The dissipative linear boltzmann equation

AbstractWe introduce and discuss a linear Boltzmann equation describing dissipative interactions of a gas of test particles with a fixed background. For a pseudo-Maxwellian collision kernel, it is shown that, if the initial distribution has finite temperature, the solution converges exponentially for large time to a Maxwellian profile drifting at the same velocity as field particles and with a universal nonzero temperature which is lower than the given background temperature

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

Surface smoothness requirements for the mirrors of the IXO X-ray telescope

The International X-ray Observatory (IXO) is a very ambitious mission, aimed at the X-ray observation of the early Universe. This makes IXO extremely demanding in terms of effective area and angular resolution. In particular, the HEW requirement below 10 keV is 5 arcsec Half-Energy Width (HEW). At higher photon energies, the HEW is expected to increase, and the angular resolution to be correspondingly degraded, due to the increasing relevance of the X-ray scattering off the reflecting surfaces. Therefore, the HEW up to 40 keV is required to be better than 30 arcsec, even though the IXO goal is to achieve an angular resolution as close as possible to 5 arcsec also at this energy. To this end, the roughness of the reflecting surfaces has to not exceed a tolerance, expressed in terms of a surface roughness PSD (Power-Spectral-Density). In this work we provide such tolerances by simulating the HEW scattering term for IXO, assuming a specific configuration for the optical module and different hypotheses on the PSD of mirrors

Plasma kisspeptin levels are associated with insulin secretion in nondiabetic individuals

To evaluate if plasma kisspeptin concentrations are associated with insulin secretion, as suggested by recent in vitro studies, independently of confounders. 261 nondiabetic subjects were stratified into tertiles according to kisspeptin values. Insulin secretion was assessed using indexes derived from oral glucose tolerance test (OGTT). After adjusting for age, gender, and BMI, subjects in the highest (tertile 3) kisspeptin group exhibited significantly lower values of insulinogenic index, corrected insulin response (CIR30), and Stumvoll indexes for first-phase and second-phase insulin release as compared with low (tertile 1) or intermediate (tertile 2) kisspeptin groups. Univariate correlations between kisspeptin concentration and metabolic variables showed that kisspeptin concentration was significantly and positively correlated with age, blood pressure, and 2-h post-load glucose, and inversely correlated with BMI, and waist circumference. There was an inverse relationship between kisspeptin levels and OGTT-derived indexes of glucose-stimulated insulin secretion. A multivariable regression analysis in a model including all the variables significantly correlated with kisspeptin concentration showed thar age (β = -0.338, P<0.0001), BMI (β = 0.272, P<0.0001), 2-h post-load glucose (β = -0.229, P<0.0001), and kisspeptin (β = -0.105, P = 0.03) remained associated with insulinogenic index. These factors explained 34.6% of the variance of the insulinogenic index. In conclusion, kisspeptin concentrations are associated with insulin secretion independently of important determinants of glucose homeostasis such as gender, age, adiposity, 2-h post-load glucose, and insulin sensitivity

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

Insulin-like growth factor-1 is a negative modulator of glucagon secretion

Glucagon secretion involves a combination of paracrine, autocrine, hormonal, and autonomic neural mechanisms. Type 2 diabetes often presents impaired glucagon suppression by insulin and glucose. Insulin-like growth factor-I (IGF-1) has elevated homology with insulin, and regulates pancreatic β-cells insulin secretion. Insulin and IGF-1 receptors share considerable structure homology and function. We hypothesized the existence of a mechanism linking the inhibition of α-cells glucagon secretion to IGF-1. Herein, we evaluated the association between plasma IGF-1 and glucagon levels in 116 nondiabetic adults. After adjusting for age gender and BMI, fasting glucagon levels were positively correlated with 2-h post-load glycaemia, HOMA index and fasting insulin, and were negatively correlated with IGF-1 levels. In a multivariable regression, the variables independently associated to fasting glucagon were circulating IGF-1 levels, HOMA index and BMI, explaining 20.7% variation. To unravel the molecular mechanisms beneath IGF-1 and glucagon association, we investigated whether IGF-1 directly modulates glucagon expression and secretion in an in vitro model of α-cells. Our data showed that IGF-1 inhibits the ability of low glucose concentration to stimulate glucagon expression and secretion via activation of the phosphatidylinositol-3-kinase/Akt/FoxO1 pathway. Collectively, our results suggest a new regulatory role of IGF-1 on α-cells biological function

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