The Steady Boltzmann and Navier-Stokes Equations

The paper discusses the similarities and the differences in the mathematical theories of the steady Boltzmann and incompressible Navier-Stokes equations posed in a bounded domain. First we discuss two different scaling limits in which solutions of the steady Boltzmann equation have an asymptotic behavior described by the steady Navier-Stokes Fourier system. Whether this system includes the viscous heating term depends on the ratio of the Froude number to the Mach number of the gas flow. While the steady Navier-Stokes equations with smooth divergence-free external force always have at least one smooth solutions, the Boltzmann equation with the same external force set in the torus, or in a bounded domain with specular reflection of gas molecules at the boundary may fail to have any solution, unless the force field is identically zero. Viscous heating seems to be of key importance in this situation. The nonexistence of any steady solution of the Boltzmann equation in this context seems related to the increase of temperature for the evolution problem, a phenomenon that we have established with the help of numerical simulations on the Boltzmann equation and the BGK model.Comment: 55 pages, 4 multiple figure

Asymptotic Theory of Slightly Rarefied Gas Flow and Force on a Closed Body

Steady gas flows at small Knudsen numbers around arbitrary bodies (asymptotic behavior for small Knudsen numbers of the solution of time-independent boundary value problems of the Boltzmann equation over a general domain) are considered when the Reynolds number of the system is of the order of unity. The generalized slip flow theory developed for the Boltzmann-Krook-Welander equation is extended for the standard Boltzmann equation. From the result, the effect of gas rare faction on the flow (the relation between Boltzmann and hydrodynamic systems) is clarified, and several features of the force on a closed body in the gas are derived

A force acting on an oblate spheroid with discontinuous surface temperature in a slightly rarefied gas

An oblate spheroid, the respective hemispheroids of which are kept at different uniform temperatures, placed in a rarefied gas at rest is considered. The explicit formula for the force acting on the spheroid (radiometric force) is obtained for small Knudsen numbers. This is a model of a vane of the Crookes radiometer. The analysis is performed for a general axisymmetric distribution of the surface temperature of the spheroid, allowing abrupt changes. Although the generalized slip flow theory, established by Sone (Rarefied Gas Dynamics, vol. 1, 1969, pp. 243–253), is available for general rarefied gas flows at small Knudsen numbers, it cannot be applied to the present problem because of the abrupt temperature changes. However, if it is combined with the symmetry relations for the linearized Boltzmann equation developed recently by Takata (J. Stat. Phys., vol. 136, 2009, pp. 751–784), one can bypass the difficulty. To be more specific, the force acting on the spheroid in the present problem can be generated from the solution of the adjoint problem to which the generalized slip flow theory can be applied, i.e. the problem in which the same spheroid with a uniform surface temperature is placed in a uniform flow of a rarefied gas. The analysis of the present paper follows this strategy

Ten years\u27 progress of Syowa Station, Antarctica, as a global geodesy network site

Progress of geodesy programs at Syowa Station since our former review in 1933 is summarized.As for Very Long Baseline Interferometry (VLBI),Global Positioning System (GPS),and Doppler Orbitography Radiopositioning Integrated by Satellites(DORIS),Syowa Station isa participating station in an international network and hasobtained an International Earth Rotation Service (IERS)dome number.Time series of about /years show change of position by plate motion. Detection of vertical motion by glacial isostatic adjustment is still under investigation. More than 20000 synthetic aperture radar (SAR) scenes have been received from the European Remote Sensing satellite-1 and -2 (ERS-1/-2) and the Japan Earth Resources satellite-1 (JERS-1) by the Syowa 11-m multipurpose antenna. Several case studies by interferometric SAR analyses have shown characteristic features of the ice grounding zones,ice dynamics and Digital Elevation Model (DEM)estimates.As for absolute gravimeter (AG) measurements, Syowa Station is registered as the International Absolute Gravity Basestation Network (IAGBN)0417 point. Observa tionswith an FG5 gravimeter were made for two summer seasons 5 years apart, and they showed consistent results within 2μGal difference. The superconducting gravimeter (SG) observations with a TT70 (#016 ) produced many scientific results in the two streamlines of tidal bands and normal mode bands.Especially, the first evidence of incessant excitation of the Earth \u27s free oscillations (background free oscillations)is noted as an important contribution from the Syowa SG observations.The Gravity Recovery And Climate Experiment (GRACE) satellite will bring an important advance for the study of ice-water-air mass circulation and its interaction with the solid-earth.The local potential fields calibrated by connecting to the station observatory data should give appropriate ground-truth information for the regional-scale satellite data,which reflects the continuing important role of Syow

Expression of glutathione S-transferase P-form in primary cultured rat liver parenchymal cells by coplanar polychlorinated biphenyl congeners is suppressed by protein kinase inhibitors and dexamethasone

AbstractGlutathione S-transferase P-form (GST-P, EC 2.5.1.18) mRNA was expressed by epidermal growth factor as well as by 3,4,5,3',4'-penta-chlorinated biphenyl (PenCB) in primary cultured rat liver parenchymal cells. The expression of GST-P was suppressed by inhibitors of protein kinase C and dexamethasone, an antagonist of AP-1 transcription factor activity, whereas expression of cytochrome P4501A2 by PenCB was not affected by these reagents. The AP-1 related transcription factor may be essential for the expression of GST-P by PenCB as also may be a protein kinase C type enzyme

The social boders of the ethical theme

Тема этического получает новый поворот в свете вопросов статуса социальной структуры. Методологические основания открытого общества не выдерживают критики с позиций морального консерватизма.The ethical theme acquires a new turn in the light of questioning social structure status. Open society has no reliable methodological grounds to counterfeit moral conservative critique

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar–Gross–Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., “A diffusion model for rarefied flows in curved channels, ” Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation

Temperature, pressure, and concentration jumps for a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation

The half-space problem of the temperature, pressure, and concentration jumps for a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. First, the problem is shown to be reduced to three elemental ones: the problem of the jumps caused by the net evaporation or condensation, that caused by the gradient of temperature, and that caused by the gradient of concentration. Then, the latter two are investigated numerically in the present contribution because the first problem has already been studied [Yasuda, Takata, and Aoki, Phys. Fluids 17, 047105 (2005)]. The numerical method is a finite-difference one, in which the complicated collision integrals are computed by the extension of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] to the case of a gas mixture. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic quantities but also at the level of the velocity distribution function. In addition, accurate formulas of the temperature, pressure, and concentration jumps are constructed for arbitrary values of the concentration of the background reference state by the use of the Chebyshev polynomial approximation. The solution of the corresponding problem of a vapor-gas mixture and that of the temperature-jump problem on a simple solid wall are also obtained as special cases of the present problem