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.Comment: 5 pages, 5 figures, submitted to J. Chem. Phy

Universality class of the pair contact process with diffusion

The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2), beta=0.28(2) and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that PCPD falls in the same universality class as DP.Comment: 8 pages, 8 figures, accepted by Phys. Rev. E (not yet published

Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems

The dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high-dimensional space with fixed hypercylindrical scatterers with specific orientations and positions. In this paper, the similarities in the Lyapunov exponents are investigated between systems of many particles and high-dimensional billiards with cylindrical scatterers which have isotropically distributed orientations and homogeneously distributed positions. The dynamics of the isotropic billiard are calculated using a Monte-Carlo simulation, and a reorthogonalization process is used to find the Lyapunov exponents. The results are compared to numerical results for systems of many hard particles as well as the analytical results for the high-dimensional Lorentz gas. The smallest three-quarters of the positive exponents behave more like the exponents of hard-disk systems than the exponents of the Lorentz gas. This similarity shows that the hard-disk systems may be approximated by a spatially homogeneous and isotropic system of scatterers for a calculation of the smaller Lyapunov exponents, apart from the exponent associated with localization. The method of the partial stretching factor is used to calculate these exponents analytically, with results that compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR

Binary continuous random networks

Many properties of disordered materials can be understood by looking at idealized structural models, in which the strain is as small as is possible in the absence of long-range order. For covalent amorphous semiconductors and glasses, such an idealized structural model, the continuous-random network, was introduced 70 years ago by Zachariasen. In this model, each atom is placed in a crystal-like local environment, with perfect coordination and chemical ordering, yet longer-range order is nonexistent. Defects, such as missing or added bonds, or chemical mismatches, however, are not accounted for. In this paper we explore under which conditions the idealized CRN model without defects captures the properties of the material, and under which conditions defects are an inherent part of the idealized model. We find that the density of defects in tetrahedral networks does not vary smoothly with variations in the interaction strengths, but jumps from close-to-zero to a finite density. Consequently, in certain materials, defects do not play a role except for being thermodynamical excitations, whereas in others they are a fundamental ingredient of the ideal structure.Comment: Article in honor of Mike Thorpe's 60th birthday (to appear in J. Phys: Cond Matt.

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.Comment: 7 pages, 2 postscript figure

Event-based relaxation of continuous disordered systems

A computational approach is presented to obtain energy-minimized structures in glassy materials. This approach, the activation-relaxation technique (ART), achieves its efficiency by focusing on significant changes in the microscopic structure (events). The application of ART is illustrated with two examples: the structure of amorphous silicon, and the structure of Ni80P20, a metallic glass.Comment: 4 pages, revtex, epsf.sty, 3 figure

Universality in the pair contact process with diffusion

The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time or of system length and extrapolate asymptotically towards values consistent with the directed percolation universality class. We argue that an intermediate regime exists where the effective critical dynamics resembles that of a parity conserving process.Comment: 8 Pages, 9 figures, final version as publishe

Towards device-size atomistic models of amorphous silicon

The atomic structure of amorphous materials is believed to be well described by the continuous random network model. We present an algorithm for the generation of large, high-quality continuous random networks. The algorithm is a variation of the "sillium" approach introduced by Wooten, Winer, and Weaire. By employing local relaxation techniques, local atomic rearrangements can be tried that scale almost independently of system size. This scaling property of the algorithm paves the way for the generation of realistic device-size atomic networks.Comment: 7 pages, 3 figure

Equilibrium crystal shapes in the Potts model

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of $q$. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing $q$, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR