arXiv subjects

G. T. Barkema

Publications and source records attributed to G. T. Barkema.

At least 55 records · Page 3Linked to original sources

arXiv2000

Symmetry effects and equivalences in lattice models of hydrophobic interaction

We establish the equivalence of a recently introduced discrete model of the hydrophobic interaction, as well as its extension to continuous state variables, with the Ising model in a magnetic field with temperature-dependent strength. In order to capture the effect of symmetries of the solvent particles we introduce a generalized multi-state model. We solve this model - which is not of the Ising type - exactly in one dimension. Our findings suggest that a small increase in symmetry decreases the amplitude of the solvent-mediated part of the potential of mean force between solute particles and enhances the solubility in a very simple fashion. High symmetry decreases also the range of the attractive potential. This weakening of the hydrophobic effect observed in the model is in agreement with the notion that the effect is entropic in origin.

cond-mat.stat-mech↗

arXiv2000

Relation between Raman spectra and Structure of Amorphous Silicon

In 1985, Beeman, Tsu and Thorpe established an almost linear relation between the Raman transverse-optic (TO) peak width and the spread in mean bond angle in a-Si. This relation is often used to estimate the latter quantity in experiments. In the last decade, there has been significant progress in the computer generation of sample networks of amorphous silicon. Exploiting this progress, this manuscript presents a more accurate determination of the relation between the TO peak width and angular spread using 1000-atom configurations. Also investigated and quantified are the relations between the TO peak frequency and the ratio of the intensities of the transverse-acoustic (TA) and TO peak, both as functions of the angular spread. As this spread decreases, the TA/TO intensity ratio decreases and the TO peak frequency increases. These relations offer additional ways to obtain structural information on a-Si from Raman measurements.

cond-mat↗

arXiv2000

A cluster algorithm for Potts models with fixed spin densities

A cluster algorithm is presented for the simulation of the q-state Potts models in which the number of spins is conserved in each state. The algorithm constructs Fortuin-Kasteleyn cluster configurations from spin configurations, in a way identical to the Swendsen-Wang algorithm; the spin assignment to these clusters is however different, and conserves the number of spins for each state. Compared to traditional non-local spin-exchange algorithms, the cluster algorithm presented here suffers less from critical slowing down, and consequently is more efficient near the critical temperature.

cond-mat↗

arXiv2000

Model of Hydrophobic Attraction in Two and Three Dimensions

An earlier one-dimensional lattice model of hydrophobic attraction is extended to two and three dimensions and studied by Monte Carlo simulation. The solvent-mediated contribution to the potential of mean force between hydrophobic solute molecules and the solubility of the solute are determined. As in the earlier model, an inverse relation is observed between the strength and range of the hydrophobic attraction. The mean force no longer varies monotonically with distance, as it does in one dimension, but has some oscillations, reflecting the greater geometrical complexity of the lattice in the higher dimensions. In addition to the strong attraction at short distances, there is now also a local minimum in the potential of depth about $kT$ at a distance of three lattice spacings in two dimensions and one of depth about $2kT$ at a distance of two lattice spacings in three dimensions. The solubility of the solute is found to decrease with increasing temperature at low temperatures, which is another signature of the hydrophobic effect and also agrees with what had been found in the one-dimensional model.

cond-mat↗

arXiv1999

High-quality continuous random networks

The continuous random network (CRN) model is an idealized model for perfectly coordinated amorphous semiconductors. The quality of a CRN can be assessed in terms of topological and configurational properties, including coordination, bond-angle distributions and deformation energy. Using a variation on the sillium approach proposed 14 years ago by Wooten, Winer and Weaire, we present 1000-atom and 4096-atom configurations with a degree of strain significantly less than the best CRN available at the moment and, for the first time, comparable to experimental results.

cond-mat.mtrl-sci↗

arXiv1999

Susceptibility amplitude ratios in the two-dimensional Potts model and percolation

The high-temperature susceptibility of the $q$-state Potts model behaves as $Γ|T-T_c|^{-γ}$ as $T\to T_c+$, while for $T\to T_c-$ one may define both longitudinal and transverse susceptibilities, with the same power law but different amplitudes $Γ_L$ and $Γ_T$. We extend a previous analytic calculation of the universal ratio $Γ/Γ_L$ in two dimensions to the low-temperature ratio $Γ_T/Γ_L$, and test both predictions with Monte Carlo simulations for $q=3$ and 4. The data for $q=4$ are inconclusive owing to large corrections to scaling, while for $q=3$ they appear consistent with the prediction for $Γ_T/Γ_L$, but not with that for $Γ/Γ_L$. A simple extrapolation of our analytic results to $q\to1$ indicates a similar discrepancy with the corresponding measured quantities in percolation. We point out that stronger assumptions were made in the derivation of the ratio $Γ/Γ_L$, and our work suggests that these may be unjustified.

cond-mat.stat-mech↗

arXiv1999

Activated mechanisms in amorphous silicon: an activation-relaxation-technique study

At low temperatures, dynamics in amorphous silicon occurs through a sequence of discrete activated events that locally reorganize the topological network. Using the activation-relaxation technique, a data base containing over 8000 such events is generated, and the events are analyzed with respect to their energy barrier and asymmetry, displacement and volume expansion/contraction. Special attention is paid to those events corresponding to diffusing coordination defects. The energetics is not clearly correlated with the displacement, nor with the defect density in well relaxed configurations. We find however some correlation with the local volume expansion: it tends to increase by about 4 eV/Å$^3$. The topological properties of these events are also studied; they show an unexpectedly rich diversity.

