2,759 research outputs found
The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
We define the topological entropy per unit volume in parabolic PDE's such as
the complex Ginzburg-Landau equation, and show that it exists, and is bounded
by the upper Hausdorff dimension times the maximal expansion rate. We then give
a constructive implementation of a bound on the inertial range of such
equations. Using this bound, we are able to propose a finite sampling algorithm
which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur
Four-states phase diagram of proteins
A four states phase diagram for protein folding as a function of temperature
and solvent quality is derived from an improved 2-d lattice model taking into
account the temperature dependence of the hydrophobic effect. The phase diagram
exhibits native, globule and two coil-type regions. In agreement with
experiment, the model reproduces the phase transitions indicative of both warm
and cold denaturations. Finally, it predicts transitions between the two coil
states and a critical point.Comment: 7 pages, 5 figures. Accepted for publication in Europhysics Letter
Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems
In this paper, we prove an inequality, which we call "Devroye inequality",
for a large class of non-uniformly hyperbolic dynamical systems (M,f). This
class, introduced by L.-S. Young, includes families of piece-wise hyperbolic
maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas),
unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound
for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K
is any separately Holder continuous function of n variables. In particular, we
can deal with observables which are not Birkhoff averages. We will show in
\cite{CCS} some applications of Devroye inequality to statistical properties of
this class of dynamical systems.Comment: Corrected version; To appear in Nonlinearit
A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion
We study numerically the magnetic susceptibility of the hierarchical model
with Ising spins () above the critical temperature and for two
values of the epsilon parameter. The integrations are performed exactly, using
recursive methods which exploit the symmetries of the model. Lattices with up
to sites have been used. Surprisingly, the numerical data can be fitted
very well with a simple power law of the form for the {\it whole} temperature range. The numerical values for
agree within a few percent with the values calculated with a high-temperature
expansion but show significant discrepancies with the epsilon-expansion. We
would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request),
uses phyzzx.te
Warm and Cold Denaturation in the Phase Diagram of a Protein Lattice Model
Studying the properties of the solvent around proteins, we propose a much
more sophisticated model of solvation than temperature-independent pairwise
interactions between monomers, as is used commonly in lattice representations.
We applied our model of solvation to a 16-monomer chain constrained on a
two-dimensional lattice. We compute a phase diagram function of the temperature
and a solvent parameter which is related to the pH of the solution. It exhibits
a native state in which the chain coalesces into a unique compact conformation
as well as a denatured state. Under certain solvation conditions, both warm and
cold denaturations occur between the native and the denatured states. A good
agreement is found with the data obtained from calorimetric experiments,
thereby validating the proposed model.Comment: 7 pages, 2 figure
Thermodynamic Limit Of The Ginzburg-Landau Equations
We investigate the existence of a global semiflow for the complex
Ginzburg-Landau equation on the space of bounded functions in unbounded domain.
This semiflow is proven to exist in dimension 1 and 2 for any parameter values
of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some
restrictions on the parameters but cover nevertheless some part of the
Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]
New Abundances for Old Stars - Atomic Diffusion at Work in NGC 6397
A homogeneous spectroscopic analysis of unevolved and evolved stars in the
metal-poor globular cluster NGC 6397 with FLAMES-UVES reveals systematic trends
of stellar surface abundances that are likely caused by atomic diffusion. This
finding helps to understand, among other issues, why the lithium abundances of
old halo stars are significantly lower than the abundance found to be produced
shortly after the Big Bang.Comment: 8 pages, 7 colour figures, 1 table; can also be downloaded via
http://www.eso.org/messenger
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