Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions

We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest

A role for jasmonates in the release of dormancy by cold stratification in wheat

Hydration at low temperatures, commonly referred to as cold stratification, is widely used for releasing dormancy and triggering germination in a wide range of species including wheat. However, the molecular mechanism that underlies its effect on germination has largely remained unknown. Our previous studies showed that methyl-jasmonate, a derivative of jasmonic acid (JA), promotes dormancy release in wheat. In this study, we found that cold-stimulated germination of dormant grains correlated with a transient increase in JA content and expression of JA biosynthesis genes in the dormant embryos after transfer to 20 (o)C. The induction of JA production was dependent on the extent of cold imbibition and precedes germination. Blocking JA biosynthesis with acetylsalicylic acid (ASA) inhibited the cold-stimulated germination in a dose-dependent manner. In addition, we have explored the relationship between JA and abscisic acid (ABA), a well-known dormancy promoter, in cold regulation of dormancy. We found an inverse relationship between JA and ABA content in dormant wheat embryos following stratification. ABA content decreased rapidly in response to stratification, and the decrease was reversed by addition of ASA. Our results indicate that the action of JA on cold-stratified grains is mediated by suppression of two key ABA biosynthesis genes, TaNCED1 and TaNCED2.This project was funded by a CSIRO Office of the Chief Executive PDF scheme

Thermal Structure of Clear Lake, Iowa

Summer water temperatures in the shallow areas of Clear Lake were slightly higher and had a greater daily range than temperatures measured in the limnetic zone. The lake was not thermally stratified, although small differences sometimes were found between surface and bottom temperatures at the deepest point. Temperatures measured in the Clear Lake Water Treatment Plant were representative of those measured in the limnetic zone of the lake and provide a useful index of temperature conditions in the lake as a whole. The average annual temperature curve is asymmetrical, with the highest temperature falling on August 5 and the lowest occurring 119 days later on November 30. The median and mean lake temperatures were 51° and 53.7°F. The median date of ice breakup was April 3 and the median date of freezing was November 27

Logarithmic observables in critical percolation

Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1. The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters. In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly. We confirm its numerical value by extensive Monte-Carlo simulations.Comment: 11 pages, 2 figures. V2: as publishe

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

Dense loops, supersymmetry, and Goldstone phases in two dimensions

Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that this phase is generic for -2< N <2 when crossings of loops are allowed, and distinct from the model of non-crossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].Comment: RevTeX, 5 pages, 3 postscript figure