343 research outputs found
Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
We perform a detailed study of the relaxation towards equilibrium in the
Hamiltonian Mean-Field (HMF) model, a prototype for long-range interactions in
-particle dynamics. In particular, we point out the role played by the
infinity of stationary states of the associated Vlasov dynamics. In this
context, we derive a new general criterion for the stability of any spatially
homogeneous distribution, and compare its analytical predictions with numerical
simulations of the Hamiltonian, finite , dynamics. We then propose and
verify numerically a scenario for the relaxation process, relying on the Vlasov
equation. When starting from a non stationary or a Vlasov unstable stationary
initial state, the system shows initially a rapid convergence towards a stable
stationary state of the Vlasov equation via non stationary states: we
characterize numerically this dynamical instability in the finite system by
introducing appropriate indicators. This first step of the evolution towards
Boltzmann-Gibbs equilibrium is followed by a slow quasi-stationary process,
that proceeds through different stable stationary states of the Vlasov
equation. If the finite system is initialized in a Vlasov stable homogenous
state, it remains trapped in a quasi-stationary state for times that increase
with the nontrivial power law . Single particle momentum distributions
in such a quasi-stationary regime do not have power-law tails, and hence cannot
be fitted by the -exponential distributions derived from Tsallis statistics.Comment: To appear in Physica
Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows
We present a theoretical description for the equilibrium states of a large
class of models of two-dimensional and geophysical flows, in arbitrary domains.
We account for the existence of ensemble inequivalence and negative specific
heat in those models, for the first time using explicit computations. We give
exact theoretical computation of a criteria to determine phase transition
location and type. Strikingly, this criteria does not depend on the model, but
only on the domain geometry. We report the first example of bicritical points
and second order azeotropy in the context of systems with long range
interactions.Comment: 4 pages, submitted to Phys. Rev. Let
Topological Solitons and Folded Proteins
We propose that protein loops can be interpreted as topological domain-wall
solitons. They interpolate between ground states that are the secondary
structures like alpha-helices and beta-strands. Entire proteins can then be
folded simply by assembling the solitons together, one after another. We
present a simple theoretical model that realizes our proposal and apply it to a
number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data
Bank codes). In all the examples that we have considered we are able to
construct solitons that reproduce secondary structural motifs such as
alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall
root-mean-square-distance accuracy of around 0.7 Angstrom or less for the
central alpha-carbons, i.e. within the limits of current experimental accuracy.Comment: 4 pages, 4 figure
Tensor products and statistics
AbstractA dictionary between operator-based and matrix-based languages in multivariate statistical analysis is proposed. Then this formulary is applied to asymptotic factorial analyses, especially for giving asymptotic covariance matrices and operators in an explicit form. Finally, we present the mathematical foundations on which are based the functional tools, i.e. tensor products of linear spaces, of vectors, and of operators
Lyapunov exponents as a dynamical indicator of a phase transition
We study analytically the behavior of the largest Lyapunov exponent
for a one-dimensional chain of coupled nonlinear oscillators, by
combining the transfer integral method and a Riemannian geometry approach. We
apply the results to a simple model, proposed for the DNA denaturation, which
emphasizes a first order-like or second order phase transition depending on the
ratio of two length scales: this is an excellent model to characterize
as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure
Algebraic Correlation Function and Anomalous Diffusion in the HMF model
In the quasi-stationary states of the Hamiltonian Mean-Field model, we
numerically compute correlation functions of momenta and diffusion of angles
with homogeneous initial conditions. This is an example, in a N-body
Hamiltonian system, of anomalous transport properties characterized by non
exponential relaxations and long-range temporal correlations. Kinetic theory
predicts a striking transition between weak anomalous diffusion and strong
anomalous diffusion. The numerical results are in excellent agreement with the
quantitative predictions of the anomalous transport exponents. Noteworthy, also
at statistical equilibrium, the system exhibits long-range temporal
correlations: the correlation function is inversely proportional to time with a
logarithmic correction instead of the usually expected exponential decay,
leading to weak anomalous transport properties
1-d gravity in infinite point distributions
The dynamics of infinite, asymptotically uniform, distributions of
self-gravitating particles in one spatial dimension provides a simple toy model
for the analogous three dimensional problem. We focus here on a limitation of
such models as treated so far in the literature: the force, as it has been
specified, is well defined in infinite point distributions only if there is a
centre of symmetry (i.e. the definition requires explicitly the breaking of
statistical translational invariance). The problem arises because naive
background subtraction (due to expansion, or by "Jeans' swindle" for the static
case), applied as in three dimensions, leaves an unregulated contribution to
the force due to surface mass fluctuations. Following a discussion by
Kiessling, we show that the problem may be resolved by defining the force in
infinite point distributions as the limit of an exponentially screened pair
interaction. We show that this prescription gives a well defined (finite) force
acting on particles in a class of perturbed infinite lattices, which are the
point processes relevant to cosmological N-body simulations. For identical
particles the dynamics of the simplest toy model is equivalent to that of an
infinite set of points with inverted harmonic oscillator potentials which
bounce elastically when they collide. We discuss previous results in the
literature, and present new results for the specific case of this simplest
(static) model starting from "shuffled lattice" initial conditions. These show
qualitative properties (notably its "self-similarity") of the evolution very
similar to those in the analogous simulations in three dimensions, which in
turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added
discussion in section IV), matches final version to appear in PR
Two-Color Coherent Photodissociation of Nitrogen Oxide in Intense Laser Fields
A simple one-dimensional semi-classical model with a Morse potential is used
to investigate the possibility of two-color infrared multi-photon dissociation
of vibrationally excited nitrogen oxide. The amplitude ratio effects and
adiabatic effects are investigated. Some initial states are found to have
thresholds smaller than expected from single-mode considerations and multiple
thresholds exist for initial states up to 32.
PACS: 42.50.HzComment: 3 pages, old papers, add source files to replace original postscrip
Breather trapping and breather transmission in a DNA model with an interface
We study the dynamics of moving discrete breathers in an interfaced piecewise
DNA molecule.
This is a DNA chain in which all the base pairs are identical and there
exists an interface such that the base pairs dipole moments at each side are
oriented in opposite directions.
The Hamiltonian of the Peyrard--Bishop model is augmented with a term that
includes the dipole--dipole coupling between base pairs. Numerical simulations
show the existence of two dynamical regimes. If the translational kinetic
energy of a moving breather launched towards the interface is below a critical
value, it is trapped in a region around the interface collecting vibrational
energy. For an energy larger than the critical value, the breather is
transmitted and continues travelling along the double strand with lower
velocity. Reflection phenomena never occur.
The same study has been carried out when a single dipole is oriented in
opposite direction to the other ones.
When moving breathers collide with the single inverted dipole, the same
effects appear. These results emphasize the importance of this simple type of
local inhomogeneity as it creates a mechanism for the trapping of energy.
Finally, the simulations show that, under favorable conditions, several
launched moving breathers can be trapped successively at the interface region
producing an accumulation of vibrational energy. Moreover, an additional
colliding moving breather can produce a saturation of energy and a moving
breather with all the accumulated energy is transmitted to the chain.Comment: 15 pages, 11 figure
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