Phonons from powder diffraction: a quantitative model-independent evaluation

We describe a model-independent approach for the extraction of detailed lattice dynamics information from neutron powder diffraction data, based on a statistical analysis of atomistic configurations generated using reverse Monte Carlo structural refinement. Phonon dispersion curves for MgO extracted in this way are shown to reproduce many of the important features found in those determined independently using neutron triple-axis spectroscopy. By means of molecular dynamics simulations, we quantify the extent to which the diffraction data are sensitive to lattice dynamics in this system.     

High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine

Results of atmospheric propagation for a high-speed, large-actuator-number adaptive optics system are presented. The system uses a microelectromechanical system- (MEMS-) based spatial light modulator correction device with 1024 actuators. Tests over a 1.35-km path achieved correction speeds in excess of 800 Hz and Strehl ratios close to 0.5. The wave-front sensor was based on a quadrature interferometer that directly measures phase. This technique does not require global wave-front reconstruction, making it relatively insensitive to scintillation and phase residues. The results demonstrate the potential of large-actuator-number MEMS-based spatial light modulators to replace conventional deformable mirrors.     

A multidimensional discrete variable representation basis obtained by simultaneous diagonalization

Direct product basis functions are frequently used in quantum dynamics calculations, but they are poor in the sense that many such functions are required to converge a spectrum, compute a rate constant, etc. Much better, contracted, basis functions, that account for coupling between coordinates, can be obtained by diagonalizing reduced dimension Hamiltonians. If a direct product basis is used, it is advantageous to use discrete variable representation (DVR) basis functions because matrix representations of functions of coordinates are diagonal in the DVR. By diagonalizing matrices representing coordinates it is straightforward to obtain the DVR that corresponds to any direct product basis. Because contracted basis functions are eigenfunctions of reduced dimension Hamiltonians that include coupling terms they are not direct product functions. The advantages of contracted basis functions and the advantages of the DVR therefore appear to be mutually exclusive. A DVR that corresponds to contracted functions is unknown. In this paper we propose such a DVR. It spans the same space as a contracted basis, but in it matrix representations of coordinates are diagonal. The DVR basis functions are chosen to achieve maximal diagonality of coordinate matrices. We assess the accuracy of this DVR by applying it to model four-dimensional problems.     

Intersections of polynomial orbits, and a dynamical Mordell–Lang conjecture

We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell–Lang conjecture. Mathematics Subject Classification (1991) Primary 14G25; Secondary 37F10, 11C08     

Unusual structures in some alkyl cyanoterphenyls

The phase behaviour of three alkyl cyanoterphenyls has been investigated with the particular objective of elucidating their unusual phase behaviour and determining the structure of the new, and so far uncharacterized, phase (E') appearing between the smectic A_d and the crystal E' phases. In the course of this work complications arose from the appearance of yet another phase which appears only on cooling but for which no characteristic X-ray diffraction pattern could be obtained. The E phase appears to have the orthorhombic symmetry characteristic of the E phase but has a complex temperature dependent packing in the c direction. This is driven by the competition between a density wave and an antiferroelectric pair ordering which results in a locked-in structure with a periodicity of three times that of the underlying density wave.     

Solution self-assembly and adsorption at the air-water interface of the monorhamnose and dirhamnose rhamnolipids and their mixtures

The self-assembly in solution and adsorption at the air-water interface, measured by small-angle neutron scattering, SANS, and neutron reflectivity, NR, of the monorhamnose and dirhamnose rhamnolipids (R1, R2) and their mixtures, are discussed. The production of the deuterium-labeled rhamnolipids (required for the NR studies) from a Pseudomonas aeruginosa culture and their separation into the pure R1 and R2 components is described. At the air-water interface, R1 and R2 exhibit Langmuir-like adsorption isotherms, with saturated area/molecule values of about 60 and 75 ?(2), respectively. In R1/R2 mixtures, there is a strong partitioning of R1 to the surface and R2 competes less favorably because of the steric or packing constraints of the larger R2 dirhamnose headgroup. In dilute solution (<20 mM), R1 and R2 form small globular micelles, L(1), with aggregation numbers of about 50 and 30, respectively. At higher solution concentrations, R1 has a predominantly planar structure, L(α) (unilamellar, ULV, or bilamellar, BLV, vesicles) whereas R2 remains globular, with an aggregation number that increases with increasing surfactant concentration. For R1/R2 mixtures, solutions rich in R2 are predominantly micellar whereas solutions rich in R1 have a more planar structure. At an intermediate composition (60 to 80 mol % R1), there are mixed L(α)/L(1) and L(1)/L(α) regions. However, the higher preferred curvature associated with R2 tends to dominate the mixed R1/R2 microstructure and its associated phase behavior.