Orthogonality of case's eigenfunctions in one-speed transport theory

The eigenfunctions of the one-speed transport equation, as introduced by Case, are shown to have more general orthogonality properties than previously known. In particular, for isotropic scattering, partial range and "two-media" orthogonality relations are derived. An extension to linearly anisotropic scattering is indicated. These results facilitate the application of Case's method to one-speed transport problems in plane geometry.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32078/1/0000127.pd

Measuring CMB polarisation with the Planck mission

In this paper, we discuss why and how the Planck mission, originally designed and proposed for mapping CMB intensity fluctuations, has been revised for polarisation measurement capability as well

Integral representation of the linear Boltzmann operator for granular gas dynamics with applications

We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of the collision operator in an Hilbert space setting, generalizing results from T. Carleman to granular gases. In the same way, we obtain from this integral representation of the gain operator that the semigroup in L^1(\R \times \R,\d \x \otimes \d\v) associated to the linear Boltzmann equation for dissipative hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic

Insights into the Second Law of Thermodynamics from Anisotropic Gas-Surface Interactions

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions in "equilibrium", even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics.Comment: 28 pages, 11 figure