New results for virial coefficients of hard spheres in D dimensions

We present new results for the virial coefficients B_k with k <= 10 for hard spheres in dimensions D=2,...,8.Comment: 10 pages, 5 figures, to appear in conference proceedings of STATPHYS 2004 in Pramana - Journal of Physic

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

Making Institutions Work for Women

Aruna Rao looks at how change is happening through the daily grind of gender equality activists. She argues that in order to achieve basic development objectives we need both better delivery and better accountability for a range services to women – not just education and health, but also agricultural extension, land registration and property protection, regulation of labour markets, and safety. She also argues that institutional insiders and outsiders need to support each others’ different but complementary roles as change agents. Development (2006) 49, 63–67. doi:10.1057/palgrave.development.1100207