10,631 research outputs found
Reflection positive affine actions and stochastic processes
In this note we continue our investigations of the representation theoretic
aspects of reflection positivity, also called Osterwalder--Schrader positivity.
We explain how this concept relates to affine isometric actions on real Hilbert
spaces and how this is connected with Gaussian processes with stationary
increments
A statistical study of the global structure of the ring current
[1] In this paper we derive the average configuration of the ring current as a function of the state of the magnetosphere as indicated by the Dst index. We sort magnetic field data from the Combined Release and Radiation Effects Satellite (CRRES) by spatial location and by the Dst index in order to produce magnetic field maps. From these maps we calculate local current systems by taking the curl of the magnetic field. We find both the westward (outer) and the eastward (inner) components of the ring current. We find that the ring current intensity varies linearly with Dst as expected and that the ring current is asymmetric for all Dst values. The azimuthal peak of the ring current is located in the afternoon sector for quiet conditions and near midnight for disturbed conditions. The ring current also moves closer to the Earth during disturbed conditions. We attempt to recreate the Dst index by integrating the magnetic perturbations caused by the ring current. We find that we need to multiply our computed disturbance by a factor of 1.88 ± 0.27 and add an offset of 3.84 ± 4.33 nT in order to get optimal agreement with Dst. When taking into account a tail current contribution of roughly 25%, this agrees well with our expectation of a factor of 1.3 to 1.5 based on a partially conducting Earth. The offset that we have to add does not agree well with an expected offset of approximately 20 nT based on solar wind pressure
Generalized CMB initial conditions with pre-equality magnetic fields
The most general initial conditions of CMB anisotropies, compatible with the
presence of pre-equality magnetic fields, are derived. When the plasma is
composed by photons, baryons, electrons, CDM particles and neutrinos, the
initial data of the truncated Einstein-Boltzmann hierarchy contemplate one
magnetized adiabatic mode and four (magnetized) non-adiabatic modes. After
obtaining the analytical form of the various solutions, the Einstein-Boltzmann
hierarchy is numerically integrated for the corresponding sets of initial data.
The TT, TE and EE angular power spectra are illustrated and discussed for the
magnetized generalization of the CDM-radiation mode, of the baryon-radiation
mode and of the non-adiabatic mode of the neutrino sector. Mixtures of initial
conditions are examined by requiring that the magnetized adiabatic mode
dominates over the remaining non-adiabatic contributions. In the latter case,
possible degeneracies between complementary sets of initial data might be
avoided through the combined analysis of the TT, TE and EE angular power
spectra at high multipoles (i.e. ).Comment: 28 pages, 24 included figures in eps styl
A spiral-like disk of ionized gas in IC 1459: Signature of a merging collision
The authors report the discovery of a large (15 kpc diameter) H alpha + (NII) emission-line disk in the elliptical galaxy IC 1459, showing weak spiral structure. The line flux peaks strongly at the nucleus and is more concentrated than the stellar continuum. The major axis of the disk of ionized gas coincides with that of the stellar body of the galaxy. The mass of the ionized gas is estimated to be approx. 1 times 10 (exp 5) solar mass, less than 1 percent of the total mass of gas present in IC 1459. The total gas mass of 4 times 10(exp 7) solar mass has been estimated from the dust mass derived from a broad-band color index image and the Infrared Astronomy Satellite (IRAS) data. The authors speculate that the presence of dust and gas in IC 1459 is a signature of a merger event
An extension of Wiener integration with the use of operator theory
With the use of tensor product of Hilbert space, and a diagonalization
procedure from operator theory, we derive an approximation formula for a
general class of stochastic integrals. Further we establish a generalized
Fourier expansion for these stochastic integrals. In our extension, we
circumvent some of the limitations of the more widely used stochastic integral
due to Wiener and Ito, i.e., stochastic integration with respect to Brownian
motion. Finally we discuss the connection between the two approaches, as well
as a priori estimates and applications.Comment: 13 page
Analysis of unbounded operators and random motion
We study infinite weighted graphs with view to \textquotedblleft limits at
infinity,\textquotedblright or boundaries at infinity. Examples of such
weighted graphs arise in infinite (in practice, that means \textquotedblleft
very\textquotedblright large) networks of resistors, or in statistical
mechanics models for classical or quantum systems. But more generally our
analysis includes reproducing kernel Hilbert spaces and associated operators on
them. If is some infinite set of vertices or nodes, in applications the
