Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Abstract Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved

Kinetic models for reactive mixtures: Problems and applications

Problems related to physical consistency and practical application of kinetic BGK models for reactive mixtures are investigated. In particular, two approximation strategies are discussed, relevant to the different physical scenarios of slow and fast chemical reactions, respectively. The former is tested versus the steady shock problem in comparison to available hydrodynamic results. For the latter, allowing for an explicit proof of the H-theorem, a preliminary sample is shown of the space homogeneous calculations in progress

Qualitative analysis of kinetic-based models for tumor-immune system interaction

A mathematical model, based on a mesoscopic approach, describing the competition between tumor cells and immune system in terms of kinetic integro-differential equations is presented. Four interacting populations are considered, representing, respectively, tumors cells, cells of the host environment, cells of the immune system, and interleukins, which are capable to modify the tumor-immune system interaction and to contribute to destroy tumor cells. The internal state variable (activity) measures the capability of a cell of prevailing in a binary interaction. Under suitable assumptions, a closed set of autonomous ordinary differential equations is then derived by a moment procedure and two three-dimensional reduced systems are obtained in some partial quasi-steady state approximations. Their qualitative analysis is finally performed, with particular attention to equilibria and their stability, bifurcations, and their meaning. Results are obtained on asymptotically autonomous dynamical systems, and also on the occurrence of a particular backward bifurcation

Shock wave structure of multi-temperature Euler equations from kinetic theory for a binary mixture

A multi-temperature hydrodynamic limit of kinetic equations is employed for the analysis of the steady shock problem in a binary mixture. Numerical results for varying parameters indicate possible occurrence of either smooth profiles or of weak solutions with one or two discontinuities. \ua9 2014 Springer Science+Business Media Dordrecht

Design and advancement status of the Beam Expander Testing X-ray facility (BEaTriX)

The BEaTriX (Beam Expander Testing X-ray facility) project is an X-ray apparatus under construction at INAF/OAB to generate a broad (200 x 60 mm2), uniform and low-divergent X-ray beam within a small lab (6 x 15 m2). BEaTriX will consist of an X-ray source in the focus a grazing incidence paraboloidal mirror to obtain a parallel beam, followed by a crystal monochromation system and by an asymmetrically-cut diffracting crystal to perform the beam expansion to the desired size. Once completed, BEaTriX will be used to directly perform the quality control of focusing modules of large X-ray optics such as those for the ATHENA X-ray observatory, based on either Silicon Pore Optics (baseline) or Slumped Glass Optics (alternative), and will thereby enable a direct quality control of angular resolution and effective area on a number of mirror modules in a short time, in full X-ray illumination and without being affected by the finite distance of the X-ray source. However, since the individual mirror modules for ATHENA will have an optical quality of 3-4 arcsec HEW or better, BEaTriX is required to produce a broad beam with divergence below 1-2 arcsec, and sufficient flux to quickly characterize the PSF of the module without being significantly affected by statistical uncertainties. Therefore, the optical components of BEaTriX have to be selected and/or manufactured with excellent optical properties in order to guarantee the final performance of the system. In this paper we report the final design of the facility and a detailed performance simulation.Comment: Accepted paper, pre-print version. The finally published manuscript can be downloaded from http://dx.doi.org/10.1117/12.223895

Electro-osmotic flows inside triangular microchannels

This work presents a numerical investigation of both pure electro-osmotic and combined electro-osmotic/pressure-driven flows inside triangular microchannels. A finite element analysis has been adopted to solve the governing equations for the electric potential and the velocity field, accounting for a finite thickness of the electric double layer. The influence of non-dimensional parameters such as the aspect ratio of the cross-section, the electrokinetic diameter and the ratio of the pressure force to the electric force on the flow behavior has been investigated. Numerical results point out that the velocity field is significantly influenced by the aspect ratio of the cross section and the electrokinetic diameter. More specifically, the aspect ratio plays an important role in determining the maximum volumetric flow rate, while the electrokinetic diameter is crucial to establishing the range of pressures that may be sustained by the electro-osmotic flow. Numerical results are also compared with two correlations available in the literature which enable to assess the volumetric flow rate and the pressure head for microchannels featuring a rectangular, a trapezoidal or an elliptical cross-section

Active shape correction of a thin glass/plastic X-ray mirror

Optics for future X-ray telescopes will be characterized by very large aperture and focal length, and will be made of lightweight materials like glass or plastic in order to keep the total mass within acceptable limits. Optics based on thin slumped glass foils are currently in use in the NuSTAR telescope and are being developed at various institutes like INAF/OAB, aiming at improving the angular resolution to a few arcsec HEW. Another possibility would be the use of thin plastic foils, being developed at SAO and the Palermo University. Even if relevant progresses in the achieved angular resolution were recently made, a viable possibility to further improve the mirror figure would be the application of piezoelectric actuators onto the non-optical side of the mirrors. In fact, thin mirrors are prone to deform, so they require a careful integration to avoid deformations and even correct forming errors. This however offers the possibility to actively correct the residual deformation. Even if other groups are already at work on this idea, we are pursuing the concept of active integration of thin glass or plastic foils with piezoelectric patches, fed by voltages driven by the feedback provided by X-rays, in intra-focal setup at the XACT facility at INAF/OAPA. In this work, we show the preliminary simulations and the first steps taken in this project