The effect of forward and backward scattering on the law of darkening for the Milne problem and the spherical albedo

A synthetic kernel is used to study the effect of forward and backward scattering on the law of darkening for the Milne problem and the spherical albedo.     

Non-gray radiative transfer

The normal-mode-expansion technique is used to establish the solution of the Milne problem basic to a generalized equation of radiative transfer. The non-gray model used includes the effects of absorption, scattering and losses due to photo-electric ionizations and collisions of the second kind. Accurate numerical results are presented for such physical quantities as the extrapolation distance, the integrated Planck function and the angular distribution of the exit intensity for selected values of the basic parameters.     

Radiation transport in plane-parallel media with non-uniform surface illumination

Fourier and other integral transform techniques are used to reduce the problem of radiation transport in plane-parallel media with non-uniform surface illumination to a convenient computational form, and theF _N method is used to provide a basis for approximate solutions.     

A point source in a finite sphere

Exact analysis and the F_N method are used to compute the radiation field due to a point source of radiation located at the center of a finite sphere.     

On computing the Chapman-Enskog functions for viscosity and heat transfer and the Burnett functions

Hermite cubic splines and collocation are used to solve, in an efficient and accurate way, the Chapman-Enskog equations for viscosity and heat transfer and to compute the Burnett functions required for Poiseuille-flow problems based on rigid-sphere collisions and the linearized Boltzmann equation.     

Particular solutions of the equation of transfer

Particular solutions corresponding to various forms for the inhomogeneous source term are established for the equation of transfer with Lth order anisotropic scattering.     

On the Origin of the Heterogeneous Emission from Pyrene Sequestered Within Tetramethylorthosilicate-Based Xerogels: A Decay-Associated Spectra and O2 Quenching Study

Steady-state and time-resolved fluorescence spectroscopy are used to determine the local microheterogeneity surrounding pyrene molecules sequestered within tetramethylorthosilicate-derived xerogels. After compensation for the intrinsic background emission from the xerogel, we find that the pyrene intensity decay kinetics are best described by a two-term rate law. This is consistent with the pyrene molecules distributing primarily into two microenvironments. Under ambient conditions, the individual pyrene microenvironments exhibit excited-state fluorescence lifetimes that differ by 100 ns. However, the pyrene I₁ to I₃ band ratios that are associated with each microenvironment are statistically equivalent to one another. These results show that the local dipolarity surrounding these pyrene microenvironments are similar, but the decay rates associated with each microenvironment are very different. The longer-lived pyrene species (Environment #1) constitutes 1/2 of the total fluorescence and it exhibits an O₂ quenching sensitivity (K_sv1) of (5.19 ± 0.52 × 10^–3 %O₂ ^–1 and a bimolecular quenching constant (k_q1) of (2.30 ± 0.23) × 10⁴ %O₂ ^–1 s^–1. Environment #2, associated with the shorter-lived pyrene species, exhibits an O₂ quenching sensitivity (K_sv2) of (2.31 ± 0.16) × 10^–2 %O₂ ^–1 and a bimolecular quenching constant (k_q2) of (2.11 ± 0.23) × 10⁵ %O₂ ^–1 s^–1. These results are interpreted as follows: Environment #1 consists of pyrene molecules sequestered within a relatively rigid siloxane network wherein non-radiative decay pathways are lessened, but these pyrene molecules are not quenched readily by O₂. Environment #2 consists of pyrene molecules adsorbed onto surface silanols within the xerogel. These pyrene molecules are quenched by the silanols and they are simultaneously more accessible to O₂ compared to Environment #1.