Related papers: A simple model of DNA denaturation and mutually av…

Correlation length exponent $\nu$ for long linear DNA molecules was determined by direct measurement of the average end-to-end distance as a function of the contour length $s$ by means of atomic force microscopy (AFM). Linear DNA, up to…

In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…

We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable partial reflector. These processes serve as a simplified models…

Oscillatory sheared suspensions, when observed stroboscopically, exhibit a reversible-irreversible transition as a function of the strain amplitude, which is a kind of absorbing phase transition. So far studies of this transition focused on…

We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…

We study one- and two-dimensional models which undergo a transition between active and absorbing phases. The transition point in these models is of novel type: jump of the order parameter coincides with its power-law singularity. Some…

The $N$-step random walk, elongated in the vicinity of a disc (in 2D) or a sphere (in 3D) of radius $R$, demonstrates a non-algebraic stretched exponential decay $P_N\sim \exp\left(-{\rm const}\, N^{1/3}\right)$ for the first return…

Many biological processes involve one dimensional diffusion over a correlated inhomogeneous energy landscape with a correlation length $\xi_c$. Typical examples are specific protein target location on DNA, nucleosome repositioning, or DNA…

We investigate the voltage-driven transport of hybridized DNA through membrane channels. As membrane channels are typically too narrow to accommodate hybridized DNA, the dehybridization of the DNA is the critical rate limiting step in the…

We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…

As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the…

In a 1976 paper published in Science, Knuth presented an algorithm to sample (non-uniform) self-avoiding walks crossing a square of side k. From this sample, he constructed an estimator for the number of such walks. The quality of this…

We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…

First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes…

We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by…

Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…

We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is…

We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large…

We introduce a family of models incorporating random segmental substitutions and point mutations and demonstrate that such models reproduce algebraic length distributions of exact matches with the slope $-4$ observed earlier in pairwise…

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…