essential ingredient going into the definition is a reproducing kernel Hilbert
space; it measures the differences of functions on evaluated on pairs of
points in . And the Hilbert norm-squared in will represent
a suitable measure of energy. Associated unbounded operators will define a
notion or dissipation, it can be a graph Laplacian, or a more abstract
unbounded Hermitian operator defined from the reproducing kernel Hilbert space
under study. We prove that there are two closed subspaces in reproducing kernel
Hilbert space which measure quantitative notions of limits at
infinity in , one generalizes finite-energy harmonic functions in
, and the other a deficiency index of a natural operator in
associated directly with the diffusion. We establish these
results in the abstract, and we offer examples and applications. Our results
are related to, but different from, potential theoretic notions of
\textquotedblleft boundaries\textquotedblright in more standard random walk
models. Comparisons are made.Comment: 38 pages, 4 tables, 3 figure
The Topology of The Cosmic Microwave Background Anisotropy on The Scale 1 degree
In this paper we develop the theory of clusterization of peaks in a Gaussian
random field. We have obtained new mathematical results from this theory and
the theory of percolation and have proposed a topological method of analysis of
sky maps based on these results. We have simulated sky maps of
the cosmic microwave background anisotropy expected from different cosmological
models with resolution in order to demonstrate how this method can
be used for detection of non-Gaussian noise in the maps and detection of the
Doppler-peak in the spectrum of perturbation of \gD T/T.Comment: 34 pages, 12 postscript figures are available upon request from
[email protected]
ISO far-infrared observations of rich galaxy clusters II. Sersic 159-03
The far-infrared emission from rich galaxy clusters is investigated. Maps
have been obtained by ISO at 60, 100, 135, and 200 microns using the PHT-C
camera. Ground based imaging and spectroscopy were also acquired. Here we
present the results for the cooling flow cluster Sersic 159-03. An infrared
source coincident with the dominant cD galaxy is found. Some off-center sources
are also present, but without any obvious counterparts.Comment: 6 pages, 4 postscript figures, accepted for publication in `Astronomy
and Astrophysics
Experimental aerodynamic characteristics for a cylindrical body of revolution with side strakes and various noses at angles of attack from 0 degrees to 58 degrees and Mach numbers from 0.6 to 2.0
For a body of revolution with afterbody side strakes, an experimental investigation was conducted in the Ames 6- by 6-Foot Wind Tunnel to determine the effects on the aerodynamic characteristics of forebody geometry, nose strakes, body side strakes, Reynolds number, Mach number, and angle of attack. Aerodynamic force and moment characteristics were measured for the straked cylindrical afterbody (cylinder fineness ratio of 7) with tangent ogive noses of fineness ratio 2.5 to 5.0. In addition, the straked cylinder afterbody was tested with an ogive nose having a rounded tip and an ogive nose with two different nose strake arrangements. The data demonstrate that the aerodynamic characteristics for a body of revolution with side strakes can be significantly affected by changes in nose fineness ratio, nose bluntness, Reynolds number, Mach number, and, of course, angle of attack. Removing the strakes from the cylindrical aftersection greatly decreased the lift, but this removal hardly changed the maximum magnitudes of the undesirable side forces that developed at angles of attack greater than about 25 deg for subsonic Mach numbers
Essential selfadjointness of the graph-Laplacian
We study the operator theory associated with such infinite graphs as
occur in electrical networks, in fractals, in statistical mechanics, and even
in internet search engines. Our emphasis is on the determination of spectral
data for a natural Laplace operator associated with the graph in question. This
operator will depend not only on , but also on a prescribed
positive real valued function defined on the edges in . In electrical
network models, this function will determine a conductance number for each
edge. We show that the corresponding Laplace operator is automatically
essential selfadjoint. By this we mean that is defined on the dense
subspace (of all the real valued functions on the set of vertices
with finite support) in the Hilbert space . The
conclusion is that the closure of the operator is selfadjoint in
, and so in particular that it has a unique spectral resolution,
determined by a projection valued measure on the Borel subsets of the infinite
half-line. We prove that generically our graph Laplace operator
will have continuous spectrum. For a given infinite graph
with conductance function , we set up a system of finite graphs with
periodic boundary conditions such the finite spectra, for an ascending family
of finite graphs, will have the Laplace operator for as its limit.Comment: 50 pages with TOC and figure
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