361 research outputs found
Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type
A mean field theory is developed for the calculation of the surface free
energy of the staggered BCSOS, (or six vertex) model as function of the surface
orientation and of temperature. The model approximately describes surfaces of
crystals with nearest neighbor attractions and next nearest neighbor
repulsions. The mean field free energy is calculated by expressing the model in
terms of interacting directed walks on a lattice. The resulting equilibrium
shape is very rich with facet boundaries and boundaries between reconstructed
and unreconstructed regions which can be either sharp (first order) or smooth
(continuous). In addition there are tricritical points where a smooth boundary
changes into a sharp one and triple points where three sharp boundaries meet.
Finally our numerical results strongly suggest the existence of conical points,
at which tangent planes of a finite range of orientations all intersect each
other. The thermal evolution of the equilibrium shape in this model shows
strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include
Unbinding of mutually avoiding random walks and two dimensional quantum gravity
We analyze the unbinding transition for a two dimensional lattice polymer in
which the constituent strands are mutually avoiding random walks. At low
temperatures the strands are bound and form a single self-avoiding walk. We
show that unbinding in this model is a strong first order transition. The
entropic exponents associated to denaturated loops and end-segments
distributions show sharp differences at the transition point and in the high
temperature phase. Their values can be deduced from some exact arguments
relying on a conformal mapping of copolymer networks into a fluctuating
geometry, i.e. in the presence of quantum gravity. An excellent agreement
between analytical and numerical estimates is observed for all cases analized.Comment: 9 pages, 11 figures, revtex
Physics-based analysis of Affymetrix microarray data
We analyze publicly available data on Affymetrix microarrays spike-in
experiments on the human HGU133 chipset in which sequences are added in
solution at known concentrations. The spike-in set contains sequences of
bacterial, human and artificial origin. Our analysis is based on a recently
introduced molecular-based model [E. Carlon and T. Heim, Physica A 362, 433
(2006)] which takes into account both probe-target hybridization and
target-target partial hybridization in solution. The hybridization free
energies are obtained from the nearest-neighbor model with experimentally
determined parameters. The molecular-based model suggests a rescaling that
should result in a "collapse" of the data at different concentrations into a
single universal curve. We indeed find such a collapse, with the same
parameters as obtained before for the older HGU95 chip set. The quality of the
collapse varies according to the probe set considered. Artificial sequences,
chosen by Affymetrix to be as different as possible from any other human genome
sequence, generally show a much better collapse and thus a better agreement
with the model than all other sequences. This suggests that the observed
deviations from the predicted collapse are related to the choice of probes or
have a biological origin, rather than being a problem with the proposed model.Comment: 11 pages, 10 figure
Coexistence of excited states in confined Ising systems
Using the density-matrix renormalization-group method we study the
two-dimensional Ising model in strip geometry. This renormalization scheme
enables us to consider the system up to the size 300 x infinity and study the
influence of the bulk magnetic field on the system at full range of
temperature. We have found out the crossover in the behavior of the correlation
length on the line of coexistence of the excited states. A detailed study of
scaling of this line is performed. Our numerical results support and specify
previous conclusions by Abraham, Parry, and Upton based on the related bubble
model.Comment: 4 Pages RevTeX and 4 PostScript figures included; the paper has been
rewritten without including new result
Effective affinities in microarray data
In the past couple of years several studies have shown that hybridization in
Affymetrix DNA microarrays can be rather well understood on the basis of simple
models of physical chemistry. In the majority of the cases a Langmuir isotherm
was used to fit experimental data. Although there is a general consensus about
this approach, some discrepancies between different studies are evident. For
instance, some authors have fitted the hybridization affinities from the
microarray fluorescent intensities, while others used affinities obtained from
melting experiments in solution. The former approach yields fitted affinities
that at first sight are only partially consistent with solution values. In this
paper we show that this discrepancy exists only superficially: a sufficiently
complete model provides effective affinities which are fully consistent with
those fitted to experimental data. This link provides new insight on the
relevant processes underlying the functioning of DNA microarrays.Comment: 8 pages, 6 figure
Elastic Lattice Polymers
We study a model of "elastic" lattice polymer in which a fixed number of
monomers is hosted by a self-avoiding walk with fluctuating length . We
show that the stored length density scales asymptotically
for large as , where is the
polymer entropic exponent, so that can be determined from the analysis
of . We perform simulations for elastic lattice polymer loops with
various sizes and knots, in which we measure . The resulting estimates
support the hypothesis that the exponent is determined only by the
number of prime knots and not by their type. However, if knots are present, we
observe strong corrections to scaling, which help to understand how an entropic
competition between knots is affected by the finite length of the chain.Comment: 10 page
Fractional Brownian motion and the critical dynamics of zipping polymers
We consider two complementary polymer strands of length attached by a
common end monomer. The two strands bind through complementary monomers and at
low temperatures form a double stranded conformation (zipping), while at high
temperature they dissociate (unzipping). This is a simple model of DNA (or RNA)
hairpin formation. Here we investigate the dynamics of the strands at the
equilibrium critical temperature using Monte Carlo Rouse dynamics. We
find that the dynamics is anomalous, with a characteristic time scaling as
, exceeding the Rouse time . We
investigate the probability distribution function, the velocity autocorrelation
function, the survival probability and boundary behaviour of the underlying
stochastic process. These quantities scale as expected from a fractional
Brownian motion with a Hurst exponent . We discuss similarities and
differences with unbiased polymer translocation.Comment: 7 pages, 8 figure
Exons, introns and DNA thermodynamics
The genes of eukaryotes are characterized by protein coding fragments, the
exons, interrupted by introns, i.e. stretches of DNA which do not carry any
useful information for the protein synthesis. We have analyzed the melting
behavior of randomly selected human cDNA sequences obtained from the genomic
DNA by removing all introns. A clear correspondence is observed between exons
and melting domains. This finding may provide new insights in the physical
mechanisms underlying the evolution of genes.Comment: 4 pages, 8 figures - Final version as published. See also Phys. Rev.
Focus 15, story 1
Two-dimensional wetting with binary disorder: a numerical study of the loop statistics
We numerically study the wetting (adsorption) transition of a polymer chain
on a disordered substrate in 1+1 dimension.Following the Poland-Scheraga model
of DNA denaturation, we use a Fixman-Freire scheme for the entropy of loops.
This allows us to consider chain lengths of order to ,
with disorder realizations. Our study is based on the statistics of
loops between two contacts with the substrate, from which we define Binder-like
parameters: their crossings for various sizes allow a precise determination
of the critical temperature, and their finite size properties yields a
crossover exponent .We then analyse at
criticality the distribution of loop length in both regimes
and , as well as the finite-size properties of the contact
density and energy. Our conclusion is that the critical exponents for the
thermodynamics are the same as those of the pure case, except for strong
logarithmic corrections to scaling. The presence of these logarithmic
corrections in the thermodynamics is related to a disorder-dependent
logarithmic singularity that appears in the critical loop distribution in the
rescaled variable as .Comment: 12 pages, 13 figure
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