Related papers: A solvable non-directed model of polymer adsorptio…
Based on a newly developed contact-density chain-growth algorithm, we have simulated a nongrafted peptide in the vicinity of different attractive substrates. We analyzed the specificity of the peptide adsorption by focussing on the…
The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.
A lattice walk model is said to be reluctant if the defining step set has a strong drift towards the boundaries. We describe efficient random generation strategies for these walks.
We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] \times [0, L]$ on the square lattice ${\mathbb Z}^2$. The number of distinct walks…
We introduce several bilocal algorithms for lattice self-avoiding walks that provide reasonable models for the physical kinetics of polymers in the absence of hydrodynamic effects. We discuss their ergodicity in different confined…
Polymer adsorption on fractally rough walls of varying dimensionality is studied by renormalization group methods on hierarchical lattices. Exact results are obtained for deterministic walls. The adsorption transition is found continuous…
We have performed multicanonical chain-growth simulations of a polymer interacting with an adsorbing surface. The polymer, which is not explicitly anchored at the surface, experiences a hierarchy of phase transitions between conformations…
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…
We study uniform 3-star polymers with one branch tethered to an attractive surface and another branch pulled by a force away from the surface. Each branch of the 3-star lattice is modelled as a self-avoiding walk on the simple cubic lattice…
We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ for…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
A previous paper (hep-lat/9311011) proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension $D$. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension.…
In this work, we present a simple and efficient generator of polymeric linear chains, based on a random self-avoiding walk process. The chains are generated using a discrete process of growth, in cubic networks and in a finite time, without…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
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…
We provide an introductory account of a tricritical phase diagram, in the setting of a mean-field random walk model of a polymer density transition, and clarify the nature of the density transition in this context. We consider a…
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices,…
We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider a model in which the trap depth increases…