618 research outputs found
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 -state Potts model, forced into coexistence by
fixing the density of one state, is studied for , 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 . We found a roughening transition for each of
the numbers of states we studied, at temperatures that decrease with increasing
, 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
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