1,287 research outputs found
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
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
Lower order terms in Szego type limit theorems on Zoll manifolds
This is a detailed version of the paper math.FA/0212273. The main motivation
for this work was to find an explicit formula for a "Szego-regularized"
determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll
manifold. The idea of the Szego-regularization was suggested by V. Guillemin
and K. Okikiolu. They have computed the second term in a Szego type expansion
on a Zoll manifold of an arbitrary dimension. In the present work we compute
the third asymptotic term in any dimension. In the case of dimension 2, our
formula gives the above mentioned expression for the Szego-redularized
determinant of a zeroth order PsDO. The proof uses a new combinatorial
identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This
identity is related to the distribution of the maximum of a random walk with
i.i.d. steps on the real line. The proof of this combinatorial identity
together with historical remarks and a discussion of probabilistic and
algebraic connections has been published separately.Comment: 39 pages, full version, submitte
Trace functions as Laplace transforms
We study trace functions on the form t\to\tr f(A+tB) where is a
real function defined on the positive half-line, and and are
matrices such that is positive definite and is positive
semi-definite. If is non-negative and operator monotone decreasing, then
such a trace function can be written as the Laplace transform of a positive
measure. The question is related to the Bessis-Moussa-Villani conjecture.
Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc
Signature of nearly icosahedral structures in liquid and supercooled liquid Copper
A growing body of experiments display indirect evidence of icosahedral
structures in supercooled liquid metals. Computer simulations provide more
direct evidence but generally rely on approximate interatomic potentials of
unproven accuracy. We use first-principles molecular dynamics simulations to
generate realistic atomic configurations, providing structural detail not
directly available from experiment, based on interatomic forces that are more
reliable than conventional simulations. We analyze liquid copper, for which
recent experimental results are available for comparison, to quantify the
degree of local icosahedral and polytetrahedral order
DNA: From rigid base-pairs to semiflexible polymers
The sequence-dependent elasticity of double-helical DNA on a nm length scale
can be captured by the rigid base-pair model, whose strains are the relative
position and orientation of adjacent base-pairs. Corresponding elastic
potentials have been obtained from all-atom MD simulation and from
high-resolution structural data. On the scale of a hundred nm, DNA is
successfully described by a continuous worm-like chain model with homogeneous
elastic properties characterized by a set of four elastic constants, which have
been directly measured in single-molecule experiments. We present here a theory
that links these experiments on different scales, by systematically
coarse-graining the rigid base-pair model for random sequence DNA to an
effective worm-like chain description. The average helical geometry of the
molecule is exactly taken into account in our approach. We find that the
available microscopic parameters sets predict qualitatively similar mesoscopic
parameters. The thermal bending and twisting persistence lengths computed from
MD data are 42 and 48 nm, respectively. The static persistence lengths are
generally much higher, in agreement with cyclization experiments. All
microscopic parameter sets predict negative twist-stretch coupling. The
variability and anisotropy of bending stiffness in short random chains lead to
non-Gaussian bend angle distributions, but become unimportant after two helical
turns.Comment: 13 pages, 6 figures, 6 table
Polymer reptation and nucleosome repositioning
We consider how beads can diffuse along a chain that wraps them, without
becoming displaced from the chain; our proposed mechanism is analogous to the
reptation of "stored length" in more familiar situations of polymer dynamics.
The problem arises in the case of globular aggregates of proteins (histones)
that are wound by DNA in the chromosomes of plants and animals; these beads
(nucleosomes) are multiply wrapped and yet are able to reposition themselves
over long distances, while remaining bound by the DNA chain.Comment: 9 pages, including 2 figures, to be published in Phys. Rev. Let
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