Related papers: Mapping self-avoiding walk on obstacle-ridden latt…
The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched…
If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere. The ensembles of SAW's used to define these hitting densities involve walks…
The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our…
Self-avoiding walks (SAWs) were introduced in chemistry to model the real-life behavior of chain-like entities such as solvents and polymers, whose physical volume prohibits multiple occupation of the same spatial point. In mathematics, a…
We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of…
Coagulation-flocculation, the physicochemical process widely used for purification a wastewater, is affected both by chemical details of involved polymers and by the statistics of their conformations on a large scale. The latter aspect is…
Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le…
Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length $N \sim {\cal O}(10^4)$. Based on the standard simple…
We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase…
Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered…
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the…
Self-avoiding walks (SAW) are the source of very difficult problems in probabilities and enumerative combinatorics. They are also of great interest as they are, for instance, the basis of protein structure prediction in bioinformatics.…
CSAW (conditioned self-avoiding walk) is a model of protein folding that combines SAW (self-avoiding walk) with Monte-Carlo. It simulates the Brownian motion of a chain molecule in the presence of interactions, both among chain residues,…
Oriented self-avoiding walks (OSAWs) on a square lattice are studied, with binding energies between steps that are oriented parallel across a face of the lattice. By means of exact enumeration and Monte Carlo simulation, we reconstruct the…
We have analysed the recently extended series for the number of self-avoiding walks (SAWs) $C_L(1)$ that cross an $L \times L$ square between diagonally opposed corners. The number of such walks is known to grow as $\lambda_S^{L^2}.$ We…
The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean…
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…
The scaling limit of the two-dimensional self-avoiding walk (SAW) is believed to be given by the Schramm-Loewner evolution (SLE) with the parameter kappa equal to 8/3. The scaling limit of the SAW has a natural parameterization and SLE has…
We study a lattice model of a magnetic polymer where the XY spin variables are located on a self-avoiding walk (SAW) on a regular lattice in two and three dimensions. We consider the regime where both spins and conformations are dynamic,…
A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no self-intersection. In this paper we present conjectures for the…