The Nuker model for galactic nuclei

The Nuker profile, characterised by an inner and outer power-law profile smoothly merged around a break radius, is a very popular model to describe the surface brightness profile of galactic nuclei. A disadvantage of this model for dynamical studies is that the spatial density distribution that corresponds to this surface brightness profile cannot be written in terms of elementary or regular special functions. We derive a compact and elegant analytical expression for the density of the Nuker model, based the Mellin integral transform method. We use this expression to discuss the general behaviour and asymptotic expansion of the density. We also discuss the special subclass of Nuker models with an infinitely sharp break and demonstrate that these models are always characterised by non-monotonous and hence unphysical density profile. We extend our study to the dynamical structure of spherical isotropic galactic nuclei with a Nuker surface brightness profile. Based on this analysis, we extend and refine the classification of spherical isotropic galactic nuclei introduced by Tremaine et al. (1994, AJ, 107, 634). We demonstrate that both the inner density slope and the sharpness of the break between the inner and outer profiles critically determine the consistency and stability of the Nuker models.

Панорамная спектроскопия спонтанного комбинационного рассеяния для диагностики струйных реагирующих потоков с использованием перестраиваемого фильтра Лио-Эмана

The spatial-density distribution in burning a premixed methane–air swirling turbulent jet has been studied by measuring the intensity of the Stokes branch of spontaneous Raman scattering for vibrational–rotational transitions in nitrogen. An optical system comprising a Nd:YAG laser and the liquid-crystalline Lyot–Ehman tunable filter has been created and tested by measuring the temperature and density fields in a cone-shaped laminar flame. It has been established that the difference of data obtained using the Stokes component of Raman scattering in nitrogen and its ratio to the anti-Stokes component does not exceed 5% in a temperature range from 300 to 1800 K.

Numerical Simulation of Spark Plasma Sintering

A macro-scale model of spark plasma sintering (SPS) that couples electrical, thermal, stress-strain and densification components is presented. The continuum theory of sintering is incorporated enabling the evolution of the densification based on local conditions, thus a true spatial density distribution could be obtained. Specimen behavior is described through a non-linear viscous constitutive relation. The simulation is based on an FEM computer code. Several examples are shown and results are compared with experimental data available.