On Multiple Einstein Rings

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes.Comment: MNRAS, in press (extra figure included

Approximate Model Predictive Control for Nonlinear Multivariable Systems

The control of multi-input multi-output (MIMO) systems is a common problem in practical control scenarios. However in the last two decades, of the advanced control schemes, only linear model predictive control (MPC) was widely used in industrial process control (Ma-ciejowski, 2002). The fundamental common idea behind all MPC techniques is to rely o

A Simple Model for Lensing by Black Holes in Galactic Nuclei

The lensing properties of the Plummer model with a central point mass and external shear are derived, including the image multiplicities, critical curves and caustics. This provides a simple model for a flattened galaxy with a central supermassive black hole. For the Plummer model with black hole, the maximum number of images is 4, provided the black hole mass is less than an upper bound which is calculated analytically. This introduces a method to constrain black hole masses by counting images, thus applicable at cosmological distance. With shear, the maximum number of images is 6 and we illustrate the occurrence of an astroid caustic and two metamorphoses.Comment: 7 pages, 4 figures, MNRAS, in press, small changes mad

Saving primary energy consumption through exergy analysis of combine distillation and power plant / Alhassan Salami Tijani, Nazri Mohammed and Werner Witt

Industrial heat pumps are heat-recovery systems that allow the temperature of waste-heat stream to be increased to a higher, more efficient temperature. Consequently, heat pumps can improve energy efficiency in industrial processes as well as energy savings when conventional passive-heat recovery is not possible. In this paper, possible ways of saving energy in the chemical industry are considered, the objective is to reduce the primary energy (such as coal) consumption of power plant. Particularly the thermodynamic analyses of integrating backpressure turbine of a power plant with distillation units have been considered. Some practical examples such as conventional distillation unit and heat pump are used as a means of reducing primary energy consumption with tangible indications of energy savings. The heat pump distillation is operated via electrical power from the power plant. The exergy efficiency of the primary fuel is calculated for different operating range of the heat pump distillation. This is then compared with a conventional distillation unit that depends on saturated steam from a power plant as the source of energy. The results obtained show that heat pump distillation is an economic way to save energy if the temperature difference between the overhead and the bottom is small. Based on the result, the energy saved by the application of a heat pump distillation is improved compared to conventional distillation unit. Key words: Distillation units; Heat integration; Exergy/energy system modelling

Dust processing in photodissociation regions - Mid-IR emission modelling

Mid-infrared spectroscopy of dense illuminated ridges (or photodissociation regions, PDRs) suggests dust evolution. Such evolution must be reflected in the gas physical properties through processes like photo-electric heating or H_2 formation. With Spitzer Infrared Spectrograph (IRS) and ISOCAM data, we study the mid-IR emission of closeby, well known PDRs. Focusing on the band and continuum dust emissions, we follow their relative contributions and analyze their variations in terms of abundance of dust populations. In order to disentangle dust evolution and excitation effects, we use a dust emission model that we couple to radiative transfer. Our dust model reproduces extinction and emission of the standard interstellar medium that we represent with diffuse high galactic latitude clouds called Cirrus. We take the properties of dust in Cirrus as a reference to which we compare the dust emission from more excited regions, namely the Horsehead and the reflection nebula NGC 2023 North. We show that in both regions, radiative transfer effects cannot account for the observed spectral variations. We interpret these variations in term of changes of the relative abundance between polycyclic aromatic hydrocarbons (PAHs, mid-IR band carriers) and very small grains (VSGs, mid-IR continuum carriers). We conclude that the PAH/VSG abundance ratio is 2.4 times smaller at the peak emission of the Horsehead nebula than in the Cirrus case. For NGC2023 North where spectral evolution is observed across the northern PDR, we conclude that this ratio is ~5 times lower in the dense, cold zones of the PDR than in its diffuse illuminated part where dust properties seem to be the same as in Cirrus. We conclude that dust in PDRs seems to evolve from "dense" to "diffuse" properties at the small spatial scale of the dense illuminated ridge.Comment: 11 pages, 11 figures, accepted for publication in A&

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

Characterizing Ultraviolet and Infrared Observational Properties for Galaxies. I. Influences of Dust Attenuation and Stellar Population Age

The correlation between infrared-to-ultraviolet luminosity ratio and ultraviolet color, i.e. the IRX-UV relation, was regarded as a prevalent recipe for correcting extragalactic dust attenuation. Considerable dispersion in this relation discovered for normal galaxies, however, complicates its usability. In order to investigate the cause of the dispersion, in this paper, we select five nearby spiral galaxies, and perform spatially resolved studies on each of the galaxies, with a combination of ultraviolet and infrared imaging data. We measure all positions within each galaxy and divide the extracted regions into young and evolved stellar populations. By means of this approach, we attempt to discover separate effects of dust attenuation and stellar population age on the IRX-UV relation for individual galaxies. In this work, in addition to dust attenuation, stellar population age is interpreted to be another parameter in the IRX-UV function, and the diversity of star formation histories is suggested to disperse the age effects. At the same time, strong evidence shows the necessity of more parameters in the interpretation of observational data, such as variations in attenuation/extinction law. Fractional contributions of different components to the integrated luminosities of the galaxies suggest that the integrated measurements of galaxies which comprise different populations would weaken the effect of the age parameter on IRX-UV diagrams. The dependance of the IRX-UV relation on luminosity and radial distance in galaxies presents weak trends, which offers an implication of selective effects. The two-dimensional maps of the UV color and the infrared-to-ultraviolet ratio are displayed and show a disparity in the spatial distributions between the two parameters in galaxies, which offers a spatial interpretation of the scatter in the IRX-UV relation.Comment: 23 pages, 27 figures, 4 tables; accepted for publication in The Astrophysical Journal; re-typesetted in the emulateapj style; minor corrections in the figure symbols and in the tex

Modeling the interstellar aromatic infrared bands with co-added spectra of PAHs

The observed variations in profiles of the interstellar aromatic infrared bands correlate with the object type and are indicative of PAH populations existing i n different sources. Spectroscopic studies on PAHs can provide tools for the int erpretation of variations accompanying the AIBs. As the observed spectra results from a mix of possible species in the region attempt is made to model this comp osite spectra by co-adding emissions from PAHs in different size groups. Theoretical IR data of PAHs having 10 to 96 carbon atoms is used to obtain emis sion spectra. The models are taken in size groups making up of small, medium and large PAHs. The models show good profile match with observations for the 7.7 $\mu m$ complex having sub-features at 7.6 and 7.8 $\mu m$. The 7.6 $\mu m$ sub-feature dominates in the spectra of medium sized PAH cations matching observations from UV rich interstellar environments. The 7.8 $\mu m$ component is more intense in the spectra of large PAH cations (model III) correlating with observations from benign astrophysical regions. A possible interpretation for the observations of $C-H$ out-of-plane bend modes and the weak outliers on the blue side of the intense 11.2 $\mu m$ band is proposed. The models provide pointers to possible PAH populations in different regions.Comment: accepted for publication in A&