Metastable Dynamics and Spatially Inhomogeneous Equilibria in Dumbbell-Shaped Domains

The motion of internal layers for three singularly perturbed reaction diffusion problems, including the Allen–Cahn equation, is studied in a two-dimensional dumbbell-shaped domain. The channel region that connects the two attachments, or lobes, of the dumbbell is taken to be rectangular. The motion of straight-line internal layers in the channel region is analyzed by using an asymptotic projection method. It is shown that this motion is metastable and highly dependent on the local convexity properties of the boundary near the contact region between the ends of the channel and the two attachments. When the domain is nonconvex it is shown that the metastable internal layers dynamics in the channel tends, as t →∞, to a limiting, stable, spatially inhomogeneous equilibrium solution.     

Quantum theory of metallic nanocohesion

The conducting and mechanical properties of ultrasmall metallic structures are calculated using the electronic scattering matrix, evaluated in the free electron approximation. Force oscillations of the order are predicted when a metallic quantum wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance. Coherent backscattering from impurities is shown to lead to fine structure (a “quantum fingerprint”) in the force oscillations. 1997 Elsevier Science B.V. All rights reserved.     

Photocatalytic degradation of 4-chlorophenol: A mechanistically-based model

The photocatalytic degradation of 4-CP was mathematically modelled using the mechanistic insights and data presented in an earlier study [1]. The solution and surface concentrations of reacting species were calculated by solving a system of differential equations that account for oxidation reactions of dissolved and adsorbed species, adsorption and desorption, reduction of oxygen, and hole-electron recombination. The differential equations were integrated over discrete time-periods and annular regions of the photoreactor. The resulting model predicts the trends observed in studies in other laboratories using different experimental apparati. Using the model it is possible to predict effects of reactor geometry, TiO₂ loading, light intensity, and mixing on the course of TiO₂ photocatalytic oxidation. The model verifies the importance of surface reactions, and reveals the need to better understand the fate and role of oxygen in TiO₂ photocatalytic systems.     

Imaging of small molecules in tissue sections with a new intermediate-pressure MALDI linear ion trap mass spectrometer

We describe a new intermediate-pressure MALDI linear ion trap mass spectrometer and its capabilities for imaging mass spectrometry. The instrument design is described and is characterized in terms of four performance issues (1) MALDI performance at intermediate pressure; (2) analysis of samples on non-conductive and conductive glass slides; (3) critical importance of tandem mass spectrometry (both MS² and MS³) for identification of analyte species and imaging of isobaric species; (4) capability for repeated analysis of the same tissue section. Application of the new instrument to imaging phospholipids in rat brain sections is described in detail.     

Applications of capillary gas chromatography in routine toxicological analyses

Capillary columns offer the toxicologist several advantages over packed columns. We have presented a highly reproducible screening procedure based on the retention index system and have shown the use of capillary columns for routine quantitation. We are currently expanding the use of these columns in our laboratory and predict that they will be in routine use by most toxicologists in the near future.