59 research outputs found
Slow dynamics due to entropic barriers in the one-dimensional `descent model'
We propose a novel one-dimensional simple model without disorder exhibiting
slow dynamics and aging at the zero temperature limit. This slow dynamics is
due to entropic barriers. We exactly solve the statics of the model. We derive
an evolution equation for the slow modes of the dynamics which are responsible
for the aging. This equation is equivalent to a random walker on the energetic
landscape. This latter elementary model can be solved analytically up to some
basic approximations and is eventually shown to present aging by itself, as
well as a slow logarithmic relaxation of the energy: e(t) ~ 1/ln(t) at large t.Comment: 8 pages,4 figures, we add analytical development of the energy-energy
correlation function showing aging, and figures 1 and
A formula for the number of tilings of an octagon by rhombi
We propose the first algebraic determinantal formula to enumerate tilings of
a centro-symmetric octagon of any size by rhombi. This result uses the
Gessel-Viennot technique and generalizes to any octagon a formula given by
Elnitsky in a special case.Comment: New title. Minor improvements. To appear in Theoretical Computer
Science, special issue on "Combinatorics of the Discrete Plane and Tilings
Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry
We perform Transition matrix Monte Carlo simulations to evaluate the entropy
of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational
symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We
confirm analytic predictions of N. Destainville et al., J. Stat. Phys. 120, 799
(2005) and M. Widom et al., J. Stat. Phys. 120, 837 (2005), in particular that
the large size and large D limits commute, and that entropy becomes insensible
to size, phason strain and boundary conditions at large D. We are able to infer
finite D and finite size scalings of entropy. We also show that phason elastic
constants can be estimated for any D by measuring the relevant perpendicular
space fluctuations.Comment: Accepted for publication in Eur. Phys. J.
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions
Three-dimensional integer partitions provide a convenient representation of
codimension-one three-dimensional random rhombus tilings. Calculating the
entropy for such a model is a notoriously difficult problem. We apply
transition matrix Monte Carlo simulations to evaluate their entropy with high
precision. We consider both free- and fixed-boundary tilings. Our results
suggest that the ratio of free- and fixed-boundary entropies is
, and can be interpreted as the ratio of the
volumes of two simple, nested, polyhedra. This finding supports a conjecture by
Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in
three-dimensional random tilings
Flip dynamics in octagonal rhombus tiling sets
We investigate the properties of classical single flip dynamics in sets of
two-dimensional random rhombus tilings. Single flips are local moves involving
3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We
determine the ergodic times of these dynamical systems (at infinite
temperature): they grow with the system size like ;
these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets
and a powerful tool from probability theory, the coupling technique. We also
point out the interesting occurrence of Gumbel distributions.Comment: 5 Revtex pages, 4 figures; definitive versio
Two-dimensional random tilings of large codimension: new progress
Two-dimensional random tilings of rhombi can be seen as projections of
two-dimensional membranes embedded in hypercubic lattices of higher dimensional
spaces. Here, we consider tilings projected from a -dimensional space. We
study the limiting case, when the quantity , and therefore the number of
different species of tiles, become large. We had previously demonstrated [ICQ6]
that, in this limit, the thermodynamic properties of the tiling become
independent of the boundary conditions. The exact value of the limiting entropy
and finite corrections remain open questions. Here, we develop a mean-field
theory, which uses an iterative description of the tilings based on an analogy
with avoiding oriented walks on a random tiling. We compare the quantities
so-obtained with numerical calculations. We also discuss the role of spatial
correlations.Comment: Proceedings of the 7th International Conference on Quasicrystals
(ICQ7, Stuttgart), 4 pages, 4 figure
Detection of confinement and jumps in single molecule membrane trajectories
We propose a novel variant of the algorithm by Simson et al. [R. Simson, E.D.
Sheets, K. Jacobson, Biophys. J. 69, 989 (1995)]. Their algorithm was developed
to detect transient confinement zones in experimental single particle tracking
trajectories of diffusing membrane proteins or lipids. We show that our
algorithm is able to detect confinement in a wider class of confining potential
shapes than Simson et al.'s one. Furthermore it enables to detect not only
temporary confinement but also jumps between confinement zones. Jumps are
predicted by membrane skeleton fence and picket models. In the case of
experimental trajectories of -opioid receptors, which belong to the family
of G-protein-coupled receptors involved in a signal transduction pathway, this
algorithm confirms that confinement cannot be explained solely by rigid fences.Comment: 4 pages, 3 figure
Thermodynamics of nano-cluster phases: a unifying theory
We propose a unifying, analytical theory accounting for the self-organization
of colloidal systems in nano- or micro-cluster phases. We predict the
distribution of cluter sizes with respect to interaction parameters and colloid
concentration. In particular, we anticipate a proportionality regime where the
mean cluster size grows proportionally to the concentration, as observed in
several experiments. We emphasize the interest of a predictive theory in soft
matter, nano-technologies and biophysics.Comment: 4 pages, 1 figur
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