Correlated exponential functions in high precision calculations for diatomic molecules

Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation is found, which is suited for the numerical evaluation. Together with recurrence relations, it makes possible the calculation of the two-center two-electron integral with arbitrary powers of electron distances. Alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can be used in cases when recurrences lose stability. Separate analysis is devoted to molecular integrals with integer powers of interelectronic distances $r_{12}$ and the vanishing corresponding nonlinear parameter. Several methods of their evaluation are proposed.Comment: 26 pages, includes two tables with exemplary calculation

Model Analysis of Spillway and Stilling Basin of Porcupine Dam

Introduction: The Engineering Experiment Station at Utah State University was engaged by the Utah Water and Power Board to make a model analysis of the spillway and stilling basin of the Porcupine Dam. This dam will be located on the East Fork of Litle Bear River, just east of Avon, Utah. It will be approximately 650 feet long and 160 feet high, composed of zones earth fill with rock rip-rap facing. The spillway will have a reinforced concrete inlet section and the remainder of the chute and stilling basin will be excavated out of the rock and leck unlined. The design-flow and the elevation of the spillway crest were both determined by the Water and Power Board. The purpose of the model study was to design an economical spillway that would carry the design-flow with a minimum of head over the crest. Also, studies were made to determine whether or not there were danger of the toe of the dam being undermined by the swirling waters from the stilling basin. Several radically different designs were tested as were a number of variations in each design. Only part of these are detailed in this report. Pictures of the final design are included

Oxygen and blood flow: players in the pathogenesis of glaucoma

The increase of IOP in POAG is due an increased resistance of aqueous outflow through the trabecular meshwork (TM). The exact mechanisms leading to the corresponding changes in the TM are not yet known. We know, however, that all risk factors for arteriosclerosis are also risk factors for an increase in IOP. RESULTS: The association between IOP increase and these factors is relatively weak but nevertheless significant. Similar to the pathogenesis of arteriosclerosis, oxidative stress plays a role in the development of TM damage. Even less is known about the pathogenesis of glaucomatous optic neuropathy (GON). Obviously the risk factors for arteriosclerosis play a role via increasing the IOP. When corrected for IOP, however, these factors only play a minor role. In contrast, factors associated with disturbed autoregulation, in particular a systemic primary vascular dysregulation (PVD), increase the risk for GON. This is best observed in normal tension glaucoma patients. An insufficient autoregulation increases the chance for an unstable ocular perfusion and thereby an unstable oxygen supply. This, in turn, leads to oxidative stress. The concentration of superoxide (O(2)(-)) within the axons of the optic nerve head increases. If neighboring astrocytes are activated, either by mechanical or by ischemic stress, in excess produced nitric oxide (NO) molecules diffuse also into the axons and fuse with oxygen. The resulting peroxynitrat (ONOO(-)) diffuses within the axons towards the retina and the lateral geniculate nucleus and induces apoptosis

Corporate social responsibility as a defense against knowledge spillovers: evidence from the inevitable disclosure doctrine

Research Summary: We examine whether companies respond to the threat of knowledge leakage by strategically increasing their engagement in corporate social responsibility (CSR). To obtain exogenous variation in the threat of knowledge leakage, we exploit a natural experiment provided by the rejection of the inevitable disclosure doctrine (IDD) by several U.S. states. Using a difference-in-differences methodology we find that, following the rejection of the IDD, companies significantly increase their CSR. Our proposed rationale is that CSR helps mitigate knowledge leakage by i) reducing employees’ propensity to join a rival firm, and ii) reducing employees’ propensity to disclose the firm’s valuable knowledge even if they join a rival firm. Evidence from a laboratory experiment, an online experiment, and a survey of knowledge workers is supportive of these arguments. Managerial Summary: We study the role of CSR in companies’ response to the threat of knowledge leakage—a major managerial challenge that has important implications for firms’ innovation and competitiveness. We use three different research designs (an analysis of companies’ CSR policies in response to an increased threat of knowledge leakage; a survey of knowledge workers; and an experiment conducted both online and in a laboratory setting). The results show that CSR is perceived to mitigate the threat of knowledge leakage. In particular, i) CSR reduces knowledge workers’ propensity to join rival firms (i.e., they are less likely to “walk”) and, even if they do, ii) CSR reduces their propensity to disclose the firm’s valuable knowledge to their new employer (i.e., they are less likely to “talk”)

