Estimating Particle Shape and Orientation Using Volume Tensors

We develop statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles. We focus on the case where particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle shape and orientation, and we derive stereological estimators of the tensors. These estimators are combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends on the orientation and shape of the particles. For instance, if the distribution of the typical particle is invariant under rotations, then the covariance matrix is proportional to the identity matrix. We develop a non-parametric test for such isotropy. A flexible Lévy-based particle model is proposed, which may be analysed using a generalized method of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex.

A Ladder Operator Solution to the Particle in a Box Problem

A ladder operator solution to the particle in a box problem of elementary quantum mechanics is presented, although the pedagogical use of this method for this problem is questioned.

Characterization of the East Houston particulate matter <2.5 atmosphere; a novel method for desorbing organic constituents from airborne particulates

I have developed a novel approach to test for toxic organic substances adsorbed onto ultra fine particulate particles present in the ambient air in Northeast Houston, Texas. These particles are predominantly carbon soot with an aerodynamic diameter (AD) of <2.5 μm. If present in the ambient air, many of the organic substances will be absorbed to the surface of the particles (which act just like a charcoal air filter), and may be adducted into the respiratory system. Once imbedded into the lungs these particles may release the adsorbed toxic organic substances with serious health consequences. I used a Airmetrics portable Minivol air sampler time drawing the ambient air through collection filters samples from 6 separate sites in Northeast Houston, an area known for high ambient PM 2.5 released from chemical plants and other sources (e.g. vehicle emissions).(1) In practice, the mass of the collected particles were much less than the mass of the filters. My technique was designed to release the adsorbed organic substances on the fine carbon particles by heating the filter samples that included the PM 2.5 particles prior to identification by gas chromatography/mass spectrometry (GCMS). The results showed negligible amounts of target chemicals from the collection filters. However, the filters alone released organic substances and GCMS could not distinguish between the organic substances released from the soot particles from those released from the heated filter fabric. However, an efficacy tests of my method using two wax burning candles that released soot revealed high levels of benzene. This suggests that my method has the potential to reveal the organic substances adsorbed onto the PM 2.5 for analysis. In order to achieve this goal, I must refine the particle collection process which would be independent of the filters; the filters upon heating also release organic substances obscuring the contribution from the soot particles. To obtain pure soot particles I will have to filter more air so that the soot particles can be shaken off the filters and then analyzed by my new technique. ^