Standard Diffusion Theory Research Articles

Sustenance of a black hole in a galactic nucleus

We examine the class of models in which a QSO is powered by a massive black hole accreting gas produced in a dense galactic nucleus. Application of the standard loss-cone diffusion theory shows that, for reasonable stellar densities, tidal disruption of stars cannot provide an effective source of fuel. Tidal disruption may be effective if collective effects enhance the rate of diffusion into disruptive orbits. In the absence of enhanced relaxation, stellar collisions can provide sufficient gas at lower densities than are required for tidal disruption. This process still requires densities higher than can be associated with the isothermal core of a normal galaxy; for example, collisions in a nucleus of mass 10/sup 9/ M/sub sun/ pc/sup -3/ release gas at a rate approx.1 M/sub sun/ yr/sup -1/ as a result of coalescence followed by rapid stellar evolution.Less extreme densities are required if active nuclei store mass during quiescent periods and this mass then becomes available through an instability, feeding the hole for a shorter period of intense activity. A mechanism for such intermittent activity may be storage and release of gas in a disk.

Extension of Linearly Anisotropic Asymptotic Neutron Diffusion Theory to Reflected Systems

The extension of asymptotic diffusion theory to reflected systems by applying discontinuous halfspace boundary conditions is demonstrated. Critical size calculations for two-region infinite planes, spheres, and infinite cylinders show significant improvement over standard diffusion theory calculations with continuity boundary conditions.

Calculation of mean number of electron-gas-atom elastic collisions

A Monte Carlo calculation of the mean number of elastic collisions involving gas atoms and an electron diffusing between two infinite perfectly absorbing planar electrodes has been carried out. The values obtained agree with those calculated by Bartels and Nordstrom in 1931 to within 12%, throughout the range of gas pressure and electrode separation investigated, but are considerably higher than the values obtained from work based on standard diffusion theory. It is shown that such calculations are unlikely to be reliable except at high gas pressure and large electrode separation.

Calibration of a porometer in terms of diffusive resistance

The rate of pressure drop in a convenient leaf-porometer is shown to be a simple function of several separable components of flow resistance. Those due to stomata are arrived at by measuring or estimating the others. Stomatal resistance is also calculated from viscous flow theory and the observed dimensions of sample stomata or their replicas. Measured and calculated values for barley agree moderately well, thus justifying the model used in calculation. With standard molecular diffusion theory, the same dimensions give the diffusive resistance of the stomata, which is the quantity of interest in transpiration or assimilation studies. With suitable averaging procedures to relate the properties of single pores to those of whole leaves, a simplified theoretical relation between viscous and diffusive resistance is found permitting conversion of porometer readings directly into diffusive resistances.