Weak Cosmic Censorship: As Strong as Ever

Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.Comment: 4 page

Breakup of the aligned H2_2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates

We have carried out calculations of the triple-differential cross section for one-photon double ionization of molecular hydrogen for a central photon energy of $75$~eV, using a fully {\it ab initio}, nonperturbative approach to solve the time-dependent \Schro equation in prolate spheroidal coordinates. The spatial coordinates $\xi$ and $\eta$ are discretized in a finite-element discrete-variable representation. The wave packet of the laser-driven two-electron system is propagated in time through an effective short iterative Lanczos method to simulate the double ionization of the hydrogen molecule. For both symmetric and asymmetric energy sharing, the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions. A notable exception, however, concerns the predictions of the recent time-independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [Phys.~Rev.~A~{\bf 82}, 023423 (2010)]. Extensive tests of the numerical implementation were performed, including the effect of truncating the Neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections. We observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing. In the parallel geometry, when the ejected electrons are collected along the direction of the laser polarization axis, back-to-back escape is the dominant channel for strongly asymmetric energy sharing, while it is completely forbidden if the two electrons share the excess energy equally.Comment: 17 pages, 9 figure

Greybody Factors for Brane Scalar Fields in a Rotating Black-Hole Background

We study the evaporation of (4+n)-dimensional rotating black holes into scalar degrees of freedom on the brane. We calculate the corresponding absorption probabilities and cross-sections obtaining analytic solutions in the low-energy regime, and compare the derived analytic expressions to numerical results, with very good agreement. We then consider the high-energy regime, construct an analytic high-energy solution to the scalar-field equation by employing a new method, and calculate the absorption probability and cross-section for this energy regime, finding again a very good agreement with the exact numerical results. We also determine the high-energy asymptotic value of the total cross-section, and compare it to the analytic results derived from the application of the geometrical optics limit.Comment: Latex file, 30 pages, 5 figures, typos corrected, version published in Phys. Rev.

Microscopic dynamics of thin hard rods

Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalised Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualtitative agreement for higher densities.Comment: 21 pages, 6 figures, v2: clarifications and improved readabilit

The nature of science as a foundation for fostering a better understanding of evolution

Misunderstandings of the nature of science (NOS) contribute greatly to resistance to evolutionary theory especially among non-scientific audiences. Here we delineate three extended instructional examples that make extensive use of NOS to establish a foundation upon which to more successfully introduce evolution. Specifically, these instructional examples enable students to consider evolutionary biology using NOS as a lens for interpretation of evolutionary concepts. We have further found, through our respective research efforts and instructional experiences, that a deep understanding of NOS helps students understand and accept the scientific validity of evolution and, conversely, that evolution provides an especially effective context for helping students and teachers to develop a deep understanding of the nature of science. Based on our research and instructional experiences, we introduce six key factors necessary for enhanced instructional success in teaching evolution. These factors are: (1) foster a deep understanding of NOS; (2) use NOS as a lens for evolution instruction; (3) explicitly compare evolution to alternative explanations; (4) focus on human evolution (where possible); (5) explicitly recognize the power of historical inference and (6) use active, social learning. Finally, we elaborate and ground these key factors in supporting literature

Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime

The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived {\it analytically}. We show that there exists a critical mass parameter, $\mu_c$, below which increasing the mass $\mu$ of the field increases the oscillation frequency $\Re(\omega)$ of the resonance. On the other hand, above the critical field mass increasing the mass $\mu$ increases the damping rate $\Im(\omega)$ of the mode. We confirm our analytical results by numerical computations.Comment: 6 page