Cuernavaca
(Mexico) and show that the bus arrivals display probability distributions
conforming those given by the Unitary Ensemble of random matrices. | physics |
7,806 | Superconvergence of period doubling cascade in trapezoid maps | nlin.CD | In the symmetric and the asymmetric trapezoid maps, as a slope of the
trapezoid is increased, the period doubling cascade occurs and the symbolic
sequence of periodic points is the Metropolis-Stein-Stein sequence and the
convergence of the onset point of the period 2^m solution to the accumulation
point is exponentiall... | physics |
7,807 | Periodic orbit action correlations in the Baker map | nlin.CD | Periodic orbit action correlations are studied for the piecewise linear,
area-preserving Baker map. Semiclassical periodic orbit formulae together with
universal spectral statistics in the corresponding quantum Baker map suggest
the existence of universal periodic orbit correlations. The calculation of
periodic orbit s... | physics |
7,808 | Spectral statistics for unitary transfer matrices of binary graphs | nlin.CD | Quantum graphs have recently been introduced as model systems to study the
spectral statistics of linear wave problems with chaotic classical limits. It
is proposed here to generalise this approach by considering arbitrary, directed
graphs with unitary transfer matrices. An exponentially increasing contribution
to the ... | physics |
7,809 | Mean- Field Approximation and a Small Parameter in Turbulence Theory | nlin.CD | Numerical and physical experiments on two-dimensional (2d) turbulence show
that the differences of transverse components of velocity field are well
described by a gaussian statistics and Kolmogorov scaling exponents. In this
case the dissipation fluctuations are irrelevant in the limit of small
viscosity. In general, o... | physics |
7,810 | Temporal correlation function in 3-D Turbulence | nlin.CD | We observe oscillatory decay in the two-point, non-equal time, velocity
correlation function of homogeneous, isotropic turbulence. We found this
through a direct numerical simulation (DNS) of the three dimensional
Navier-Stokes ($3-D$ NS) equation. We give an approximate analytic theory which
explains this oscillatory ... | physics |
7,811 | Statistics of pressure and of pressure-velocity correlations in isotropic turbulence | nlin.CD | Some pressure and pressure-velocity correlation in a direct numerical
simulations of a three-dimensional turbulent flow at moderate Reynolds numbers
have been analyzed. We have identified a set of pressure-velocity correlations
which posseses a good scaling behaviour. Such a class of pressure-velocity
correlations are ... | physics |
7,812 | Approximate renormalization for the break-up of invariant tori with three frequencies | nlin.CD | We construct an approximate renormalization transformation for Hamiltonian
systems with three degrees of freedom in order to study the break-up of
invariant tori with three incommensurate frequencies which belong to the cubic
field $Q(\tau)$, where $\tau^3+\tau^2-2\tau-1=0$. This renormalization has two
fixed points~: ... | physics |
7,813 | Levy Anomalous Diffusion and Fractional Fokker--Planck Equation | nlin.CD | We demonstrate that the Fokker-Planck equation can be generalized into a
'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional
space differentiations, in order to encompass the wide class of anomalous
diffusions due to a Levy stable stochastic forcing. A precise determination of
this equation ... | physics |
7,814 | Hamiltonian mappings and circle packing phase spaces | nlin.CD | We introduce three area preserving maps with phase space structures which
resemble circle packings. Each mapping is derived from a kicked Hamiltonian
system with one of three different phase space geometries (planar, hyperbolic
or spherical) and exhibits an infinite number of coexisting stable periodic
orbits which app... | physics |
7,815 | Quantum Graphs: A model for Quantum Chaos | nlin.CD | We study the statistical properties of the scattering matrix associated with
generic quantum graphs. The scattering matrix is the quantum analogue of the
classical evolution operator on the graph. For the energy-averaged spectral
form factor of the scattering matrix we have recently derived an exact
combinatorial expre... | physics |
7,816 | Measuring Information Transfer | nlin.CD | An information theoretic measure is derived that quantifies the statistical
coherence between systems evolving in time. The standard time delayed mutual
information fails to distinguish information that is actually exchanged from
shared information due to common history and input signals. In our new
approach, these inf... | physics |
7,817 | Detection of Nonlinear Coupling and its Application to Cardiorespiratory Interaction | nlin.CD | We present here a modification of the Lagrangian measures technique, which
allows a reliable detection of interdependency among simultaneous measurements
of different variables. This method is applied to a simulated multivariate time
series and to a bivariate cardiorespiratory signal. By using this methodology,
it is p... | physics |
7,818 | Applying Blind Chaos Control to Find Periodic Orbits | nlin.CD | Analysis of the PPF chaos control method used in biological experiments shows
