A new proof of the Howe Conjecture

The Howe Conjecture, which has formulations for both a reductive -adic group and its Lie algebra, is a statement about the finite dimensionality of certain spaces of -invariant distributions. Howe proved the algebra version of the conjecture for via a method of descent. Harish-Chandra extended Howe's method, when the characteristic is zero, to arbitrary reductive Lie algebras. Harish-Chandra then used the conjecture, in both its Lie algebra and group formulations, as a fundamental underpinning of his approach to harmonic analysis on the group and Lie algebra. Many properties of -invariant distributions, which for real Lie groups follow from differential equations, in the -adic case are consequences of the Howe Conjecture and other facts, e.g. properties of orbital integrals. Clozel proved the group Howe Conjecture in characteristic zero via a method very different than Howe's and Harish-Chandra's descent methods. We give a new proof of the group Howe Conjecture via the Bruhat-Tits building. A key tool in our proof is the geodesic convexity of the displacement function. Highlights of the proof are that it is valid in all characteristics, it has similarities to Howe's and Harish-Chandra's methods, and it has similarities to the existence proof of an unrefined minimal K-type.

     

Computational and experimental study of the cluster size distribution in MAPLE

A combined experimental and computational study is performed to investigate the origin and characteristics of the surface features observed in SEM images of thin polymer films deposited in matrix-assisted pulsed laser evaporation (MAPLE). Analysis of high-resolution SEM images of surface morphologies of the films deposited at different fluences reveals that the mass distributions of the surface features can be well described by a power-law, Y(N) ∝ N^−t, with exponent −t ≈ −1.6. Molecular dynamic simulations of the MAPLE process predict a similar size distribution for large clusters observed in the ablation plume. A weak dependence of the cluster size distributions on fluence and target composition suggests that the power-law cluster size distribution may be a general characteristic of the ablation plume generated as a result of an explosive decomposition of a target region overheated above the limit of its thermodynamic stability. Based on the simulation results, we suggest that the ejection of large matrix-polymer clusters, followed by evaporation of the volatile matrix, is responsible for the formation of the surface features observed in the polymer films deposited in MAPLE experiments.     

The TEM characterization of the lamellar structure of osteoporotic human trabecular bone

The lamellar structure of osteoporotic human trabecular bone was characterized experimentally by means of transmission electron microscopy (TEM). More specifically, the TEM was used to determine if trabecular bone exhibits similar lamellar structural motifs as cortical bone by analyzing unmineralized, mineralized and demineralized bone, and to study the influence of the osteocyte network on the lamellar structure of osteoporotic trabecular bone. Comparison with normal trabecular bone is included. This paper summarizes partial results of a larger study, which addressed the characterization of the hierarchical structure of normal versus osteoporotic human trabecular bone [Rubin, M.A., 2001. Multiscale characterization of the ultrastructure of trabecular bone in osteoporotic and normal humans and in two inbred strains of mice. MS Thesis, Georgia Institute of Technology.] at several structural scales.     

How do quasicrystals grow?

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.     

The effect of pH on the room-temperature phosphorescence properties of several purine and pyrimidine derivatives

Room-temperature phosphorescence (RTP) spectra of eleven purines and pyrimidines adsorbed on Whatman No. 40 filter paper have been determined in acidic, neutral and basic media. RTP excitation and emission wavelengths do not vary significantly with pH. For most compounds, use of basic (pH approximately 13) solutions yields stronger RTP signals than use of neutral or acidic (pH approximately 1.6) solutions. Exceptions are adenine, theobromine and theophylline, which give larger RTP signals when in neutral than in basic conditions. The existence of differences in phosphorescence quantum yields between the various ionic species as well as of specific pH-related interactions with the substrate is discussed. Absolute limits of detection, ranging between 0.4 and 38 ng for selected compounds, depend on the pH of the analyte solution.     

Ion Association in Lanthanide Chloride Solutions

A better understanding of the solution chemistry of the lanthanide (Ln) salts in water would have wide ranging implications in materials processing, waste management, element tracing, medicine and many more fields. This is particularly true for minerals processing, given governmental concerns about lanthanide security of supply and the drive to identify environmentally sustainable processing routes. Despite much effort, even in simple systems, the mechanisms and thermodynamics of Ln^III association with small anions remain unclear. In the present study, molecular dynamics (MD), using a newly developed force field, provide new insights into LnCl₃(aq) solutions. The force field accurately reproduces the structure and dynamics of Nd³⁺, Gd³⁺ and Er³⁺ in water when compared to calculations using density functional theory (DFT). Adaptive-bias MD simulations show that the mechanisms for ion pairing change from dissociative to associative exchange depending upon cation size. Thermodynamics of association reveal that whereas ion pairing is favourable, the equilibrium distribution of species at low concentration is dominated by weakly bound solvent-shared and solvent-separated ion pairs, rather than contact ion pairs, reconciling a number of contrasting observations of Ln^III–Cl association in the literature. In addition, we show that the thermodynamic stabilities of a range of inner sphere and outer sphere coordination complexes are comparable and that the kinetics of anion binding to cations may control solution speciation distributions beyond ion pairs. The techniques adopted in this work provide a framework with which to investigate more complex solution chemistries of cations in water.     

An experimental-theoretical analysis of protein adsorption on peptidomimetic polymer brushes

Surface-grafted water-soluble polymer brushes are being intensely investigated for preventing protein adsorption to improve biomedical device function, prevent marine fouling, and enable applications in biosensing and tissue engineering. In this contribution, we present an experimental-theoretical analysis of a peptidomimetic polymer brush system with regard to the critical brush density required for preventing protein adsorption at varying chain lengths. A mussel adhesive-inspired DOPA-Lys (DOPA = 3,4-dihydroxy-phenylalanine; Lys = lysine) pentapeptide surface grafting motif enabled aqueous deposition of our peptidomimetic polypeptoid brushes over a wide range of chain densities. Critical densities of 0.88 nm(-2) for a relatively short polypeptoid 10-mer to 0.42 nm(-2) for a 50-mer were identified from measurements of protein adsorption. The experiments were also compared with the protein adsorption isotherms predicted by a molecular theory. Excellent agreements in terms of both the polymer brush structure and the critical chain density were obtained. Furthermore, atomic force microscopy (AFM) imaging is shown to be useful in verifying the critical brush density for preventing protein adsorption. The present coanalysis of experimental and theoretical results demonstrates the significance of characterizing the critical brush density in evaluating the performance of an antifouling polymer brush system. The high fidelity of the agreement between the experiments and molecular theory also indicate that the theoretical approach presented can aid in the practical design of antifouling polymer brush systems.