5,172 research outputs found
An L^2-Index Theorem for Dirac Operators on S^1 * R^3
An expression is found for the -index of a Dirac operator coupled to a
connection on a vector bundle over . Boundary
conditions for the connection are given which ensure the coupled Dirac operator
is Fredholm. Callias' index theorem is used to calculate the index when the
connection is independent of the coordinate on . An excision theorem due
to Gromov, Lawson, and Anghel reduces the index theorem to this special case.
The index formula can be expressed using the adiabatic limit of the
-invariant of a Dirac operator canonically associated to the boundary. An
application of the theorem is to count the zero modes of the Dirac operator in
the background of a caloron (periodic instanton).Comment: 14 pages, Latex, to appear in the Journal of Functional Analysi
Singularities in Speckled Speckle
Speckle patterns produced by random optical fields with two (or more) widely
different correlation lengths exhibit speckle spots that are themselves highly
speckled. Using computer simulations and analytic theory we present results for
the point singularities of speckled speckle fields: optical vortices in scalar
(one polarization component) fields; C points in vector (two polarization
component) fields. In single correlation length fields both types of
singularities tend to be more{}-or{}-less uniformly distributed. In contrast,
the singularity structure of speckled speckle is anomalous: for some sets of
source parameters vortices and C points tend to form widely separated giant
clusters, for other parameter sets these singularities tend to form chains that
surround large empty regions. The critical point statistics of speckled speckle
is also anomalous. In scalar (vector) single correlation length fields phase
(azimuthal) extrema are always outnumbered by vortices (C points). In contrast,
in speckled speckle fields, phase extrema can outnumber vortices, and azimuthal
extrema can outnumber C points, by factors that can easily exceed for
experimentally realistic source parameters
Ab-initio elastic tensor of cubic TiAlN alloy: the dependence of the elastic constants on the size and shape of the supercell model
In this study we discuss the performance of approximate SQS supercell models
in describing the cubic elastic properties of B1 (rocksalt)
TiAlN alloy by using a symmetry based projection technique. We
show on the example of TiAlN alloy, that this projection
technique can be used to align the differently shaped and sized SQS structures
for a comparison in modeling elasticity. Moreover, we focus to accurately
determine the cubic elastic constants and Zener's type elastic anisotropy of
TiAlN. Our best supercell model, that captures accurately both
the randomness and cubic elastic symmetry, results in GPa,
GPa and GPa with 3% of error and for Zener's
elastic anisotropy with 6% of error. In addition, we establish the general
importance of selecting proper approximate SQS supercells with symmetry
arguments to reliably model elasticity of alloys. In general, we suggest the
calculation of nine elastic tensor elements - , , ,
, , , , and , to evaluate and
analyze the performance of SQS supercells in predicting elasticity of cubic
alloys via projecting out the closest cubic approximate of the elastic tensor.
The here described methodology is general enough to be applied in discussing
elasticity of substitutional alloys with any symmetry and at arbitrary
composition.Comment: Submitted to Physical Review
Polarization of tightly focused laser beams
The polarization properties of monochromatic light beams are studied. In
contrast to the idealization of an electromagnetic plane wave, finite beams
which are everywhere linearly polarized in the same direction do not exist.
Neither do beams which are everywhere circularly polarized in a fixed plane. It
is also shown that transversely finite beams cannot be purely transverse in
both their electric and magnetic vectors, and that their electromagnetic energy
travels at less than c. The electric and magnetic fields in an electromagnetic
beam have different polarization properties in general, but there exists a
class of steady beams in which the electric and magnetic polarizations are the
same (and in which energy density and energy flux are independent of time).
Examples are given of exactly and approximately linearly polarized beams, and
of approximately circularly polarized beams.Comment: 9 pages, 6 figure
Teachers’ Perceptions of Needs and Supports for Handwriting Instruction in Kindergarten
Background: This study was designed to explore the perceived needs of kindergarten teachers as well as the supports they require in preparing children for success in the area of handwriting.
Methods: A phenomenological research design was used and nine kindergarten teachers employed at four elementary schools in a school district in Illinois participated in the study. Semi-structured interviews were completed to discuss the perceptions of teachers related to challenges they face and the supports they require in promoting the occupational task of handwriting among the children in their classrooms.
Results: The results from this pilot study revealed that overall the teachers felt that the lack of a curriculum and formalized training impacted their teaching practices related to handwriting instruction.
Conclusion: The teachers stated that gaps in their knowledge base relating to developmental progression, the ability to assist struggling students, an awareness of strategies to use, and the IEP process contributed to their challenges in teaching handwriting to kindergarten students
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