that it can robustly control a wider class of systems than previously believed,
including those without stable manifolds. This can be exploited to find the
locations of unstable periodic orbits by varying the parameters of the control
system. | physics |
7,819 | Microscopic chaos and diffusion | nlin.CD | We investigate the connections between microscopic chaos, defined on a
dynamical level and arising from collisions between molecules, and diffusion,
characterized by a mean square displacement proportional to the time. We use a
number of models involving a single particle moving in two dimensions and
colliding with fix... | physics |
7,820 | Spiral Turbulence: From the Oxidation of CO on Pt(110) to Ventricular Fibrillation | nlin.CD | We give a brief overview of systems that show spiral patterns and
spatiotemporally chaotic states. We concentrate on two physical systems: (1)
the oxidation of CO on Pt(110) and (2) ventricular fibrillation in hearts. The
equations that have been suggested as simple models for these two different
systems are closely re... | physics |
7,821 | Anomalous Scaling in Passive Scalar Advection and Lagrangian Shape Dynamics | nlin.CD | The problem of anomalous scaling in passive scalar advection, especially with
$\delta$-correlated velocity field (the Kraichnan model) has attracted a lot of
interest since the exponents can be computed analytically in certain limiting
cases. In this paper we focus, rather than on the evaluation of the exponents,
on el... | physics |
7,822 | Bubbling and bistability in two parameter discrete systems | nlin.CD | We present a graphical analysis of the mechanisms underlying the occurrences
of bubbling sequences and bistability regions in the bifurcation scenario of a
special class of one dimensional two parameter maps. The main result of the
analysis is that whether it is bubbling or bistability is decided by the sign
of the thi... | physics |
7,823 | Turbulence Driven by a Deterministic Chaotic Dynamics | nlin.CD | In the inertial range of fully developed turbulence, we model the vertex
network dynamics by an iterated unimodular map having the universal behavior.
Inertial range anomalous scaling for the pair correlation functions of the
velocity and the local energy dissipation is established as a consequence of
the chaotic behav... | physics |
7,824 | Breaking time reversal symmetry in chaotic driven Rydberg atoms | nlin.CD | We consider the dynamics of Rydberg states of the hydrogen atom driven by a
microwave field of elliptical polarization, with a possible additional static
electric field. We concentrate on the effect of a resonant weak field - whose
frequency is close to the Kepler frequency of the electron around the nucleus -
which es... | physics |
7,825 | Phase synchronization in coupled nonidentical excitable systems and array enhanced coherence resonance | nlin.CD | We study the dynamics of a lattice of coupled nonidentical Fitz Hugh-Nagumo
system subject to independent external noise. It is shown that these stochastic
oscillators can lead to global synchronization behavior {\sl without an
external signal}. With the increase of the noise intensity, the system exhibits
coherence re... | physics |
7,826 | Scale Dependent Intermittency and Conformal Invariance in Turbulence | nlin.CD | We present a conformal theory for intermittent scalar fields. As an example,
we consider the energy flux from large to small scales in the developed
turbulent flow. The conformal correlation functions are found in the inertial
range of scales. In the simplest case, the theory leads to the log-normal
model. Parameters o... | physics |
7,827 | Estimation of initial conditions from a scalar time series | nlin.CD | We introduce a method to estimate the initial conditions of a mutivariable
dynamical system from a scalar signal. The method is based on a modified
multidimensional Newton-Raphson method which includes the time evolution of the
system. The method can estimate initial conditions of periodic and chaotic
systems and the r... | physics |
7,828 | Dynamic Algorithm for Parameter Estimation and Its Applications | nlin.CD | We consider a dynamic method, based on synchronization and adaptive control,
to estimate unknown parameters of a nonlinear dynamical system from a given
scalar chaotic time series. We present an important extension of the method
when time series of a scalar function of the variables of the underlying
dynamical system i... | physics |
7,829 | Dimension of interaction dynamics | nlin.CD | A method allowing to distinguish interacting from non-interacting systems
based on available time series is proposed and investigated. Some facts
concerning generalized Renyi dimensions that form the basis of our method are
proved. We show that one can find the dimension of the part of the attractor of
the system conne... | physics |
7,830 | Simple Denoising Algorithm Using Wavelet Transform | nlin.CD | We have presented a new and alternative algorithm for noise reduction using
the methods of discrete wavelet transform and numerical differentiation of the
data. In our method the threshold for reducing noise comes out automatically.
