4,369 research outputs found
Rational invariants of even ternary forms under the orthogonal group
In this article we determine a generating set of rational invariants of
minimal cardinality for the action of the orthogonal group on
the space of ternary forms of even degree . The
construction relies on two key ingredients: On one hand, the Slice Lemma allows
us to reduce the problem to dermining the invariants for the action on a
subspace of the finite subgroup of signed permutations. On the
other hand, our construction relies in a fundamental way on specific bases of
harmonic polynomials. These bases provide maps with prescribed
-equivariance properties. Our explicit construction of these
bases should be relevant well beyond the scope of this paper. The expression of
the -invariants can then be given in a compact form as the
composition of two equivariant maps. Instead of providing (cumbersome) explicit
expressions for the -invariants, we provide efficient algorithms
for their evaluation and rewriting. We also use the constructed
-invariants to determine the -orbit locus and
provide an algorithm for the inverse problem of finding an element in
with prescribed values for its invariants. These are
the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application,
refinement of Definition 3.1. To appear in "Foundations of Computational
Mathematics
Constraints on the average magnetic field strength of relic radio sources 0917+75 and 1401-33 from XMM-Newton observations
We observed two relic radio sources, 0917+75 and 1401-33, with the XMM-Newton
X-ray observatory. We did not detect any X-ray emission, thermal or
non-thermal, in excess of the local background level from either target. This
imposes new upper limits on the X-ray flux due to inverse Compton scattering of
photons from the cosmic microwave background by relativistic electrons in the
relic sources, and new lower limits on the magnetic field strength from the
relative strength of the radio and X-ray emission. The combination of radio and
X-ray observations provides a measure of the magnetic field independent of
equipartition or minimum energy assumptions. Due to increasing sensitivity of
radio observations, the known population of cluster relics has been growing;
however, studies of non-thermal X-ray emission from relics remain scarce. Our
study adds to the small sample of relics studied in X-rays. In both relics, our
field strength lower limits are slightly larger than estimates of the
equipartition magnetic field.Comment: 11 pages, 5 figures. Accepted by MNRA
Effects of Bulk and Surface Conductivity on the Performance of CdZnTe Pixel Detectors
We studied the effects of bulk and surface conductivity on the performance of
high-resistivity CdZnTe (CZT) pixel detectors with Pt contacts. We emphasize
the difference in mechanisms of the bulk and surface conductivity as indicated
by their different temperature behaviors. In addition, the existence of a thin
(10-100 A) oxide layer on the surface of CZT, formed during the fabrication
process, affects both bulk and surface leakage currents. We demonstrate that
the measured I-V dependencies of bulk current can be explained by considering
the CZT detector as a metal-semiconductor-metal system with two back-to-back
Schottky-barrier contacts. The high surface leakage current is apparently due
to the presence of a low-resistivity surface layer that has characteristics
which differ considerably from those of the bulk material. This surface layer
has a profound effect on the charge collection efficiency in detectors with
multi-contact geometry; some fraction of the electric field lines originated on
the cathode intersects the surface areas between the pixel contacts where the
charge produced by an ionizing particle gets trapped. To overcome this effect
we place a grid of thin electrodes between the pixel contacts; when the grid is
negatively biased, the strong electric field in the gaps between the pixels
forces the electrons landing on the surface to move toward the contacts,
preventing the charge loss. We have investigated these effects by using CZT
pixel detectors indium bump bonded to a custom-built VLSI readout chip
Correlation between magnetic interactions and domain structure in A1 FePt ferromagnetic thin films
We have investigated the relationship between the domain structure and the
magnetic interactions in a series of FePt ferromagnetic thin films of varying
thickness. As-made films grow in the magnetically soft and chemically
disordered A1 phase that may have two distinct domain structures. Above a
critical thickness nm the presence of an out of plane
anisotropy induces the formation of stripes, while for planar
domains occur.
