Nonequilibrium Time Reversibility with Maps and Walks

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt’s and Zermélo’s paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the irreversible Second Law of Thermodynamics (Loschmidt’s) as well as periodic in the time (Zermélo’s, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals’ information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here.     

Metal Ion Recognition. Interaction of New Oxygen-Nitrogen Donor Macrocycles with Selected Transition and Post-Transition Metal Ions

As part of an ongoing investigation of the factors influencing metal ionrecognition, we have investigated structure/function relationships involvingthe metal-ion binding by three new N-benzyl-substituted, 15- and 16-membered,macrocyclic ligands incorporating N₂O ₃- and N ₃O ₃-donor sets (withthe N ₃O ₃-system consisting of a N ₂O ₃-macrocyclic ring with an attachedCH ₂CH ₂NCH ₂C ₆H ₅ pendant arm). Selected solid complexes of thelatter ligand were isolated and the X-ray structures of individual Ni(II) and Ag(I) complexeswere obtained.Where solubility permitted, potentiometric titration studies in 95% methanolwere employed to investigate the binding affinities of all three ligand derivativestowards Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Ag(I) and Pb(II). The 15-memberedN ₂O ₃-ring was found to be selective for Ag(I) over the other six metalsinvestigated, including Cu(II). However, the presence of a further nitrogen donorin the form of the pendant benzylamine functionality in the N ₃O ₃-donorsystem results in an increase in its binding affinity for Ag(I) but an even greaterincrease occurs for Cu(II). As a consequence, the latter ion is now more stronglybound than Ag(I). The factors influencing these respective selectivities are discussed.     

Three-component Heck–Diels–Alder cascade processes involving alkylallenes, aryl iodides and dienophiles

A wide variety of aryl/heteroaryl iodides undergo an intermolecular Heck reaction with alkylallenes to furnish 1,3-dienes. These subsequently react in situ with various dienophiles to give Diels–Alder adducts. The chemistry has been extended to incorporate cyclisation-anion capture methodology and the stereochemistry of the products has been determined.     

Alteration of foliar flavonoid chemistry induced by enhanced UV-B radiation in field-grown Pinus ponderosa, Quercus rubra and Pseudotsuga menziesii

Chromatographic analyses of foliage from several tree species illustrate the species-specific effects of UV-B radiation on both quantity and composition of foliar flavonoids. Pinus ponderosa, Quercus rubra and Pseudotsuga menziesii were field-grown under modulated ambient (1x) and enhanced (2x) biologically effective UV-B radiation. Foliage was harvested seasonally over a 3-year period, extracted, purified and the flavonoid fraction applied to a mu Bondapak/C(18) column HPLC system sampling at 254 nm. Total flavonoid concentrations in Quercus rubra foliage were more than twice (leaf area basis) that of the other species; Pseudotsuga menziesii foliage had intermediate levels and P. ponderosa had the lowest concentrations of total flavonoids. No statistically significant UV-B radiation-induced effects were found in total foliar flavonoid concentrations for any species; however, concentrations of specific compounds within each species exhibited significant treatment effects. Higher (but statistically insignificant) levels of flavonoids were induced by UV-B irradiation in 1- and 2-year-old P. ponderosa foliage. Total flavonoid concentrations in 2-year-old needles increased by 50% (1x ambient UV-B radiation) or 70% (2x ambient UV-B radiation) from that of 1-year-old tissue. Foliar flavonoids of Q. rubra under enhanced UV-B radiation tended to shift from early-eluting compounds to less polar flavonoids eluting later. There were no clear patterns of UV-B radiation effects on 1-year-old P. menziesii foliage. However, 2-year-old tissue had slightly higher foliar flavonoids under the 2x UV-B radiation treatment compared to ambient levels. Results suggest that enhanced UV-B radiation will alter foliar flavonoid composition and concentrations in forest tree species, which could impact tissue protection, and ultimately, competition, herbivory or litter decomposition.     

Fast-atom bombardment and tandem mass spectrometry of macrolide antibiotics

Molecular weights of macrolide antibiotics can be determined from either (M + H)⁺ or (M + Met)⁺, the latter desorbed from alkali metal salt-saturated matrices. The ion chemistry of macrolides, as determined by tandem mass spectrometry (MS/MS), is different for ions produced as metallated than those formed as (M + H)⁺ species. An explanation for these differences is the location of the charge. For protonated species, the charge is most likely situated on a functional group with high proton affinity, such as the dimethylamino group of the ammo sugar. The alkali metal ion, however, is bonded to the highly oxygenated aglycone. As a result, the collision-activated dissociation spectra of protonated macrolides are simple with readily identifiable fragment ions in both the high and low mass regions but no fragments in the middle mass range. In contrast, the cationized species give complex spectra with many abundant ions, most of which are located in the high mass range. The complementary nature of the fragmentation of these two species recommends the study of both by MS/MS when determining the structure or confirming the identity of these biomaterials.     

Multiscale data sampling and function extension

We introduce a multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nyström interpolation method. The multiscale extension (MSE) method is based on mutual distances between data points. It uses a coarse-to-fine hierarchy of the multiscale decomposition of a Gaussian kernel. It generates a sequence of subsamples, which we refer to as adaptive grids, and a sequence of approximations to a given empirical function on the data, as well as their extensions to any newly-arrived data point. The subsampling is done by a special decomposition of the associated Gaussian kernel matrix in each scale in the hierarchical procedure.     

Prioritized OWA aggregation

We indicate that the problem of prioritized criteria arises in situations in which there exists a relationship between the criteria so that lack of satisfaction by the higher priority criteria cannot be readily compensated for by satisfaction by lower priority criteria. Typical of this situation is the relationship between safety and cost. We consider the problem of criteria aggregation in this environment. Central to our approach is the use of importance weights to enforce this prioritization imperative. We apply our use of priority based importance weights to the case where the scope of the criteria aggregation is an OWA type aggregation.     

PIV space-time resolution of flow behind blast waves

An ultra-high speed, time-resolved particle image velocimetry (PIV) system is developed to measure velocity fields created by explosive detonators. When initiated into a gas, the detonators generate blast waves that propagate outwards from the origin of initiation at supersonic speeds. The PIV system consists of a custom eight-pulse Nd:YAG laser system and an ultra-high speed camera system comprising four dual-frame CCD cameras optically combined to share a single optic axis. The system is capable of sampling the flow field four times at up to 333 MHz or eight times at up to 8 MHz. System development is discussed, and preliminary application to the complex flow behind the blast wave from an exploding bridge wire detonator is demonstrated.