4 research outputs found
Energy Localization in the Peyrard-Bishop DNA model
We study energy localization on the oscillator-chain proposed by Peyrard and
Bishop to model the DNA. We search numerically for conditions with initial
energy in a small subgroup of consecutive oscillators of a finite chain and
such that the oscillation amplitude is small outside this subgroup for a long
timescale. We use a localization criterion based on the information entropy and
we verify numerically that such localized excitations exist when the nonlinear
dynamics of the subgroup oscillates with a frequency inside the reactive band
of the linear chain. We predict a mimium value for the Morse parameter (the only parameter of our normalized model), in agreement with the
numerical calculations (an estimate for the biological value is ).
For supercritical masses, we use canonical perturbation theory to expand the
frequencies of the subgroup and we calculate an energy threshold in agreement
with the numerical calculations
A New Method for Computing Topological Pressure
The topological pressure introduced by Ruelle and similar quantities describe
dynamical multifractal properties of dynamical systems. These are important
characteristics of mesoscopic systems in the classical regime. Original
definition of these quantities are based on the symbolic description of the
dynamics. It is hard or impossible to find symbolic description and generating
partition to a general dynamical system, therefore these quantities are often
not accessible for further studies. Here we present a new method by which the
symbolic description can be omitted. We apply the method for a mixing and an
intermittent system.Comment: 8 pages LaTeX with revtex.sty, the 4 postscript figures are included
using psfig.tex to appear in PR