39 research outputs found
Maximal Lyapunov exponent at Crises
We study the variation of Lyapunov exponents of simple dynamical systems near
attractor-widening and attractor-merging crises. The largest Lyapunov exponent
has universal behaviour, showing abrupt variation as a function of the control
parameter as the system passes through the crisis point, either in the value
itself, in the case of the attractor-widening crisis, or in the slope, for
attractor merging crises. The distribution of local Lyapunov exponents is very
different for the two cases: the fluctuations remain constant through a merging
crisis, but there is a dramatic increase in the fluctuations at a widening
crisis.Comment: 22kb plus 3 figures available on request; to appear in Phys. Rev.
Growth Algorithms for Lattice Heteropolymers at Low Temperatures
Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are
proposed and tested on simple models of lattice heteropolymers. Both are found
to outperform not only the previous version of PERM, but also all other
stochastic algorithms which have been employed on this problem, except for the
core directed chain growth method (CG) of Beutler & Dill. In nearly all test
cases they are faster in finding low-energy states, and in many cases they
found new lowest energy states missed in previous papers. The CG method is
superior to our method in some cases, but less efficient in others. On the
other hand, the CG method uses heavily heuristics based on presumptions about
the hydrophobic core and does not give thermodynamic properties, while the
present method is a fully blind general purpose algorithm giving correct
Boltzmann-Gibbs weights, and can be applied in principle to any stochastic
sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres
Dynamical signatures of ‘phase transitions’: chaos in finite clusters
Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article
Perfectly Translating Lattices on a Cylinder
We perform molecular dynamics simulations on an interacting electron gas
confined to a cylindrical surface and subject to a radial magnetic field and
the field of the positive background. In order to study the system at lowest
energy states that still carry a current, initial configurations are obtained
by a special quenching procedure. We observe the formation of a steady state in
which the entire electron-lattice cycles with a common uniform velocity.
Certain runs show an intermediate instability leading to lattice
rearrangements. A Hall resistance can be defined and depends linearly on the
magnetic field with an anomalous coefficient reflecting the manybody
contributions peculiar to two dimensions.Comment: 13 pages, 5 figure
Structure optimization in an off-lattice protein model
We study an off-lattice protein toy model with two species of monomers
interacting through modified Lennard-Jones interactions. Low energy
configurations are optimized using the pruned-enriched-Rosenbluth method
(PERM), hitherto employed to native state searches only for off lattice models.
For 2 dimensions we found states with lower energy than previously proposed
putative ground states, for all chain lengths . This indicates that
PERM has the potential to produce native states also for more realistic protein
models. For , where no published ground states exist, we present some
putative lowest energy states for future comparison with other methods.Comment: 4 pages, 2 figure
Curvature fluctuations and Lyapunov exponent at Melting
We calculate the maximal Lyapunov exponent in constant-energy molecular
dynamics simulations at the melting transition for finite clusters of 6 to 13
particles (model rare-gas and metallic systems) as well as for bulk rare-gas
solid. For clusters, the Lyapunov exponent generally varies linearly with the
total energy, but the slope changes sharply at the melting transition. In the
bulk system, melting corresponds to a jump in the Lyapunov exponent, and this
corresponds to a singularity in the variance of the curvature of the potential
energy surface. In these systems there are two mechanisms of chaos -- local
instability and parametric instability. We calculate the contribution of the
parametric instability towards the chaoticity of these systems using a recently
proposed formalism. The contribution of parametric instability is a continuous
function of energy in small clusters but not in the bulk where the melting
corresponds to a decrease in this quantity. This implies that the melting in
small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev
Long Range Magnetic Order and the Darwin Lagrangian
We simulate a finite system of confined electrons with inclusion of the
Darwin magnetic interaction in two- and three-dimensions. The lowest energy
states are located using the steepest descent quenching adapted for velocity
dependent potentials. Below a critical density the ground state is a static
Wigner lattice. For supercritical density the ground state has a non-zero
kinetic energy. The critical density decreases with for exponential
confinement but not for harmonic confinement. The lowest energy state also
depends on the confinement and dimension: an antiferromagnetic cluster forms
for harmonic confinement in two dimensions.Comment: 5 figure