Related papers: Branched Polymers
Let K be the convex hull of the path of a standard brownian motion B(t) in R^n, taken at time 0 < t < 1. We derive formulas for the expected volume and surface area of K. Moreover, we show that in order to approximate K by a discrete…
We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure $\nu_\lambda$ for all $\lambda>0$. We follow in part a previous incomplete unpublished work of the first named author with M.…
The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density \sigma, assuming good solvent conditions. A phenomenological scaling theory, describing the…
We prove a law of large numbers for the volumes of families of random hyperbolic mapping tori and Heegaard splittings providing a sharp answer to a conjecture of Dunfield and Thurston.
We consider random polytopes in the $d$-dimensional Euclidean space that are the convex hulls i.i.d. random points selected according to beta-prime distributions. These distributions are rotationally symmetric, heavy-tailed, and their…
We study the conformational properties of complex Gaussian polymers containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered at $n$ branching points to either a linear polymer backbone (generalized bottlebrush…
The a.s. existence of a polymer probability in the infinite volume limit is readily obtained under general conditions of weak disorder from standard theory on multiplicative cascades or branching random walk. However, speculations in the…
In this work we present a new model for the form factor of a star polymer consisting of self-avoiding branches. This new model incorporates excluded volume effects and is derived from the two point correlation function for a star polymer..…
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex…
By quantitative studies of statistics of polymer stretching in a random flow and of a flow field we demonstrate that the stretching of polymer molecules in a 3D random flow occurs rather sharply via the coil-stretch transition at the value…
A number of recent experiments have provided detailed observations of the configurations of long DNA strands under nano-to-micrometer sized confinement. We therefore revisit the problem of an excluded volume polymer chain confined between…
We estimate the mean first time, called the mean rotation time (MRT), for a planar random polymer to wind around a point. This polymer is modeled as a collection of n rods, each of them being parameterized by a Brownian angle. We are led to…
For various polymers with different topological structures we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We call polymers with nontrivial topology topological…
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
We consider the branching capacity of the range of a simple random walk on $\mathbb Z^d$, with $d \ge 5$, and show that it falls in the same universality class as the volume and the capacity of the range of simple random walks and branching…
For a directed polymer in a random medium lying on an infinite cylinder, that is in 1+1 dimensions with finite width and periodic boundary conditions on the transverse direction, the winding number is simply the algebraic number of turns…
We obtain a new upper estimate on the Euclidean diameter of the intersection of the kernel of a random matrix with iid rows with a given convex body. The proof is based on a small-ball argument rather than on concentration and thus the…
In this paper the excluded volume of binary similar hyperparticles with small size difference in D-dimensional Euclidean spaces R2, R3, and R4 is studied using two different statistical geometry approaches. These geometric approaches,…
We investigate $(2+1)$-dimensional discretized directed polymers in Gaussian random media. By numerically calculating the probability distribution function of overlap between two independent and identical systems on a common random…