Related papers: A random walker on a ratchet
We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force…
We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles. The main results are devoted to the study of the generating function and the limiting…
Kinesin-1 is an ATP-driven, two-headed motor protein that transports intracellular cargoes along microtubule. Based on recent experimental observations, we formulate a mechanochemical model for it, in which forward/backward/futile cycle of…
The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and…
An inchworm processive mechanism is proposed to explain the motion of dimeric molecular motors such as kinesin. We present here preliminary results for this mechanism focusing on observables like mean velocity, coupling ratio and efficiency…
A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The…
Transport of a Brownian particle moving in a periodic potential is investigated in the presence of symmetric unbiased external force. The viscous medium is alternately in contact with the two heat reservoirs. We present the analytical…
We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…
We consider the continuous time random walk model (CTRW) of tracer's motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported in Holzner et al. Phys. Rev. E 92, 013015…
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically…
We consider a multi-type branching random walk with displacements that have either regularly varying or semi-exponential tails. We investigate the asymptotic behavior of the rightmost particle in irreducible and reducible regimes and…
Branching random walks on multidimensional lattice with heavy tails and a constant branching rate are considered. It is shown that under these conditions (heavy tails and constant rate), the front propagates exponentially fast, but the…
Myosin-V is a highly processive dimeric protein that walks with 36nm steps along actin tracks, powered by coordinated ATP hydrolysis reactions in the two myosin heads. No previous theoretical models of the myosin-V walk reproduce all the…
The classical walking behaviors of a single atom in an amplitude-modulated standing wave lattice beyond the internal dynamics are investigated. Based on a simple effective model, we identify a diversity of dynamic regimes of atomic motion…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions…
We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., {\em Proc.…
The cell cytoskeleton is a striking example of "active" medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown recently to have a spectacular impact on the mechanical and rheological properties of the cellular…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
Consider two random walks on $\mathbb{Z}$. The transition probabilities of each walk is dependent on trajectory of the other walker i.e. a drift $p>1/2$ is obtained in a position the other walker visited twice or more. This simple model has…