737 research outputs found
Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''
In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained
a theoretical expression for the maximum Lyapunov exponent of a
dilute gas. They conclude that is proportional to the cube root of
the self-diffusion coefficient , independent of the range of the interaction
potential. They validate their conjecture with numerical data for a dense
one-component plasma, a system with long-range forces. We claim that their
result is highly non-generic. We show in the following that it does not apply
to a gas of hard spheres, neither in the dilute nor in the dense phase.Comment: 1 page, Revtex - 1 PS Figs - Submitted to Physical Review Letter
Aluminum-, Calcium- And Titanium-Rich Oxide Stardust In Ordinary Chondrite Meteorites
We report isotopic data for a total of 96 presolar oxide grains found in
residues of several unequilibrated ordinary chondrite meteorites. Identified
grain types include Al2O3, MgAl2O4, hibonite (CaAl12O19) and Ti oxide. This
work greatly increases the presolar hibonite database, and is the first report
of presolar Ti oxide. O-isotopic compositions of the grains span previously
observed ranges and indicate an origin in red giant and asymptotic giant branch
(AGB) stars of low mass (<2.5 MSun) for most grains. Cool bottom processing in
the parent AGB stars is required to explain isotopic compositions of many
grains. Potassium-41 enrichments in hibonite grains are attributable to in situ
decay of now-extinct 41Ca. Inferred initial 41Ca/40Ca ratios are in good
agreement with model predictions for low-mass AGB star envelopes, provided that
ionization suppresses 41Ca decay. Stable Mg and Ca isotopic ratios of most of
the hibonite grains reflect primarily the initial compositions of the parent
stars and are generally consistent with expectations for Galactic chemical
evolution, but require some local interstellar chemical inhomogeneity. Very
high 17O/16O or 25Mg/24Mg ratios suggest an origin for some grains in binary
star systems where mass transfer from an evolved companion has altered the
parent star compositions. A supernova origin for the hitherto enigmatic
18O-rich Group 4 grains is strongly supported by multi-element isotopic data
for two grains. The Group 4 data are consistent with an origin in a single
supernova in which variable amounts of material from the deep 16O-rich interior
mixed with a unique end-member mixture of the outer layers. The Ti oxide grains
primarily formed in low-mass AGB stars. They are smaller and rarer than
presolar Al2O3, reflecting the lower abundance of Ti than Al in AGB envelopes.Comment: Accepted for publication in ApJ; 47 pages, 13 figure
Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering
In recent work a deterministic and time-reversible boundary thermostat called
thermostating by deterministic scattering has been introduced for the periodic
Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the
nonlinear properties of this new dynamical system by numerically calculating
its Lyapunov exponents. Based on a revised method for computing Lyapunov
exponents, which employs periodic orthonormalization with a constraint, we
present results for the Lyapunov exponents and related quantities in
equilibrium and nonequilibrium. Finally, we check whether we obtain the same
relations between quantities characterizing the microscopic chaotic dynamics
and quantities characterizing macroscopic transport as obtained for
conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript
Simple deterministic dynamical systems with fractal diffusion coefficients
We analyze a simple model of deterministic diffusion. The model consists of a
one-dimensional periodic array of scatterers in which point particles move from
cell to cell as defined by a piecewise linear map. The microscopic chaotic
scattering process of the map can be changed by a control parameter. This
induces a parameter dependence for the macroscopic diffusion coefficient. We
calculate the diffusion coefficent and the largest eigenmodes of the system by
using Markov partitions and by solving the eigenvalue problems of respective
topological transition matrices. For different boundary conditions we find that
the largest eigenmodes of the map match to the ones of the simple
phenomenological diffusion equation. Our main result is that the difffusion
coefficient exhibits a fractal structure by varying the system parameter. To
understand the origin of this fractal structure, we give qualitative and
quantitative arguments. These arguments relate the sequence of oscillations in
the strength of the parameter-dependent diffusion coefficient to the
microscopic coupling of the single scatterers which changes by varying the
control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.
