14,324 research outputs found
Pistons modeled by potentials
In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function associated with a scalar field living on
an interval in a background potential. Although, as a model for a
piston, it seems reasonable to assume a potential having compact support within
, we provide a formalism that can be applied to any sufficiently smooth
potential.Comment: 10 pages, LaTeX. A typo in eq. (3.5) has been corrected. In
"Cosmology, Quantum Vacuum and Zeta Functions: In Honour of Emilio Elizalde",
Eds. S.D. Odintsov, D. Saez-Gomez, and S. Xambo-Descamps. (Springer 2011) pp
31
Generalization of Linearized Gouy-Chapman-Stern Model of Electric Double Layer for Nanostructured and Porous Electrodes: Deterministic and Stochastic Morphology
We generalize linearized Gouy-Chapman-Stern theory of electric double layer
for nanostructured and morphologically disordered electrodes. Equation for
capacitance is obtained using linear Gouy-Chapman (GC) or
Debye-ckel equation for potential near complex
electrode/electrolyte interface. The effect of surface morphology of an
electrode on electric double layer (EDL) is obtained using "multiple scattering
formalism" in surface curvature. The result for capacitance is expressed in
terms of the ratio of Gouy screening length and the local principal radii of
curvature of surface. We also include a contribution of compact layer, which is
significant in overall prediction of capacitance. Our general results are
analyzed in details for two special morphologies of electrodes, i.e.
"nanoporous membrane" and "forest of nanopillars". Variations of local shapes
and global size variations due to residual randomness in morphology are
accounted as curvature fluctuations over a reference shape element.
Particularly, the theory shows that the presence of geometrical fluctuations in
porous systems causes enhanced dependence of capacitance on mean pore sizes and
suppresses the magnitude of capacitance. Theory emphasizes a strong influence
of overall morphology and its disorder on capacitance. Finally, our predictions
are in reasonable agreement with recent experimental measurements on
supercapacitive mesoporous systems
Measurement of Electron Trapping in the CESR Storage Ring
The buildup of low-energy electrons has been shown to affect the performance
of a wide variety of particle accelerators. Of particular concern is the
persistence of the cloud between beam bunch passages, which can impose
limitations on the stability of operation at high beam current. We have
obtained measurements of long-lived electron clouds trapped in the field of a
quadrupole magnet in a positron storage ring, with lifetimes much longer than
the revolution period. Based on modeling, we estimate that about 7% of the
electrons in the cloud generated by a 20-bunch train of 5.3 GeV positrons with
16-ns spacing and population survive longer than 2.3 s in a
quadrupole field of gradient 7.4 T/m. We have observed a non-monotonic
dependence of the trapping effect on the bunch spacing. The effect of a witness
bunch on the measured signal provides direct evidence for the existence of
trapped electrons. The witness bunch is also observed to clear the cloud,
demonstrating its effectiveness as a mitigation technique.Comment: 6 pages, 9 figures, 28 citation
Cocliques of maximal size in the prime graph of a finite simple group
In this paper we continue our investgation of the prime graph of a finite
simple group started in http://arxiv.org/abs/math/0506294 (the printed version
appeared in [1]). We describe all cocliques of maximal size for all finite
simple groups and also we correct mistakes and misprints from our previous
paper. The list of correction is given in Appendix of the present paper.Comment: published version with correction
The challenges of staying together while moving fast
We report on the results of an empirical study conducted with 35 experienced software developers from 22 high-tech companies, including Google, Facebook, Microsoft, Intel, and others. The goal of the study was to elicit challenges that these developers face, potential solutions that they envision to these challenges, and research initiatives that they think would deliver useful results.
Challenges identified by the majority of the study participants relate to the collaborative nature of the work: the availability and discoverability of information, communication, collaborative planning and integration with work of others. Almost all participants also addressed the advantages and disadvantages of the current "fast to the market" trend, and the toll it takes on the quality of the software that they are able to deliver and on their professional and personal satisfaction as software engineers.
