IRREVERSIBLE SELF AVOIDING WALKS

Random walks on self-avoiding walks (SAWs) are studied using Monte Carlo techniques on a square lattice (with nearest-neighbour hopping along the chain and between SAW points which are nearest neighbours on the embedding lattice). The average of the square of the end-to-end distance for random walks of t steps on SAWs of length N is fitted to the scaling forms (Rt2) varies as Ndelta tk (for t or approximately=Ntheta ), where theta approximately=2 nu s/k; nu s being the average end-to-end distance exponent for SAWs. The observed value of the exponent delta is supported by the authors' real space renormalisation group result for the conductivity of SAW chains. The exponent k has been related to the 'effective' fractal dimension of the SAW chain.

In this paper, we study non-trapped self-avoiding walks (SAWs), which are SAWs that can be extended to an arbitrary length. We apply the flatPERM Monte Carlo method for this purpose, generating non-trapped SAWs of length up to 1024 on the square, triangular and hexagonal lattices, and calculating their number and mean squared end-to-end distance. We find strong numerical evidence that the growth constant μ and entropic and metric exponents γ and ν are identical for non-trapped and all SAWs, and in particular that the exponents are also universal for non-trapped SAWs. We also calculate the limiting ratio of non-trapped to all SAWs. We see some evidence of an n−1/2 correction-to-scaling term which is not present for all SAWs.

Self-avoiding walks on deterministic and random fractals: Numerical results

Study on the mechanism of helium platelets formation at low temperatures in SiC from the perspective of atomic diffusion

Information gathering and processing can be particularly useful to enhance the efficiency of living organisms when searching or foraging under uncertain scenarios. Assuming that such situations can be conveniently modeled through random walk models, a case that has been widely explored in the physical literature is the generation of self-avoiding trajectories as a mechanism to increase the area of the region explored and so the search efficiency. Additionally, other mechanisms as the ability to prospect the possible outcomes from choosing between different paths/trajectories could potentially enhance such efficiency even further. Here we use an extension of the classical true self-avoiding random walk model to explore that idea. We evaluate numerically how the coverage time of such random walk model gets modified when a basic prospection mechanism, which allows the walker to anticipate the outcome of possible future paths, is introduced. We analyze the level of prospection that is required to optimize the mean coverage time in a regular domain and report two relevant findings. First, we observe that increasing more and more the information used for prospection is just optimal provided the organism can process it adequately (which occurs when the self-avoidance mechanism is reliable enough), but it can be even detrimental when self-avoidance (i.e. memory) is poor or impaired. Second, we surprisingly find that prospection carried out at different time scales can be as optimal as one based on a fixed large prospection time scale. We claim that such results may capture some basic traits from the real strategies used by higher organisms when searching under uncertainty.

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks (SAW) interacting with (alternate) sites on the surface of the honeycomb lattice is A key identity used in that proof depends on the existence of a parafermionic observable for SAW interacting with a surface on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed for the honeycomb lattice persist irrespective of lattice. This permits the accurate estimation of the critical fugacity for the corresponding problem for the square and triangular lattices. We consider both edge and site weighting, and results of unprecedented precision are achieved. We also prove the corresponding result for the edge-weighted case for the honeycomb lattice.

We performed Monte Carlo simulations to study catalytic surface reaction of the type ½A2 + BA → A2B. We chose two different types of catalytic surfaces in our studies: one represented by a square lattice (coordination number four) and the other represented by a triangular lattice (coordination number six). The whole process can be described by a single parameter, which is taken as the relative adsorption of BA molecules. In our model, we always need two nearest neighbor sites to the adsorption of both molecules. After deposition, the A2 molecules dissociate occupying two nearest neighbor sites, while the BA molecules stay bound. The reaction occurs only when a free A atom is nearest neighbor of a B atom of the BA molecule. In spite of each reaction freeing three empty sites on the lattice, this model does not exhibit any reactive window for both lattices. Only when we introduce processes like the diffusion of BA molecules or free A atoms, or desorption of BA molecules, the catalytic surface can become active for some values of deposition rate yBA. As to be expected, the reactivity over the triangular lattice is higher than that observed on the square lattice.

In this study, we show the convergence and new properties of persistence length, , for the self-avoiding random walk model (SAW) using Monte Carlo data. We generate high precision estimates of several conformational quantities with a pivot algorithm for the square, hexagonal, triangular, cubic and diamond lattices with path lengths of 103 steps. For each lattice, we accurately estimate the asymptotic limit , which corroborates the convergence of to a constant value, and allows us to check the universality on the curves. Based on the estimates we make an ansatz for dependency with lattice cell and spatial dimension, we also find a new geometric interpretation for the persistence length.

