Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Simulations of lattice animals and trees

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is {\it not} the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. In addition to the partition sum (number of different animals) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is {\it not} very efficient for the `classical' model for collapsing animals.Comment: 17 pages RevTeX, 29 figures include

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe

On directed interacting animals and directed percolation

We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable animals) as special cases and its collapse transition is equivalent to a directed bond percolation threshold. Precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n=17. The crossover region in the vicinity of the collapse transition is analyzed in detail and the crossover exponent $\phi$ is determined directly from the singular part of the free energy. We show using scaling arguments and an exact relation due to Dhar that $\phi$ is equal to the Fisher exponent $\sigma$ governing the size distribution of large directed percolation clusters.Comment: 23 pages, 3 figures; J. Phys. A 35 (2002) 272

Random Walks with Long-Range Self-Repulsion on Proper Time

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in good agreement with Monte Carlo simulations in two dimensions. A numerical study of the scaling functions and of the efficiency of the algorithm is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included) IFUP-Th 13/92 and SNS 14/9

Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

We evaluate the virial coefficients B_k for k<=10 for hard spheres in dimensions D=2,...,8. Virial coefficients with k even are found to be negative when D>=5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D>=5. Further analysis provides evidence that negative virial coefficients will be seen for some k>10 for D=4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D=3.Comment: 33 pages, 12 figure

Afrikaans as Standaard Gemiddelde Europees:Wanneer ‘n lid uit sy taalarea beweeg

A recent trend in the study of Standard Average European is the extraterritorial perspective of examining the extent to which non-European languages have converged with this Sprachbund as a result of contact with one or more of its members. The present article complements this line of research in that it investigates the extent to which a European language has diverged from Standard Average European after leaving the linguistic area. The focus is on Dutch, a nuclear member of the Sprachbund, and Afrikaans, its colonial offshoot. The two languages are compared with respect to twelve of the most distinctive linguistic features of Standard Average European. Afrikaans is found to share ten of them with Dutch, including anticausative prominence and formally distinguished intensifiers and reflexives, and could therefore still be considered a core member of the Sprachbund, despite deviations in the expression of negative pronouns and the grammaticality of external possessor constructions. This relatively low degree of divergence may be attributed to the continuity from Settler Dutch to at least the variety of Afrikaans on which the standard language is based and to the important role that Dutch continued to play in the history of Afrikaans

Parallel Excluded Volume Tempering for Polymer Melts

We have developed a technique to accelerate the acquisition of effectively uncorrelated configurations for off-lattice models of dense polymer melts which makes use of both parallel tempering and large scale Monte Carlo moves. The method is based upon simulating a set of systems in parallel, each of which has a slightly different repulsive core potential, such that a thermodynamic path from full excluded volume to an ideal gas of random walks is generated. While each system is run with standard stochastic dynamics, resulting in an NVT ensemble, we implement the parallel tempering through stochastic swaps between the configurations of adjacent potentials, and the large scale Monte Carlo moves through attempted pivot and translation moves which reach a realistic acceptance probability as the limit of the ideal gas of random walks is approached. Compared to pure stochastic dynamics, this results in an increased efficiency even for a system of chains as short as $N = 60$ monomers, however at this chain length the large scale Monte Carlo moves were ineffective. For even longer chains the speedup becomes substantial, as observed from preliminary data for $N = 200$

Revival of the magnetar PSR J1622-4950: observations with MeerKAT, Parkes, XMM-Newton, Swift, Chandra, and NuSTAR

New radio (MeerKAT and Parkes) and X-ray (XMM-Newton, Swift, Chandra, and NuSTAR) observations of PSR J1622-4950 indicate that the magnetar, in a quiescent state since at least early 2015, reactivated between 2017 March 19 and April 5. The radio flux density, while variable, is approximately 100x larger than during its dormant state. The X-ray flux one month after reactivation was at least 800x larger than during quiescence, and has been decaying exponentially on a 111+/-19 day timescale. This high-flux state, together with a radio-derived rotational ephemeris, enabled for the first time the detection of X-ray pulsations for this magnetar. At 5%, the 0.3-6 keV pulsed fraction is comparable to the smallest observed for magnetars. The overall pulsar geometry inferred from polarized radio emission appears to be broadly consistent with that determined 6-8 years earlier. However, rotating vector model fits suggest that we are now seeing radio emission from a different location in the magnetosphere than previously. This indicates a novel way in which radio emission from magnetars can differ from that of ordinary pulsars. The torque on the neutron star is varying rapidly and unsteadily, as is common for magnetars following outburst, having changed by a factor of 7 within six months of reactivation.Comment: Published in ApJ (2018 April 5); 13 pages, 4 figure