Comparison of models and lattice-gas simulations for Liesegang patterns

For more than a century Liesegang patterns – self-organized, quasi-periodic structures occurring in diffusion-limited chemical reactions with two components – have been attracting scientists. The pattern formation can be described by four basic empirical laws. In addition to many experiments, several models have been devised to understand the formation of the bands and rings. Here we review the most important models and complement them with detailed three-dimensional lattice-gas simulations. We show how the mean-field predictions can be reconciled with experimental data by a redefinition of the distances suggested by our lattice-gas simulations.     

Microbial adhesion to poly(ethylene oxide) brushes: influence of polymer chain length and temperature

Glass surfaces were modified by end-grafting poly(ethylene oxide) (PEO) chains having molecular weights of 526, 2000, or 9800 Da. Characterization using water contact angles, ellipsometry, and X-ray photoelectron spectroscopy confirmed the presence of the PEO brushes on the surface with estimated lengths in water of 2.8-, 7.5-, and 23.7-nm, respectively. Adhesion of two bacterial (Staphylococcus epidermidis and Pseudomonas aeruginosa) and two yeast (Candida albicans and Candida tropicalis) strains to these brushes was studied and compared to their adhesion to bare glass. For the bacterium P. aeruginosa and the yeast C. tropicalis, adhesion to the 2.8-nm brush was comparable to their adhesion on bare glass, whereas adhesion to the 7.5- and 23.7-nm brushes was greatly reduced. For S. epidermidis, adhesion was only slightly higher to the 2.8-nm brush than that to the longer brushes. Adhesion of the yeast C. albicans to the PEO brushes was lower than that to glass, but no differences in adhesion were found between the three brush lengths. After passage of an air bubble, nearly all microorganisms adhering to a brush were removed, irrespective of brush length, whereas retention of the adhering organisms on glass was much higher. No significant differences were found in adhesion nor retention between experiments conducted at 20 and those conducted at 37 degrees C.     

Pitch of amplitude-modulated irregular-rate stimuli in acoustic and electric hearing

The pitch of stimuli was studied under conditions where place-of-excitation was held constant, and where pitch was therefore derived from "purely temporal" cues. In experiment 1, the acoustical and electrical pulse trains consisted of pulses whose amplitudes alternated between a high and a low value, and whose interpulse intervals alternated between 4 and 6 ms. The attenuated pulses occurred after the 4-ms intervals in condition A, and after the 6-ms intervals in condition B. For both normal-hearing subjects and cochlear implantees, the period of an isochronous pulse train equal in pitch to this "4-6" stimulus increased from near 6 ms at the smallest modulation depth to nearly 10 ms at the largest depth. Additionally, the modulated pulse trains in condition A were perceived as being lower in pitch than those in condition B. Data are interpreted in terms of increased refractoriness in condition A, where the larger pulses are more closely followed by the smaller ones than in condition B. Consistent with this conclusion, the A-B difference was reduced at longer interpulse intervals. These findings provide a measure of supra-threshold effects of refractoriness on pitch perception, and increase our understanding of coding of temporal information in cochlear implant speech processing schemes.     

An equivariant Brauer semigroup and the symmetric imprimitivity theorem

Suppose that is a second countable locally compact transformation group. We let denote the set of Morita equivalence classes of separable dynamical systems where is a -algebra and is compatible with the given -action on . We prove that is a commutative semigroup with identity with respect to the binary operation for an appropriately defined balanced tensor product on -algebras. If and act freely and properly on the left and right of a space , then we prove that and are isomorphic as semigroups. If the isomorphism maps the class of to the class of , then is Morita equivalent to .