Related papers: Trajectories of directed lattice paths
We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of…
We perform equilibrium computer simulations of a two-dimensional pinned flexible polymer exposed to a quenched disorder potential consisting of hard disks. We are especially interested in the high-density regime of the disorder, where…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results for this model continue to hold for a more general reference…
We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t') for photons moving to the right (left) direction.…
We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this…
We consider two-dimensional system of particles localized on randomly distributed sites of squared lattice with anisotropic transfer matrix elements between localized sites. By summing of "diffusion ladder" and "cooperon ladder" type…
Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance 1 << D << N^\nu (\nu = 3/4…
Prudent walks are self-avoiding walks which cannot step towards an already occupied vertex. We introduce a new model of adsorbing prudent walks on the square lattice, which start on an impenetrable surface and accrue a fugacity $a$ with…
The diameter of the graph of a $d$-dimensional lattice polytope $P \subseteq [0,k]^{n}$ is known to be at most $dk$ due to work by Kleinschmidt and Onn. However, it is an open question whether the monotone diameter, the shortest guaranteed…
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…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
The transport of polymers with folded configurations across membrane pores is investigated theoretically by analyzing simple discrete stochastic models. The translocation dynamics is viewed as a sequence of two events: motion of the folded…
We report molecular dynamics simulation results on the equilibrium properties of polymer thin films adsorbed onto flat and curved substrates. We first systematically determine the contact angle of polymer droplets on flat substrates as a…
We consider the internal dynamics of the polymer molecule which is injected in the chaotic flow with strong mean shear component. The flow geometry corresponds to the recent experiments on the elastic turbulence (Groisman, Steinberg 2000).…
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 consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and…
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…
We study the static properties of a semiflexible polymer exposed to a quenched random environment by means of computer simulations. The polymer is modeled as two-dimensional Heisenberg chain. For the random environment we consider hard…
We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can…