Thomas Prellberg
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View article: Zeros of conditional Gaussian analytic functions, random sub-unitary matrices and q-series
Zeros of conditional Gaussian analytic functions, random sub-unitary matrices and q-series Open
We investigate radial statistics of zeros of hyperbolic Gaussian Analytic Functions (GAF) of the form $φ(z) = \sum_{k\ge 0} c_k z^k$ given that $|φ(0)|^2=t$ and assuming coefficients $c_k$ to be independent standard complex normals. We obt…
View article: Improving convergence of generalised Rosenbluth sampling for branched polymer models by uniform sampling
Improving convergence of generalised Rosenbluth sampling for branched polymer models by uniform sampling Open
Sampling with the generalised atmospheric Rosenbluth method (GARM) is a technique for estimating the distributions of lattice polymer models that has had some success in the study of linear polymers and lattice polygons. In this paper we w…
View article: Improving Convergence of Generalised Rosenbluth Sampling for Branched Polymer Models by Uniform Sampling
Improving Convergence of Generalised Rosenbluth Sampling for Branched Polymer Models by Uniform Sampling Open
Sampling with the Generalised Atmospheric Rosenbluth Method (GARM) is a technique for estimating the distributions of lattice polymer models that has had some success in the study of linear polymers and lattice polygons. In this paper we w…
View article: On the universality class of the special adsorption point of two-dimensional lattice polymers
On the universality class of the special adsorption point of two-dimensional lattice polymers Open
In recent work [PRE 100, 022121 (2019)] evidence was found that the surface adsorption transition of interacting self-avoiding trails (ISATs) placed on the square lattice displays a non-universal behavior at the special adsorption point (S…
View article: Multicritical scaling in a lattice model of vesicles
Multicritical scaling in a lattice model of vesicles Open
Vesicles, or closed fluctuating membranes, have been modeled in two dimensions by self-avoiding polygons, weighted with respect to their perimeter and enclosed area, with the simplest model given by area-weighted excursions. These models g…
View article: Adsorption of two-dimensional polymers with two- and three-body self-interactions
Adsorption of two-dimensional polymers with two- and three-body self-interactions Open
Using extensive Monte Carlo simulations, we investigate the surface adsorption of self-avoiding trails on the triangular lattice with two- and three-body on-site monomer-monomer interactions. In the parameter space of two-body, three-body,…
View article: Adsorption of interacting self-avoiding trails in two dimensions
Adsorption of interacting self-avoiding trails in two dimensions Open
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…
View article: Skew Schur Function Representation of Directed Paths in a Slit
Skew Schur Function Representation of Directed Paths in a Slit Open
In this work, we establish a general relationship between the enumeration of weighted directed paths and skew Schur functions, extending work by Bousquet-Mélou, who expressed generating functions of discrete excursions in terms of rectangu…
View article: Enumerating path diagrams in connection with $q$-tangent and $q$-secant numbers
Enumerating path diagrams in connection with $q$-tangent and $q$-secant numbers Open
We enumerate height-restricted path diagrams associated with $q$-tangent and $q$-secant numbers by considering convergents of continued fractions, leading to expressions involving basic hypergeometric functions. Our work generalises some r…
View article: Phase transitions in solvent-dependent polymer adsorption in three dimensions
Phase transitions in solvent-dependent polymer adsorption in three dimensions Open
We consider the phase diagram of self-avoiding walks (SAWs) 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…
View article: Exact solution of pulled, directed vesicles with sticky walls in two dimensions
Exact solution of pulled, directed vesicles with sticky walls in two dimensions Open
We analyse a directed lattice vesicle model incorporating both the binding-unbinding transition and the vesicle inflation-deflation transition. From the exact solution, we derive the phase diagram for this model and elucidate scaling prope…
View article: Adsorption of neighbor-avoiding walks on the simple cubic lattice
Adsorption of neighbor-avoiding walks on the simple cubic lattice Open
We investigate neighbor-avoiding walks on the simple cubic lattice in the\npresence of an adsorbing surface. This class of lattice paths has been less\nstudied using Monte Carlo simulations. Our investigation follows on from our\nprevious …
View article: Universality of crossover scaling for the adsorption transition of lattice polymers
Universality of crossover scaling for the adsorption transition of lattice polymers Open
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 intermonomer interactions. Moreover, it has been conjectu…
View article: Anomalous polymer collapse winding angle distributions
Anomalous polymer collapse winding angle distributions Open
In two dimensions polymer collapse has been shown to be complex with multiple\nlow temperature states and multi-critical points. Recently, strong numerical\nevidence has been provided for a long-standing prediction of universal scaling\nof…
View article: Dataset: Anomalous polymer collapse winding angle distributions
Dataset: Anomalous polymer collapse winding angle distributions Open
This data set provides the basis for the publication "Anomalous polymer collapse winding angle distributions”. The data set contains the code used to run the simulations, the simulation results, and the data analysis itself.