Nuclear spin echo spectra are observed for three phases ( alpha H, alpha I, alpha L) of CoV alloys with 11.4-21.8 at.% V at 4.2K in zero external field. The 59Co spectra have three peaks and the hyperfine fields corresponding to the peak frequencies at 15.0 at.% V are: 136, 155, 174 kOe for the alpha H phase; 137, 165 195 kOe for the alpha I phase; and 141, 168, 201 kOe for the alpha L phase. On the reasonable assumption that Co atoms with more than four vanadium atoms at their nearest-neighbour (NN) sites do not have magnetic moments, the hyperfine fields obtained in a given phase are attributed, in order from the largest value, to Co atoms with one, two and three vanadium atoms at the NN sites, respectively. These Co atoms with one to three V neighbours seem to have well defined localised moments that do not differ very much from those in Co metal.

We present the results of Monte Carlo simulation for self-avoiding walks on a percolation cluster for square and simple cubic lattices performed very close to the percolation thresholds and estimate critical exponents \ensuremath{\nu} and \ensuremath{\gamma} defined by the disorder averages of the mean-square radius of gyration and the number of self-avoiding walks, respectively. Our results for \ensuremath{\nu} indicate a behavior rather similar to the self-avoiding walks on fully occupied lattice unlike the large increase in \ensuremath{\nu} reported in the only previous work of this kind by Kremer given for the diamond lattice. Our results for \ensuremath{\gamma} suggest an increase from the full lattice value just at ${p}_{c}$ in three dimensions, while in two dimensions the asymptotic behavior appears to be similar to that of the ordinary self-avoiding walks. We also consider the possible crossover from fractal to Euclidean behavior and discuss the reasons why no crossover scaling is observed for the mean-square radius of gyration in the present calculation.

Superconductivity in the t- t′- J model

Two-dimensional condensation of atoms adsorbed on a hexagonally packed crystalline surface: CVM theory incorporated with three kinds of sites

A long-range interacting 1/\ensuremath{\Vert}r${\ensuremath{\Vert}}^{\ensuremath{\omega}}$ true self-avoiding walk is introduced. A Flory argument gives the scaling exponent \ensuremath{\nu}=2/(\ensuremath{\omega}+2) for the end-to-end distance. For a Coulomb interaction this yields \ensuremath{\nu}=2/d, which implies that four is the upper critical dimension for growing polyelectrolytes. A Monte Carlo simulation is consistent with this conclusion.

Dichloromethane, CH{sub 2}Cl{sub 2}, adsorbs dissociatively on a Pd(100) surface at room temperature with C, Cl, and H adsorbing into 4-fold sites while H tends to diffuse underneath the surface layer with increasing CH{sub 2}Cl{sub 2} exposures. Combined AES, TDS, LEED, and HREELS observations and Monte Carlo simulations suggest a model in which C and Cl adsorb at next nearest neighbor (NNN) sites having a Cl-C-Cl angle of 90{degree} and exclude adsorption on all the nearest neighbor (NN) and Cl-Cl NNN adsorption sites. Atomic Cl desorbs at 1,100 K with the activation energy of desorption of ca. 68 kcal/mol. Oxygen-precovered surface with p(2{times}2) structure completely inhibits CH{sub 2}Cl{sub 2} adsorption while CH{sub 2}Cl{sub 2}-precovered surface is very reactive toward oxygen in the temperature range 350-510 K. The selectivity of oxidation of carbon fragments to CO increases with CH{sub 2}Cl{sub 2} preexposures, i.e., Cl-C-Cl coverages. A Monte-Carlo simulation of the oxidation of surface carbon by surface oxygen atoms resulted in a semiquantitative account of the observed rates of production of CO and CO{sub 2} as a function of chlorine coverage.

Monte Carlo simulations have been reviewed for several models of dense polymer systems: (i) a system of very short (N= 16 links) freely joined chains with Lennard-Jones interactions in the continuum, (ii) self-avoiding walks on a diamond lattice with up to N= 200 links and (iii) pearl-necklace chains with up to N= 98 hard spheres. The cases of both a mobile and a frozen-in environment have been considered. The dynamics of displacements and the structure factors have been studied and interpreted in terms of the Rouse model and the reptation model, paying particular attention to the crossover between these models. Only for the frozen-environment case is reptation fully verified, while for models (i) and (ii) simple Rouse behaviour is found and for model (iii) relaxation with a diffusion constant D∝N–2.0 ± 0.2 and disengagement time τd∝N3.4 ± 0.4 is found, but the monomer displacements are in disagreement with reptation laws. A brief comparison with pertinent experiments has been made, and the crossover between the Rouse model and the Zimm model is considered briefly.