927 research outputs found
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
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
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 H 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 ~eV, using a fully {\it ab initio}, nonperturbative approach to solve
the time-dependent \Schro equation in prolate spheroidal coordinates. The
spatial coordinates and 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
Evaporation of a Kerr black hole by emission of scalar and higher spin particles
We study the evolution of an evaporating rotating black hole, described by
the Kerr metric, which is emitting either solely massless scalar particles or a
mixture of massless scalar and nonzero spin particles. Allowing the hole to
radiate scalar particles increases the mass loss rate and decreases the angular
momentum loss rate relative to a black hole which is radiating nonzero spin
particles. The presence of scalar radiation can cause the evaporating hole to
asymptotically approach a state which is described by a nonzero value of . This is contrary to the conventional view of black hole
evaporation, wherein all black holes spin down more rapidly than they lose
mass. A hole emitting solely scalar radiation will approach a final asymptotic
state described by . A black hole that is emitting scalar
particles and a canonical set of nonzero spin particles (3 species of
neutrinos, a single photon species, and a single graviton species) will
asymptotically approach a nonzero value of only if there are at least 32
massless scalar fields. We also calculate the lifetime of a primordial black
hole that formed with a value of the rotation parameter , the minimum
initial mass of a primordial black hole that is seen today with a rotation
parameter , and the entropy of a black hole that is emitting scalar or
higher spin particles.Comment: 22 pages, 13 figures, RevTeX format; added clearer descriptions for
variables, added journal referenc
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