The algorithm has been applied to three model flow systems - Lorenz,
Autocatalator, and... | physics |
7,831 | On the stability of long-range sound propagation through a structured ocean | nlin.CD | Several acoustic experiments show a surprising degree of stability in wave
fronts propagating over multi-megameter ranges through the ocean's sound
channel despite the presence of random-like, sound speed fluctuations. Previous
works have pointed out the existence of chaos in simplified ray models
incorporating structu... | physics |
7,832 | Properties of Stationary Nonequilibrium States in the Thermostatted Lorentz Gas I: the One Particle System | nlin.CD | We study numerically and analytically the properties of the stationary state
of a particle moving under the influence of an electric field $\bE$ in a two
dimensional periodic Lorentz gas with the energy kept constant by a Gaussian
thermostat. Numerically the current appears to be a continuous function of
$\bE$ whose de... | physics |
7,833 | Spurious Lyapunov Exponents Computed Using the Eckmann-Ruelle Procedure | nlin.CD | Lyapunov exponents can be difficult to determine from experimental data. In
particular, when using embedding theory to build chaotic attractors in a
reconstruction space, extra "spurious" Lyapunov exponents arise that are not
Lyapunov exponents of the original system. By studying the local linearization
matrices that a... | physics |
7,834 | Fractal Dimension of Higher-Dimensional Chaotic Repellors | nlin.CD | Using examples we test formulae previously conjectured to give the fractal
information dimension of chaotic repellors and their stable and unstable
manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents
and the characteristic escape time from the repellor. Our main example, a
three-dimensional ch... | physics |
7,835 | On a generalization of the logistic map | nlin.CD | A family of non-conjugate chaotic maps generalizing the well-known logistic
function is defined, and some of its basic properties studied. A simple formula
for the Lyapunov exponents of all the maps contained in this family is given
based on the construction of conjugacies. Moreover, it is shown that, despite
the dissi... | physics |
7,836 | Spectral statistics in chaotic systems with a point interaction | nlin.CD | We consider quantum systems with a chaotic classical limit that are perturbed
by a point-like scatterer. The spectral form factor K(tau) for these systems is
evaluated semiclassically in terms of periodic and diffractive orbits. It is
shown for order tau^2 and tau^3 that off-diagonal contributions to the form
factor wh... | physics |
7,837 | Influence of diffraction on the spectrum and wavefunctions of an open system | nlin.CD | In this paper, we demonstrate the existence and significance of diffractive
orbits in an open microwave billiard, both experimentally and theoretically.
