Hydrodynamic states of phonons in insulators

The Chapman-Enskog method is generalized for accounting the effect of kinetic modes on hydrodynamic evolution. Hydrodynamic states of phonon system of insulators have been studied in a small drift velocity approximation. For simplicity, the investigation was carried out for crystals of the cubic class symmetry. It has been found that in phonon hydrodynamics, local equilibrium is violated even in the approximation linear in velocity. This is due to the absence of phonon momentum conservation law that leads to a drift velocity relaxation. Phonon hydrodynamic equations which take dissipative processes into account have been obtained. The results were compared with the standard theory based on the local equilibrium validity. Integral equations have been obtained for calculating the objects of the theory (including viscosity and heat conductivity). It has been shown that in low temperature limit, these equations are solvable by iterations. Steady states of the system have been considered and an expression for steady state heat conductivity has been obtained. It coincides with the famous result by Akhiezer in the leading low temperature approximation. It has been established that temperature distribution in the steady state of insulator satisfies a condition of heat source absence.Comment: 10 page

Generalization of the Grad method in plasma physics

The Grad method is generalized based on the Bogolyubov idea of the functional hypothesis for states at the end of relaxation processes in a system. The Grad problem (i.e., description of the Maxwell relaxation) for a completely ionized spatially uniform two-component electron-ion plasma is investigated using the Landau kinetic equation. The component distribution functions and time evolution equations for parameters describing the state of a system are calculated, and corrections are obtained to the known results in a perturbation theory in a small electron-to-ion mass ratio.Comment: 10 pages, 2 table

On relaxation phenomena in a two-component plasma

The relaxation of temperatures and velocities of the components of a quasi-equilibrium two-component homogeneous completely ionized plasma is investigated on the basis of a generalization of the Chapman-Enskog method applied to the Landau kinetic equation. The generalization is based on the functional hypothesis in order to account for the presence of kinetic modes of the system. In the approximation of a small difference of the component temperatures and velocities, it is shown that relaxation really exists (the relaxation rates are positive). The proof is based on the arguments that are valid for an arbitrary two-component system. The equations describing the temperature and velocity kinetic modes of the system are investigated in a perturbation theory in the square root of the small electron-to-ion mass ratio. The equations of each order of this perturbation theory are solved with the help of the Sonine polynomial expansion. Corrections to the known Landau results related to the distribution functions of the plasma and relaxation rates are obtained. The hydrodynamic theory based on these results should take into account a violation of local equilibrium in the presence of relaxation processes.Comment: 18 page

The asymmetric sandwich theorem

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.Comment: 17 page

An XMM-Newton look at the strongly variable radio-weak BL Lac Fermi J1544-0639

Fermi J1544-0639/ASASSN-17gs/AT2017egv was identified as a gamma-ray/optical transient on May 15, 2017. Subsequent multiwavelength observations suggest that this source may belong to the new class of radio-weak BL Lacs. We studied the X-ray spectral properties and short-term variability of Fermi J1544-0639 to constrain the X-ray continuum emission mechanism of this peculiar source. We present the analysis of an XMM-Newton observation, 56 ks in length, performed on February 21, 2018. The source exhibits strong X-ray variability, both in flux and spectral shape, on timescales of ~10 ks, with a harder-when-brighter behaviour typical of BL Lacs. The X-ray spectrum is nicely described by a variable broken power law, with a break energy of around 2.7 keV consistent with radiative cooling due to Comptonization of broad-line region photons. We find evidence for a `soft excess', nicely described by a blackbody with a temperature of ~0.2 keV, consistent with being produced by bulk Comptonization along the jet.Comment: 11 pages, 12 figures. Accepted for publication in Astronomy & Astrophysic