Lyapunov Exponents from Kinetic Theory for a Dilute, Field-driven Lorentz Gas
Positive and negative Lyapunov exponents for a dilute, random,
two-dimensional Lorentz gas in an applied field, , in a steady state
at constant energy are computed to order . The results are:
where
are the exponents for the field-free Lorentz gas,
, is the mean free time between collisions,
is the charge, the mass and is the speed of the particle. The
calculation is based on an extended Boltzmann equation in which a radius of
curvature, characterizing the separation of two nearby trajectories, is one of
the variables in the distribution function. The analytical results are in
excellent agreement with computer simulations. These simulations provide
additional evidence for logarithmic terms in the density expansion of the
diffusion coefficient.Comment: 7 pages, revtex, 3 postscript figure
Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality
We discuss the role played by the Lyapunov exponents in the dynamics of
Zhang's model of Self-Organized Criticality. We show that a large part of the
spectrum (slowest modes) is associated with the energy transpor in the lattice.
In particular, we give bounds on the first negative Lyapunov exponent in terms
of the energy flux dissipated at the boundaries per unit of time. We then
establish an explicit formula for the transport modes that appear as diffusion
modes in a landscape where the metric is given by the density of active sites.
We use a finite size scaling ansatz for the Lyapunov spectrum and relate the
scaling exponent to the scaling of quantities like avalanche size, duration,
density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear
Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
The foundations of the chaotic scattering theory for transport and
reaction-rate coefficients for classical many-body systems are considered here
in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is
employed to obtain an expression for the escape-rate for a phase space
trajectory to leave a finite open region of phase space for the first time.
This expression relates the escape rate to the difference between the sum of
the positive Lyapunov exponents and the K-S entropy for the fractal set of
trajectories which are trapped forever in the open region. This result is well
known for systems of a few degrees of freedom and is here extended to systems
of many degrees of freedom. The formalism is applied to smooth hyperbolic
systems, to cellular-automata lattice gases, and to hard sphere sytems. In the
latter case, the goemetric constructions of Sinai {\it et al} for billiard
systems are used to describe the relevant chaotic scattering phenomena. Some
applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file.
Figures are available on request from [email protected]
Can disorder induce a finite thermal conductivity in 1D lattices?
We study heat conduction in one dimensional mass disordered harmonic and
anharmonic lattices. It is found that the thermal conductivity of the
disordered anharmonic lattice is finite at low temperature, whereas it diverges
as at high temperature. Moreover, we demonstrate that a
unique nonequilibrium stationary state in the disordered harmonic lattice does
not exist at all.Comment: 4 pages with 4 eps figure
Curvature fluctuations and Lyapunov exponent at Melting
We calculate the maximal Lyapunov exponent in constant-energy molecular
dynamics simulations at the melting transition for finite clusters of 6 to 13
particles (model rare-gas and metallic systems) as well as for bulk rare-gas
solid. For clusters, the Lyapunov exponent generally varies linearly with the
total energy, but the slope changes sharply at the melting transition. In the
bulk system, melting corresponds to a jump in the Lyapunov exponent, and this
corresponds to a singularity in the variance of the curvature of the potential
energy surface. In these systems there are two mechanisms of chaos -- local
instability and parametric instability. We calculate the contribution of the
parametric instability towards the chaoticity of these systems using a recently
proposed formalism. The contribution of parametric instability is a continuous
function of energy in small clusters but not in the bulk where the melting
corresponds to a decrease in this quantity. This implies that the melting in
small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev
Wave transmission, phonon localization and heat conduction of 1D Frenkel-Kontorova chain
We study the transmission coefficient of a plane wave through a 1D finite
quasi-periodic system -- the Frenkel-Kontorova (FK) model -- embedding in an
infinite uniform harmonic chain. By varying the mass of atoms in the infinite
uniform chain, we obtain the transmission coefficients for {\it all}
eigenfrequencies. The phonon localization of the incommensurated FK chain is
also studied in terms of the transmission coefficients and the Thouless
exponents. Moreover, the heat conduction of Rubin-Greer-like model for FK chain
at low temperature is calculated. It is found that the stationary heat flux
, and depends on the strength of the external
potential.Comment: 15 pages in Revtex, 8 EPS figure
- …