Radiative Transfer

The discrete ordinates method (DOM) and discrete transfer method (DTM) were evaluated from the viewpoints of both predictive accuracy and computational economy by comparing their predictions with exact solutions available from a box-shaped enclosure problem with steep ...

The application of physics to art history, art conservation and archaeology is currently a growing area of research. Astronomy and astrophysics have made significant contributions to imaging science which has in turn contributed to the developments of many other fields ranging from biological science to the study of art history, archaeology and art conservation. This paper will discuss how knowledge traditionally associated with astrophysics have made impact on the
study of cultural heritage. Examples will be drawn from recent research carried out in my research group.

In this study we extend the results given in a previous report regarding the propagation features of high-frequency energy in slender structures to the case of three-dimensional porous media. The mathematical theory of microlocal analysis of hyperbolic partial differential equations shows that the energy associated to their high-frequency solutions (in a sense to be precised) satisfies Liouville-type transport equations, or radiative transfer equations for randomly heterogeneous materials. For long propagation times these equations can be asymptotically approached by diffusion equations. Some classical results of the engineering mechanics literature about the heat conduction analogy and the statistical energy analysis of structural vibrations at high frequencies are recovered in this process. The purpose of this report is to focus on such a diffusive regime for isotropic porous media.

Climate models differ in their responses to imposed forcings, such as increased greenhouse gas concentrations, due to different climate feedback strengths. Feedbacks in NCAR’s Community Atmospheric Model (CAM) are separated into two components: the change in climate components in response to an imposed forcing and the “radiative kernel,” the effect that climate changes have on the top-of-the-atmosphere (TOA) radiative budget. This technique’s usefulness depends on the linearity of the feedback processes. For the case of CO2 doubling, the sum of the effects of water vapor, temperature, and surface albedo changes on the TOA clear-sky flux is similar to the clear-sky flux changes directly calculated by CAM. When monthly averages are used rather than values from every time step, the global-average TOA shortwave change is underestimated by a quarter, partially as a result of intramonth correlations of surface albedo with the radiative kernel. The TOA longwave flux changes do not depend o...

A system of exact linear integral equations for the source function, intensity and flux is presented for a two-dimensional cylindrical medium consisting of up to four layers with reflecting boundaries between the layers. Properties that may change from layer to layer are the single scattering albedo, optical thickness, and refractive index. The incident radiation is collimated and has a Bessel function distribution. The Bessel function boundary condition reduces the two-dimensional problem to a one-dimensional problem. Superposition is then used to derive the solution for any other boundary condition that is Hankel transformable. A special case of a Gaussian distribution that models a laser beam is presented. Some one-dimensional numerical results are presented for the source function and intensity within one and two layer media. Two-dimensional results are presented for back-scattered intensity due to the laser beam boundary condition. Only the conservative case is considered; optical thicknesses of 2.0 and 5.0 are considered; and refractive indices of 1.00 and 1.33 are considered.

The 3.3 micron PAH feature is undetected for the majority of the sample (97%), with typical upper limits of 5E-16 W/m^2. Compact 11.2 micron PAH emission is seen directly towards 1 out of the 53 Spitzer Short-High spectra, for a source that is borderline embedded. For all 12 sources with both VLT and Spitzer spectra, no PAH features are detected in either. In total, PAH features are detected toward at most 1 out of 63 (candidate) embedded protostars (<~ 2%), even lower than observed for class II T Tauri stars with disks (11-14%). Assuming typical class I stellar and envelope parameters, the absence of PAHs emission is most likely explained by the absence of emitting carriers through a PAH abundance at least an order of magnitude lower than in molecular clouds but similar to that found in disks. Thus, most PAHs likely enter the protoplanetary disks frozen out in icy layers on dust grains and/or in coagulated form.

This research is dedicated to the simulation of the transient response of beam trusses under impulse loads. The latter lead to the propagation of high-frequency waves in such built up structures. In the aerospace industry, that phenomenon may penalize the functioning of the structures or the equipments attached to them on account of the vibrational energy carried by the waves. It is also observed experimentally that high-frequency wave propagation evolves into a diffusive vibrational state at late times. The goal of this study is then to develop a robust model of high-frequency wave propagation within three-dimensional beam trusses in order to be able to recover, for example, this diffusion regime. On account of the small wavelengths and the high modal density, the modelling of high-frequency wave propagation is hardly feasible by classical finite elements or other methods describing the displacement fields directly. Thus, an approach dealing with the evolution of an estimator of the energy density of each propagating mode in a Timoshenko beam has been used. It provides information on the local behavior of the structures while avoiding some limitations related to the small wavelengths of high-frequency waves. After a comparison between some reduced-order beam kinematics and the Lamb model of wave propagation in a circular waveguide, the Timoshenko kinematics has been selected for the mechanical modelling of the beams. It may be shown that the energy densities of the propagating modes in a Timoshenko beam obey transport equations. Two groups of energy modes have been isolated: the longitudinal group that gathers the compressional and the bending energetic modes, and the transverse group that gathers the shear and torsional energetic modes. The reflection/transmission phenomena taking place at the junctions between beams have also been investigated. For this purpose, the power flow reflection/transmission operators have been derived from the continuity of the displacements and efforts at the junctions. Some characteristic features of a high-frequency behavior at beam junctions have been highlighted such as the decoupling between the rotational and translational motions. It is also observed that the energy densities are discontinuous at the junctions on account of the power flow reflection/transmission phenomena. Thus a discontinuous finite element method has been implemented, in order to solve the transport equations they satisfy. The numerical scheme has to be weakly dissipative and dispersive in order to exhibit the aforementioned diffusive regime arising at late times. That is the reason why spectral-like approximation functions for spatial discretization, and strong-stability preserving Runge-Kutta schemes for time integration have been used. Numerical simulations give satisfactory results because they indeed highlight the outbreak of such a diffusion state. The latter is characterized by the following: (i) the spatial spread of the energy over the truss, and (ii) the equipartition of the energy between the different modes. The last part of the thesis has been devoted to the development of a time reversal processing, that could be useful for future works on structural health monitoring of complex, multi-bay trusses.