3,574 research outputs found
On the polar decomposition of right linear operators in quaternionic Hilbert spaces
In this article we prove the existence of the polar decomposition for densely
defined closed right linear operators in quaternionic Hilbert spaces: If is
a densely defined closed right linear operator in a quaternionic Hilbert space
, then there exists a partial isometry such that . In
fact is unique if . In particular, if is separable
and is a partial isometry with , then we prove that
if and only if either or .Comment: 17 page
Models of Galaxy Clusters with Thermal Conduction
We present a simple model of hot gas in galaxy clusters, assuming hydrostatic
equilibrium and energy balance between radiative cooling and thermal
conduction. For five clusters, A1795, A1835, A2199, A2390 and RXJ1347.5-1145,
the model gives a good description of the observed radial profiles of electron
density and temperature, provided we take the thermal conductivity to
be about 30% of the Spitzer conductivity. Since the required is
consistent with the recent theoretical estimate of Narayan & Medvedev (2001)
for a turbulent magnetized plasma, we consider a conduction-based equilibrium
model to be viable for these clusters. We further show that the hot gas is
thermally stable because of the presence of conduction. For five other
clusters, A2052, A2597, Hydra A, Ser 159-03 and 3C295, the model requires
unphysically large values of to fit the data. These clusters must have
some additional source of heat, most likely an active galactic nucleus since
all the clusters have strong radio galaxies at their centers. We suggest that
thermal conduction, though not dominant in these clusters, may nevertheless
play a significant role by preventing the gas from becoming thermally unstable.Comment: Published in ApJ; 22 pages, including 2 tables, 4 figures; typos
corrected to match the published versio
Squeezing in Multivariate Spin Systems
In contrast to the canonically conjugate variates , representing the
position and momentum of a particle in the phase space distributions, the three
Cartesian components, ,, of a spin- system constitute
the mutually non-commuting variates in the quasi-probabilistic spin
distributions. It can be shown that a univariate spin distribution is never
squeezed and one needs to look into either bivariate or trivariate
distributions for signatures of squeezing. Several such distributions result if
one considers different characteristic functions or moments based on various
correspondence rules. As an example, discrete probability distribution for an
arbitrary spin-1 assembly is constructed using Wigner-Weyl and Margenau-Hill
correspondence rules. It is also shown that a trivariate spin-1 assembly
resulting from the exposure of nucleus with non-zero quadrupole moment to
combined electric quadrupole field and dipole magnetic field exhibits squeezing
in cerain cases.Comment: 13 pages, 1 Table, Presented at ICSSUR-05, Franc
Determination of the spin-flip time in ferromagnetic SrRuO3 from time-resolved Kerr measurements
We report time-resolved Kerr effect measurements of magnetization dynamics in
ferromagnetic SrRuO3. We observe that the demagnetization time slows
substantially at temperatures within 15K of the Curie temperature, which is ~
150K. We analyze the data with a phenomenological model that relates the
demagnetization time to the spin flip time. In agreement with our observations
the model yields a demagnetization time that is inversely proportional to T-Tc.
