Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we use conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

     

Statistics of particle velocities in dense granular flows

We present measurements of the particle velocity distribution in the slow flow of granular material through vertical channels. The velocities of particles adjacent to the smooth, transparent front face of the channel were determined by video imaging and particle tracking. We find that the mean velocity changes sharply in shear layers near the side walls, but remains constant in a substantial core. The velocity distribution is non-Gaussian, is anisotropic, and follows a power law at large velocities. Remarkably, the distribution is identical in the shear layer and the core. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.     

Regeneration of C4H10 dry reforming catalyst by nonthermal plasma

Carbon deposition via coke formation is one of the critical problems causing catalyst deactivation during the reforming of hydrocarbons.An effort was made to regenerate the catalyst（Ni/7-alumina） by oxidation methods.Two approaches were carried out for the regeneration of the deactivated catalyst.The first one involves the plasma treatment of the deactivated catalyst in the presence of dry air over a temperature range of 300～500℃,while the second one only the thermal treatment in the same temperature range.The performance of the regenerated catalyst was evaluated in terms of C₄H₁₀ and CO₂ conversions and the physicochemical characteristics were examined using a surface area analyzer,an elemental analyzer,scanning electron microscopy（SEM） and transmission electron microscopy（TEM）.It was observed that the carbon deposit （coke） on the catalyst was about 9.89 wt%after reforming C₄H₁₀ for 5 h at 540℃.The simple thermal treatment at 400℃reduced carbon content to 6.59 wt%whereas it was decreased to 3.25 wt%by the plasma and heat combination.The specific surface area was fully restored to the original state by the plasma-assisted regeneration at 500℃.As far as the catalytic activity is concerned,the fresh and regenerated catalysts exhibited similar C₄H₁₀ and CO₂ conversion efficiencies.     

Long-term follow-up of 82 patients with chronic disease of the thoracic aorta using spin-echo and cine gradient magnetic resonance imaging

The objective of this study to examine the clinical impact of magnetic resonance imaging in long-term follow-up of patients (pts) with chronic disease of the thoracic aorta such as coarctation of the aorta, chronic aortic dissection and true aortic aneurysm. A total of 322 magnetic resonance examinations obtained in 82 pts with chronic disease of the thoracic aorta (31 pts with coarctation of the aorta (CoA), 29 pts with chronic aortic dissection and 22 pts with true aneurysm) over a period of 0.25 to 13.5 (mean +/- SD: 6.5 +/- 3.4) years were retrospectively reviewed. Diameters of the thoracic aorta were measured at predefined levels and morphological and functional parameters of special interest were analysed in each patient group. Pts were classified as having constant or progressive disease and clinical end-points were defined as (re-)operation or death. 43 pts (52%) (CoA 15 pts, chronic dissection 16 pts, true aneurysm 12 pts) had constant findings. None of them underwent (re-)operation and seven patients (16%) died, three of them from their aortic disease more than five years later after their last magnetic resonance examination, one from an arrhythmogenic event, and in the remaining 3 pts the cause of death could not be definitely established. 39 pts (48%) (CoA 16 pts, chronic dissection 13 pts, true aneurysm 10 pts) had progressive disease as demonstrated by repetitive magnetic resonance imaging. Of these 39 pts 24 pts underwent (re-)operation, in 15 pts operation was postponed. Four pts died from their aortic disease. Repetitive magnetic resonance imaging is a clinically feasible technique for long-term follow-up of pts with chronic disease of the thoracic aorta because it can detect progressive disease in a large subset of pts requiring elective surgery. The results of magnetic resonance imaging provided the rationale for either (re-)operation or conservative management, thus guiding patient management.