163 research outputs found
Polymer collapse and crystallization in bond fluctuation models
While the -collapse of single long polymers in bad solvents is
usually a continuous (tri-critical) phase transition, there are exceptions
where it is preempted by a discontinuous crystallization (liquid
solid) transition. For a version of the bond-fluctuation
model (a model where monomers are represented as cubes, and
bonds can have lengths between 2 and ) it was recently shown by F.
Rampf {\it et al.} that there exist distinct collapse and crystallization
transitions for long but {\it finite} chains. But as the chain length goes to
infinity, both transition temperatures converge to the same , i.e.
infinitely long polymers collapse immediately into a solid state. We explain
this by the observation that polymers crystallize in the Rampf {\it et al.}
model into a non-trivial cubic crystal structure (the `A15' or `CrSi'
Frank-Kasper structure) which has many degenerate ground states and, as a
consequence, Bloch walls. If one controlls the polymer growth such that only
one ground state is populated and Bloch walls are completely avoided, the
liquid-solid transition is a smooth cross-over without any sharp transition at
all.Comment: 4 page
Self-trapping self-repelling random walks
Although the title seems self-contradictory, it does not contain a misprint.
The model we study is a seemingly minor modification of the "true self-avoiding
walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in
it are self-repelling up to a characteristic time (which depends on
various parameters), but spontaneously (i.e., without changing any control
parameter) become self-trapping after that. For free walks, is
astronomically large, but on finite lattices the transition is easily
observable. In the self-trapped regime, walks are subdiffusive and
intermittent, spending longer and longer times in small areas until they escape
and move rapidly to a new area. In spite of this, these walks are extremely
efficient in covering finite lattices, as measured by average cover times.Comment: 5 pages main paper + 5 pages supplementary materia
Sequential Monte Carlo Methods for Protein Folding
We describe a class of growth algorithms for finding low energy states of
heteropolymers. These polymers form toy models for proteins, and the hope is
that similar methods will ultimately be useful for finding native states of
real proteins from heuristic or a priori determined force fields. These
algorithms share with standard Markov chain Monte Carlo methods that they
generate Gibbs-Boltzmann distributions, but they are not based on the strategy
that this distribution is obtained as stationary state of a suitably
constructed Markov chain. Rather, they are based on growing the polymer by
successively adding individual particles, guiding the growth towards
configurations with lower energies, and using "population control" to eliminate
bad configurations and increase the number of "good ones". This is not done via
a breadth-first implementation as in genetic algorithms, but depth-first via
recursive backtracking. As seen from various benchmark tests, the resulting
algorithms are extremely efficient for lattice models, and are still
competitive with other methods for simple off-lattice models.Comment: 10 pages; published in NIC Symposium 2004, eds. D. Wolf et al. (NIC,
Juelich, 2004
Universality and Asymptotic Scaling in Drilling Percolation
We present simulations of a 3-d percolation model studied recently by K.J.
Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)], obtained with a new and
more efficient algorithm. They confirm most of their results in spite of larger
systems and higher statistics used in the present paper, but we also find
indications that the results do not yet represent the true asymptotic behavior.
The model is obtained by replacing the isotropic holes in ordinary Bernoulli
percolation by randomly placed and oriented cylinders, with the constraint that
the cylinders are parallel to one of the three coordinate axes. We also
speculate on possible generalizations.Comment: 4 pages, 4 figure
On the Continuum Time Limit of Reaction-Diffusion Systems
The parity conserving branching-annihilating random walk (pc-BARW) model is a
reaction-diffusion system on a lattice where particles can branch into
offsprings with even and hop to neighboring sites. If two or more particles
land on the same site, they immediately annihilate pairwise. In this way the
number of particles is preserved modulo two. It is well known that the pc-BARW
with in 1 spatial dimension has no phase transition (it is always
subcritical), if the hopping is described by a continuous time random walk. In
contrast, the 1-d pc-BARW has a phase transition when formulated in
discrete time, but we show that the continuous time limit is non-trivial: When
the time step , the branching and hopping probabilities at the
critical point scale with different powers of . These powers are
different for different microscopic realizations. Although this phenomenon is
not observed in some other reaction-diffusion systems like, e.g. the contact
process, we argue that it should be generic and not restricted to the 1-d
pc-BARW model.Comment: 3 pages, including 2 figure
Tricritical directed percolation in 2+1 dimensions
We present detailed simulations of a generalization of the Domany-Kinzel
model to 2+1 dimensions. It has two control parameters and which
describe the probabilities of a site to be wetted, if exactly of its
"upstream" neighbours are already wetted. If depends only weakly on ,
the active/adsorbed phase transition is in the directed percolation (DP)
universality class. If, however, increases fast with so that the
formation of inactive holes surrounded by active sites is suppressed, the
transition is first order. These two transition lines meet at a tricritical
point. This point should be in the same universality class as a tricritical
transition in the contact process studied recently by L\"ubeck. Critical
exponents for it have been calculated previously by means of the field
theoretic epsilon-expansion (, with in the present case).
Rather poor agreement is found with either.Comment: 10 pages, including 10 figures; accepted for JSTA
Temporal scaling at Feigenbaum points and non-extensive thermodynamics
We show that recent claims for the non-stationary behaviour of the logistic
map at the Feigenbaum point based on non-extensive thermodynamics are either
wrong or can be easily deduced from well-known properties of the Feigenbaum
attractor. In particular, there is no generalized Pesin identity for this
system, the existing "proofs" being based on misconceptions about basic notions
of ergodic theory. In deriving several new scaling laws of the Feigenbaum
attractor, thorough use is made of its detailed structure, but there is no
obvious connection to non-extensive thermodynamics.Comment: accepted for Phys. Rev. Let
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