Magnetic interactions have been characterized using the well known DCD-IRM
remanence protocols, plots, and magnetic viscosity measurements. We
have observed a strong correlation between the domain configuration and the
sign of the magnetic interactions. Planar domains are associated with positive
exchange-like interactions, while stripe domains have a strong negative
dipolar-like contribution. In this last case we have found a close correlation
between the interaction parameter and the surface dipolar energy of the stripe
domain structure. Using time dependent magnetic viscosity measurements, we have
also estimated an average activation volume for magnetic reversal, nm which is approximately
independent of the film thickness or the stripe period.Comment: 25 pages, 11 figure
Theory of magnetic domains in uniaxial thin films
For uniaxial easy axis films, properties of magnetic domains are usually
described within the Kittel model, which assumes that domain walls are much
thinner than the domains. In this work we present a simple model that includes
a proper description of the magnetostatic energy of domains and domain walls
and also takes into account the interaction between both surfaces of the film.
Our model describes the behavior of domain and wall widths as a function of
film thickness, and is especially well suited for the strong stripe phase. We
prove the existence of a critical value of magneto-crystalline anisotropy above
which stripe domains exist for any film thickness and justify our model by
comparison with exact results. The model is in good agreement with experimental
data for hcp cobalt.Comment: 15 pages, 7 figure
Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors
We calculate the magnetization torque due to the spin polarization of the
itinerant electrons by deriving the kinetic spin Bloch equations based on the
- model. We find that the first-order gradient of the magnetization
inhomogeneity gives rise to the current-induced torques, which are consistent
to the previous works. At the second-order gradient, we find an effective
magnetic field perpendicular to the spin stiffness filed. This field is
proportional to the nonadiabatic parameter . We show that this vertical
spin stiffness term can significantly modify the domain-wall structure in
ferromagnetic semiconductors and hence should be included in the
Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.Comment: 7 pages, 4 figure
Giant Planar Hall Effect in Epitaxial (Ga,Mn)As Devices
Large Hall resistance jumps are observed in microdevices patterned from
epitaxial (Ga,Mn)As layers when subjected to a swept, in-plane magnetic field.
This giant planar Hall effect is four orders of magnitude greater than
previously observed in metallic ferromagnets. This enables extremely sensitive
measurements of the angle-dependent magnetic properties of (Ga,Mn)As. The
magnetic anisotropy fields deduced from these measurements are compared with
theoretical predictions.Comment: 3 figure
A series of coverings of the regular n-gon
We define an infinite series of translation coverings of Veech's double-n-gon
for odd n greater or equal to 5 which share the same Veech group. Additionally
we give an infinite series of translation coverings with constant Veech group
of a regular n-gon for even n greater or equal to 8. These families give rise
to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To
appear in Geometriae Dedicata.
Blue Variable Stars from the MACHO database I: Photometry and Spectroscopy of the LMC sample
We present the photometric properties of 1279 blue variable stars within the
LMC. Photometry is derived from the MACHO database. The lightcurves of the
sample exhibit a variety of quasi-periodic and aperiodic outburst behavior. A
characteristic feature of the photometric variation is that the objects are
reddest when at maximum outburst. A subset of 102 objects were examined
spectroscopically. Within this subset, 91% exhibited Balmer emission in at
least one epoch, in some cases with spectacular spectral variability. The
variability observed in the sample is consistent with the establishment and
maintenance of the Be phenomenon.Comment: 19 pages, AJ accepte
Antiferromagnetic interlayer exchange coupling across an amorphous metallic spacer layer
By means of magneto-optical Kerr effect we observe for the first time
antiferromagnetic coupling between ferromagnetic layers across an amorphous
metallic spacer layer. Biquadratic coupling occurs at the transition from a
ferromagnetically to an antiferromagnetically coupled region. Scanning
tunneling microscopy images of all involved layers are used to extract
thickness fluctuations and to verify the amorphous state of the spacer. The
observed antiferromagnetic coupling behavior is explained by RKKY interaction
taking into account the amorphous structure of the spacer material.Comment: Typset using RevTex, 4 pages with 4 figures (.eps
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