View article: Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares
Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares Open
We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice bui…
View article: Phase diagram of twist storing lattice polymers in variable solvent quality
Phase diagram of twist storing lattice polymers in variable solvent quality Open
When double stranded DNA is turned in experiments it undergoes a transition. We use an interacting self-avoiding walk on a three-dimensional fcc lattice weighted by writhe to relate to these experiments and treat this problem via simulatio…
View article: Writhe induced phase transition in unknotted self-avoiding polygons
Writhe induced phase transition in unknotted self-avoiding polygons Open
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 o…
View article: Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice
Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice Open
We consider a model of semiflexible interacting self-avoiding trails (sISATs) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting sel…
View article: Higher-Order Airy Scaling in Deformed Dyck Paths
Higher-Order Airy Scaling in Deformed Dyck Paths Open
We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, ‘jumps’ orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with r…
View article: Scaling in area-weighted generalized Motzkin paths
Scaling in area-weighted generalized Motzkin paths Open
We consider a generalized version of Motzkin paths, where horizontal steps have length $\ell$, with $\ell$ being a fixed positive integer. We first give the general functional equation for the area-length generating function of this model.…
View article: The role of three-body interactions in two-dimensional polymer collapse
The role of three-body interactions in two-dimensional polymer collapse Open
Various interacting lattice path models of polymer collapse in two dimensions\ndemonstrate different critical behaviours. This difference has been without a\nclear explanation. The collapse transition has been variously seen to be in the\n…
View article: Forces and pressures in adsorbing partially directed walks
Forces and pressures in adsorbing partially directed walks Open
journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Forces and pressures in adsorbing partially directed walks copyright_information: © 2016 IOP Publishing Ltd date_received: 2015-10-02 date…
View article: Winding angle distributions for two-dimensional collapsing polymers
Winding angle distributions for two-dimensional collapsing polymers Open
We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for $N$-step walks is compatible with …
View article: Phase Diagram of Twist Storing Lattice Polymers in Variable Solvent\n Quality
Phase Diagram of Twist Storing Lattice Polymers in Variable Solvent\n Quality Open
When double stranded DNA is turned in experiments it undergoes a transition.\nWe use an interacting self-avoiding walk on a three-dimensional fcc lattice\nweighted by writhe to relate to these experiments and treat this problem via\nsimula…
View article: Self-attracting polymers in two dimensions with three low-temperature phases
Self-attracting polymers in two dimensions with three low-temperature phases Open
We study via Monte Carlo simulation a generalisation of the so-called vertex interacting self-avoiding walk (VISAW) model on the square lattice. The configurations are actually not self-avoiding walks but rather restricted self-avoiding tr…
View article: Uniform asymptotics of area-weighted Dyck paths
Uniform asymptotics of area-weighted Dyck paths Open
Using the generalized method of steepest descents for the case of two coalescing saddle points, we derive an asymptotic expression for the bivariate generating function of Dyck paths, weighted according to their length and their area in th…
View article: On the Number of Walks in a Triangular Domain
On the Number of Walks in a Triangular Domain Open
We consider walks on a triangular domain that is a subset of the triangular lattice. We then specialise this by dividing the lattice into two directed sublattices with different weights. Our central result is an explicit formula for the ge…