Long-range interactions in the ozone molecule: spectroscopic and dynamical points of view

Using the multipolar expansion of the electrostatic energy, we have characterized the asymptotic interactions between an oxygen atom O$(^3P)$ and an oxygen molecule O$_2(^3\Sigma_g^-)$, both in their electronic ground state. We have calculated the interaction energy induced by the permanent electric quadrupoles of O and O$_2$ and the van der Waals energy. On one hand we determined the 27 electronic potential energy surfaces including spin-orbit connected to the O$(^3P)$ + O$_2(^3\Sigma_g^-)$ dissociation limit of the O--O$_2$ complex. On the other hand we computed the potential energy curves characterizing the interaction between O$(^3P)$ and a O$_2(^3\Sigma_g^-)$ molecule in its lowest vibrational level and in a low rotational level. Such curves are found adiabatic to a good approximation, namely they are only weakly coupled to each other. These results represent a first step for modeling the spectroscopy of ozone bound levels close to the dissociation limit, as well as the low energy collisions between O and O$_2$ thus complementing the knowledge relevant for the ozone formation mechanism.Comment: Submitted to J. Chem. Phys. after revisio

Minimum time aircraft trajectories between two points in range altitude space

Calculus of variations used to determine minimum time aircraft trajectories between two fixed points in range-altitude spac

Limit points in the range of the commuting probability function on finite groups

If G is a finite group, then Pr(G) denotes the fraction of ordered pairs of elements of G which commute. We show that, if l \in (2/9,1] is a limit point of the function Pr on finite groups, then l \in \Q and there exists an e = e_l > 0 such that Pr(G) \not\in (l - e_l, l) for any finite group G. These results lend support to some old conjectures of Keith Joseph.Comment: 11 pages, no figure

Complexity and line of critical points in a short-range spin-glass model

We investigate the critical behavior of a three-dimensional short-range spin glass model in the presence of an external field \eps conjugated to the Edwards-Anderson order parameter. In the mean-field approximation this model is described by the Adam-Gibbs-DiMarzio approach for the glass transition. By Monte Carlo numerical simulations we find indications for the existence of a line of critical points in the plane (\eps,T) which separates two paramagnetic phases and terminates in a critical endpoint. This line of critical points appears due to the large degeneracy of metastable states present in the system (configurational entropy) and is reminiscent of the first-order phase transition present in the mean-field limit. We propose a scenario for the spin-glass transition at \eps=0, driven by a spinodal point present above $T_c$, which induces strong metastability through Griffiths singularities effects and induces the absence of a two-step shape relaxation curve characteristic of glasses.Comment: 5 pages, 4 postscript figure, revte

A renormalisation group approach to two-body scattering in the presence of long-range forces

We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible fixed points of the short-range potential as this cut-off is lowered to zero. The expansions around these fixed points define the power countings for the corresponding effective field theories. Expansions around nontrivial fixed points are shown to correspond to distorted-wave versions of the effective-range expansion. These methods are applied to scattering in the presence of Coulomb, Yukawa and repulsive inverse-square potentials.Comment: 22 pages (RevTeX), 4 figure

On non-round points of the boundary of the numerical range and an application to non-selfadjoint Schr\"odinger operators

We show that non-round boundary points of the numerical range of an unbounded operator (i.e. points where the boundary has infinite curvature) are contained in the spectrum of the operator. Moreover, we show that non-round boundary points, which are not corner points, lie in the essential spectrum. This generalizes results of H\"ubner, Farid, Spitkovsky and Salinas and Velasco for the case of bounded operators. We apply our results to non-selfadjoint Schr\"odinger operators, showing that in this case the boundary of the numerical range can be non-round only at points where it hits the essential spectrum.Comment: Shortened version. To appear in Journal of Spectral Theor

Connecting species’ geographical distributions to environmental variables: range maps versus observed points of occurrence

Connecting the geographical occurrence of a species with underlying environmental variables is fundamental for many analyses of life history evolution and for modeling species distributions for both basic and practical ends. However, raw distributional information comes principally in two forms: points of occurrence (specific geographical coordinates where a species has been observed), and expert-prepared range maps. Each form has potential short-comings: range maps tend to overestimate the true occurrence of a species, whereas occurrence points (because of their frequent non-random spatial distribution) tend to underestimate it. Whereas previous comparisons of the two forms have focused on how they may differ when estimating species richness, less attention has been paid to the extent to which the two forms actually differ in their representation of a species’ environmental associations. We assess such differences using the globally distributed avian order Galliformes (294 species). For each species we overlaid range maps obtained from IUCN and point-of-occurrence data obtained from GBIF on global maps of four climate variables and elevation. Over all species, the median difference in distribution centroids was 234 km, and median values of all five environmental variables were highly correlated, although there were a few species outliers for each variable. We also acquired species’ elevational distribution mid-points (mid-point between minimum and maximum elevational extent) from the literature; median elevations from point occurrences and ranges were consistently lower (median −420 m) than mid-points. We concluded that in most cases occurrence points were likely to produce better estimates of underlying environmental variables than range maps, although differences were often slight. We also concluded that elevational range mid-points were biased high, and that elevation distributions based on either points or range maps provided better estimates

Optimal Color Range Reporting in One Dimension

Color (or categorical) range reporting is a variant of the orthogonal range reporting problem in which every point in the input is assigned a \emph{color}. While the answer to an orthogonal point reporting query contains all points in the query range $Q$, the answer to a color reporting query contains only distinct colors of points in $Q$. In this paper we describe an O(N)-space data structure that answers one-dimensional color reporting queries in optimal $O(k+1)$ time, where $k$ is the number of colors in the answer and $N$ is the number of points in the data structure. Our result can be also dynamized and extended to the external memory model

Phase diagrams and free-energy landscapes for model spin-crossover materials with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions

We present phase diagrams, free-energy landscapes, and order-parameter distributions for a model spin-crossover material with a two-step transition between the high-spin and low-spin states (a square-lattice Ising model with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions) [P. A. Rikvold et al., Phys. Rev. B 93, 064109 (2016)]. The results are obtained by a recently introduced, macroscopically constrained Wang-Landau Monte Carlo simulation method [C. H. Chan, G. Brown, and P. A. Rikvold, Phys. Rev. E 95, 053302 (2017)]. The method's computational efficiency enables calculation of thermodynamic quantities for a wide range of temperatures, applied fields, and long-range interaction strengths. For long-range interactions of intermediate strength, tricritical points in the phase diagrams are replaced by pairs of critical end points and mean-field critical points that give rise to horn-shaped regions of metastability. The corresponding free-energy landscapes offer insights into the nature of asymmetric, multiple hysteresis loops that have been experimentally observed in spin-crossover materials characterized by competing short-range interactions and long-range elastic interactions.Comment: 35 pages, 20 figure