Semiclassical Theory of Inelastic Collisions II. Momentum Space Formulation

The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation. Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed

Pelvic trauma : WSES classification and guidelines

Complex pelvic injuries are among the most dangerous and deadly trauma related lesions. Different classification systems exist, some are based on the mechanism of injury, some on anatomic patterns and some are focusing on the resulting instability requiring operative fixation. The optimal treatment strategy, however, should keep into consideration the hemodynamic status, the anatomic impairment of pelvic ring function and the associated injuries. The management of pelvic trauma patients aims definitively to restore the homeostasis and the normal physiopathology associated to the mechanical stability of the pelvic ring. Thus the management of pelvic trauma must be multidisciplinary and should be ultimately based on the physiology of the patient and the anatomy of the injury. This paper presents the World Society of Emergency Surgery (WSES) classification of pelvic trauma and the management Guidelines.Peer reviewe

NON-ADIABATIC ELASTIC SCATTERING

Author Institution: Department of Chemistry, Massachusetts Institute of TechnologyElastic scattering of high energy (0.5-1.0 keV relative energy) atomic and molecular beams has been extensively used as an experimental method for determining interaction potentials of the order of 1.0 to 10 eV. Measurements of the total cross-section for scattering at angles greater than an effective detector aperture (about $10^{-2}$ radians), as a function of relative energy, yield information about the scattering potential on the assumption that it is invariant to the beam velocity (adiabatic approximation). A previous study showed that under the experimental conditions the high angular momentum in the ``typical'' collision leads to significant Coriolis shifts in the effective potential, and these shifts were estimated by simple calculations for the $He_{2}$ system (for which a serious discrepancy of 10 eV at 0.5 A between adiabatic theory and experimental values exists); the calculated shifts were about 25% of the discrepancy. The present work reports the results from: a) An elaborate study of the Coriolis shifts in the analogous problem of scattering in the repulsive state of $H_{2}$; since the effect is a one-electron effect, analogy with $He_{2}$ should be approximately valid. It is concluded that the simple type of calculations made for $He_{2}$ suffice to include almost all of the Coriolis effects. b) A more critical study of the theory of potentials for elastic scattering in the conditions of interest, in order to more firmly establish the validity of the Coriolis shift calculations. c) Analysis of elastic scattering with velocity-dependent potentials. The results are rather surprising, showing that the scattering ``amplifies'' the velocity dependence (due mainly to Coriolis shifts) so that if routine analysis of cross-sections as function of energy is made, the potentials inferred may differ from adiabatic theory by quantities of the order of several times larger than the actual velocity-dependent shifts themselves. Numerical calculations are presented for $H_{2}$ and some estimates made for $He_{2}$

NON-ADIABATIC EFFECTS IN THE HIGH-ENERGY SCATTERING OF NORMAL HELIUM ATOMS

Author Institution: Department of Chemistry, Massachusetts Institute of Technology“There is a large discrepancy $(\sim 9$ e.v.) between the calculated adiabatic electronic energy of the ground state $(X^{1} \Sigma_{g}^{+})$ of the system $He_{2}$ and the effective scattering potential deduced from experiments with high-energy (2 kev) atomic helium beams, at small interatomic distances (0.53 Angstrom). A theory of the potential including non-adiabacity is presented: the non-adiabacity arises from the high angular momentum of the ``measuring collisions’’. Perturbation theory is employed to give an estimate of the magnitude of non-adiabacity in agreement with the experimental discrepancy at 0.53 {\AA} and to predict the observed agreement of adiabatic theory and experiment at 1.06 {\AA}. A variational calculation is presented which gives about 25% of the discrepancy by inclusion of only a few discrete states. A pseudo-Hamiltonian is introduced as a means of including virtual continuum contributions, which are very important, and a description is given of calculations now under way to include the continuum. It is hoped that most of the discrepancy can be calculated variationally.