Orbits that diffract off of a sharp edge of the system are found to have a
strong influence on the transmission spectrum of the system, especially in the
regime where ... | physics |
7,838 | The Scalings of Scalar Structure Functions in a Velocity Field with Coherent Vortical Structures | nlin.CD | In planar turbulence modelled as an isotropic and homogeneous collection of
2-D non-interacting compact vortices, the structure functions S_p(r) of a
statistically stationary passive scalar field have the following scaling
behaviour in the limit where the P\'eclet number Pe -> \infty S_p(r) ~
constant+\ln({\frac{r}{LPe... | physics |
7,839 | Generalized Flows, Intrinsic Stochasticity, and Turbulent Transport | nlin.CD | The study of passive scalar transport in a turbulent velocity field leads
naturally to the notion of generalized flows which are families of probability
distributions on the space of solutions to the associated ODEs, which no longer
satisfy the uniqueness theorem for ODEs. Two most natural regularizations of
this probl... | physics |
7,840 | Direct-interaction electrodynamics of a two-electron atom | nlin.CD | We study numerically the dynamical system of a two-electron atom with the
Darwin interaction as a model to investigate scale-dependent effects of the
relativistic action-at-a-distance electrodynamics. This dynamical system
consists of a small perturbation of the Coulomb dynamics for energies in the
atomic range. The ke... | physics |
7,841 | Singular continuous spectra in a pseudo-integrable billiard | nlin.CD | The pseudo-integrable barrier billiard invented by Hannay and McCraw [J.
Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier
placed on a symmetry axis -- is generalized. It is proven that the flow on
invariant surfaces of genus two exhibits a singular continuous spectral
component. | physics |
7,842 | Hyperbolic Magnetic Billiards on Surfaces of Constant Curvature | nlin.CD | We consider classical billiards on surfaces of constant curvature, where the
charged billiard ball is exposed to a homogeneous, stationary magnetic field
perpendicular to the surface.
We establish sufficient conditions for hyperbolicity of the billiard
dynamics, and give lower estimation for the Lyapunov exponent. Th... | physics |
7,843 | Hierarchy of Chaotic Maps with an Invariant Measure | nlin.CD | We give hierarchy of one-parameter family F(a,x) of maps of the interval
[0,1] with an invariant measure. Using the measure, we calculate
Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of
these maps analytically, where the results thus obtained have been approved
with numerical simulation. ... | physics |
7,844 | Fredholm methods for billiard eigenfunctions in the coherent state representation | nlin.CD | We obtain a semiclassical expression for the projector onto eigenfunctions by
means of the Fredholm theory. We express the projector in the coherent state
basis, thus obtaining the semiclassical Husimi representation of the stadium
eigenfunctions, which is written in terms of classical invariants: periodic
points, thei... | physics |
7,845 | Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis | nlin.CD | We study the behaviour of the Standard map critical function in a
neighbourhood of a fixed resonance, that is the scaling law at the fixed
resonance. We prove that for the fundamental resonance the scaling law is
linear. We show numerical evidence that for the other resonances $p/q$, $q \geq
2$, $p \neq 0$ and $p$ and ... | physics |
7,846 | The Markovian metamorphosis of a simple turbulent cascade model | nlin.CD | Markovian properties of a discrete random multiplicative cascade model of
log-normal type are discussed. After taking small-scale resummation and
breaking of the ultrametric hierarchy into account, qualitative agreement with
Kramers-Moyal coefficients, recently deduced from a fully developed turbulent
flow, is achieved... | physics |
7,847 | Using Topological Statistics to Detect Determinism in Time Series | nlin.CD | Statistical differentiability of the measure along the reconstructed
trajectory is a good candidate to quantify determinism in time series. The
procedure is based upon a formula that explicitly shows the sensitivity of the
measure to stochasticity. Numerical results for partially surrogated time
series and series deriv... | physics |
7,848 | Variational principles in the analysis of traffic flows. (Why it is worth to go against the flow.) | nlin.CD | By means of a novel variational approach and using dual maps techniques and
general ideas of dynamical system theory we derive exact results about several
models of transport flows, for which we also obtain a complete description of
their limit (in time) behavior in the space of configurations. Using these
results we s... | physics |
