A new approach to the homogenization of heterogeneous media for neutron diffusion calculations
Mathematical formulation for homogenization of heterogeneous media for neutron diffusion transport theory
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Mathematical formulation for homogenization of heterogeneous media for neutron diffusion transport theory
Mathematical model for neutron diffusion mechanics in heterogeneous media with vacuum channels
We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack. c2002 John Wiley & Sons, Ltd.
This is the first attempt to analyze both radiation and detailed kinetics on the burning and extinction of a solid fuel in a stagnation-point diffusion flame. We present a detailed and comparatively accurate computational model of a solid fuel flame along with a quantitative study of the kinetics mechanism, radiation interactions, and the extinction limits of the flame. A detailed kinetics model for the burning of solid trioxane (a trimer of formaldehyde) is coupled with a narrowband radiation model, with carbon dioxide, carbon monoxide, and water vapor as the gas-phase participating media. The solution of the solid trioxane diffusion flame over the flammable regime is presented in some detail, as this is the first solution of a heterogeneous trioxane flame. We identify high-temperature and low-temperature reaction paths for the heterogeneous trioxane flame. We then compare the adiabatic solution to solutions that include Surface radiation only and gas-phase and surface radiation using a black surface model. The analysis includes discussion of detailed flame chemistry over the flammable regime and, in particular, at the low stretch extinction limit. We emphasize the low stretch regime of the radiatively participating flame, since this is the region representative of microgravity flames. When only surface radiation is included, two extinction limits exist (the blow-off limit, and the low stretch radiative limit), and the burning rate and maximum flame temperatures are lower, as expected. With the inclusion of surface and gas-phase radiation, results show that, while flame temperatures are lower, the burning rate of the trioxane diffusion flame may actually increase at low stretch rate due to radiative feedback from the flame to the surface.
The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.