THE VALENCE-BOND METHOD FOR LATTICE ELECTRON STUDIES

$^{1}$ L. F. Mattheiss, Phys. Rev. 123, 1209 (1961). $^{2}$ J. W. Moskowitz, J. Chem. Phys. 37, 677 (1962).Author Institution: Department of Chemistry, Massachusetts Institute of TechnologyIn a model lattice with one electron per atom the band theory gives an adequate description for the electron behavior only at small lattice spacings. At very large separations the lowest state corresponds to electrons localized on individual atoms. The transition between these limiting cases is of great interest to the theory of solids and of conjugated molecules. Most critical studies on this problem have been restricted to finite lattices of hydrogen atoms as the model systems, with most attention fixed to date on the 2N-membered rings. The hexagonal $H_{6}$ ring has been studied completely; a full configuration interaction study was made by $Mattheiss^{1}$ and the ``alternant molecular orbital'' study by $Moskowitz^{2}$. Mattheiss' calculation may be regarded as the ``exact'' results by which other methods may be evaluated. The valence-bond method has never been applied to problems of lattices because of the large number of canonical singlets which are in full resonance. On the other hand it is physically realistic, emphasizing localization and correlation of nearest neighbor electrons. We have employed the valence-bond method as a partial description of the wave function for model lattices, working out the energy expressions using a) orthogonal atomic orbitals, b) ionic character in each pair bond (the same in every bond), c) ``nearest neighbor bonds only''. For the 2N-membered rings this restricts the VB set to the $Kekul\'{e}$ structures. In order to represent true delocalization of electrons, dominant at short distances, the lowest molecular orbital wave function was also included. With such a simple three-term wave function, with one variable parameter (ionic character in the VB terms) we obtained lower energies for the ground singlet in $H_{6}$ than any other calculation except that of Mattheiss. The method has significant advantages in comparison with the ``alternant m. o.'' method, and is not identical to it. We believe it brings some rather helpful physical insight into the treatment of the lattice problem. Extension of the method to other model systems and possible implications of our results to date are discussed

Ontogenetic spatial distributions of red grouper (Epinephelus morio) and gag grouper (Mycteroperca microlepis) in the U.S. Gulf of Mexico

•We developed statistical models for red and gag grouper juveniles and adults.•Predictions concur with understanding of grouper distributions in the Gulf of Mexico.•Our approach identified potential spawning grounds for gag grouper.•Our study will help improve the maps fed into ecosystem models of the Gulf of Mexico. Mapping the spatial distributions of fish populations is an integral component of ecosystem-based fisheries management (EBFM). Particularly for red grouper (Epinephelus morio) and gag grouper (“gag”; Mycteroperca microlepis), two economically important species, the lack of mapping due to data limitations (i.e., inconsistent capture in research surveys) has left a critical gap in the science needed to assess how ecosystem processes and EBFM measures in the Gulf of Mexico (GOM) impact their population dynamics. We combined multiple fisheries-dependent and fisheries-independent data sources to map the long-term spatial distributions of older juveniles and adults of red and gag groupers in the U.S. GOM, using spatio-temporal binomial generalized linear mixed models (GLMMs). Spatio-temporal binomial GLMMs rely on the idea that probability of encounter at a given site is more similar to probability of encounter at nearby sites than to probability of encounter at geographically remote locations; this tenet allows one to estimate a smoothed surface depicting how probability of encounter varies spatially. Our spatio-temporal binomial GLMMs do not integrate environmental covariates, yet they account for the effects of year and research survey. The distribution maps produced from the predictions of the spatio-temporal binomial GLMMs aligned with the current understanding of the long-term ontogenetic spatial distributions of red and gag groupers in the U.S. GOM. Red grouper was predicted to be encountered throughout the West Florida Shelf (WFS), primarily at depths ranging from 20 to 60m. Both older juvenile and adult female gags were predicted to be encountered from Apalachicola, Florida, to the region northwest of Tampa, Florida, along the 20m depth contour, especially in Apalachee Bay. The probability of encounter of adult female gag was also high in the Florida Middle Grounds and in deeper (>40m) areas of the WFS. The probability of encounter of adult male gag was highest along the edge of the WFS, both inside recognized spawning grounds (including the Madison-Swanson marine protected area) and outside, i.e., below 27°N (including Pulley Ridge). The distribution maps produced are valuable for understanding the ecology of grouper species and can be used as a basis for further analyses. Our spatio-temporal binomial GLMM framework will serve many important EBFM projects, including the construction of reliable distribution maps in bulk for spatially explicit ecosystem models of the GOM, which will improve spatial distributions and species spatial overlaps in spatially explicit ecosystem models and, therefore, the trophic interactions predicted by these models