4,373 research outputs found
Mathematical Analysis of the BIBEE Approximation for Molecular Solvation: Exact Results for Spherical Inclusions
We analyze the mathematically rigorous BIBEE (boundary-integral based
electrostatics estimation) approximation of the mixed-dielectric continuum
model of molecular electrostatics, using the analytically solvable case of a
spherical solute containing an arbitrary charge distribution. Our analysis,
which builds on Kirkwood's solution using spherical harmonics, clarifies
important aspects of the approximation and its relationship to Generalized Born
models. First, our results suggest a new perspective for analyzing fast
electrostatic models: the separation of variables between material properties
(the dielectric constants) and geometry (the solute dielectric boundary and
charge distribution). Second, we find that the eigenfunctions of the
reaction-potential operator are exactly preserved in the BIBEE model for the
sphere, which supports the use of this approximation for analyzing
charge-charge interactions in molecular binding. Third, a comparison of BIBEE
to the recent GB theory suggests a modified BIBEE model capable of
predicting electrostatic solvation free energies to within 4% of a full
numerical Poisson calculation. This modified model leads to a
projection-framework understanding of BIBEE and suggests opportunities for
future improvements.Comment: 33 pages, 5 figure
Nuclear Structure Calculations and Modern Nucleon-Nucleon Potentials
We study ground-state properties of the doubly magic nuclei 4He, 16O, and
40Ca employing the Goldstone expansion and using as input four different
high-quality nucleon-nucleon (NN) potentials. The short-range repulsion of
these potentials is renormalized by constructing a smooth low-momentum
potential V-low-k. This is used directly in a Hartree-Fock approach and
corrections up to third order in the Goldstone expansion are evaluated.
Comparison of the results shows that they are only slightly dependent on the
choice of the NN potential.Comment: 5 pages, submitted to Physical Review
Two-band second moment model and an interatomic potential for caesium
A semi-empirical formalism is presented for deriving interatomic potentials
for materials such as caesium or cerium which exhibit volume collapse phase
transitions. It is based on the Finnis-Sinclair second moment tight binding
approach, but incorporates two independent bands on each atom. The potential is
cast in a form suitable for large-scale molecular dynamics, the computational
cost being the evaluation of short ranged pair potentials. Parameters for a
model potential for caesium are derived and tested
Effect of partially-screened nuclei on fast-electron dynamics
We analyze the dynamics of fast electrons in plasmas containing partially
ionized impurity atoms, where the screening effect of bound electrons must be
included. We derive analytical expressions for the deflection and slowing-down
frequencies, and show that they are increased significantly compared to the
results obtained with complete screening, already at sub-relativistic electron
energies. Furthermore, we show that the modifications to the deflection and
slowing down frequencies are of equal importance in describing the runaway
current evolution. Our results greatly affect fast-electron dynamics and have
important implications, e.g. for the efficacy of mitigation strategies for
runaway electrons in tokamak devices, and energy loss during relativistic
breakdown in atmospheric discharges.Comment: 6 pages, 3 figures, fixed minor typo
Black Hole Production in Particle Collisions and Higher Curvature Gravity
The problem of black hole production in transplanckian particle collisions is
revisited, in the context of large extra dimensions scenarios of TeV-scale
gravity. The validity of the standard description of this process (two
colliding Aichelburg-Sexl shock waves in classical Einstein gravity) is
questioned. It is observed that the classical spacetime has large curvature
along the transverse collision plane, as signaled by the curvature invariant
(R_ijkl)^2. Thus quantum gravity effects, and in particular higher curvature
corrections to the Einstein gravity, cannot be ignored. To give a specific
example of what may happen, the collision is re-analyzed in the
Einstein-Lanczos-Lovelock gravity theory, which modifies the Einstein-Hilbert
Lagrangian by adding a particular `Gauss-Bonnet' combination of curvature
squared terms. The analysis uses a series of approximations, which reduce the
field equations to a tractable second order nonlinear PDE of the Monge-Ampere
type. It is found that the resulting spacetime is significantly different from
the pure Einstein case in the future of the transverse collision plane. These
considerations cast serious doubts on the geometric cross section estimate,
which is based on the classical Einstein gravity description of the black hole
production process.Comment: 36 pp, v2: quantum wavelength limit on particle size and shock width
included; curvature estimate lowered but still well above Planck value; small
modifications throughout; conclusions unchange
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