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

Gravitational Lensing by Rotating Naked Singularities

We model massive compact objects in galactic nuclei as stationary, axially-symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are a static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are function of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightingly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The point-like caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure

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

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

Gravitational lensing in braneworld gravity: formalism and applications

In this article, we develop a formalism which is different from the standard lensing scenario and is necessary for understanding lensing by gravitational fields which arise as solutions of the effective Einstein equations on the brane. We obtain general expressions for measurable quantities such as time delay, deflection angle, Einstein ring and magnification. Subsequently, we estimate the deviations (relative to the standard lensing scenario) in the abovementioned quantities by considering the line elements for clusters and spiral galaxies obtained by solving the effective Einstein equations on the brane. Our analysis reveals that gravitational lensing can be a useful tool for testing braneworld gravity as well as the existence of extra dimensions.Comment: 20 pages, 1 figure, 2 tables. Accepted for publication in Classical and Quantum Gravit

Surface modification of mineral dust particles by sulphuric acid processing: Implications for ice nucleation abilities

The ability of coated mineral dust particles to act as ice nuclei (IN) was investigated at LACIS (Leipzig Aerosol Cloud Interaction Simulator) during the FROST1- and FROST2-campaigns (Freezing of dust). Sulphuric acid was condensed on the particles which afterwards were optionally humidified, treated with ammonia vapour and/or heat. By means of aerosol mass spectrometry we found evidence that processing of mineral dust particles with sulphuric acid leads to surface modifications of the particles. These surface modifications are most likely responsible for the observed reduction of the IN activation of the particles. The observed particle mass spectra suggest that different treatments lead to different chemical reactions on the particle surface. Possible chemical reaction pathways and products are suggested and the implications on the IN efficiency of the treated dust particles are discussed

Corrigendum to "Laboratory investigations of the impact of mineral dust aerosol on cold cloud formation" published in Atmos. Chem. Phys., 10, 11955–11968, 2010

No abstract available

Gravitational Lensing and f(R) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f(R) extended theories of gravity. Starting from an exact solution of the f(R) field equations, which corresponds to the Schwarzschild-de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the non linearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.Comment: 7 Pages, RevTex, 1 eps figure; references added; revised to match the version accepted for publication in General Relativity and Gravitatio