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.Comment: 19 pages, 2 figure

Partitioning 3D space for parallel many-particle stimulations

In a common approach for parallel processing applied to simulations of manyparticle systems with short-ranged interactions and uniform density, the simulation cell is partitioned into domains of equal shape and size, each of which is assigned to one processor. We compare the commonly used simple-cubic (SC) domain shape to domain shapes chosen as the Voronoi cells of BCC and FCC lattices. The latter two are found to result in superior partitionings with respect to communication overhead. Other domain shapes, relevant for a small number of processors, are also discussed. The higher eciency with BCC and FCC partitionings is demonstrated in simulations of the sillium model for amorphous silicon

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.Comment: 17 pages including 6 PostScript figures, typeset with LaTeX 2e using the Elsevier macro package elsart.cl

DNA electrophoresis studied with the cage model

The cage model for polymer reptation, proposed by Evans and Edwards, and its recent extension to model DNA electrophoresis, are studied by numerically exact computation of the drift velocities for polymers with a length L of up to 15 monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by a regime where the velocity decreases exponentially with the applied electric field strength. In agreement with de Gennes' reptation arguments, we find that asymptotically for large polymers the diffusion coefficient D decreases quadratically with polymer length; for the cage model, the proportionality coefficient is DL^2=0.175(2). Additionally we find that the leading correction term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of kink representation approac

Energy landscape of relaxed amorphous silicon

We analyze the structure of the energy landscape of a well-relaxed 1000-atom model of amorphous silicon using the activation-relaxation technique (ART nouveau). Generating more than 40,000 events starting from a single minimum, we find that activated mechanisms are local in nature, that they are distributed uniformly throughout the model and that the activation energy is limited by the cost of breaking one bond, independently of the complexity of the mechanism. The overall shape of the activation-energy-barrier distribution is also insensitive to the exact details of the configuration, indicating that well-relaxed configurations see essentially the same environment. These results underscore the localized nature of relaxation in this material.Comment: 8 pages, 12 figure

An analysis of the fluctuations of the geomagnetic dipole

The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core.Comment: 11 pages, 6 figure

Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique

The potential energy surface (PES) of Lennard-Jones clusters is investigated using the activation-relaxation technique (ART). This method defines events in the configurational energy landscape as a two-step process: (a) a configuration is first activated from a local minimum to a nearby saddle-point and (b) is then relaxed to a new minimum. Although ART has been applied with success to a wide range of materials such as a-Si, a-SiO2 and binary Lennard-Jones glasses, questions remain regarding the biases of the technique. We address some of these questions in a detailed study of ART-generated events in Lennard-Jones (LJ) clusters, a system for which much is already known. In particular, we study the distribution of saddle-points, the pathways between configurations, and the reversibility of paths. We find that ART can identify all trajectories with a first-order saddle point leaving a given minimum, is fully reversible, and samples events following the Boltzmann weight at the saddle point.Comment: 8 pages, 7 figures in postscrip

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

DMRG studies of the effect of constraint release on the viscosity of polymer melts

The scaling of the viscosity of polymer melts is investigated with regard to the molecular weight. We present a generalization of the Rubinstein-Duke model, which takes constraint releases into account and calculate the effects on the viscosity by the use of the Density Matrix Renormalization Group (DMRG) algorithm. Using input from Rouse theory the rates for the constraint release are determined in a self consistent way. We conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity.Comment: 6 pages, 8 figure