Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

Gamow-Teller GT+ distributions in nuclei with mass A=90-97

We investigate the Gamow-Teller strength distributions in the electron-capture direction in nuclei having mass A=90-97, assuming a 88Sr core and using a realistic interaction that reasonably reproduces nuclear spectroscopy for a wide range of nuclei in the region as well as experimental data on Gamow-Teller strength distributions. We discuss the systematics of the distributions and their centroids. We also predict the strength distributions for several nuclei involving stable isotopes that should be experimentally accessible for one-particle exchange reactions in the near future.Comment: 9 pages, 10 figures (from 17 eps files), to be submitted to Phys.Rev.C; corrected typos, minor language change

Poissonian bursts in e-mail correspondence

Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend the analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data depart from the known correlations of Poissonian statistics. The analysis shows that the higher-order statistics from the empirical data is indistinguishable from that of randomly reordered time series, thus demonstrating that e-mail correspondence is no more bursty or correlated than a Poisson process. Furthermore synthetic data sets generated by a cascading Poisson process replicate the burstiness and correlations observed in the empirical data. Finally, a simple rescaling analysis using the best-estimate rate of activity, confirms that the empirically observed correlations arise from a non-homogeneus Poisson process

Boundary Effects in the One Dimensional Coulomb Gas

We use the functional integral technique of Edwards and Lenard to solve the statistical mechanics of a one dimensional Coulomb gas with boundary interactions leading to surface charging. The theory examined is a one dimensional model for a soap film. Finite size effects and the phenomenon of charge regulation are studied. We also discuss the pressure of disjunction for such a film. Even in the absence of boundary potentials we find that the presence of a surface affects the physics in finite systems. In general we find that in the presence of a boundary potential the long distance disjoining pressure is positive but may become negative at closer interplane separations. This is in accordance with the attractive forces seen at close separations in colloidal and soap film experiments and with three dimensional calculations beyond mean field. Finally our exact results are compared with the predictions of the corresponding Poisson-Boltzmann theory which is often used in the context of colloidal and thin liquid film systems.Comment: 28 pages, LATEX2e, 11 figures, uses styles[12pt] resubmission because of minor corrections to tex

Beneficiation of ilmenite from lumar analog

The results reported were obtained on a meteoric eucrite sample called Millbillillie Sample no. 173. Optical microscopy studies of the sample showed it to consist of ilmenite, troilite, and transparent gangue. The transparent gangue consisted of feldspar (anorthite), pyroxenes, olivines, and opaques. Troilite was present in minor quantities. Screen assay analyses of the 30, 100, 200, and 400 US mesh screen fractions showed that minor concentration of titanium occurred in the 200 x 400 and -400 mesh screen fractions. Scanning electron microscopy (SEM) studies of the bulk sample showed the presence of a variety of ilmenite grains, ranging from 50 microns down to less than 1 micron without any evidence of liberation. Electron Diffraction Scans (EDS) confirmed the ratio of Fe to Ti in the ilmenite grains. Dry magnetic separation in a Frantz Isodynamic Separator was found to be effective only at sizes finer than 150 microns (100 US mesh) and more so at 200 mesh (74 microns). In each case, dedusting of the sample to remove -400 mesh (-0.037 microns) fines was required. Liberation size was determined to be 200 mesh and finer. The highest grade concentrate assaying 3.45 percent Ti was produced by magnetic separation of the -200 + 400 mesh screen fraction assaying 0.44 Ti (from a -30 mesh sample) at a current setting of 0.35 AMP. This concentrate contained 21.2 percent of the Ti values in the screen fraction with 2.72 weight percent of feed to test. The results can be projected to a sample stage ground to -200 mesh. Magnetic separation of the 200 + 400 mesh (-0.074 + 0.037 microns) should produce a concentrate accounting for 1.41 weight percent of the feed. This concentrate will analyze 3.45 percent Ti and contain 10.3 percent of the Ti values in the feed. By changing the Frantz Magnetic Separator settings, a lower grade concentrate analyzing 0.98 percent Ti can be produced at an increased recovery of 25.4 percent. The concentrate weight will be 11.7 percent of the feed. It must be emphasized that improved grades and recoveries can be obtained with the -400 mesh fines. However, beneficiation of these extremely fine materials is not possible in a practical process scheme

Skill set profile clustering: the empty K-means algorithm with automatic specification of starting cluster centers

While students’ skill set profiles can be estimated with formal cognitive diagnosis models [8], their computational complexity makes simpler proxy skill estimates attractive [1, 4, 6]. These estimates can be clustered to generate groups of similar students. Often hierarchical agglomerative clustering or k-means clustering is utilized, requiring, for K skills, the specification of 2^K clusters. The number of skill set profiles/clusters can quickly become computationally intractable. Moreover, not all profiles may be present in the population. We present a flexible version of k-means that allows for empty clusters. We also specify a method to determine efficient starting centers based on the Q-matrix. Combining the two substantially improves the clustering results and allows for analysis of data sets previously thought impossible