An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.

Influence of a Counterion on the Ion Atmosphere of an Anion: A Molecular Dynamics Study of LiX and CsX (X = F-, Cl-, I-) in Methanol

We report molecular dynamics (MD) simulations to explore the influence of a counterion on the structure and dynamics of cationic and anionic solvation shells for various ions in methanol at 298 K. We show that the variation in ionic size of either the cation or the anion in an ion pair influences the solvation structure of the other ion as well as the diffusivity in an electrolyte solution of methanol. The extent of ionic association between the cation and its counteranion of different ionic sizes has been investigated by analyzing the radial distribution functions (RDFs) and the orientation of methanol molecules in the first solvation shell (FSS) of ions. It is shown that the methanol in the FSS of the anion as well the cation exhibit quite different radial and orientational structures as compared to methanol which lie in the FSS of either the anion or the cation but not both. We find that the coordination number (CN) of F-, Cr-, and I- ions decreases with increasing size of the anion which is contrary to the trend reported for the anions in H2O. The mean residence time (MRT) of methanol molecules in the FSS of ions has been calculated using the stable states picture (SSP) approach. It is seen that the ion-counterion interaction has a considerable influence on the MRT of methanol molecules in the FSS of ions. We also discuss the stability order of the ion-counterion using the potentials of mean force (PMFs) for ion pairs with ions of different sizes. The PMF plots reveal that the Li+-F- pair (small-small) is highly stable and the Li+-I- pair is least stable (small-large) in electrolyte solutions.

Onset of plane layer magnetoconvection at low Ekman number

We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth's tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra-c and critical wavenumber a(c) are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number. (ratio of the Lorentz force to the Coriolis force). E is varied from 10(-9) to 10(-2) and. from 10(-3) to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E-one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E < 10(-6) and establish a map in the (E, Lambda) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal. (C) 2015 AIP Publishing LLC.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.