7,849 | Study of Regular and Irregular States in Generic Systems | nlin.CD | In this work we semiclassically analyzed the high lying eigenstates of a
mixed type Hamiltonian system. For the regular states we employ the
Einstein-Brillouin-Keller quantization, while for the chaotic states, following
the principle of uniform semiclassical condensation, we obtain a prediction for
their wavefunction ... | physics |
7,850 | Experimental study of generic billiards with microwave resonators | nlin.CD | In this work we study the eigenstates and the energy spectra of a generic
billiard system with the use of microwave resonators. This is possible due to
the exact correspondence between the Schroedinger equation and the electric
field equations of the lowest modes in thin microwave resonators. We obtain a
good agreement... | physics |
7,851 | Topics in quantum chaos of generic systems | nlin.CD | We review the main ideas and results in the stationary problems of quantum
chaos in generic (mixed) systems, whose classical dynamics has regular
(invariant tori) and chaotic regions coexisting in the phase space. First we
discuss the universality classes of spectral fluctuations (GOE/GUE for ergodic
systems, and Poiss... | physics |
7,852 | Forecasting confined spatiotemporal chaos with genetic algorithms | nlin.CD | A technique to forecast spatiotemporal time series is presented. it uses a
Proper Ortogonal or Karhunen-Lo\`{e}ve Decomposition to encode large
spatiotemporal data sets in a few time-series, and Genetic Algorithms to
efficiently extract dynamical rules from the data. The method works very well
for confined systems disp... | physics |
7,853 | Regular and Irregular States in Generic Systems | nlin.CD | In this work we present the results of a numerical and semiclassical analysis
of high lying states in a Hamiltonian system, whose classical mechanics is of a
generic, mixed type, where the energy surface is split into regions of regular
and chaotic motion. As predicted by the principle of uniform semiclassical
condensa... | physics |
7,854 | Test of the Quantum Chaoticity Criterion for Diamagnetic Kepler Problem | nlin.CD | The earlier suggested criterion of quantum chaoticity, borrowed from the
nuclear compound resonance theory, is used in the analysis of the quantum
diamagnetic Kepler problem (the spinless charged particle motion in the Coulomb
and homogenious magnetic fields). | physics |
7,855 | On the Green function of linear evolution equations for a region with a boundary | nlin.CD | We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems. | physics |
7,856 | Statistics of soliton-bearing systems with additive noise | nlin.CD | We present a consistent method to calculate the probability distribution of
soliton parameters in systems with additive noise. Even though a weak noise is
considered, we are interested in probabilities of large fluctuations (generally
non-Gaussian) which are beyond perturbation theory. Our method is a further
developme... | physics |
7,857 | A method to find unstable periodic orbits for the diamagnetic Kepler Problem | nlin.CD | A method to determine the admissibility of symbolic sequences and to find the
unstable periodic orbits corresponding to allowed symbolic sequences for the
diamagnetic Kepler problem is proposed by using the ordering of stable and
unstable manifolds. By investigating the unstable periodic orbits up to length
6, a one to... | physics |
7,858 | A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series | nlin.CD | We describe methods of estimating the entire Lyapunov spectrum of a spatially
extended system from multivariate time-series observations. Provided that the
coupling in the system is short range, the Jacobian has a banded structure and
can be estimated using spatially localised reconstructions in low embedding
dimension... | physics |
7,859 | Bounds for Turbulent Transport | nlin.CD | We present rigorous bounds for the average heat transport in Boussinesq
Rayleigh-Benard convection. | physics |
7,860 | Localization of Eigenfunctions in the Stadium Billiard | nlin.CD | We present a systematic survey of scarring and symmetry effects in the
stadium billiard. The localization of individual eigenfunctions in Husimi phase
space is studied first, and it is demonstrated that on average there is more
localization than can be accounted for on the basis of random-matrix theory,
even after remo... | physics |
7,861 | Boundary effects in extended dynamical systems | nlin.CD | In the framework of spatially extended dynamical systems, we present three
examples in which the presence of walls lead to dynamic behavior qualitatively
different from the one obtained in an infinite domain or under periodic
boundary conditions. For a nonlinear reaction-diffusion model we obtain
