939 research outputs found
The Steep Nekhoroshev's Theorem
Revising Nekhoroshev's geometry of resonances, we provide a fully
constructive and quantitative proof of Nekhoroshev's theorem for steep
Hamiltonian systems proving, in particular, that the exponential stability
exponent can be taken to be ) ('s
being Nekhoroshev's steepness indices and the number of degrees of
freedom)
The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.Comment: 12 pages, submitted to Journal of Statistical Physic
A rigorous implementation of the Jeans--Landau--Teller approximation
Rigorous bounds on the rate of energy exchanges between vibrational and
translational degrees of freedom are established in simple classical models of
diatomic molecules. The results are in agreement with an elementary
approximation introduced by Landau and Teller. The method is perturbative
theory ``beyond all orders'', with diagrammatic techniques (tree expansions) to
organize and manipulate terms, and look for compensations, like in recent
studies on KAM theorem homoclinic splitting.Comment: 23 pages, postscrip
The nonequilibrium Ehrenfest gas: a chaotic model with flat obstacles?
It is known that the non-equilibrium version of the Lorentz gas (a billiard
with dispersing obstacles, electric field and Gaussian thermostat) is
hyperbolic if the field is small. Differently the hyperbolicity of the
non-equilibrium Ehrenfest gas constitutes an open problem, since its obstacles
are rhombi and the techniques so far developed rely on the dispersing nature of
the obstacles. We have developed analytical and numerical investigations which
support the idea that this model of transport of matter has both chaotic
(positive Lyapunov exponent) and non-chaotic steady states with a quite
peculiar sensitive dependence on the field and on the geometry, not observed
before. The associated transport behaviour is correspondingly highly irregular,
with features whose understanding is of both theoretical and technological
interest
Effective stability of the Trojan asteroids
We study the spatial circular restricted problem of three bodies in the light
of Nekhoroshev theory of stability over large time intervals. We consider in
particular the Sun-Jupiter model and the Trojan asteroids in the neighborhood
of the Lagrangian point . We find a region of effective stability around
the point such that if the initial point of an orbit is inside this
region the orbit is confined in a slightly larger neighborhood of the
equilibrium (in phase space) for a very long time interval. By combining
analytical methods and numerical approximations we are able to prove that
stability over the age of the universe is guaranteed on a realistic region, big
enough to include one real asteroid. By comparing this result with the one
obtained for the planar problem we see that the regions of stability in the two
cases are of the same magnitude.Comment: 9 pages, 2 figures, Astronomy & Astrophysics in pres
Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice
We investigate the connection between local and global dynamics in the Fermi
-- Pasta -- Ulam (FPU) -- model from the point of view of stability of
its simplest periodic orbits (SPOs). In particular, we show that there is a
relatively high mode of the linear lattice, having one
particle fixed every two oppositely moving ones (called SPO2 here), which can
be exactly continued to the nonlinear case for and whose
first destabilization, , as the energy (or ) increases for {\it
any} fixed , practically {\it coincides} with the onset of a ``weak'' form
of chaos preceding the break down of FPU recurrences, as predicted recently in
a similar study of the continuation of a very low () mode of the
corresponding linear chain. This energy threshold per particle behaves like
. We also follow exactly the properties of
another SPO (with ) in which fixed and moving particles are
interchanged (called SPO1 here) and which destabilizes at higher energies than
SPO2, since . We find that, immediately after
their first destabilization, these SPOs have different (positive) Lyapunov
spectra in their vicinity. However, as the energy increases further (at fixed
), these spectra converge to {\it the same} exponentially decreasing
function, thus providing strong evidence that the chaotic regions around SPO1
and SPO2 have ``merged'' and large scale chaos has spread throughout the
lattice.Comment: Physical Review E, 18 pages, 6 figure
Study of Liapunov Exponents and the Reversibility of Molecular Dynamics Algorithms
We study the question of lack of reversibility and the chaotic nature of the
equations of motion in numerical simulations of lattice QCD.Comment: latex file with 3 pages, 1 figure. Talk presented at Lattice'96 by C.
Li
Time-reversal focusing of an expanding soliton gas in disordered replicas
We investigate the properties of time reversibility of a soliton gas,
originating from a dispersive regularization of a shock wave, as it propagates
in a strongly disordered environment. An original approach combining
information measures and spin glass theory shows that time reversal focusing
occurs for different replicas of the disorder in forward and backward
propagation, provided the disorder varies on a length scale much shorter than
the width of the soliton constituents. The analysis is performed by starting
from a new class of reflectionless potentials, which describe the most general
form of an expanding soliton gas of the defocusing nonlinear Schroedinger
equation.Comment: 7 Pages, 6 Figure
Using SAS functions and high resolution isotope data to unravel travel time distributions in headwater catchments
Acknowledgments. We are grateful to the European Research Council (ERC) VeWa project (GA335910) and NERC/JIP SIWA project (NE/MO19896/1) for funding. A.R. acknowledges the financial support from the ENAC school at EPFL. C.B. acknowledges support from the University of Costa Rica (project 217-B4-239 and the Isotope Network for Tropical Ecosystem Studies (ISONet)). Data to support this study are provided by the Northern Rivers Institute, University of Aberdeen and are available by the authors. The authors wish to thank Ype van der Velde, Arash Massoudieh, Jean-Raynald de Dreuzy and an anonymous referee for the useful review comments.Peer reviewedPublisher PD
Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems
Boundary effects in the stepwise structure of the Lyapunov spectra and the
corresponding wavelike structure of the Lyapunov vectors are discussed
numerically in quasi-one-dimensional systems consisting of many hard-disks.
Four kinds of boundary conditions constructed by combinations of periodic
boundary conditions and hard-wall boundary conditions are considered, and lead
to different stepwise structures of the Lyapunov spectra in each case. We show
that a spatial wavelike structure with a time-oscillation appears in the
spatial part of the Lyapunov vectors divided by momenta in some steps of the
Lyapunov spectra, while a rather stationary wavelike structure appears in the
purely spatial part of the Lyapunov vectors corresponding to the other steps.
Using these two kinds of wavelike structure we categorize the sequence and the
kinds of steps of the Lyapunov spectra in the four different boundary condition
cases.Comment: 33 pages, 25 figures including 10 color figures. Manuscript including
the figures of better quality is available from
http://newt.phys.unsw.edu.au/~gary/step.pd
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