67 research outputs found
Writhe induced phase transition in unknotted self-avoiding polygons
Abstract. Recently it has been argued that weighting the writhe of unknotted self-avoiding polygons can be related to possible experiments that turn double stranded DNA. We first solve exactly a directed model and demonstrate that in such a subset of polygons the problem of weighting their writhe is associated with a phase transition. We then analyse simulations using the Wang-Landau algorithm to observe scaling in the fluctuations of the writhe that is compatible with a second-order phase transition in a undirected self-avoiding polygon model. Crucially, we conclude that the transition becomes apparent when the polygon is stretched sufficiently with a pulling force
Universality of crossover scaling for the adsorption transition of lattice polymers
Recently, it has been proposed that the adsorption transition for a single
polymer in dilute solution, modeled by lattice walks in three dimensions, is
not universal with respect to inter-monomer interactions. It has also been
conjectured that key critical exponents , measuring the growth of the
contacts with the surface at the adsorption point, and , which
measures the finite-size shift of the critical temperature, are not the same.
However, applying standard scaling arguments the two key critical exponents
should be identical, thus pointing to a potential breakdown of these standard
scaling arguments. This is in contrast to the well studied situation in two
dimensions, where there are exact results from conformal field theory: these
exponents are both accepted to be and universal. We use the flatPERM
algorithm to simulate self-avoiding walks and trails on the hexagonal, square
and simple cubic lattices up to length to investigate these claims.
Walks can be seen as a repulsive limit of inter-monomer interaction for trails,
allowing us to probe the universality of adsorption. For each model we analyze
several thermodynamic properties to produce different methods of estimating the
critical temperature and the key exponents. We test our methodology on the
two-dimensional cases and the resulting spread in values for and
indicates that there is a systematic error that exceeds the
statistical error usually reported. We further suggest a methodology for
consistent estimation of the key adsorption exponents which gives
in three dimensions. We conclude that in three
dimensions these critical exponents indeed differ from the mean-field value of
, but cannot find evidence that they differ from each other. Importantly,
we also find no substantive evidence of any non-universality in the polymer
adsorption transition
Adsorption of interacting self-avoiding trails in two dimensions
We investigate the surface adsorption transition of interacting self-avoiding
square lattice trails onto a straight boundary line. The character of this
adsorption transition depends on the strength of the bulk interaction, which
induces a collapse transition of the trails from a swollen to a collapsed
phase, separated by a critical state. If the trail is in the critical state,
the universality class of the adsorption transition changes; this is known as
the special adsorption point. Using flatPERM, a stochastic growth Monte Carlo
algorithm, we simulate the adsorption of self-avoiding interacting trails on
the square lattice using three different boundary scenarios which differ with
respect to the orientation of the boundary and the type of surface interaction.
We confirm the expected phase diagram, showing swollen, collapsed, and adsorbed
phases in all three scenarios, and confirm universality of the normal
adsorption transition at low values of the bulk interaction strength.
Intriguingly, we cannot confirm universality of the special adsorption
transition. We find different values for the exponents; the most likely
explanation is that this is due to the presence of strong corrections to
scaling at this point.Comment: 10 pages, 8 figure
Phase transitions in solvent-dependent polymer adsorption in three dimensions
We consider the phase diagram of self-avoiding walks (SAW) on the simple
cubic lattice subject to surface and bulk interactions, modeling an adsorbing
surface and variable solvent quality for a polymer in dilute solution,
respectively. We simulate SAWs at specific interaction strengths to focus on
locating certain transitions and their critical behavior. By collating these
new results with previous results we sketch the complete phase diagram and show
how the adsorption transition is affected by changing the bulk interaction
strength. This expands on recent work considering how adsorption is affected by
solvent quality. We demonstrate that changes in the adsorption crossover
exponent coincide with phase boundaries.Comment: 5 pages, 3 figure
Adsorption of neighbor-avoiding walks on the simple cubic lattice
We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous results using self-avoiding walks and self-avoiding trails. The connection is that neighbor-avoiding walks are equivalent to the infinitely repulsive limit of self-avoiding walks with monomer-monomer interactions. Such repulsive interactions can be seen to enhance the excluded volume effect. We calculate the critical behavior of the adsorption transition for neighbor-avoiding walks, finding a critical temperature of
T
a
=
3.274
(
9
)
and a crossover exponent of
Ï•
=
0.482
(
13
)
, which is consistent with the exponent for self-avoiding walks and trails, leading to an overall combined estimate for three dimensions of
Ï•
3D
=
0.484
(
7
)
. While questions of universality have previously been raised regarding the value of adsorption exponents in three dimensions, our results indicate that the value of
Ï•
in the strongly repulsive regime does not differ from its noninteracting value. However, it is clearly different from the mean-field value of
1
/
2
and therefore not superuniversal
Genetic Associations with Plasma B12, B6, and Folate Levels in an Ischemic Stroke Population from the Vitamin Intervention for Stroke Prevention (VISP) Trial
Background: B vitamins play an important role in homocysteine metabolism, with vitamin deficiencies resulting in increased levels of homocysteine and increased risk for stroke. We performed a genome-wide association study (GWAS) in 2,100 stroke patients from the Vitamin Intervention for Stroke Prevention (VISP) trial, a clinical trial designed to determine whether the daily intake of high-dose folic acid, vitamins B6, and B12 reduce recurrent cerebral infarction.
Methods: Extensive quality control (QC) measures resulted in a total of 737,081 SNPs for analysis. Genome-wide association analyses for baseline quantitative measures of folate, Vitamins B12, and B6 were completed using linear regression approaches, implemented in PLINK.
Results: Six associations met or exceeded genome-wide significance (P ≤ 5 × 10−08). For baseline Vitamin B12, the strongest association was observed with a non-synonymous SNP (nsSNP) located in the CUBN gene (P = 1.76 × 10−13). Two additional CUBN intronic SNPs demonstrated strong associations with B12 (P = 2.92 × 10−10 and 4.11 × 10−10), while a second nsSNP, located in the TCN1 gene, also reached genome-wide significance (P = 5.14 × 10−11). For baseline measures of Vitamin B6, we identified genome-wide significant associations for SNPs at the ALPL locus (rs1697421; P = 7.06 × 10−10 and rs1780316; P = 2.25 × 10−08). In addition to the six genome-wide significant associations, nine SNPs (two for Vitamin B6, six for Vitamin B12, and one for folate measures) provided suggestive evidence for association (P ≤ 10−07).
Conclusion: Our GWAS study has identified six genome-wide significant associations, nine suggestive associations, and successfully replicated 5 of 16 SNPs previously reported to be associated with measures of B vitamins. The six genome-wide significant associations are located in gene regions that have shown previous associations with measures of B vitamins; however, four of the nine suggestive associations represent novel finding and warrant further investigation in additional populations
A directed walk model of a long chain polymer in a slit with attractive walls
C1 - Journal Articles Referee
On the non-universality of a critical exponent for self-avoiding walks
We have extended the enumeration of self-avoiding walks on the Manhattan lattice from 28 to 53 steps and for self-avoiding polygons from 48 to 84 steps. Analysis of this data suggests that the walk generating function exponent γ = 1.3385 ± 0.003, which is different from the corresponding exponent on the square, triangular and honeycomb lattices. This provides numerical support for an argument recently advanced by Cardy, to the effect that excluding walks with parallel nearest-neighbour steps should cause a change in the exponent γ. The lattice topology of the Manhattan lattice precludes such parallel steps. © 1998 Elsevier Science B.V
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