On the formation of current sheets in response to the compression or expansion of a potential magnetic field

The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089] that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite non-zero current.Comment: Accepted for publication in Ap

Carbohydrates in the North Sea during spring blooms of <i>Phaeocystis</i>: a specific fingerprint

Regional and temporal variation in the composition of water-soluble carbohydrates from Phaeocystis colonies sampled in the southern North Sea was small during spring 1994, except for a high variability in the contribution of glucose. Glucose is universally present in storage products of microalgae; the relative constancy of the carbohydrate pattern of the other monosaccharides suggests that these are part of the more refractory colony mucus. In all Phaeocystis samples arabinose dominated, followed by xylose (Belgian coast) or galactose and mannose (Dutch coast). Rhamnose, glucuronate and O-methylated sugars were present in lower amounts. The latter, always present in samples containing Phaeocystis, may be typical for North Sea strains. The sugar patterns we report here differ from those presented in the literature concerning Phaeocystis-derived material, and also from the sugar fingerprint in the preceding diatom bloom. The Phaeocystis mucus apparently behaves as particulate matter since it was retained on filters of over 1 um. This characteristic together with its refractory nature, typical of 'transparent exopolymer particles' (TEPs), must have consequences for the heterotrophic microbial community in terms of adherence and substrate availability

Scaling function and universal amplitude combinations for self-avoiding polygons

We analyze new data for self-avoiding polygons, on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function. The results imply universal amplitude combinations for all area moments and suggest that rooted self-avoiding polygons may satisfy a $q$-algebraic functional equation.Comment: 9 page

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

Punctured polygons and polyominoes on the square lattice

We use the finite lattice method to count the number of punctured staircase and self-avoiding polygons with up to three holes on the square lattice. New or radically extended series have been derived for both the perimeter and area generating functions. We show that the critical point is unchanged by a finite number of punctures, and that the critical exponent increases by a fixed amount for each puncture. The increase is 1.5 per puncture when enumerating by perimeter and 1.0 when enumerating by area. A refined estimate of the connective constant for polygons by area is given. A similar set of results is obtained for finitely punctured polyominoes. The exponent increase is proved to be 1.0 per puncture for polyominoes.Comment: 36 pages, 11 figure

Perimeter Generating Functions For The Mean-Squared Radius Of Gyration Of Convex Polygons

We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the generating functions. In all cases the size exponent $\nu=1$.Comment: 8 pages, 1 figur

Using environmental DNA for detection of Batrachochytrium salamandrivorans in natural water

Rapid, early, and reliable detection of invasive pathogenic microorganisms is essential in order to either predict or delineate an outbreak, and monitor appropriate mitigation measures. The chytrid fungus Batrachochytrium salamandrivorans is expanding in Europe, and infection with this fungus may cause massive mortality in urodelans (salamanders and newts). In this study, we designed and validated species‐specific primers and a probe for detection of B. salamandrivorans in water. In a garden pond in close proximity to the B. salamandrivorans index site in the Netherlands, B. salamandrivorans‐infected newts had been detected in 2015 and have been monitored since. In 2016 and 2017, no B. salamandrivorans was detected at this site, but in 2018 B. salamandrivorans flared up in this isolated pond which allowed validation of the technique in situ. We here present the development of an environmental DNA technique that successfully detects B. salamandrivorans DNA in natural waterbodies even at low concentrations. This technique may be further validated to play a role in B. salamandrivorans range delineation and surveillance in both natural waterbodies and in captive collections

Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 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