38,596 research outputs found
Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization
The major and minor axes of the polarization ellipses that surround singular
lines of circular polarization in three dimensional optical ellipse fields are
shown to be organized into Mobius strips. These strips can have either one or
three half-twists, and can be either right- or left-handed. The normals to the
surrounding ellipses generate cone-like structures. Two special projections,
one new geometrical, and seven new topological indices are developed to
characterize the rather complex structures of the Mobius strips and cones.
These eight indices, together with the two well-known indices used until now to
characterize singular lines of circular polarization, could, if independent,
generate 16,384 geometrically and topologically distinct lines. Geometric
constraints and 13 selection rules are discussed that reduce the number of
lines to 2,104, some 1,150 of which have been observed in practice; this number
of different C lines is ~ 350 times greater than the three types of lines
recognized previously. Statistical probabilities are presented for the most
important index combinations in random fields. It is argued that it is
presently feasible to perform experimental measurements of the Mobius strips
and cones described here theoretically
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
Linear systems solvers - recent developments and implications for lattice computations
We review the numerical analysis' understanding of Krylov subspace methods
for solving (non-hermitian) systems of equations and discuss its implications
for lattice gauge theory computations using the example of the Wilson fermion
matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES
are close to optimal for the Wilson fermion matrix. Consequently,
preconditioning appears to be the crucial issue for further improvements.Comment: 7 pages, LaTeX using espcrc2.sty, 2 figures, 9 eps-files, Talk
presented at LATTICE96(algorithms), submitted to Nucl. Phys. B, Proc. Supp
DVCS on nuclei: Observability and Consequences
In this paper, we discuss the feasibility of measuring deeply virtual Compton
scattering (DVCS) on nuclei in a collider setting, as for example, the planned
high-luminosity Electron-Ion-Collider (EIC). We demonstrate that employing our
recent model for nuclear generalized parton distributions (nGPDs), the
one-photon unpolarized DVCS cross section as well as the azimuthal- and spin
asymmetry are of the same size as in the proton case. This will allow for an
experimental extraction of nuclear GPDs with high precision shedding new light
on nuclear shadowing at small and the interplay of shadowing and
nuclear enhancement at .Comment: 9 pages, 18 figures, uses EPJ style format, final version to appear
in EPJ
Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear Polarization
The minor axes of, and the normals to, the polarization ellipses that
surround singular lines of linear polarization in three dimensional optical
ellipse fields are shown to be organized into Mobius strips and into structures
we call rippled rings (r-rings). The Mobius strips have two full twists, and
can be either right- or left-handed. The major axes of the surrounding ellipses
generate cone-like structures. Three orthogonal projections that give rise to
15 indices are used to characterize the different structures. These indices, if
independent, could generate 839,808 geometrically and topologically distinct
lines; selection rules are presented that reduce the number of lines to 8,248,
some 5,562 of which have been observed in a computer simulation. Statistical
probabilities are presented for the most important index combinations in random
fields. It is argued that it is presently feasible to perform experimental
measurements of the Mobius strips, r-rings, and cones described here
theoretically
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