An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

Dynamic stability of weakly damped oscillators with elastic impacts and wear

The dynamics of non-linear oscillators comprising of a single-degree-of-freedom system and beams with elastic two-sided amplitude constraints subject to harmonic loads is analyzed. The beams are clamped at one end, and constrained against unilateral contact sites near the other end. The structures are modelled by a Bernoulli-type beam supported by springs using the finite element method. Rayleigh damping is assumed. Symmetric and elastic double-impact motions, both harmonic and sub-harmonic, are studied by way of a Poincaré mapping that relates the states at subsequent impacts. Stability and bifurcation analyses are performed for these motions, and domains of instability are delineated. Impact work rate, which is the rate of energy dissipation to the impacting surfaces, is evaluated and discussed. In addition, an experiment conducted by Moon and Shaw on the vibration of a cantilevered beam with one-sided amplitude constraining stop is modelled. Bifurcation observed in the experiment could be captured.     

Comparison of localization and delocalization indices obtained with Hartree-Fock and conventional correlated methods: effect of Coulomb correlation

Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.     

Deflection of laser-produced ions in laser-induced thermal-desorption/fourier-transform mass spectrometry for surface analysis

A method for deflecting ions, such as K⁺, produced outside a Fourier-transform mass spectrometer cell during laser-induced thermal desorption, is described. This technique has been shown to deflect laser-generated K and Ti ions from two Ti foil samples (biomedical implant model surfaces), yielding mass spectra of coadsorbed organic species. Further studies characterizing the laser desorption/deflection parameters have shown that ion deflection improves with higher deflection voltages and greater sample to Fourier-transform mass spectrometry cell separation. Higher laser power densities resulted in greater surface ion production; hence higher deflection voltages were necessary. A 6% increase in laser power necessitated a fourfold increase in deflection voltage for the Ti sample.     

Membrane ion-exchange chromatography for process-scale antibody purification

Microemulsion electrokinetic chromatography (MEEKC) was evaluated as a screening tool for the indirect measurement of octanol–water partition coefficients (log P_o/w) of pesticide compounds. Over 80 pesticide compounds representing a variety of structural characteristics were studied, and good correlation of log P_o/w with the logarithm of the retention factor was found. The microemulsion system studied allowed the separation of compounds in the log P_o/w range of −1 to 7. In addition, a smaller set of simple organic molecules that vary in structural features was evaluated and compared to the pesticide log P_o/w calibration. The pesticide and simple organic molecule log P_o/w calibration lines were statistically similar. This suggests that a universal set of standard compounds may be employed for the log P_o/w calibration to provide measurements for a variety of compounds with good accuracy.     

Recoil spectrometry: Ion accelerator based elemental characterisation of surface layers

Recoil Spectrometry covers a group of techniques that are very similar to the well known Rutherford backscattering Spectrometry technique, but with the important difference that one measures the recoiling target atom rather than the projectile ion. This makes it possible to determine both the identity of the recoil and its depth of origin from its energy and velocity, using a suitable detector system. The incident ion is typically high-energy (30–100MeV)³⁵C1,⁸¹Br or¹²⁷I. Low concentrations of light elements such as C, O and N can be profiled in a heavy matrix such as Fe or GaAs. Here we present an overview of mass and energy dispersive recoil Spectrometry and illustrate its successful use in some typical applications.