20,973 research outputs found
Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation
We enunciate and prove here a generalization of Geroch's famous conjecture
concerning analytic solutions of the elliptic Ernst equation. Our
generalization is stated for solutions of the hyperbolic Ernst equation that
are not necessarily analytic, although it can be formulated also for solutions
of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic
case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to
proof contained in pape
Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves
A method is presented for solving the characteristic initial value problem
for the collision and subsequent nonlinear interaction of plane gravitational
or gravitational and electromagnetic waves in a Minkowski background. This
method generalizes the monodromy transform approach to fields with nonanalytic
behaviour on the characteristics inherent to waves with distinct wave fronts.
The crux of the method is in a reformulation of the main nonlinear symmetry
reduced field equations as linear integral equations whose solutions are
determined by generalized (``dynamical'') monodromy data which evolve from data
specified on the initial characteristics (the wavefronts).Comment: 4 pages, RevTe
Infrared astronomy
The role and contributions of Frank McDonald in extending high energy astrophysics to the sub-eV photon energy range (in putting infrared astronomy into orbit) are discussed
Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem
We consider the collisions of plane gravitational and electromagnetic waves
with distinct wavefronts and of arbitrary polarizations in a Minkowski
background. We first present a new, completely geometric formulation of the
characteristic initial value problem for solutions in the wave interaction
region for which initial data are those associated with the approaching waves.
We present also a general approach to the solution of this problem which
enables us in principle to construct solutions in terms of the specified
initial data. This is achieved by re-formulating the nonlinear dynamical
equations for waves in terms of an associated linear problem on the spectral
plane. A system of linear integral ``evolution'' equations which solve this
spectral problem for specified initial data is constructed. It is then
demonstrated explicitly how various colliding plane wave space-times can be
constructed from given characteristic initial data.Comment: 33 pages, 3 figures, LaTeX. Accepted for publication in Classical and
Quantum Gravit
Clustering of DIRBE Light and IR Background
We outline a new method for estimating the cosmic infrared background using
the spatial and spectral correlation properties of infrared maps. The cosmic
infrared background from galaxies should have a minimum fluctuation of the
order of 10\% on angular scales of the order of 1\deg. We show that a linear
combination of maps at different wavelengths can greatly reduce the
fluctuations produced by foreground stars, while not eliminating the
fluctuations of the background from high redshift galaxies. The method is
potentially very powerful, especially at wavelengths where the foreground is
bright but smooth.Comment: 7 pages postcript, talk at "Unveiling the cosmic infrared background"
workshop, College Park, M
Maximal multihomogeneity of algebraic hypersurface singularities
From the degree zero part of logarithmic vector fields along an algebraic
hypersurface singularity we indentify the maximal multihomogeneity of a
defining equation in form of a maximal algebraic torus in the embedded
automorphism group. We show that all such maximal tori are conjugate and in
one-to-one correspondence to maxmimal tori in the degree zero jet of the
embedded automorphism group.
The result is motivated by Kyoji Saito's characterization of quasihomogeneity
for isolated hypersurface singularities and extends its formal version and a
result of Hauser and Mueller.Comment: 5 page
Manufacturing with the Sun
Concentrated solar radiation is now a viable alternative source for many advanced manufacturing processes. Researchers at the National Renewable Energy Laboratory (NREL) have demonstrated the feasibility of processes such as solar induced surface transformation of materials (SISTM), solar based manufacturing, and solar pumped lasers. Researchers are also using sunlight to decontaminate water and soils polluted with organic compounds; these techniques could provide manufacturers with innovative alternatives to traditional methods of waste management. The solar technology that is now being integrated into today's manufacturing processes offer greater potential for tomorrow, especially as applied to the radiation abundant environment available in space and on the lunar surface
Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
For the fields depending on two of the four space-time coordinates only, the
spaces of local solutions of various integrable reductions of Einstein's field
equations are shown to be the subspaces of the spaces of local solutions of the
``null-curvature'' equations constricted by a requirement of a universal (i.e.
solution independent) structures of the canonical Jordan forms of the unknown
matrix variables. These spaces of solutions of the ``null-curvature'' equations
can be parametrized by a finite sets of free functional parameters -- arbitrary
holomorphic (in some local domains) functions of the spectral parameter which
can be interpreted as the monodromy data on the spectral plane of the
fundamental solutions of associated linear systems. Direct and inverse problems
of such mapping (``monodromy transform''), i.e. the problem of finding of the
monodromy data for any local solution of the ``null-curvature'' equations with
given canonical forms, as well as the existence and uniqueness of such solution
for arbitrarily chosen monodromy data are shown to be solvable unambiguously.
The linear singular integral equations solving the inverse problems and the
explicit forms of the monodromy data corresponding to the spaces of solutions
of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction
The Growing Mismatch Between Patient Longevity and the Service Life of Implantable Cardioverter-Defibrillators
Implantable cardioverter-defibrillators (ICDs) are lifesaving devices. Over 100,000 patients received ICDs in 2004 at a cost of $2 billion for the pulse generators alone. Because of expanded indications and coverage by Medicare, the number of ICD implantations and replacements is expected to increase dramatically during the next decade. The average ICD patient at our institution now lives nearly 10 years after the procedure. However, the service life of pulse generators has decreased from 4.7 ± 1 year for single-chamber units to 4.0 ± 1 year for dual-chamber devices. This mismatch between patient longevity and the service life of ICDs poses a significant clinical and economic burden that must be addressed. One near-term solution is for manufacturers to provide devices with larger batteries so that most patients can have an ICD pulse generator that lasts a lifetime. For the long-term, more robust or renewable energy sources are needed
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