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 $\phi$, measuring the growth of the contacts with the surface at the adsorption point, and $1/\delta$, 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 $1/2$ 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 $1024$ 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 $\phi$ and $1/\delta$ 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 $\phi=1/\delta=0.484(4)$ in three dimensions. We conclude that in three dimensions these critical exponents indeed differ from the mean-field value of $1/2$, 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 ϕ = 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 ϕ 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 ϕ 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

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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

Self-avoiding walks in a slab with attractive walls

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