A Geometric Approach to Integrability of Abel Differential Equations

A geometric approach is used to study the Abel first-order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to characterise some particular examples of integrable Abel equations. Second order Abel equations will be discussed and the inverse problem of the Lagrangian dynamics is analysed: the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class. The study is carried out by means of the Darboux polynomials and Jacobi multipliers.     

Stereochemical analysis of ferrocene and the uncertainty of fluorescence XAFS data

Methods for the quantification of statistically valid measures of the uncertainties associated with X‐ray absorption fine structure (XAFS) data obtained from dilute solutions using fluorescence measurements are developed. Experimental data obtained from 10 mM solutions of the organometallic compound ferrocene, Fe(C₅H₅)₂, are analysed within this framework and, following correction for various electronic and geometrical factors, give robust estimates of the standard errors of the individual measurements. The reliability of the refinement statistics of standard current XAFS structure approaches that do not include propagation of experimental uncertainties to assess subtle structural distortions is assessed in terms of refinements obtained for the staggered and eclipsed conformations of the C₅H₅ rings of ferrocene. Standard approaches (XFIT, IFEFFIT) give refinement statistics that appear to show strong, but opposite, preferences for the different conformations. Incorporation of experimental uncertainties into an IFEFFIT‐like analysis yield refinement statistics for the staggered and eclipsed forms of ferrocene which show a far more realistic preference for the eclipsed form which accurately reflects the reliability of the analysis. Moreover, the more strongly founded estimates of the refined parameter uncertainties allow more direct comparison with those obtained by other techniques. These XAFS‐based estimates of the bond distances have accuracies comparable with those obtained using single‐crystal diffraction techniques and are superior in terms of their use in comparisons of experimental and computed structures.     

Beyond the N = 50 shell closure: High-spin excitations of 87Kr and ground-state spin of 87Br

The ⁸⁷Kr nucleus has been produced as fission fragment in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85MeV bombarding energy and studied with the Euroball IV array. High-spin states of this neutron-rich isotope have been identified for the first time. Its level scheme has been obtained up to 6.3MeV excitation energy and spin I ∼ 23/2ℏ. Its structure is interpreted by analogy with those of the heavier isotones. The proposed configurations involve both proton and neutron excitations from several sub-shells located close to the Fermi levels, particularly νd_5/2, πp_3/2f_5/2 and πg_9/2. Moreover, a revised spin value of 5/2^- for the ⁸⁷Br ground state is proposed.     

Long-lived mesoscopic entanglement outside the Lamb-Dicke regime

We create entangled states of the spin and motion of a single 40Ca+ ion in a linear ion trap. We theoretically study and experimentally observe the behavior outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the motional coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed up to Deltaalpha=5.1 with coherence time 170 micros and mean phonon excitation n = 16.     

Epitaxial LSMO films grown on MgO single crystalline substrates

The manganite La_0.67Sr_0.33MnO₃ (LSMO) layers are deposited on single crystal MgO(0 0 1) substrates using a magnetron dc sputtering. The crystalline perfection of the layers, both the as-prepared and the annealed, are characterized by X-ray diffraction technique, rocking curve measurements, Rutherford backscattering spectroscopy (RBS) and transmission electron microscopy (TEM). TEM analyses give evidence of the epitaxial growth of the annealed LSMO with a nanocrystalline surface layer. The temperature dependence of resistance in the 77-340 K range is measured by a standard four-probe technique. While the as-prepared film does not show any transition from paramagnetic to ferromagnetic state, the film annealed in oxygen shows steep R(T) dependence with a peak at 330 K and maximal slope (dR/dT) at 290 K where the maximal sensitivity is 3% K⁻¹.     

A radial mode ultrasonic horn for the inactivation of Escherichia coli K12

Tuned cylindrical radial mode ultrasonic horns offer advantages over ultrasonic probes in the design of flow-through devices for bacterial inactivation. This study presents a comparison of the effectiveness of a radial horn and probe in the inactivation of Escherichia coli K12. The radial horn is designed using finite element analysis and the predicted modal parameters are validated using experimental modal analysis. A validated finite element model of the probe is also presented. Visual studies of the cavitation fields produced by the radial horn and probe are carried out using luminol and also backlighting to demonstrate the advantages of radial horns in producing a more focused cavitation field with widely dispersed streamers. Microbiological studies show that, for the same power density, better inactivation of E. coli K12 is achieved using the radial horn and, also, the radial horn offers greater achievable power density resulting in further improvements in bacterial inactivation. The radial horn is shown to be more effective than the probe device and offers opportunities to design in-line flow-through devices for processing applications.     

A memory function model for the velocity autocorrelation function and the self-diffusion coefficient in simple dense fluids

A memory-function model is used to compute the velocity autocorrelation function and the self-diffusion coefficient of a dense Lennard-Jones fluid from the zero-time correlation functions of the molecular velocity and its first two time derivatives. It is shown that these zero-time correlation functions can be evaluated in terms of the radial distribution function and the pair potential only, i.e. without considering higher order correlation functions. Since molecular dynamics results are available for the radial distribution function as well as the velocity autocorrelation function and the self-diffusion coefficient, a rigorous test of the chosen memory function is possible. The agreement is reasonable, although generally not within the error bands of the molecular dynamics results.     

Magnetic anisotropies of late transition metal atomic clusters

We analyze the impact of the magnetic anisotropy on the geometric structure and magnetic ordering of small atomic clusters of palladium, iridium, platinum, and gold. We have employed a noncollinear implementation of density functional theory where the spin-orbit interaction has been included self-consistently. The size of the clusters ranges from two to five, six, or seven atoms, depending on the element. Our results highlight the relevance of the spin-orbit interaction in the magnetic properties of small atomic clusters made of fourth- and fifth-row elements.