We also make a direct comparison of the spin flip rate and the Gilbert damping
coefficient showing that their ratio very close to kBTc, indicating a common
origin for these phenomena
The extraordinary Hall effect in coherent epitaxial tau (Mn,Ni)Al thin films on GaAs
Ultrathin coherent epitaxial films of ferromagnetic tau(Mn,Ni)0.60Al0.40 have been grown by molecular beam epitaxy on GaAs substrates. X-ray scattering and cross-sectional transmission electron microscopy measurements confirm that the c axis of the tetragonal tau unit cell is aligned normal to the (001) GaAs substrate. Measurements of the extraordinary Hall effect (EHE) show that the films are perpendicularly magnetized, exhibiting EHE resistivities saturating in the range of 3.3-7.1 muOMEGA-cm at room temperature. These values of EHE resistivity correspond to signals as large as +7 and -7 mV for the two magnetic states of the film with a measurement current of 1 mA. Switching between the two magnetic states is found to occur at distinct field values that depend on the previously applied maximum field. These observations suggest that the films are magnetically uniform. As such, tau(Mn,Ni)Al films may be an excellent medium for high-density storage of binary information
4-[(E)-(4-Methylphenyl)iminomethyl]phenol
In the title compound, C14H13NO, the two rings show significant deviation from coplanarity, with a dihedral angle between the two planes of 49.40 (5)°. The hydroxy group is involved in an intermolecular O—H⋯N hydrogen bond, forming an extended one-dimensional zigzag chain along (001)
4-Bromo-N-(4-hydroxybenzylidene)aniline
In the title compound, C13H10BrNO, the benzene ring planes are inclined at an angle of 48.85 (17)°, resulting in a nonplanar molecule. A characteristic of aromatic Schiff bases with N-aryl substituents is that the terminal phenyl rings are twisted relative to the HC=N plane. In this case, the HC=N unit makes dihedral angles of 11.1 (4) and 38.5 (3)° with the hydroxybenzene and bromobenzene rings, respectively. In the crystal, the molecules are linked by O—H⋯N hydrogen bonds to form infinite (C8) chains along the b axis
Critical thickness and orbital ordering in ultrathin La0.7Sr0.3MnO3 films
Detailed analysis of transport, magnetism and x-ray absorption spectroscopy
measurements on ultrathin La0.7Sr0.3MnO3 films with thicknesses from 3 to 70
unit cells resulted in the identification of a lower critical thickness for a
non-metallic, non-ferromagnetic layer at the interface with the SrTiO3 (001)
substrate of only 3 unit cells (~12 Angstrom). Furthermore, linear dichroism
measurements demonstrate the presence of a preferred (x2-y2) in-plane orbital
ordering for all layer thicknesses without any orbital reconstruction at the
interface. A crucial requirement for the accurate study of these ultrathin
films is a controlled growth process, offering the coexistence of
layer-by-layer growth and bulk-like magnetic/transport properties.Comment: 22 pages, 6 figures, accepted for publication in Physical Review
The detection of patients at risk of gastrointestinal toxicity during pelvic radiotherapy by electronic nose and FAIMS : a pilot study
It is well known that the electronic nose can be used to identify differences between human health and disease for a range of disorders. We present a pilot study to investigate if the electronic nose and a newer technology, FAIMS (Field Asymmetric Ion Mobility Spectrometry), can be used to identify and help inform the treatment pathway for patients receiving pelvic radiotherapy, which frequently causes gastrointestinal side-effects, severe in some. From a larger group, 23 radiotherapy patients were selected where half had the highest levels of toxicity and the others the lowest. Stool samples were obtained before and four weeks after radiotherapy and the volatiles and gases emitted analysed by both methods; these chemicals are products of fermentation caused by gut microflora. Principal component analysis of the electronic nose data and wavelet transform followed by Fisher discriminant analysis of FAIMS data indicated that it was possible to separate patients after treatment by their toxicity levels. More interestingly, differences were also identified in their pre-treatment samples. We believe these patterns arise from differences in gut microflora where some combinations of bacteria result to give this olfactory signature. In the future our approach may result in a technique that will help identify patients at “high risk” even before radiation treatment is started
A duality relation for fluid spacetime
We consider the electromagnetic resolution of gravitational field. We show
that under the duality transformation, in which active and passive electric
parts of the Riemann curvature are interchanged, a fluid spacetime in comoving
coordinates remains invariant in its character with density and pressure
transforming, while energy flux and anisotropic pressure remaining unaltered.
Further if fluid admits a barotropic equation of state,
where , which will transform to . Clearly the stiff fluid and dust are dual to each-other
while , will go to flat spacetime. However the n and the deSitter ) universes ar e self-dual.Comment: 5 pages, LaTeX version, Accepted in Classical Quantum Gravity as a
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