473 research outputs found
Topological events on wave dislocation lines: birth and death of small loops, and reconnection
In three-dimensional space, a wave dislocation, that is, a quantized (optical) vortex or phase singularity, is a line zero of a complex scalar wavefunction. As a 'time' parameter varies, the topology of the vortex can change by encounter with a line of vanishing vorticity (curl of the current associated with the wavefunction). An isolated critical point of the field intensity, sliding along the zero-vorticity line like a bead on a wire, meets the vortex as it encounters the line, and so participates in the singular event. Local expansio n and gauge and coordinates transformations show that the vortex topology can change generically by the appearance or disappearance of a loop, or by the reconnection of branches of a pair of hyperbolas
Polarization singularities in the clear sky
Ideas from singularity theory provide a simple account of the pattern of polarization directions in daylight. The singularities (two near the Sun and two near the anti-Sun) are points in the sky where the polarization line pattern has index +1/2 and the intensity of polarization is zero. The singularities are caused by multiple scattering that splits into two each of the unstable index +1 singularities at the Sun and anti-Sun, which occur in the single-dipole scattering (Rayleigh) theory. The polarization lines are contours of an elliptic integral. For the intensity of polarization (unnormalized degree), it is necessary to incorporate the strong depolarizing effect of multiple scattering near the horizon. Singularity theory is compared with new digital images of sky polarization, and gives an excellent description of the pattern of polarization directions. For the intensity of polarization, the theory can reproduce not only the zeros but also subtle variations in the polarization maxima
Vortex knots in light
Optical vortices generically arise when optical beams are combined. Recently, we reported how several laser beams containing optical vortices could be combined to form optical vortex loops, links and knots embedded in a light beam (Leach et al 2004 Nature 432 165). Here, we describe in detail the experiments in which vortex loops form these structures. The experimental construction follows a theoretical model originally proposed by Berry and Dennis, and the beams are synthesized using a programmable spatial light modulator and imaged using a CCD camera
The super-oscillating superlens
We demonstrate a lens that creates a sub-wavelength focal spot beyond the near-field by exploiting the phenomenon of super-oscillation
Large scale directional anomalies in the WMAP 5yr ILC map
We study the alignments of the low multipoles of CMB anisotropies with
specific directions in the sky (i.e. the dipole, the north Ecliptic pole, the
north Galactic pole and the north Super Galactic pole). Performing
random extractions we have found that: 1) separately quadrupole and octupole
are mildly orthogonal to the dipole but when they are considered together, in
analogy to \cite{Copi2006}, we find an unlikely orthogonality at the level of
0.8% C.L.; 2) the multipole vectors associated to are unlikely aligned
with the dipole at C.L.; 3) the multipole vectors associated to
are mildly orthogonal to the dipole but when we consider only maps
that show exactly the same correlation among the multipoles as in the observed
WMAP 5yr ILC, these multipole vectors are unlikely orthogonal to the dipole at
C.L..Comment: 12 pages, 10 figures, 3 tables. Accepted for publication in JCAP. Few
references added and some typos correcte
Non-parametric characterization of blast loads
Mathematical analysis of blast pressures has typically involved the empirical fitting of parametric models, which assumes a specific function shape. In reality, the true shape of the blast pressure is unknown and may lack a parametric form, particularly in the negative phase following arrival of the secondary shock. In this work, we develop a non-parametric (NP) representation that makes few assumptions and relies on the observed experimental data to fit a unique and previously unknown model. This differs from traditional approaches by not arbitrarily selecting a single, restrictive class of functions and estimating a minimal set of parameters, but rather estimating the underlying function class for which the blast pressure is generated; learning the model directly from the observed data. The method was applied to experimental blast measurements and the NP estimates matched the experimental data with a high degree of accuracy, both qualitatively and quantitatively. The NP approach was shown to significantly outperform other commonly used approaches, near-perfectly track the entire pressure and specific impulse history and predicting experimental peak specific impulse to within ±0.5% in all cases (compared to ±5.0% for a trained artificial neural network (ANN) and ±7.5% for the UFC semi-empirical approach). The NP approach predicts experimental net specific impulses (positive and negative phases combined) with a maximum variation of 2.7%, compared to maximum variations of −116% and 55% for the UFC and ANN approaches, respectively. Since the framework is probabilistic in nature, it can naturally account for random noise in sensor measurements, which are typically more pronounced in blast experiments than many other machine learning applications
Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
Using coherent-state techniques, we prove a sampling theorem for Majorana's
(holomorphic) functions on the Riemann sphere and we provide an exact
reconstruction formula as a convolution product of samples and a given
reconstruction kernel (a sinc-type function). We also discuss the effect of
over- and under-sampling. Sample points are roots of unity, a fact which allows
explicit inversion formulas for resolution and overlapping kernel operators
through the theory of Circulant Matrices and Rectangular Fourier Matrices. The
case of band-limited functions on the Riemann sphere, with spins up to , is
also considered. The connection with the standard Euler angle picture, in terms
of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App
Vortex lines of the electromagnetic field
Relativistic definition of the phase of the electromagnetic field, involving
two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to
extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C.
Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded
in the solutions of wave equations from Schroedinger wave mechanics to Maxwell
theory. It is shown that time evolution of vortex lines has universal features;
in Maxwell theory it is very similar to that in Schroedinger wave mechanics.
Connection with some early work on geometrodynamics is established. Simple
examples of solutions of Maxwell equations with embedded vortex lines are
given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.
High-energy physics with particles carrying non-zero orbital angular momentum
Thanks to progress in optics in the past two decades, it is possible to
create photons carrying well-defined non-zero orbital angular momentum (OAM).
Boosting these photons into high-energy range preserving their OAM seems
feasible. Intermediate energy electrons with OAM have also been produced
recently. One can, therefore, view OAM as a new degree of freedom in
high-energy collisions and ask what novel insights into particles' structure
and interactions it can bring. Here we discuss generic features of scattering
processes involving particles with OAM in the initial state. We show that they
make it possible to perform a Fourier analysis of a plane wave cross section
with respect to the azimuthal angles of the initial particles, and to probe the
autocorrelation function of the amplitude, a quantity inaccessible in plane
wave collisions.Comment: 7 pages, 1 figure, talk given at the workshop "30 years of strong
interactions", Spa, Belgium, 6-8 April 201
Deterministically Driven Avalanche Models of Solar Flares
We develop and discuss the properties of a new class of lattice-based
avalanche models of solar flares. These models are readily amenable to a
relatively unambiguous physical interpretation in terms of slow twisting of a
coronal loop. They share similarities with other avalanche models, such as the
classical stick--slip self-organized critical model of earthquakes, in that
they are driven globally by a fully deterministic energy loading process. The
model design leads to a systematic deficit of small scale avalanches. In some
portions of model space, mid-size and large avalanching behavior is scale-free,
being characterized by event size distributions that have the form of
power-laws with index values, which, in some parameter regimes, compare
favorably to those inferred from solar EUV and X-ray flare data. For models
using conservative or near-conservative redistribution rules, a population of
large, quasiperiodic avalanches can also appear. Although without direct
counterparts in the observational global statistics of flare energy release,
this latter behavior may be relevant to recurrent flaring in individual coronal
loops. This class of models could provide a basis for the prediction of large
solar flares.Comment: 24 pages, 11 figures, 2 tables, accepted for publication in Solar
Physic
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