923 research outputs found
New Universality of Lyapunov Spectra in Hamiltonian Systems
A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian
systems. The universality appears in middle energy regime and is different from
another universality which can be reproduced by random matrices in the
following two points. One is that the new universality appears in a limited
range of large i/N rather than the whole range, where N is degrees of freedom.
The other is Lyapunov spectra do not behave linearly while random matrices give
linear behavior even on 3D lattice. Quadratic terms with smaller nonlinear
terms of potential functions play an intrinsic role in the new universality.Comment: 19 pages, 16 Encapsulated Postscript figures, LaTeX (100 kb
Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems
Time dependent mode structure for the Lyapunov vectors associated with the
stepwise structure of the Lyapunov spectra and its relation to the momentum
auto-correlation function are discussed in quasi-one-dimensional many-hard-disk
systems. We demonstrate mode structures (Lyapunov modes) for all components of
the Lyapunov vectors, which include the longitudinal and transverse components
of their spatial and momentum parts, and their phase relations are specified.
These mode structures are suggested from the form of the Lyapunov vectors
corresponding to the zero-Lyapunov exponents. Spatial node structures of these
modes are explained by the reflection properties of the hard-walls used in the
models. Our main interest is the time-oscillating behavior of Lyapunov modes.
It is shown that the largest time-oscillating period of the Lyapunov modes is
twice as long as the time-oscillating period of the longitudinal momentum
auto-correlation function. This relation is satisfied irrespective of the
particle number and boundary conditions. A simple explanation for this relation
is given based on the form of the Lyapunov vector.Comment: 39 pages, 21 figures, Manuscript including the figures of better
quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm
Dimension dependent energy thresholds for discrete breathers
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. We study the existence of energy thresholds for discrete breathers,
i.e., the question whether, in a certain system, discrete breathers of
arbitrarily low energy exist, or a threshold has to be overcome in order to
excite a discrete breather. Breather energies are found to have a positive
lower bound if the lattice dimension d is greater than or equal to a certain
critical value d_c, whereas no energy threshold is observed for d<d_c. The
critical dimension d_c is system dependent and can be computed explicitly,
taking on values between zero and infinity. Three classes of Hamiltonian
systems are distinguished, being characterized by different mechanisms
effecting the existence (or non-existence) of an energy threshold.Comment: 20 pages, 5 figure
Statistical-mechanical formulation of Lyapunov exponents
We show how the Lyapunov exponents of a dynamic system can in general be
expressed in terms of the free energy of a (non-Hermitian) quantum many-body
problem. This puts their study as a problem of statistical mechanics, whose
intuitive concepts and techniques of approximation can hence be borrowed.Comment: 10 pages, 3 figures, RevTex
Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach
We investigate the laws that rule the behavior of the largest Lyapunov
exponent (LLE) in many particle systems with long range interactions. We
consider as a representative system the so-called Hamiltonian alpha-XY model
where the adjustable parameter alpha controls the range of the interactions of
N ferromagnetic spins in a lattice of dimension d. In previous work the
dependence of the LLE with the system size N, for sufficiently high energies,
was established through numerical simulations. In the thermodynamic limit, the
LLE becomes constant for alpha greater than d whereas it decays as an inverse
power law of N for alpha smaller than d. A recent theoretical calculation based
on Pettini's geometrization of the dynamics is consistent with these numerical
results (M.-C. Firpo and S. Ruffo, cond-mat/0108158). Here we show that the
scaling behavior can also be explained by a random matrix approach, in which
the tangent mappings that define the Lyapunov exponents are modeled by random
simplectic matrices drawn from a suitable ensemble.Comment: 5 pages, no figure
Large Deviation Approach to the Randomly Forced Navier-Stokes Equation
The random forced Navier-Stokes equation can be obtained as a variational
problem of a proper action. By virtue of incompressibility, the integration
over transverse components of the fields allows to cast the action in the form
of a large deviation functional. Since the hydrodynamic operator is nonlinear,
the functional integral yielding the statistics of fluctuations can be
practically computed by linearizing around a physical solution of the
hydrodynamic equation. We show that this procedure yields the dimensional
scaling predicted by K41 theory at the lowest perturbative order, where the
perturbation parameter is the inverse Reynolds number. Moreover, an explicit
expression of the prefactor of the scaling law is obtained.Comment: 24 page
Evaluation of the Quality of Commercial Fish Feeds in India with Respect to Microbiological Parameters
This paper describes the first comprehensive study of the quality of commercial fish feeds in India with regard to microbiological indices. Quality of feed is an important parameter that has a direct impact on the outcome of any aquaculture system. Microbiological parameters such as total plate count (TPC), Escherichia coli (CFUg-1), coliformes (CFUg-1), Enterobacteriaceae (CFUg-1) and yeast and mould (CFUg-1) counts were analysed using 3M™ Petrifilm™ as per guidelines. The TPC ranged from 2.0 × 102 to3.13 × 104 CFUg-1 in different feeds. Presence of E. coli was detected in one of the feeds with 1.15×102 CFUg-1. Coliform bacteria were not detected in any of the feeds. Enterobacteriaceae was present in three feeds in the range of 5.45 × 102 to 1.58×103 CFUg-1. Yeast and mould count ranged from <10 to 1.68 × 104 CFUg-1 in the feeds analyzed. The results obtained from the present study indicate that the feeds were contaminated with micro-organisms. As far as Indian scenario is concerned, there exist several feed companies which do not comply with the quality regulations and specifications as laid down by the Bureau of Indian Standards (BIS). In addition, specifications are not available for aqua feeds regarding the acceptable levels of microbiological parameters. Hence the present study calls for a standardized code of quality to be observed by feed manufacturing companies for quality products
From multiplicative noise to directed percolation in wetting transitions
A simple one-dimensional microscopic model of the depinning transition of an
interface from an attractive hard wall is introduced and investigated. Upon
varying a control parameter, the critical behaviour observed along the
transition line changes from a directed-percolation to a multiplicative-noise
type. Numerical simulations allow for a quantitative study of the multicritical
point separating the two regions, Mean-field arguments and the mapping on a yet
simpler model provide some further insight on the overall scenario.Comment: 4 pages, 3 figure
Topics in chaotic dynamics
Various kinematical quantities associated with the statistical properties of
dynamical systems are examined: statistics of the motion, dynamical bases and
Lyapunov exponents. Markov partitons for chaotic systems, without any attempt
at describing ``optimal results''. The Ruelle principle is illustrated via its
relation with the theory of gases. An example of an application predicts the
results of an experiment along the lines of Evans, Cohen, Morriss' work on
viscosity fluctuations. A sequence of mathematically oriented problems
discusses the details of the main abstract ergodic theorems guiding to a proof
of Oseledec's theorem for the Lyapunov exponents and products of random
matricesComment: Plain TeX; compile twice; 30 pages; 140K Keywords: chaos,
nonequilibrium ensembles, Markov partitions, Ruelle principle, Lyapunov
exponents, random matrices, gaussian thermostats, ergodic theory, billiards,
conductivity, gas.
Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom
We study the one-dimensional discrete model. We compare two
equilibrium properties by use of molecular dynamics simulations: the Lyapunov
spectrum and the time dependence of local correlation functions. Both
properties imply the existence of a dynamical crossover of the system at the
same temperature. This correlation holds for two rather different regimes of
the system - the displacive and intermediate coupling regimes. Our results
imply a deep connection between slowing down of relaxations and phase space
properties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev.
E, accepted for publicatio
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