Related papers: Mapping onto ideal chains overestimates self-entan…
Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and…
The interplay of topological constraints and persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three dimensional lattice model. We ask if the results are consistent with…
We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that…
Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these…
A wide variety of real-life networks share two remarkable generic topological properties: scale-free behavior and modular organization, and it is natural and important to study how these two features affect the dynamical processes taking…
Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly related to other discrete structures. While walks restricted to…
We present a new simulation technique to study systems of polymers functionalized by reactive sites that bind/unbind forming reversible linkages. Functionalized polymers feature self-assembly and responsive properties that are unmatched by…
We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semi-dilute solutions. Our main result is that…
Polymer melts undergoing large deformation by uniaxial elongation are studied by molecular dynamics simulations of bead-spring chains in melts. Applying a primitive path analysis to strongly deformed polymer melts, the role of topological…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single…
One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these…
We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step…
The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact…
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…
We present computer simulations to examine probability distributions of gyration radius for the no-thickness closed polymers of N straight segments of equal length. We are particularly interested in the conditional distributions when the…
Polymer chains undergoing a continuous adsorption-desorption transition are studied through extensive computer simulations. A three-dimensional self-avoiding walk lattice model of a polymer chain grafted onto a surface has been treated for…
Random walks cannot, in general, be pushed forward by quasi-isometries. Tame Markov chains were introduced as a `quasi-isometry invariant' are a generalization of random walks. In this paper, we construct several examples of tame Markov…
Simulations in which a globular ring polymer with delocalized knots is separated in two interacting loops by a slipping link, or in two non-interacting globuli by a wall with a hole, show how the minimal crossing number of the knots…
Designing optimal structure favorable to diffusion and effectively controlling the trapping process are crucial in the study of trapping problem---random walks with a single trap. In this paper, we study the trapping problem occurring on…