3,815 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
Complexity for extended dynamical systems
We consider dynamical systems for which the spatial extension plays an
important role. For these systems, the notions of attractor, epsilon-entropy
and topological entropy per unit time and volume have been introduced
previously. In this paper we use the notion of Kolmogorov complexity to
introduce, for extended dynamical systems, a notion of complexity per unit time
and volume which plays the same role as the metric entropy for classical
dynamical systems. We introduce this notion as an almost sure limit on orbits
of the system. Moreover we prove a kind of variational principle for this
complexity.Comment: 29 page
Dynamics of kinks in the Ginzburg-Landau equation: Approach to a metastable shape and collapse of embedded pairs of kinks
We consider initial data for the real Ginzburg-Landau equation having two
widely separated zeros. We require these initial conditions to be locally close
to a stationary solution (the ``kink'' solution) except for a perturbation
supported in a small interval between the two kinks. We show that such a
perturbation vanishes on a time scale much shorter than the time scale for the
motion of the kinks. The consequences of this bound, in the context of earlier
studies of the dynamics of kinks in the Ginzburg-Landau equation, [ER], are as
follows: we consider initial conditions whose restriction to a bounded
interval have several zeros, not too regularly spaced, and other zeros of
are very far from . We show that all these zeros eventually disappear
by colliding with each other. This relaxation process is very slow: it takes a
time of order exponential of the length of
Hierarchical renormalization goup fixed points
Hierarchical renormalization group transformations are related to
non-associative algebras. Non-trivial infrared fixed points are shown to be
solutions of polynomial equations. At the example of a scalar model in
dimensions some methods for the solution of these algebraic equations
are presented.Comment: Contribution to Lat94, 27 Sep -- 1 Oct 1994, Bielefeld, 6 pages,
latex, no figure
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
Abundance Analysis of the Halo Giant HD122563 with Three-Dimensional Model Stellar Atmospheres
We present a preliminary local thermodynamic equilibrium (LTE) abundance
analysis of the template halo red giant HD122563 based on a realistic,
three-dimensional (3D), time-dependent, hydrodynamical model atmosphere of the
very metal-poor star. We compare the results of the 3D analysis with the
abundances derived by means of a standard LTE analysis based on a classical,
1D, hydrostatic model atmosphere of the star. Due to the different upper
photospheric temperature stratifications predicted by 1D and 3D models, we find
large, negative, 3D-1D LTE abundance differences for low-excitation OH and Fe I
lines. We also find trends with lower excitation potential in the derived Fe
LTE abundances from Fe I lines, in both the 1D and 3D analyses. Such trends may
be attributed to the neglected departures from LTE in the spectral line
formation calculations.Comment: 4 pages, 4 figures, contribution to proceedings for Joint Discussion
10 at the IAU General Assembly, Rio de Janeiro, Brazil, August 200
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]
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