13,896 research outputs found
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
By numerical calculation, the Planck spectrum with zero-point radiation is
shown to satisfy a natural maximum-entropy principle whereas alternative
choices of spectra do not. Specifically, if we consider a set of
conducting-walled boxes, each with a partition placed at a different location
in the box, so that across the collection of boxes the partitions are uniformly
spaced across the volume, then the Planck spectrum correspond to that spectrum
of random radiation (having constant energy kT per normal mode at low
frequencies and zero-point energy (1/2)hw per normal mode at high frequencies)
which gives maximum uniformity across the collection of boxes for the radiation
energy per box. The analysis involves Casimir energies and zero-point radiation
which do not usually appear in thermodynamic analyses. For simplicity, the
analysis is presented for waves in one space dimension.Comment: 11 page
Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
The formulae for Planck length, Hawking temperature and Unruh-Davies
temperature are derived by using only laws of classical physics together with
the Heisenberg principle. Besides, it is shown how the Hawking relation can be
deduced from the Unruh relation by means of the principle of equivalence; the
deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure
Homogeneous heterotic supergravity solutions with linear dilaton
I construct solutions to the heterotic supergravity BPS-equations on products
of Minkowski space with a non-symmetric coset. All of the bosonic fields are
homogeneous and non-vanishing, the dilaton being a linear function on the
non-compact part of spacetime.Comment: 36 pages; v2 conclusion updated and references adde
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
On Lagerstrom’s Model of Slow Incompressible Viscous Flow
The model discussed is a nonlinear boundary value problem which contains a parameter that models the Reynolds number. The matched asymptotic expansions, an inner “Stokes” expansion valid near the inner boundary and an outer “Oseen” expansion valid away from it, that describe the solutions of the model problem for small are extended. Numerical calculations show that these matched expansions have only a small range of usefulness, with the addition of further terms generally causing a worse, rather than better, approximation at moderate values of . Far better results are achieved when a single expansion, the outer expansion, is used throughout. The additional terms that have been calculated then consistently give improved approximations for all . It is also rigorously proved that an iterative method of solution of the model equation based on the outer “Oseen” approximation, converges for all to a unique solution.\ud
The results presented here for Lagerstrom’s model suggest that iterative improvement of the Oseen expansion may be an effective method of approximation of viscous flows at moderate Reynolds number
New non compact Calabi-Yau metrics in D=6
A method for constructing explicit Calabi-Yau metrics in six dimensions in
terms of an initial hyperkahler structure is presented. The equations to solve
are non linear in general, but become linear when the objects describing the
metric depend on only one complex coordinate of the hyperkahler 4-dimensional
space and its complex conjugated. This situation in particular gives a dual
description of D6-branes wrapping a complex 1-cycle inside the hyperkahler
space, which was studied by Fayyazuddin. The present work generalize the
construction given by him. But the explicit solutions we present correspond to
the non linear problem. This is a non linear equation with respect to two
variables which, with the help of some specific anzatz, is reduced to a non
linear equation with a single variable solvable in terms of elliptic functions.
In these terms we construct an infinite family of non compact Calabi-Yau
metrics.Comment: A numerical error has been corrected together with the corresponding
analysis of the metri
Techniques for measuring atmospheric aerosols at the High Resolution Fly's Eye experiment
We describe several techniques developed by the High Resolution Fly's Eye
experiment for measuring aerosol vertical optical depth, aerosol horizontal
attenuation length, and aerosol phase function. The techniques are based on
measurements of side-scattered light generated by a steerable ultraviolet laser
and collected by an optical detector designed to measure fluorescence light
from cosmic-ray air showers. We also present a technique to cross-check the
aerosol optical depth measurement using air showers observed in stereo. These
methods can be used by future air fluorescence experiments.Comment: Accepted for publication in Astroparticle Physics Journal 16 pages, 9
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