Quantifying density fluctuations in water at a hydrophobic surface: evidence for critical drying

Employing smart Monte Carlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility $\chi(z)$, increase rapidly for distances $z$ within $1$ or $2$ molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle $\theta$, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: $\cos(\theta)\to -1$. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations

On some properties of the water-vapor spectrum and their relations to atmospheric radiation

In the present paper we investigate the physical consequences of the fact that the water vapor spectrum in the far infrared consists of a large number of narrow lines. It will be shown that the average width of these lines is much smaller than the intervals which could be resolved with the spectrographs used hitherto. For thick layer of vapor complete absorption is nevertheless reached in most parts of the spectrum. It can be shown that under such circumstances the total absorption is approximately proportional to the air pressure in the absorbing layers and is inversely proportional to the square root of the absolute temperature. There is an additional variation with temperature of a more complex type which cannot yet be quantitatively evaluated from the available measurements, but it is probably not very large

A Phylogenetic Analysis of the African Plant Genus Palisota (family Commelinaceae) based on Chloroplast DNA Sequences

The plant genus Palisota (family Commelinaceae, or spiderwort family) consists of approximately 20 species and is distributed throughout the forests of tropical Africa. The genus exhibits several unusual morphological characteristics, and as a result has been difficult to classify based on morphology. Molecular phylogenetic studies have placed it near the base of Commelinaceae, but the exact placement of Palisota within the family is not clear. As the African continent has become more arid in recent geological times, the forests have receded, reducing the habitat for Palisota species and potentially impacting speciation and extinction rates within the genus. The goal of this study is to sequence the chloroplast-encoded gene rbcL in several additional species of Palisota and its relatives in order to: 1) determine the phylogenetic relationship of the genus with respect to other members of Commelinaceae; 2) evaluate phylogenentic relationships among species of Palisota; and 3) infer relative speciation/extinction rates within the genus. Additionally, we are exploring the use of other molecular regions for phylogenetic analysis with the genus

On some fundamental results about higher-rank graphs and their C*-algebras

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated to a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph {\Lambda} is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of infinite-path spaces when the k-graph is row finite with no sources. We conclude with a short direct proof of the characterisation, originally due to Robertson and Sims, of simplicity of the C*-algebra of a row-finite k-graph with no sources.Comment: 21 pages, two pictures prepared using TiK

Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of accurate simulation results with theory

We report a detailed study, using state-of-the-art simulation and theoretical methods, of the depletion potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q=\sigma_s/\sigma_b. Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir, \eta_s^r. Two specialized Monte Carlo simulation schemes --the geometrical cluster algorithm, and staged particle insertion-- are deployed to obtain accurate depletion potentials for a number of combinations of q\leq 0.1 and \eta_s^r. After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely \eta_s^r=0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this \eta_s^r. The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small sphere packing fractions that we consider. The effective potentials from simulation, DFT and the morphometric approximation were used to compute the second virial coefficient B_2 as a function of \eta_s^r. Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity towards fluid fluid phase separation in additive binary hard sphere mixtures with q\leq 0.1.Comment: 16 pages, 9 figures, revised treatment of morphometric approximation and reordered some materia

Understanding the physics of hydrophobic solvation

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations.The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones (LJ) solvent and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e.~as the solute radius $R_s\to\infty$. Focusing on the radial density profile $\rho(r)$ and a sensitive spatial measure of fluctuations, the local compressibility profile $\chi(r)$, our binding potential analysis provides explicit predictions for the manner in which the key features of $\rho(r)$ and $\chi(r)$ scale with $R_s$, the strength of solute-water attraction $\varepsilon_{sf}$, and the deviation from liquid-vapor coexistence of the chemical potential, $\delta\mu$. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such our theory provides a firm basis for understanding the physics of hydrophobic solvation.Comment: 18 page

Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics

We investigate the origin of the density depletion and enhanced density fluctuations that occur in water in the vicinity of an extended hydrophobic solute. We argue that both phenomena are remnants of the critical drying surface phase transition that occurs at liquid-vapor coexistence in the macroscopic planar limit, ie. as the solute radius $R_s\to\infty$. Focusing on the density profile $\rho(r)$ and a sensitive spatial measure of fluctuations, the local compressibility profile $\chi(r)$, we develop a scaling theory which expresses the extent of the density depletion and enhancement in compressibility in terms of $R_s$, the strength of solute-water attraction $\varepsilon_s$, and the deviation from liquid-vapor coexistence $\delta\mu$. Testing the predictions against results of classical density functional theory for a simple solvent and Grand Canonical Monte Carlo simulations of a popular water model, we find that the theory provides a firm physical basis for understanding how water behaves at a hydrophobe.Comment: 5 pages, 4 figures. To appear in Phys. Rev. Let

Factors Associated with the Enactment of Safety Belt and Motorcycle Helmet Laws.

It has been shown that road safety laws, such as motorcycle helmet and safety belt laws, have a significant effect in reducing road fatalities. Although an expanding body of literature has documented the effects of these laws on road safety, it remains unclear which factors influence the likelihood that these laws are enacted. This study attempts to identify the factors that influence the decision to enact safety belt and motorcycle helmet laws. Using panel data from 31 countries between 1963 and 2002, our results reveal that increased democracy, education level, per capita income, political stability, and more equitable income distribution within a country are associated with the enactment of road safety laws