cond-mat.dis-nn↗

arXiv1999

Elementary mechanisms governing the dynamics of silica

A full understanding of glasses requires an accurate atomistic picture of the complex activated processes that constitute the low-temperature dynamics of these materials. To this end, we generate over five thousand activated events in silica glass, using the activation-relaxation technique; these atomistic mechanisms are analysed and classified according to their activation energies, their topological properties and their spatial extend. We find that these are collective processes, involving ten to hundreds of atoms with a continuous range of activation energies; that diffusion and relaxation occurs through the creation, annihilation and motion of single dangling bonds; and that silicon and oxygen have essentially the same diffusivity.

cond-mat↗

arXiv1998

Reptation of star polymers in a network: Monte Carlo results of diffusion coefficients

We report on Monte Carlo results of diffusion coefficients of lattice star polymers trapped inside a fixed network (de Gennes model). It is found that our data are in agreement with the Helfand-Pearson exponential factor α=0.29. For the pre-exponential power law exponent we find β=2. In contrast to existing theoretical predictions, we find that the number of arms f leads to a pre-exponential factor of the form exp(-0.75 f).

cond-mat↗

arXiv1998

Exploring structural mechanisms in disordered materials using the activation-relaxation technique

Structural mechanisms in disordered materials like amorphous semi-conductors and glasses can be explored with the activation-relaxation technique (ART). The application of a sequence of such mechanisms allows for the generation of well-relaxed structures. The method and its application in the study of the microscopic changes in amorphous silicon and silica glass are reviewed, and two recent improvements are presented.

cond-mat↗

arXiv1998

Long-time dynamics of de Gennes' model for reptation

Diffusion of a polymer in a gel is studied within the framework of de Gennes' model for reptation. Our results for the scaling of the diffusion coefficient D and the longest relaxation time tau are markedly different from the most recently reported results, and are in agreement with de Gennes' reptation arguments: D ~ 1/N^2 and tau ~ N^3. The leading exponent of the finite-size corrections to the diffusion coefficient is consistent with the value of -2/3 that was reported for the Rubinstein model. This agreement suggests that its origin might be physical rather than an artifact of these models.

cond-mat↗

arXiv1998

Identification of relaxation and diffusion mechanisms in amorphous silicon

The dynamics of amorphous silicon at low temperatures can be characterized by a sequence of discrete activated events, through which the topological network is locally reorganized. Using the activation-relaxation technique, we create more than 8000 events, providing an extensive database of relaxation and diffusion mechanisms. The generic properties of these events - size, number of atoms involved, activation energy, etc. - are discussed and found to be compatible with experimental data. We introduce a complete and unique classification of defects based on their topological properties and apply it to study of events involving only four-fold coordinated atoms. For these events, we identify and present in detail three dominant mechanisms.

cond-mat↗

arXiv1997

Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique

A detailed description of the activation-relaxation technique (ART) is presented. This method defines events in the configurational energy landscape of disordered materials, such as a-Si, glasses and polymers, in a two-step process: first, a configuration is activated from a local minimum to a nearby saddle-point; next, the configuration is relaxed to a new minimum; this allows for jumps over energy barriers much higher than what can be reached with standard techniques. Such events can serve as basic steps in equilibrium and kinetic Monte Carlo schemes.

cond-mat↗

arXiv1997

Two-dimensional oriented self-avoiding walks with parallel contacts

Two closely related models of oriented self-avoiding walks (OSAWs) on a square lattice are studied. We use the pruned-enriched Rosenbluth method to determine numerically the phase diagram. Both models have three phases: a tight-spiral phase in which the binding of parallel steps dominates, a collapsed phase when the binding of anti-parallel steps dominates, and a free (open coil) phase. We show that the system features a first-order phase transition from the free phase to the tight-spiral phase, while both other transitions are continuous. The location of the phases is determined accurately. We also study turning numbers and gamma exponents in various regions of the phase diagram.

cond-mat↗

arXiv1997

Monte Carlo simulation of ice models

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models.

cond-mat.stat-mech↗

arXiv1997

New Monte Carlo algorithms for classical spin systems

We describe a number of recently developed cluster-flipping algorithms for the efficient simulation of classical spin models near their critical temperature. These include the algorithms of Wolff, Swendsen and Wang, and Niedermeyer, as well as the limited cluster algorithm, the multigrid methods of Kandel and co-workers, and the invaded cluster algorithm. We describe the application of these algorithms to Ising, Potts, and continuous spin models. This paper is a review to appear in "Monte Carlo Methods in Chemical Physics", D. Ferguson, J. I. Siepmann, and D. G. Truhlar (eds.), Wiley, New York (1997).

cond-mat↗

arXiv1997

Diffusion constant for the repton model of gel electrophoresis

The repton model is a simple model of the "reptation" motion by which DNA diffuses through a gel during electrophoresis. In this paper we show that the model can be mapped onto a system consisting of two types of particles with hard-sphere interactions diffusing on a one-dimensional lattice. Using this mapping we formulate an efficient Monte Carlo algorithm for the model which allows us to simulate systems more than twice the size of those studied before. Our results confirm scaling hypotheses which have previously been put forward for the model. We also show how the particle version of the model can be used to construct a transfer matrix which allows us to solve exactly for the diffusion constant of small repton systems. We give results for systems of up to 20 reptons.

cond-mat.soft↗

arXiv1996

The repton model of gel electrophoresis

We discuss the repton model of agarose gel electrophoresis of DNA. We review previous results, both analytic and numerical, as well as presenting a new numerical algorithm for the efficient simulation of the model, and suggesting a new approach to the model's analytic solution.

cond-mat.soft↗