8,813 research outputs found
Tight bounds for break minimization
We consider round-robin sports tournaments with n teams and n â 1 rounds. We construct an infinite family of opponent schedules for which every home-away assignment induces at least 1/4 n(nâ2) breaks. This construction establishes a matching lower bound for a corresponding upper bound from the literature
Energy-momentum conservation in pre-metric electrodynamics with magnetic charges
A necessary and sufficient condition for energy-momentum conservation is
proved within a topological, pre-metric approach to classical electrodynamics
including magnetic as well as electric charges. The extended Lorentz force,
consisting of mutual actions by F=(E, B) on the electric current and G=(H, D)
on the magnetic current, can be derived from an energy-momentum "potential" if
and only if the constitutive relation G=G(F) satisfies a certain vanishing
condition. The electric-magnetic reciprocity introduced by Hehl and Obukhov is
seen to define a complex structure on the tensor product of 2-form pairs (F,G)
which is independent of but consistent with the Hodge star operator defined by
any Lorentzian metric. Contrary to a recent claim in the literature, it does
not define a complex structure on the space of 2-forms itself.Comment: 8 pages, 1 fugur
Infinite families of superintegrable systems separable in subgroup coordinates
A method is presented that makes it possible to embed a subgroup separable
superintegrable system into an infinite family of systems that are integrable
and exactly-solvable. It is shown that in two dimensional Euclidean or
pseudo-Euclidean spaces the method also preserves superintegrability. Two
infinite families of classical and quantum superintegrable systems are obtained
in two-dimensional pseudo-Euclidean space whose classical trajectories and
quantum eigenfunctions are investigated. In particular, the wave-functions are
expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure
Maxwell's theory on a post-Riemannian spacetime and the equivalence principle
The form of Maxwell's theory is well known in the framework of general
relativity, a fact that is related to the applicability of the principle of
equivalence to electromagnetic phenomena. We pose the question whether this
form changes if torsion and/or nonmetricity fields are allowed for in
spacetime. Starting from the conservation laws of electric charge and magnetic
flux, we recognize that the Maxwell equations themselves remain the same, but
the constitutive law must depend on the metric and, additionally, may depend on
quantities related to torsion and/or nonmetricity. We illustrate our results by
putting an electric charge on top of a spherically symmetric exact solution of
the metric-affine gauge theory of gravity (comprising torsion and
nonmetricity). All this is compared to the recent results of Vandyck.Comment: 9 pages, REVTeX, no figures; minor changes, version to be published
in Class. Quantum Gra
A General Class of Metamaterial Transformation Slabs
In this paper, we apply transformation-based optics to the derivation of a
general class of transparent metamaterial slabs. By means of analytical and
numerical full-wave studies, we explore their image displacement/formation
capabilities, and establish intriguing connections with configurations already
known in the literature. Starting from these revisitations, we develop a number
of nontrivial extensions, and illustrate their possible applications to the
design of perfect radomes, anti-cloaking devices, and focusing devices based on
double-positive (possibly nonmagnetic) media. These designs show that such
anomalous features may be achieved without necessarily relying on
negative-index or strongly resonant metamaterials, suggesting more practical
venues for the realization of these devices.Comment: 25 pages, 13 figures; minor changes in the tex
Calculations of Energy Losses due to Atomic Processes in Tokamaks with Applications to the ITER Divertor
Reduction of the peak heat loads on the plasma facing components is essential
for the success of the next generation of high fusion power tokamaks such as
the International Thermonuclear Experimental Reactor (ITER) 1 . Many present
concepts for accomplishing this involve the use of atomic processes to transfer
the heat from the plasma to the main chamber and divertor chamber walls and
much of the experimental and theoretical physics research in the fusion program
is directed toward this issue. The results of these experiments and
calculations are the result of a complex interplay of many processes. In order
to identify the key features of these experiments and calculations and the
relative role of the primary atomic processes, simple quasi-analytic models and
the latest atomic physics rate coefficients and cross sections have been used
to assess the relative roles of central radiation losses through
bremsstrahlung, impurity radiation losses from the plasma edge, charge exchange
and hydrogen radiation losses from the scrape-off layer and divertor plasma and
impurity radiation losses from the divertor plasma. This anaysis indicates that
bremsstrahlung from the plasma center and impurity radiation from the plasma
edge and divertor plasma can each play a significant role in reducing the power
to the divertor plates, and identifies many of the factors which determine the
relative role of each process. For instance, for radiation losses in the
divertor to be large enough to radiate the power in the divertor for high power
experiments, a neutral fraction of 10-3 to 10-2 and an impurity recycling rate
of netrecycle of ~ 10^16 s m^-3 will be required in the divertor.Comment: Preprint for the 1994 APSDPP meeting, uuencoded and gzipped
postscript with 22 figures, 40 pages
Semirelativistic stability of N-boson systems bound by 1/r pair potentials
We analyze a system of self-gravitating identical bosons by means of a
semirelativistic Hamiltonian comprising the relativistic kinetic energies of
the involved particles and added (instantaneous) Newtonian gravitational pair
potentials. With the help of an improved lower bound to the bottom of the
spectrum of this Hamiltonian, we are able to enlarge the known region for
relativistic stability for such boson systems against gravitational collapse
and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation,
remainder of the paper unchange
A generalized photon propagator
A covariant gauge independent derivation of the generalized dispersion
relation of electromagnetic waves in a medium with local and linear
constitutive law is presented. A generalized photon propagator is derived. For
Maxwell constitutive tensor, the standard light cone structure and the standard
Feynman propagator are reinstated
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