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

SAWdoubler: a program for counting self-avoiding walks

This article presents SAWdoubler, a package for counting the total number Z(N) of self-avoiding walks (SAWs) on a regular lattice by the length-doubling method, of which the basic concept has been published previously by us. We discuss an algorithm for the creation of all SAWs of length N, efficient storage of these SAWs in a tree data structure, and an algorithm for the computation of correction terms to the count Z(2N) for SAWs of double length, removing all combinations of two intersecting single-length SAWs. We present an efficient numbering of the lattice sites that enables exploitation of symmetry and leads to a smaller tree data structure; this numbering is by increasing Euclidean distance from the origin of the lattice. Furthermore, we show how the computation can be parallelised by distributing the iterations of the main loop of the algorithm over the cores of a multicore architecture. Experimental results on the 3D cubic lattice demonstrate that Z(28) can be computed on a dual-core PC in only 1 hour and 40 minutes, with a speedup of 1.56 compared to the single-core computation and with a gain by using symmetry of a factor of 26. We present results for memory use and show how the computation is made to fit in 4 Gbyte RAM. It is easy to extend the SAWdoubler software to other lattices; it is publicly available under the GNU LGPL license.Comment: 29 pages, 3 figure

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.

Біблійні концепти і проповідницька традиція української літератури (на прикладі концепту води)

Clinical mastitis (CM) can be caused by a wide variety of pathogens and a farmer has to start treatment before the actual causal pathogen is known. Knowing the Gram-status of CM cases would aid in the decision for the most appropriate treatment. By providing a probability distribution for the Gram-status, rather than only providing the most likely Gram-status, the involved uncertainty is visible for a farmer, thereby allowing a more informed treatment decision. The objective of this study was to examine the value of providing probability distributions for the Gram-status of CM cases to a farmer to take a more informed treatment decision. A naive Bayesian network (NBN) based on data from 274 Dutch dairy herds in which the occurrence of CM was recorded over an 18-month period was constructed. The dataset contained 3,534 CM cases, all classified accordingto their Gram-status. Two-third of the dataset was used for the construction and one-third was retained for validation. Information usually available at a dairy farm was included in the NBN under construction (parity, month in lactation, season of the year, quarter position, somatic cell count history and CM history, being sick or not, and color and texture of the milk). For getting insight in the quality of the constructed NBN, the accuracy was determined. The accuracy of classifying CM cases into Gram-positive or Gram-negative pathogens was 73%. Because only CM cases with a high probability for Gram-negative or Gram-positive pathogens will be considered for specific treatment, it was interesting to have a closer look at CM cases with probabilities > 0.90. We foundthat the accuracy of the classification increased with the calculated probability for Gram-negative or Gram-positive pathogens. The probability distributions for the Gram-status provide the farmer with considerable additional information about the most likely Gram-status of a CM case and the uncertainty involved

Fractals and dynamical chaos in a random 2D Lorentz gas with sinks

Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the asymptotic decay of the survival probability is exponential and characterized by an escape rate, which can be related to the average positive Lyapunov exponent and to the dimension of the fractal repeller of the system. For infinite systems, the survival probability obeys a stretched exponential law of the form P(c,t)~exp(-Ct^{1/2}). The transition between the two regimes is studied and we show that, for a given trap density, the non-integer dimension of the fractal repeller increases with the system size to finally reach the integer dimension of the phase space. Nevertheless, the repeller remains fractal. We determine the special scaling properties of this fractal.Comment: 40 pages, 10 figures, preprint for Physica