Related papers: Structural characterization of ice polymorphs from…
A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the…
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these…
We investigate the large-scale structure and temporal evolution of cyclonic and anticyclonic systems in the North Atlantic using persistent homology applied to daily sea-level pressure anomalies from the ERA5 reanalysis (1950-2022). By…
The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of…
Understanding the structural tendencies of nanoconfined water is of great interest for nanoscience and biology, where nano/micro-sized objects may be separated by very few layers of water. Here we investigate the properties of ice confined…
We prove quantitative sub-ballisticity for the self-avoiding walk on the hexagonal lattice. Namely, we show that with high probability a self-avoiding walk of length $n$ does not exit a ball of radius $O(n/\log{n})$. Previously, only a…
We define a new ensemble for self-avoiding walks in the upper half-plane, the fixed irredicible bridge ensemble, by considering self-avoiding walks in the upper half-plane up to their $n$-th bridge height, $Y_n$, and scaling the walk by…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We study the connective constants of weighted self-avoiding walks (SAWs) on infinite graphs and groups. The main focus is upon weighted SAWs on finitely generated, virtually indicable groups. Such groups possess so-called 'height…
We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks…
This monograph reviews our current understanding of the physical dynamics of ice crystal growth, focusing on the spontaneous formation of complex structures from water vapor (called snow crystals) as a function of temperature,…
To comprehend the complexities of the ice-water interface, we perform a study that attempts to correlate the altered dynamics of water to its perturbed structure at, and due to, the interface. The deviation from bulk values of structural…
In polymer physics it is typically assumed that excluded volume interactions are effectively screened in polymer melts. Hence, chains could be described by an effective random walk without excluded volume interactions. In this letter, we…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
These lecture notes provide a rapid introduction to a number of rigorous results on self-avoiding walks, with emphasis on the critical behaviour. Following an introductory overview of the central problems, an account is given of the…
Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green's function of a graph also known as the communicability. The walk…
We have theoretically investigated the transport properties of a ring-shaped array of small tunnel junctions, which is weakly coupled to the drain electrode. We have found that the long range interaction together with the semi-isolation of…
In this paper, we investigate a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by…
The anharmonicity of atomic motion limits the thermal conductivity in crystalline solids. However, a microscopic understanding of the mechanisms active in strong thermal insulators is lacking. In this letter, we classify 465 experimentally…
Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientation and speed fluctuations. This interplay of…