boundary-induced spati... | physics |
7,862 | An algebraic method of obtaining of symplectic coordinates in a rigid body dynamics | nlin.CD | An algebraic procedure of getting of canonical variables in a rigid body
dynamics is presented. The method is based on using a structure of an algebra
of Lie-Poisson brackets with which a Hamiltonian dynamics is set. In a
particular case of a problem of a top in a homogeneous gravitation field the
method leads to well-... | physics |
7,863 | Escape from noisy intermittent repellers | nlin.CD | Intermittent or marginally-stable repellers are commonly associated with a
power law decay in the survival fraction. We show here that the presence of
weak additive noise alters the spectrum of the Perron - Frobenius operator
significantly giving rise to exponential decays even in systems that are
otherwise regular. Im... | physics |
7,864 | Synchronization of Chaotic Maps by Symmetric Common Noise | nlin.CD | Synchronization of identical chaotic systems subjected to common noise has
been the subject of recent research. Studies on several chaotic systems have
shown that, the synchronization is actually induced by the non-zero mean of the
noise, and symmetric noise with zero-mean cannot lead to synchronization. Here
it is pre... | physics |
7,865 | Synchronization With Positive Conditional Lyapunov Exponents | nlin.CD | Synchronization of chaotic system may occur only when the largest conditional
Lyapunov exponent of the driven system is negative. The synchronization with
positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf
56}, 2272 (1997)) is a combined result of the contracting region of the system
and the f... | physics |
7,866 | Simple Driven Maps As Sensitive Devices | nlin.CD | Sensitive dependence of nonlinear systems on initial conditions or parameters
can be useful in applications. We propose in this paper that bubbling behavior
in simple driven symmetrical maps may be used as a working principle of
sensitive devices. The system is stable when there is no input and displays
bursting behavi... | physics |
7,867 | A Relationship Between Parametric Resonance and Chaos | nlin.CD | In this paper we study two types of exponential instability -- parametric
resonance and chaos. We show that a given equation may produce chaos or
parametric resonance, depending how the problem is defined. In so doing we
establish a relationship between the Floquet indices (associated with
parametric resonance) and Lya... | physics |
7,868 | Intermittency in forced two-dimensional turbulence | nlin.CD | We find strong evidence for intermittency in forced two dimensional (2D)
turbulence in a flowing soap film experiment. In the forward enstrophy cascade
the structure function scaling exponents are nearly indistinguishable from 3D
studies. Intermittency corrections are present in the inverse energy cascade as
well, but ... | physics |
7,869 | Composition of Chaotic Maps with an Invariant Measure | nlin.CD | We generate new hierarchy of many-parameter family of maps of the interval
[0,1] with an invariant measure, by composition of the chaotic maps of
reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or
equivalently Lyapunov characteristic exponent, of these maps analytically,
where the results thus ... | physics |
7,870 | Pressure spectrum and structure function in homogeneous turbulence | nlin.CD | The pressure spectrum and structure function in homogeneous steady turbulence
of an incompressible fluid is studied using direct numerical simulation. The
resolution of the simulation is up to $1024^3$ and the Taylor microscale
Reynolds number $\Rl$ is between 38 and 478. The energy spectrum is found to
have a small bu... | physics |
7,871 | Amplification of weak signals and stochastic resonance via on-off intermittency with symmetry breaking | nlin.CD | Nonlinear dynamical systems possessing reflection symmetry have an invariant
subspace in the phase space. The dynamics within the invariant subspace can be
random or chaotic. As a system parameter changes, the motion transverse to the
invariant subspace can lose stability, leading to on-off intermittency. Under
certain... | physics |
7,872 | Robustness of Supersensitivity to Small Signals in Nonlinear Dynamical Systems | nlin.CD | Nonlinear dynamical systems possessing an invariant subspace can display
interesting dynamical behavior, such as on-off intermittency and bubbling. This
letter shows that a class of such systems have amazing features of (1)
supersensitivity to small input signals and (2) robustness of the
supersensitivity in the presen... | physics |
7,873 | Extracting Messages Masked by Chaotic Signals of Time-delay Systems | nlin.CD | We show how to extract messages masked by a chaotic signal of a time-delay
system with very high dimension and many positive Lyapunov exponents. Using a
