A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.Comment: 17 pages, 8 figures, IoP style file

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

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics

Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure

Historical changes in the stomatal limitation of photosynthesis: empirical support for an optimality principle

The ratio of leaf‐internal (ci) to ambient (ca) partial pressure of CO2, defined here as χ, is an index of adjustments in both leaf stomatal conductance and photosynthetic rate to environmental conditions. Measurements and proxies of this ratio can be used to constrain vegetation models uncertainties for predicting terrestrial carbon uptake and water use. We test a theory based on the least‐cost optimality hypothesis for modelling historical changes in χ over the 1951‐2014 period, across different tree species and environmental conditions, as reconstructed from stable carbon isotopic measurements across a global network of 103 absolutely‐dated tree‐ring chronologies. The theory predicts optimal χ as a function of air temperature, vapour pressure deficit, ca and atmospheric pressure. The theoretical model predicts 39% of the variance in χ values across sites and years, but underestimates the inter‐site variability in the reconstructed χ trends, resulting in only 8% of the variance in χ trends across years explained by the model. Overall, our results support theoretical predictions that variations in χ are tightly regulated by the four environmental drivers. They also suggest that explicitly accounting for the effects of plant‐available soil water and other site‐specific characteristics might improve the predictions

Tree-ring isotopes suggest atmospheric drying limits temperature–growth responses of treeline bristlecone pine

Altitudinally separated bristlecone pine populations in the White Mountains (California, USA) exhibit differential climate-growth responses as temperature and tree-water relations change with altitude. These populations provide a natural experiment to explore the ecophysiological adaptations of this unique tree species to the twentieth century climate variability. We developed absolutely dated annual ring-width chronologies, and cellulose stable carbon and oxygen isotope chronologies from bristlecone pine growing at the treeline (~3500 m) and ~200 m below for the period AD 1710-2010. These chronologies were interpreted in terms of ecophysiological adaptations to climate variability with a dual-isotope model and a leaf gas exchange model. Ring widths show positive tree growth anomalies at treeline and consistent slower growth below treeline in relation to the twentieth century warming and associated atmospheric drying until the 1980s. Growth rates of both populations declined during and after the 1980s when growing-season temperature and atmospheric vapour pressure deficit continued to increase. Our model-based interpretations of the cellulose stable isotopes indicate that positive treeline growth anomalies prior to the 1980s were related to increased stomatal conductance and leaf-level transpiration and photosynthesis. Reduced growth since the 1980s occurred with a shift to more conservative leaf gas exchange in both the treeline and below-treeline populations, whereas leaf-level photosynthesis continued to increase in response to rising atmospheric CO2 concentrations. Our results suggest that warming-induced atmospheric drying confounds positive growth responses of apparent temperature-limited bristlecone pine populations at treeline. In addition, the observed ecophysiological responses of attitudinally separated bristlecone pine populations illustrate the sensitivity of conifers to climate change