Negative thermal expansion in ZrW2O8: mechanisms, rigid unit modes, and neutron total scattering

The local structure of the low-temperature ordered phase of the negative thermal expansion (NTE) material has been investigated by reverse Monte Carlo (RMC) modeling of neutron total scattering data. We obtain, for the first time, quantitative measurements of the extent to which the and polyhedra move as rigid units, and we show that these values are consistent with the predictions of rigid unit mode theory. We suggest that rigid unit modes are associated with the NTE. Our results do not support a recent interpretation of x-ray-absorption fine structure spectroscopy data in terms of a larger rigid structural component involving the Zr-O-W linkage.     

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.