special embedding coordinate, the infinite dimensional phase space of the
time-delay system is projected to a special three-dimensional space, which
enables us to iden... | physics |
7,874 | Decoding Information by Following Parameter Modulation With Parameter Adaptive Control | nlin.CD | It has been proposed to realize secure communication using chaotic
synchronization via transmission of binary message encoded by parameter
modulation in the chaotic system. This paper considers the use of parameter
adaptive control techniques to extract the message, based on the assumptions
that we know the equation fo... | physics |
7,875 | Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents | nlin.CD | 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, wi... | physics |
7,876 | Scaling law for the critical function of an approximate renormalization | nlin.CD | We construct an approximate renormalization for Hamiltonian systems with two
degrees of freedom in order to study the break-up of invariant tori with
arbitrary frequency. We derive the equation of the critical surface of the
renormalization map, and we compute the scaling behavior of the critical
function of one-parame... | physics |
7,877 | Symmetry-breaking on-off intermittency under modulation: Robustness of supersensitivity, resonance and information gain | nlin.CD | Nonlinear dynamical systems possessing an invariant subspace in the phase
space and chaotic or stochastic motion within the subspace often display on-off
intermittency close to the threshold of stability of the subspace. In a class
of symmetric systems, the intermittency is symmetry-breaking [Ying-Cheng Lai,
Phys. Rev.... | physics |
7,878 | The power spectrum of geodesic divergences as an early detector of chaotic motion | nlin.CD | We propose a new method for determining the stochastic or ordered nature of
trajectories in non-integrable Hamiltonian dynamical systems. The method
consists of constructing a time-series from the divergence of nearby
trajectories and then performing a power spectrum analysis of the series.
Ordered trajectories present... | physics |
7,879 | Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map | nlin.CD | It is well-known that the dynamics of the Arnold circle map is phase-locked
in regions of the parameter space called Arnold tongues. If the map is
invertible, the only possible dynamics is either quasiperiodic motion, or
phase-locked behavior with a unique attracting periodic orbit. Under the
influence of quasiperiodic... | physics |
7,880 | Detection of fixed points in spatiotemporal signals by clustering method | nlin.CD | We present a method to determine fixed points in spatiotemporal signals. A
144-dimensioanl simulated signal, similar to a Kueppers-Lortz instability, is
analyzed and its fixed points are reconstructed. | physics |
7,881 | Chaos in a well : Effects of competing length scales | nlin.CD | A discontinuous generalization of the standard map, which arises naturally as
the dynamics of a periodically kicked particle in a one dimensional infinite
square well potential, is examined. Existence of competing length scales,
namely the width of the well and the wavelength of the external field,
introduce novel dyna... | physics |
7,882 | Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations | nlin.CD | A replicator equation with mutation processes is numerically studied.
Without any mutations, two characteristics of the replicator dynamics are
known: an exponential divergence of the dominance period, and hierarchical
orderings of the attractors. A mutation introduces some new aspects: the
emergence of structurally ... | physics |
7,883 | Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions | nlin.CD | A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on
a torus for general boundary conditions (BCs), whose number ($k$) is always
finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em
all} $k$ BCs is exactly equivalent to that of the renormalized QAM (with
Planck's consta... | physics |
7,884 | Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series | nlin.CD | A practical and popular technique to extract the symbolic dynamics from
experimentally measured chaotic time series is the threshold-crossing method,
by which an arbitrary partition is utilized for determining the symbols. We
address to what extent the symbolic dynamics so obtained can faithfully
represent the phase-sp... | physics |
7,885 | Essential nonlinearities in hearing | nlin.CD | Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation
to maximize tuning and amplification. We show that in this condition several
effects are expected to be generic: compression of the dynamic range,
infinitely shrap tuning at zero input, and generation of combination tones.
