相关论文: Radius of Gyration, Contraction Factors, and Subdi…

Using a theoretical model we show that ideal ring polymers are stronger depletants than ideal linear polymers of equal radii of gyration, but not of equal hydrodynamic radii. The difference in the depletion-induced force profile is largely…

A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall. As the piston approaches the wall the…

We study analytically and numerically the winding of directed polymers of length $t$ around each other or around a rod. Unconfined polymers in pure media have exponentially decaying winding angle distributions, the decay constant depending…

We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.

The molecular dynamics simulations were used to obtain the radius of gyration of real ring polymer chains with different topological structures consisting of 360 monomers. We focus on the entropic force which is exerted by a dilute solution…

We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency…

Every irreducible outer automorphism of the free group of rank r is topologically represented by an irreducible train track map $f$ on some graph $\Gamma$ of rank r. Moreover, $f$ can always be written as a composition of folds and a graph…

We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…

Motivated by a problem arising from pharmaceutical science [B. Baeumer et al., Discr. Contin. Dyn. Sys. B 12], we study random walks on the contact graph of a bidisperse random sphere packing. For a random walk on the unweighted graph that…

An integral convex polytope ${\mathcal P}$ is said to be Gorenstein if its toric ring $K[{\mathcal P}]$ is normal and Gorenstein. In this paper, Gorenstein cut polytopes of graphs are characterized explicitly. First, we prove that…

We present a novel mechanism for resolving the mechanical rigidity of nanoscopic circular polymers that flow in a complex environment. The emergence of a regime of negative differential mobility induced by topological interactions between…

We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…

We study of the dynamics of ring polymers confined to diffuse in a background gel at low concentrations. We do this in order to probe the inter-play between topology and dynamics in ring polymers. We develop an algorithm that takes into…

We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to…

We study three resistance distance-based graph invariants: the Kirchhoff index, and two modifications, namely, the multiplicative degree-Kirchhoff index and the additive degree-Kirchhoff index. In work in press, one of the present authors…

The BKMP conjecture (2006-2008), proposed a new method to compute closed and open Gromov-Witten invariants for every toric Calabi-Yau 3-folds, through a topological recursion based on mirror symmetry. So far, this conjecture had been…

The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In…

In this paper, we present a new approach to the Kratky-Porod Model (KP) of semiflexible polymers. Our solution to the model is based on the definition of a generating function which we use to study the statistical mechanics of semiflexible…

This thesis deals with some $(1+1)$-dimensional lattice path models from the KPZ universality class: the directed random polymer with inverse-gamma weights (known as log-gamma polymer) and its zero temperature degeneration, i.e. the last…

The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…