1,260 research outputs found
Nontrivial classes in from nontrivalent graph cocycles
We construct nontrivial cohomology classes of the space of
imbeddings of the circle into , by means of Feynman diagrams. More
precisely, starting from a suitable linear combination of nontrivalent
diagrams, we construct, for every even number , a de Rham cohomology
class on . We prove nontriviality of these classes by evaluation
on the dual cycles.Comment: 10 pages, 11 figures. V2: minor changes, typos correcte
Big -ample Line Bundles
A recent paper of Totaro develops a theory of -ample bundles in
characteristic 0. Specifically, a line bundle on is -ample if for
every coherent sheaf on , there exists an integer such
that implies for
. We show that a line bundle on a complex projective scheme is
-ample if and only if the restriction of to its augmented base locus is
-ample. In particular, when is a variety and is big but fails to be
-ample, then there exists a codimension 1 subscheme of such that the
restriction of to is not -ample.Comment: 9 pages, 2 pdf figure
On the naturality of the Mathai-Quillen formula
We give an alternative proof for the Mathai-Quillen formula for a Thom form
using its natural behaviour with respect to fiberwise integration. We also
study this phenomenon in general context.Comment: 6 page
A study of electric motors for use in liquid and gaseous helium Engineering report no. 3530
Electric motor design and operation in liquid and gaseous helium environment
Link Invariants for Flows in Higher Dimensions
Linking numbers in higher dimensions and their generalization including gauge
fields are studied in the context of BF theories. The linking numbers
associated to -manifolds with smooth flows generated by divergence-free
p-vector fields, endowed with an invariant flow measure are computed in
different cases. They constitute invariants of smooth dynamical systems (for
non-singular flows) and generalizes previous results for the 3-dimensional
case. In particular, they generalizes to higher dimensions the Arnold's
asymptotic Hopf invariant for the three-dimensional case. This invariant is
generalized by a twisting with a non-abelian gauge connection. The computation
of the asymptotic Jones-Witten invariants for flows is naturally extended to
dimension n=2p+1. Finally we give a possible interpretation and implementation
of these issues in the context of string theory.Comment: 21+1 pages, LaTeX, no figure
The polarization of the planet-hosting WASP-18 system
We report observations of the linear polarization of the WASP-18 system,
which harbors a very massive ( approx 10 M_J) planet orbiting very close to its
star with an orbital period of 0.94 days. We find the WASP-18 system is
polarized at about 200 parts-per-million (ppm), likely from the interstellar
medium predominantly, with no strong evidence for phase dependent modulation
from reflected light from the planet. We set an upper limit of 40 ppm (99%
confidence level) on the amplitude of a reflected polarized light planetary
signal. We compare the results with models for a number of processes that may
produce polarized light in a planetary system to determine if we can rule out
any phenomena with this limit. Models of reflected light from thick clouds can
approach or exceed this limit, but such clouds are unlikely at the high
temperature of the WASP-18b atmosphere. Additionally, we model the expected
polarization resulting from the transit of the planet across the star and find
this has an amplitude of about 1.6 ppm, which is well below our detection
limits. We also model the polarization due to the tidal distortion of the star
by the massive planet and find this is also too small to be measured currently.Comment: 23 pages, 10 Figures, 6 Tables, Accepted to A
Cyclic cocycles on twisted convolution algebras
We give a construction of cyclic cocycles on convolution algebras twisted by
gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu
and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted
convolution algebra and twisted cohomology groups which is similar to a
construction of Mathai and Stevenson. When the groupoid is not proper, we
cannot construct an invariant connection on the gerbe; therefore to study this
algebra, we instead develop simplicial techniques to construct a simplicial
curvature 3-form representing the class of the gerbe. Then by using a JLO
formula we define a morphism from a simplicial complex twisted by this
simplicial curvature 3-form to the mixed bicomplex computing the periodic
cyclic cohomology of the twisted convolution algebras. The results in this
article were originally published in the author's Ph.D. thesis.Comment: 39 page
A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models
The algebraic definition of charges for symmetry-preserving D-branes in
Wess-Zumino-Witten models is shown to coincide with the geometric definition,
for all simple Lie groups. The charge group for such branes is computed from
the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark
Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling
In this first of three articles on the optical absorption of electrons in
half-filled Peierls-distorted chains we present analytical results for
non-interacting tight-binding electrons. We carefully derive explicit
expressions for the current operator, the dipole transition matrix elements,
and the optical absorption for electrons with a cosine dispersion relation of
band width and dimerization parameter . New correction
(``''-)terms to the current operator are identified. A broad band-to-band
transition is found in the frequency range whose shape
is determined by the joint density of states for the upper and lower Peierls
subbands and the strong momentum dependence of the transition matrix elements.Comment: 17 pages REVTEX 3.0, 2 postscript figures; hardcopy versions before
May 96 are obsolete; accepted for publication in The Philosophical Magazine
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