These effects are "... | physics |
7,886 | Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems | nlin.CD | Harmonic inversion has already been proven to be a powerful tool for the
analysis of quantum spectra and the periodic orbit orbit quantization of
chaotic systems. The harmonic inversion technique circumvents the convergence
problems of the periodic orbit sum and the uncertainty principle of the usual
Fourier analysis, ... | physics |
7,887 | Dynamics of Sawtooth Map: 1. New Numerical Results | nlin.CD | Some results of numerical study of the canonical map with a sawtooth force
are given and discovered new unexpected dynamical effects are described. In
particular, it is shown that if the values of the system parameter K belong to
the countable set determined by Ovsyannikov's theorem, separatrices of primary
resonances ... | physics |
7,888 | Aspects of the stochastic Burgers equation and their connection with turbulence | nlin.CD | 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 throug... | physics |
7,889 | Nonintegrability and Chaos in the Anisotropic Manev Problem | nlin.CD | The anisotropic Manev problem, which lies at the intersection of classical,
quantum, and relativity physics, describes the motion of two point masses in an
anisotropic space under the influence of a Newtonian force-law with a
relativistic correction term. Using an extension of the Poincare'-Melnikov
method, we first pr... | physics |
7,890 | From synchronization to multistability in two coupled quadratic maps | nlin.CD | The phenomenology of a system of two coupled quadratic maps is studied both
analytically and numerically. Conditions for synchronization are given and the
bifurcations of periodic orbits from this regime are identified. In addition,
we show that an arbitrarily large number of distinct stable periodic orbits may
be obta... | physics |
7,891 | Coherence resonance near blowout bifurcation in nonlinear dynamical systems | nlin.CD | Previous studies have shown that noise can induce coherence resonance in some
nonlinear dynamical systems close to a bifurcation of a periodic motion, such
as in excitable systems. We demonstrate that coherence resonance can be
observed in systems close to a {\sl blowout bifurcation}. It is shown that for
dynamical sys... | physics |
7,892 | Entropy Production in a Persistent Random Walk | nlin.CD | We consider a one-dimensional persisent random walk viewed as a deterministic
process with a form of time reversal symmetry. Particle reservoirs placed at
both ends of the system induce a density current which drives the system out of
equilibrium. The phase space distribution is singular in the stationary state
and has... | physics |
7,893 | About universality of lifetime statistics in quantum chaotic scattering | nlin.CD | The statistics of the resonance widths and the behavior of the survival
probability is studied in a particular model of quantum chaotic scattering (a
particle in a periodic potential subject to static and time-periodic forces)
introduced earlier in Ref.[5,6]. The coarse-grained distribution of the
resonance widths is s... | physics |
7,894 | Anomalous scaling of a passive scalar in the presence of strong anisotropy | nlin.CD | Field theoretic renormalization group and the operator product expansion are
applied to a model of a passive scalar field, advected by the Gaussian strongly
anisotropic velocity field. Inertial-range anomalous scaling behavior is
established, and explicit asymptotic expressions for the n-th order structure
functions of... | physics |
7,895 | Absence of supersensitivity to small input signals in generalized on--off systems | nlin.CD | It has recently been shown that nonlinear skew product dynamical systems with
invariant subspaces which are capable of displaying on-off intermittency can
show supersensitivity to small input signals.
Here we show that this supersensitivity is absent for more general dynamical
systems with non-skew product structure,... | physics |
7,896 | Nature of matrix elements in the quantum chaotic domain of interacting particle systems | nlin.CD | There is a newly emerging understanding that in the chaotic domain of
isolated finite interacting many particle systems smoothed densities define the
statistical description of these systems and these densities follow from
embedded (two-body) random matrix ensembles and their various deformations.
These ensembles predi... | physics |
7,897 | Exploring phase space localization of chaotic eigenstates via parametric variation | nlin.CD | In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation
measure was introduced that sensitively probes phase space localization
properties of eigenstates. It is based on a system's response to varying an
external parameter. The measure correlates level velocities with overlap
intensities between the ... | physics |
7,898 | Phase space localization of chaotic eigenstates: Violating ergodicity | nlin.CD | The correlation between level velocities and eigenfunction intensities
provides a new way of exploring phase space localization in quantized
non-integrable systems. It can also serve as a measure of deviations from
ergodicity due to quantum effects for typical observables. This paper relies on
two well known paradigms ... | physics |
7,899 | Breaking conjugate pairing in thermostatted billiards by magnetic field | nlin.CD | We demonstrate that in the thermostatted three-dimensional Lorentz gas the
symmetry of the Lyapunov spectrum can be broken by adding to the system an
external magnetic field not perpendicular to the electric field. For
perpendicular field vectors, there is a Hamiltonian reformulation of the
dynamics and the conjugate p... | physics |
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