Statistical mechanics and topology of polymer systems

Grant number: DE170100186 | Funding period: 2017 - 2021

Completed

Abstract

This project aims to study the behaviour of systems of long polymers in solution, and the effects of temperature, solvent and other environmental properties. Polymer models capture important physical properties of real-world molecules like DNA. This project will study the topology of polymer chains in tightly confined spaces. Knots and links hinder important biological processes like DNA replication, and this project will research how entanglement forms and how the biological mechanisms are used to manage it. The project is expected to have both important biological consequences and to enhance Australia's position as a centre for research in statistical mechanics.

Related publications (12)

Walks obeying two-step rules on the square lattice: full, half and quarter planes

Nicholas Beaton

2022-01-28

We consider walks on the edges of the square lattice Z2 which obey two-step rules, which allow (or forbid) steps in a given direct..

Exact solution of directed walk models of polymeric zipping with pulling in two and three dimensions

NR Beaton, AL Owczarek

2021-03-15

Alignment Percolation

Nicholas R Beaton, Geoffrey R Grimmett, Mark Holmes

2021-03-01

The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in d≥ 2 dimensions..

Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents

Nicholas R Beaton, Anthony J Guttmann, Iwan Jensen

2020-04-24

We investigate, by series methods, the behaviour of interacting self-avoiding walks (ISAWs) on the honeycomb lattice and on the sq..

Exact solution of some quarter plane walks with interacting boundaries

NR Beaton, AL Owczarek, A Rechnitzer

2019-09-13

The set of random walks with different step sets (of short steps) in the quarter plane has provided a rich set of models that have..

Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers

Nicholas R Beaton, Mathilde Bouvel, Veronica Guerrini, Simone Rinaldi

2019-07-19

The first problem addressed by this article is the enumeration of some families of pattern-avoiding inversion sequences. We solve ..

Slicings of parallelogram polyominoes: Catalan, Schroder, Baxter, and other sequences

Nicholas R Beaton, Mathilde Bouvel, Veronica Guerrini, Simone Rinaldi

2019-07-19

We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succ..

Knotting statistics for polygons in lattice tubes

NR Beaton, JW Eng, CE Soteros

2019-04-05

We study several related models of self-avoiding polygons in a tubular subgraph of the simple cubic lattice, with a particular int..

Characterising knotting properties of polymers in nanochannels

NR Beaton, JW Eng, K Ishihara, K Shimokawa, CE Soteros

2018-07-28

Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either ..

Partition function zeros of adsorbing Dyck paths

NR Beaton, EJ Janse van Rensburg

2018-03-16

The zeros of the size-n partition functions for a statistical mechanical model can be used to help understand the critical behavio..

On consecutive pattern avoiding permutations of length 4, 5 and beyond

Nicholas R Beaton, Andrew R Conway, Anthony J Guttmann

2018-01-01

We review and extend what is known about the generating functions for consecutive pattern avoiding permutations of length 4, 5 and..

Adsorbing staircase polygons subject to a force

Nicholas R Beaton

2017-12-08

We study several models of staircase polygons on the 45° rotated square lattice, which interact with an impenetrable surface while..

University of Melbourne Researchers

Nick Beaton Mathematics and Statistics