Packing 16, 17 of 18 circles in an equilateral triangle

We present new, efficient packings for 16, 17 and 18 congruent circles in an equilateral triangle. The results have been found by the use of simulated annealing and a quasi-Newton optimization technique, supplemented with some human intelligence

Outlook: Summer 2003

Alumni publication of the Boston University School of Dental Medicine

Transport of nonlinearly adsorbing compounds between stream water and sediment bed in a laboratory flume

The exchange of nonlinearly adsorbing compounds between stream water and sediment beds covered with stationary bedforms was investigated in laboratory experiments. The dominant physical exchange process is advective pumping caused by dynamic pressure variations over dunes on the bed. Observations of net mass exchange of cationic surfactants in a 5-meter long recirculating flume were used to validate the exchange model, which is based on the hydraulics of advective pumping and nonlinear adsorption isotherms derived from batch experiments. The flume experiments were conducted under steady, uniform flow conditions. The pH and ionic strength of the flume water was controlled by adding sodium chloride and sodium bicarbonate to deionized water. The sand was washed prior to every experiment. The mass exchange of cationic surfactants and bromide was determined by measuring the depletion of these compounds in the overlying water column as it mixed with the clean porewater from the bed. Porewater concentration profiles were acquired to monitor the penetration depth of the compounds in the bed. Bromide was used as a conservative tracer to observe the hydraulics of water exchange between the bed and the overlying water. Garnet sand was used as the model sediment because it had heterogeneous properties similar to natural sediments. The net mass exchange with a bed covered with stationary bedforms was greater than the exchange with a flat bed. The mass exchange of the cationic surfactants versus time observed in the flume experiments could not be modeled using linear adsorption; however, linear approximations provided upper and lower limits on the exchange. The total mass transfer of the cationic surfactants to the bed increased with their hydrocarbon chain lengths. The model for the exchange of nonlinearly adsorbing compounds solves the advection equation to track the transport of the compounds within the bed and computes the net mass flux through the bed surface. Nonlinear adsorption was modeled by the means of four different isotherm equations fitted to the batch adsorption data. The effect of the choice of isotherm on the exchange models for the flume experiments was found to be very small. The model generally predicted the flume results well without calibration. Additional model simulations were performed to provide a sensitivity analysis for the model inputs

Preparation and Characterization of Some Particulate Materials in the Aluminum Industry

Preparation and characterization techniques for the following particulate materials are reviewed: micromineralogical samples of bauxite, alumina and its trihydroxide, as well as sedimentary and respirable particles. Scanning electron microscopy (SEM), energy dispersive X-ray microanalysis (EDS) and image analysis were used to characterize the microminerals of bauxite. Comparisons were made among micromineralogical samples with various grain size fractions and the degree of weathering could be quantified. Programs were developed for characterization of the sandy and floury types of aluminum trihydroxide and alumina. We have used backscattered electron SEM images to characterize the size and shape of various aluminum trihydroxides. Comparison could be made between sandy and floury types of aluminum trihydroxide/alumina samples and the effects of technological changes could be quantified. The shape and composition of respirable particles in alumina plants were studied from the point of view of environmental protection

HETEROCYCLIZATION WITH IMINIUM SALTS AND N-YLIDES

Novel 2,3a,6a-triazaphenalene and 1-thia-2a,5a-diaza-acenaphthene ring systems were synthesized and their ring transformation reactions affording polycycles with bridgehead nitrogen atom were investigated. 1,3-Dipolar cycloaddition of isoquinoline N-ylides with azomethines and olefines were studied and the regio- and stereoselectivity of the reaction were proved by structure elucidation and quantum chemical calculations

THE EFFECT OF CRUSTAL MASSES ON GEOID ANOMALIES

An important question in geosciences is the physical interpretation of global geoid forms and the improvement of our knowledge on the inner structure of the Earth. The authors suggest a new method which separates geoid heights due to upper known density inhomo- genities from geoid heights of inner unknown mass distributions. The interpretation of remain- ing geoid forms becomes presumably simpler after removing the effect of known masses from the full geoid. This paper deals with the mathematical solution of the effects of known sur- face mass distributions capable of computer computation and presents some results of initial numerical computations