We describe in depth the identified challenges, supporting our findings with explicit quotes from the study participants. We also put these findings in context of work done by the software engineering community and outline a roadmap for possible future research initiatives
Shear modulus of the hadron-quark mixed phase
Robust arguments predict that a hadron-quark mixed phase may exist in the
cores of some "neutron" stars. Such a phase forms a crystalline lattice with a
shear modulus higher than that of the crust due to the high density and charge
separation, even allowing for the effects of charge screening. This may lead to
strong continuous gravitational-wave emission from rapidly rotating neutron
stars and gravitational-wave bursts associated with magnetar flares and pulsar
glitches. We present the first detailed calculation of the shear modulus of the
mixed phase. We describe the quark phase using the bag model plus first-order
quantum chromodynamics corrections and the hadronic phase using relativistic
mean-field models with parameters allowed by the most massive pulsar. Most of
the calculation involves treating the "pasta phases" of the lattice via
dimensional continuation, and we give a general method for computing
dimensionally continued lattice sums including the Debye model of charge
screening. We compute all the shear components of the elastic modulus tensor
and angle average them to obtain the effective (scalar) shear modulus for the
case where the mixed phase is a polycrystal. We include the contributions from
changing the cell size, which are necessary for the stability of the
lower-dimensional portions of the lattice. Stability also requires a minimum
surface tension, generally tens of MeV/fm^2 depending on the equation of state.
We find that the shear modulus can be a few times 10^33 erg/cm^3, two orders of
magnitude higher than the first estimate, over a significant fraction of the
maximum mass stable star for certain parameter choices.Comment: 22 pages, 12 figures, version accepted by Phys. Rev. D, with the
corrections to the shear modulus computation and Table I given in the erratu
Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes
The rapid and efficient exchange of ions between porous electrodes and
aqueous solutions is important in many applications, such as electrical energy
storage by super-capacitors, water desalination and purification by capacitive
deionization (or desalination), and capacitive extraction of renewable energy
from a salinity difference. Here, we present a unified mean-field theory for
capacitive charging and desalination by ideally polarizable porous electrodes
(without Faradaic reactions or specific adsorption of ions) in the limit of
thin double layers (compared to typical pore dimensions). We illustrate the
theory in the case of a dilute, symmetric, binary electrolyte using the
Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae
are available for salt adsorption and capacitive charging of the diffuse part
of the double layer. We solve the full GCS mean-field theory numerically for
realistic parameters in capacitive deionization, and we derive reduced models
for two limiting regimes with different time scales: (i) In the
"super-capacitor regime" of small voltages and/or early times where the porous
electrode acts like a transmission line, governed by a linear diffusion
equation for the electrostatic potential, scaled to the RC time of a single
pore. (ii) In the "desalination regime" of large voltages and long times, the
porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear
diffusion equations for the pore-averaged potential and salt concentration
Use of the complete basis set limit for computing highly accurate ab initio dipole moments
Calculating dipole moments with high-order basis sets is generally only
possible for the light molecules, such as water. A simple, yet highly effective
strategy of obtaining high-order dipoles with small, computationally less
expensive basis sets is described. Using the finite field method for computing
dipoles, energies calculated with small basis sets can be extrapolated to
produce dipoles that are comparable to those obtained in high order
calculations. The method reduces computational resources by approximately 50%
(allowing the calculation of reliable dipole moments for larger molecules) and
simultaneously improves the agreement with experimentally measured infrared
transition intensities. For atmospherically important molecules which are
typically too large to consider the use of large basis sets, this procedure
will provide the necessary means of improving calculated spectral intensities
by several percent
Empirical logic of finite automata: microstatements versus macrostatements
We compare the two approaches to the empirical logic of automata. The first,
called partition logic (logic of microstatements), refers to experiments on
individual automata. The second one, the logic of simulation (logic of
macrostatements), deals with ensembles of automata.Comment: late
Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities
The aim of this paper is to discuss some basic notions regarding generic
glass forming systems composed of particles interacting via soft potentials.
Excluding explicitly hard-core interaction we discuss the so called `glass
transition' in which super-cooled amorphous state is formed, accompanied with a
spectacular slowing down of relaxation to equilibrium, when the temperature is
changed over a relatively small interval. Using the classical example of a
50-50 binary liquid of N particles with different interaction length-scales we
show that (i) the system remains ergodic at all temperatures. (ii) the number
of topologically distinct configurations can be computed, is temperature
independent, and is exponential in N. (iii) Any two configurations in phase
space can be connected using elementary moves whose number is polynomially
bounded in N, showing that the graph of configurations has the `small world'
property. (iv) The entropy of the system can be estimated at any temperature
(or energy), and there is no Kauzmann crisis at any positive temperature. (v)
The mechanism for the super-Arrhenius temperature dependence of the relaxation
time is explained, connecting it to an entropic squeeze at the glass
transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR
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