6,389 research outputs found
Note on Bessaga-Klee classification
We collect several variants of the proof of the third case of the
Bessaga-Klee relative classification of closed convex bodies in topological
vector spaces. We were motivated by the fact that we have not found anywhere in
the literature a complete correct proof. In particular, we point out an error
in the proof given in the book of C.~Bessaga and A.~Pe\l czy\'nski (1975). We
further provide a simplified version of T.~Dobrowolski's proof of the smooth
classification of smooth convex bodies in Banach spaces which works
simultaneously in the topological case.Comment: 14 pages; we made few corrections, added one reference and precised
the abstrac
Rich families and elementary submodels
We compare two methods of proving separable reduction theorems in functional
analysis -- the method of rich families and the method of elementary submodels.
We show that any result proved using rich families holds also when formulated
with elementary submodels and the converse is true in spaces with fundamental
minimal system an in spaces of density . We do not know whether the
converse is true in general. We apply our results to show that a projectional
skeleton may be without loss of generality indexed by ranges of its
projections
Optical geometry analysis of the electromagnetic self-force
We present an analysis of the behaviour of the electromagnetic self-force for
charged particles in a conformally static spacetime, interpreting the results
with the help of optical geometry. Some conditions for the vanishing of the
local terms in the self-force are derived and discussed.Comment: 18 pages; 2 figure
Neutrino-driven explosions twenty years after SN1987A
The neutrino-heating mechanism remains a viable possibility for the cause of
the explosion in a wide mass range of supernova progenitors. This is
demonstrated by recent two-dimensional hydrodynamic simulations with detailed,
energy-dependent neutrino transport. Neutrino-driven explosions were not only
found for stars in the range of 8-10 solar masses with ONeMg cores and in case
of the iron core collapse of a progenitor with 11 solar masses, but also for a
``typical'' progenitor model of 15 solar masses. For such more massive stars,
however, the explosion occurs significantly later than so far thought, and is
crucially supported by large-amplitude bipolar oscillations due to the
nonradial standing accretion shock instability (SASI), whose low (dipole and
quadrupole) modes can develop large growth rates in conditions where convective
instability is damped or even suppressed. The dominance of low-mode deformation
at the time of shock revival has been recognized as a possible explanation of
large pulsar kicks and of large-scale mixing phenomena observed in supernovae
like SN 1987A.Comment: 11 pages, 6 figures; review proceeding for "Supernova 1987A: 20 Years
After: Supernovae and Gamma-Ray Bursters" AIP, New York, eds. S. Immler, K.W.
Weiler, and R. McCra
Wigner-Eckart theorem for tensor operators of Hopf algebras
We prove Wigner-Eckart theorem for the irreducible tensor operators for
arbitrary Hopf algebras, provided that tensor product of their irreducible
representation is completely reducible. The proof is based on the properties of
the irreducible representations of Hopf algebras, in particular on Schur lemma.
Two classes of tensor operators for the Hopf algebra U(su(2)) are
considered. The reduced matrix elements for the class of irreducible tensor
operators are calculated. A construction of some elements of the center of
U(su(2)) is given.Comment: 14 pages, late
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Extremal spacings between eigenvalues of random unitary matrices of size N
pertaining to circular ensembles are investigated. Explicit probability
distributions for the minimal spacing for various ensembles are derived for N =
4. We study ensembles of tensor product of k random unitary matrices of size n
which describe independent evolution of a composite quantum system consisting
of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes
large, the nearest neighbor distribution P(s) becomes Poissonian, but
statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations
from the Poissonian behavior
Modeling Interface Motion Of Combustion (MINOC). A computer code for two-dimensional, unsteady turbulent combustion
A computer code for calculating the flow field and flame propagation in a turbulent combustion tunnel is described. The model used in the analysis is the random vortex model, which allows the turbulent field to evolve as a fundamental solution to the Navier-Stokes equations without averaging or closure modeling. The program was used to study the flow field in a model combustor, formed by a rearward-facing step in a channel, in terms of the vorticity field, the turbulent shear stresses, the flame contours, and the concentration field. Results for the vorticity field reveal the formation of large-scale eddy structures in the turbulent flow downstream from the step. The concentration field contours indicate that most burning occurred around the outer edges of the large eddies of the shear layer
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