A Universal Magnification Theorem III. Caustics Beyond Codimension Five

In the final paper of this series, we extend our results on magnification invariants to the infinite family of A, D, E caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A, D, E family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real pre-images), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula.Comment: 8 page

Расчет распределения температуры по поверхности низкотемпературного композиционного электрообогревателя для предприятий агропромышленного комплекса

Получены аналитические зависимости и приведены результаты расчета численных значений распределения температур по поверхности низкотемпературного композиционного электрообогревателя, которые могут быть использованы при проектировании аналогичных изделий в различных областях сельского хозяйства и промышленности

O(a)O(a) Improvement for Quenched Wilson Fermions

We briefly describe some of our recent results for the mass spectrum and matrix elements using $O(a)$ improved fermions for quenched QCD. Where possible a comparison is made between improved and Wilson fermions.Comment: 6 pages, Latex, 11 figures, epsf.sty and buckow1.sty needed (buckow1.sty included). Talk presented at the 31st Ahrenshoop Symposium on the Theory of Elementary Particles, September 1997, Buckow, German

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Wind-driven emissions of coarse-mode particles in an urban environment

Quantifying surface–atmosphere exchange rates of particles is important for understanding the role of suspended particulate matter in radiative transfer, clouds, precipitation, and climate change. Emissions of coarse-mode particles with a diameter greater than 0.5 µm provide giant cloud condensation nuclei and ice nuclei. These emissions are critical for understanding the evolution of cloud microphysical properties yet remain poorly understood. Here we introduce a new method that uses lidar retrievals of the elastic backscatter and Doppler velocity to obtain surface number emissions of particles with a diameter greater than 0.53 µm. The technique is applied to study particle number fluxes over a 2-month period from 1 June to 10 August 2022 during the TRACER campaign at an urban site near Houston, TX, USA. We found that all the observed fluxes were positive (upwards), indicating particle emission from the surface. The fluxes followed a diurnal pattern and peaked near noon local time. Flux intensity varied through the 2 months with multi-day periods of strong fluxes and multi-day periods of weak fluxes. Emission particle number fluxes peaked near ∼ 100 cm−2 s−1. The daily averaged emission fluxes correlated with friction velocity and were anticorrelated with surface relative humidity. The emission flux can be parameterized as F= 3000 u*4, where u* is the friction velocity in m s−1 and the emission flux F is in cm−2 s−1. The u* dependence is consistent with emission from wind-driven erosion. Estimated values for the mass flux are in the lower range of literature values from non-urban sites. These results demonstrate that urban environments may play an important role in supplying coarse-mode particles to the boundary layer. We anticipate that quantification of these emissions will help constrain aerosol–cloud interaction models that use prognostic aerosol schemes.</p

Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

Image distortion in non perturbative gravitational lensing

We introduce the idea of {\it shape parameters} to describe the shape of the pencil of rays connecting an observer with a source lying on his past lightcone. On the basis of these shape parameters, we discuss a setting of image distortion in a generic (exact) spacetime, in the form of three {\it distortion parameters}. The fundamental tool in our discussion is the use of geodesic deviation fields along a null geodesic to study how source shapes are propagated and distorted on the path to an observer. We illustrate this non-perturbative treatment of image distortion in the case of lensing by a Schwarzschild black hole. We conclude by showing that there is a non-perturbative generalization of the use of Fermat's principle in lensing in the thin-lens approximation.Comment: 22 pages, 6 figures, to appear in Phys. Rev. D (January 2001

Ice Initiation by Aerosol Particles: Measured and Predicted Ice Nuclei Concentrations versus Measured Ice Crystal Concentrations in an Orographic Wave Cloud

The initiation of ice in an isolated orographic wave cloud was compared with expectations based on ice nucleating aerosol concentrations and with predictions from new ice nucleation parameterizations applied in a cloud parcel model. Measurements of ice crystal number concentrations were found to be in good agreement both with measured number concentrations of ice nuclei feeding the clouds and with ice nuclei number concentrations determined from the residual nuclei of cloud particles collected by a counterflow virtual impactor. Using lognormal distributions fitted to measured aerosol size distributions and measured aerosol chemical compositions, ice nuclei and ice crystal concentrations in the wave cloud were reasonably well predicted in a 1D parcel model framework. Two different empirical parameterizations were used in the parcel model: a parameterization based on aerosol chemical type and surface area and a parameterization that links ice nuclei number concentrations to the number concentrations of particles with diameters larger than 0.5 μm. This study shows that aerosol size distribution and composition measurements can be used to constrain ice initiation by primary nucleation in models. The data and model results also suggest the likelihood that the dust particle mode of the aerosol size distribution controls the number concentrations of the heterogeneous ice nuclei, at least for the lower temperatures examined in this case