Search results for "singularity"
showing 10 items of 352 documents
Study of η and η′ Photoproduction at MAMI
2017
The reactions γp→ηp and γp→η′p are measured from their thresholds up to the center-of-mass energy W=1.96 GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross sections are obtained with unprecedented statistical accuracy, providing fine energy binning and full production-angle coverage. A strong cusp is observed in the total cross section for η photoproduction at the energies in the vicinity of the η′ threshold, W=1896 MeV (Eγ=1447 MeV). Within the framework of a revised ηMAID isobar model, the cusp, in connection with a steep rise of the η′ total cross section from its threshold, can only be explained by a strong coupling of the poorly known N(1895)1/2− …
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
1987
AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to
Orthogonality Catastrophe and Decoherence in a Trapped-Fermion Environment
2012
The Fermi edge singularity and the Anderson orthogonality catastrophe describe the universal physics which occurs when a Fermi sea is locally quenched by the sudden switching of a scattering potential, leading to a brutal disturbance of its ground state. We demonstrate that the effect can be seen in the controllable domain of ultracold trapped gases by providing an analytic description of the out-of-equilibrium response to an atomic impurity, both at zero and at finite temperature. Furthermore, we link the transient behavior of the gas to the decoherence of the impurity, and, in particular to the amount of non-markovianity of its dynamics.
Coherent quasiparticle approximation (cQPA) and nonlocal coherence
2010
We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum…
Mössbauer gamma-ray diffraction from the molecular crystal KCN
1980
Abstract Mossbauer gamma-ray diffraction was applied to separate the elastic and inelastic scattering intensities from the (200), (400) and (600) Bragg reflections of KCN. The energy resolution of our experiment was 60 neV. The Debye-Waller factor extracted from the elastic data and the thermal diffuse inelastic data both increase towards phase transition, theoretically a logarithmic singularity was predicted.
Subwavelength beams with polarization singularities in plasmonic metamaterials
2014
We investigated the diffraction behavior of plasmonic Bessel beams propagating in metal-dielectric stratified materials and wire media. Our results reveal various regimes in which polarization singularities are selectively maintained. This polarization-pass effect can be controlled by appropriately setting the filling factor of the metallic inclusions and its internal periodic distribution. These results may have implications in the development of devices at the nanoscale level for manipulation of polarization and angular momentum of cylindrical vector beams. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2011-29120-C05-01.
Non-Homogeneity of Lateral Resolution in Integral Imaging
2013
We evaluate the lateral resolution in reconstructed integral images. Our analysis takes into account both the diffraction effects in the image capture stage and the lack of homogeneity and isotropy in the reconstruction stage. We have used Monte Carlo simulation in order to assign a value for the resolution limit to any reconstruction plane. We have modelled the resolution behavior. Although in general the resolution limit increases proportionally to the distance to the lens array, there are some periodically distributed singularity planes. The phenomenon is supported by experiments.
Elliptic equations having a singular quadratic gradient term and a changing sign datum
2012
In this paper we study a singular elliptic problem whose model is \begin{eqnarray*} - \Delta u= \frac{|\nabla u|^2}{|u|^\theta}+f(x), in \Omega\\ u = 0, on \partial \Omega; \end{eqnarray*} where $\theta\in (0,1)$ and $f \in L^m (\Omega)$, with $m\geq \frac{N}{2}$. We do not assume any sign condition on the lower order term, nor assume the datum $f$ has a constant sign. We carefully define the meaning of solution to this problem giving sense to the gradient term where $u=0$, and prove the existence of such a solution. We also discuss related questions as the existence of solutions when the datum $f$ is less regular or the boundedness of the solutions when the datum $f \in L^m (\Omega)$ with …
Positive solutions of Dirichlet and homoclinic type for a class of singular equations
2018
Abstract We study a nonlinear singular boundary value problem and prove that, depending on a relationship between exponents of power terms, the problem has either solutions of Dirichlet type or homoclinic solutions. We make use of shooting techniques and lower and upper solutions.
An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
2005
We present the first exact, complete and efficient implementation that computes for a given set P=p1,...,pn of quadric surfaces the planar map induced by all intersection curves p1∩ pi, 2 ≤ i ≤ n, running on the surface of p1. The vertices in this graph are the singular and x-extreme points of the curves as well as all intersection points of pairs of curves. Two vertices are connected by an edge if the underlying points are connected by a branch of one of the curves. Our work is based on and extends ideas developed in [20] and [9].Our implementation is complete in the sense that it can handle all kind of inputs including all degenerate ones where intersection curves have singularities or pa…