Random Distribution

This research focuses on fourth-grade (9-year-old) students’ informal and intuitive conceptions of probability and distribution revealed as they worked through a sequence of tasks. These tasks were designed to study students’ spontaneous reasoning about distributions in different settings and their understanding of probability of various binomial random events that they explored with a set of physical chance mechanisms. The data were gathered from a pilot study with four students. We analyzed the interplay of reasoning about distribution and understanding of probability. The findings suggest that students’ qualitative descriptions of distributions could be developed into the quantification of probabilities through reasoning about data in chance situations.

This study includes a detailed numerical investigation of the problem of gaseous diffusion in structures of randomly overlapping capillaries of various orientation distributions in the ordinary, transition, and Knudsen diffusion regimes. Effective diffusion coefficients are computed through a Monte Carlo simulation method based on the mean square displacement of random walkers traveling in the interior of the porous media. The simulation results reveal a strong dependence of the components of the effective diffusivity tensor of a capillary structure on its porosity, the Knudsen number, and the orientational distribution of the capillaries. The computed transition regime diffusivities are found to be in excellent agreement with those predicted by the reciprocal additivity or harmonic mean diffusivity expression (Bosanquet formula) using the computed diffusion coefficients in the ordinary and Knudsen diffusion regimes for all configurations of flow except for that parallel to unidirectional capillaries.

A probabilistic approach is presented for the analysis of open stope stability. The approach considers the inherent variability and uncertainty which are typical of rock mass properties. In this study, a series of numerical analyses were performed using FLAC to study the ...

In his seminal work, Kleinberg showed how to augment meshes using random edges, so that they become navigable; that is, greedy routing computes paths of polylogarithmic expected length between any pairs of nodes. This yields the crucial question of determining wether such an augmentation is possible for all graphs. In this paper, we answer negatively to this question by exhibiting a threshold on the doubling dimension, above which an infinite family of graphs cannot be augmented to become navigable whatever the distribution of random edges is. Precisely, it was known that graphs of doubling dimension at most O(loglogn) are navigable. We show that for doubling dimension >> log log n, an infinite family of graphs cannot be augmented to become navigable. Finally, we complete our result by studying the special case of square meshes, that we prove to always be augrnentable to become navigable.

Abstract Numerous 2: 1 clay minerals were synthesized between 100 and 250 C. For each clay mineral, octahedral sheets were occupied by two different cations A and B, the atomic ratio View the MathML source varying from zero to one. Synthetic clays were studied by ...

A probabilistic approach is presented for the analysis of open stope stability. The approach considers the inherent variability and uncertainty which are typical of rock mass properties. In this study, a series of numerical analyses were performed using FLAC to study the ...