Related papers: Vortex metrology using circular and elliptical Lag…
Vortices are topologically stable singularities at the center of a swirl of energy. Optical vortices are conventionally formed using diffractive optics or by bespoke optical elements. We report room temperature integrated lasers directly…
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as…
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of anyone of the four Chebyshev weights, considered by Gautschi and Li in \cite{gauli}. As it is well known, in the case of analytic integrands,…
The analysis of twisted (vortex) paraxial photons and electrons is fulfilled in the framework of relativistic quantum mechanics. The use of the Foldy-Wouthuysen representation radically simplifies a description of relativistic electrons and…
We derive a non-dimensional metric to quantify the expected Lagrangian persistence of objectively defined Eulerian vortices in two-dimensional unsteady flows. This persistence metric is the averaged deviation of the vorticity from its…
Laguerre-Gaussian (LG) modes are solutions of the paraxial Helmholtz equation in cylindrical coordinates and are associated with light fields carrying orbital angular momentum (OAM). It is customary to modulate such beams using phase-only…
We introduce a formalism to describe 2D-Potentials for 2D-matter (or charge) distributions with arbitrary elliptical symmetry including varying eccentricity and twisting of the iso-density curves. We use this approach to describe elliptical…
It is shown that in the modified axial gauge version of canonically quantized QCD$_{3+1}$ on a torus only nongeneric gauge field configurations allow for large gauge transformations. For the other configurations, the gauge is fixed…
A kinematical analysis applied to a sample of galaxy clusters indicates that the differences between the velocity distribution of elliptical and spiral galaxies are associated with the shape of their orbit families. The orbital anisotropies…
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel $\kappa$, which translates naturally into kernels between histograms or clouds of points. We first cover…
In TEM, a typical goal consists of making a small electron probe in the sample plane in order to obtain high spatial resolution in scanning transmission electron microscopy. In order to do so, the phase of the electron wave is corrected to…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…
The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However,…
Laguerre geometry of surfaces in $\R^3$ is given in the book of Blaschke [1], and have been studied by E.Musso and L.Nicolodi [5], [6], [7], B. Palmer [8] and other authors. In this paper we study Laguerre differential geometry of…
Particles are a widespread tool for obtaining information from fluid flows. When Eulerian data are unavailable, they may be employed to estimate flow fields or to identify coherent flow structures. Here we numerically examine the…
Introducing a spatial chirp into a pulse with a longitudinal vortex, such as a standard pulsed Laguerre-Gauss beam, results in a vortex pulse with an arbitrary orientation of the line phase singularity between longitudinal and transverse,…
The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by K.…
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…