469 research outputs found
The structure of the hard sphere solid
We show that near densest-packing the perturbations of the HCP structure
yield higher entropy than perturbations of any other densest packing. The
difference between the various structures shows up in the correlations between
motions of nearest neighbors. In the HCP structure random motion of each sphere
impinges slightly less on the motion of its nearest neighbors than in the other
structures.Comment: For related papers see:
http://www.ma.utexas.edu/users/radin/papers.htm
Generation of folk song melodies using Bayes transforms
The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models
Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries
Using exact computations we study the classical hard-core monomer-dimer
models on m x n plane lattice strips with free boundaries. For an arbitrary
number v of monomers (or vacancies), we found a logarithmic correction term in
the finite-size correction of the free energy. The coefficient of the
logarithmic correction term depends on the number of monomers present (v) and
the parity of the width n of the lattice strip: the coefficient equals to v
when n is odd, and v/2 when n is even. The results are generalizations of the
previous results for a single monomer in an otherwise fully packed lattice of
dimers.Comment: 4 pages, 2 figure
A Corpus-Based, Pilot Study of Lexical Stress Variation in American English
Phonological free variation describes the phenomenon of there being more than one pronunciation for a word without any change in meaning (e.g. because, schedule, vehicle). The term also applies to words that exhibit different stress patterns (e.g. academic, resources, comparable) with no change in meaning or grammatical category. A corpus-based analysis of free variation is a useful tool for testing the validity of surveys of speakers' pronunciation preferences for certain variants. The current paper presents the results of a corpus-based pilot study of American English, in an attempt to replicate Mompéan's 2009 study of British English
Loop models and their critical points
Loop models have been widely studied in physics and mathematics, in problems
ranging from polymers to topological quantum computation to Schramm-Loewner
evolution. I present new loop models which have critical points described by
conformal field theories. Examples include both fully-packed and dilute loop
models with critical points described by the superconformal minimal models and
the SU(2)_2 WZW models. The dilute loop models are generalized to include
SU(2)_k models as well.Comment: 20 pages, 15 figure
Small molecule screening in zebrafish: an in vivo approach to identifying new chemical tools and drug leads
In the past two decades, zebrafish genetic screens have identified a wealth of mutations that have been essential to the understanding of development and disease biology. More recently, chemical screens in zebrafish have identified small molecules that can modulate specific developmental and behavioural processes. Zebrafish are a unique vertebrate system in which to study chemical genetic systems, identify drug leads, and explore new applications for known drugs. Here, we discuss some of the advantages of using zebrafish in chemical biology, and describe some important and creative examples of small molecule screening, drug discovery and target identification
Tetromino tilings and the Tutte polynomial
We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each
tile is assigned a weight that depends on its orientation and position on the
lattice. For a particular choice of the weights, the generating function of
tilings is shown to be the evaluation of the multivariate Tutte polynomial
Z\_G(Q,v) (known also to physicists as the partition function of the Q-state
Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the
edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure
Phase Transition in a Self-repairing Random Network
We consider a network, bonds of which are being sequentially removed; that is
done at random, but conditioned on the system remaining connected
(Self-Repairing Bond Percolation SRBP). This model is the simplest
representative of a class of random systems for which forming of isolated
clusters is forbidden. It qualitatively describes the process of fabrication of
artificial porous materials and degradation of strained polymers. We find a
phase transition at a finite concentration of bonds , at which the
backbone of the system vanishes; for all the network is a dense
fractal.Comment: 4 pages, 4 figure
Influence of extended dynamics on phase transitions in a driven lattice gas
Monte Carlo simulations and dynamical mean-field approximations are performed
to study the phase transition in a driven lattice gas with nearest-neighbor
exclusion on a square lattice. A slight extension of the microscopic dynamics
with allowing the next-nearest-neighbor hops results in dramatic changes.
Instead of the phase separation into high- and low-density regions in the
stationary state the system exhibits a continuous transition belonging to the
Ising universality class for any driving. The relevant features of phase
diagram are reproduced by an improved mean-field analysis.Comment: 3 pages, 3 figure
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