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.     

Chaotic scattering in the gravitational three-body problem

We summarize some results of an ongoing study of the chaotic scattering interaction between a bound pair of stars (a binary) and an incoming field star. The stars are modeled as point masses and their equations of motion are numerically integrated for a large number of initial conditions. The global features of the resulting initial-value space maps are presented, and their evolution as a function of system parameters is discussed. We find that the maps contain regular regions separated by rivers of chaotic behavior. The probability of escape within the chaotic regions is discussed, and a straightforward explanation of the scaling present in these regions is reviewed. We investigate a statistical quantity of interest, namely the cross section for temporarily bound interactions, as a function of the third star's incoming velocity and mass. Finally, a new way of considering long-lived trajectories is presented, allowing long data sets to be qualitatively analyzed at a glance.     

Generalized negative flows in hierarchies of integrable evolution equations

A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results, several integrability properties of these generalized negative flow equation are established, including their symmetry structure, conservation laws, and bi-Hamiltonian formulation. (The results also apply to the hierarchy of ordinary negative flows). The first generalized negative flow equation is worked out explicitly for each of the following integrable equations: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Sawada-Kotera, Kaup-Kupershmidt, Kupershmidt.     

Long-term trend in CHF2Cl (HCFC-22) from high spectral resolution infrared solar absorption measurements and comparison with in situ measurements

The average tropospheric volume mixing ratio of CHF₂Cl (HCFC-22) has been retrieved from a time series of high spectral resolution ground-based infrared solar absorption spectra recorded with the McMath Fourier transform spectrometer located at the U.S. National Solar Observatory facility on Kitt Peak in southern Arizona (31.9°N, 111.6°W, 2.09 km altitude) for the time period October 1987–November 2002. The retrievals are based on fits to the well-isolated, unresolved 2ν₆ Q branch at 829.05 cm⁻¹ and the SFIT2 retrieval algorithm. The measured daily averages show a near linear rise per year in the mean tropospheric volume mixing ratio as a function of time with a best fit yielding an average increase rate of (5.66±0.15) parts per trillion (10⁻¹²) by volume per year, corresponding to (6.47±0.17)%yr⁻¹, 1 sigma, at the beginning of the time series. The tropospheric mixing ratios retrieved from the solar spectra have been compared with monthly average surface flask sampling measurements from the Climate Monitoring and Diagnostic Laboratory (CMDL) station at Niwot Ridge, Colorado (40.0°N, 105.5°W, 3013 m altitude), archived measurement from the same location, and early CMDL northern hemisphere Pacific cruise measurements. The average ratio of the retrieved tropospheric mixing ratio relative to the CMDL surface mixing ratio is 1.053 for the overlapping 1987 to 2002 time period. The retrieved mean tropospheric mixing ratio is consistent with the surface measurements within the errors estimated for the remote sensing observations.     

Experimental implementation of a self-tuning control system for decentralised velocity feedback

Simulations have previously shown that, for broadband excitation, adjusting the gain of a local velocity feedback loop to maximise their absorbed power also tends to minimise the kinetic energy of the structure under control. This paper describes an experimental implementation of multiple velocity feedback loops on a flat panel, whose gains can be controlled automatically by an algorithm that maximises their local absorbed power. Taking care to remove excessive phase shift in the control loop allows a stable feedback gain that is high enough to experimentally demonstrate the transition in control action between optimum damping and pinning of the structure. A simple search algorithm is then used to adapt the feedback gains of two control loops to maximise their local absorbed powers, thus demonstrating self-tuning. By measuring the power absorbed by each of these loops and also estimation of the kinetic energy of the plate from velocity measurements for a wide range of the two feedback gains, it is shown that not only does the adaptive algorithm converge to a set of feedback gains that maximise total power absorbed by the two feedback loops, but also that this set of feedback gains is very close to those that minimise the measured kinetic energy of the panel.     

Particle Size Characterization of an Extra Fine Milled Product

The present research aims to characterize the particle size distribution of sub micron particles suspended in a liquid. The particles milled are an organic poorly water soluble crystalline product. To characterize the size of these particles, different techniques have been tested: imaging techniques (SEM, CryoTEM), static light scattering techniques, dynamic light scattering techniques, centrifugation and flow field flow fractionation. The results indicate that the studied milled particles have a primary particle size close to 180nm and there is strong evidence of larger particles which are very likely aggregates. This is clearly seen from the Cryo TEM results. All the above mentioned techniques should in principle be able to measure samples of dispersion containing particles of ca 180 nm but several are disturbed by the presence of large aggregates. It is difficult to estimate the amount of aggregate present, but most of the time one is interested in what the primary particle size distribution is. It is clear that no single piece of equipment is capable of exactly determining the particle size distribution of our samples, but the static light scattering with low shear on mixing does give a good representation of what is seen with the image analysis by cryo TEM.     

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.     

Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

If (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V ₁ and V ₂ are spacelike separated spacetime regions, then the system ( (V ₁ ), (V ₂ ), ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A (V ₁ ), B (V ₂ ) correlated in the normal state there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V ₁ and V ₂ and disjoint from both V ₁ and V ₂ , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( (V ₁ ), (V ₂ ), ) with a locally normal and locally faithful state and suitable bounded V ₁ and V ₂ satisfies the Weak Reichenbach's Common Cause Principle.     

Study of an ultrahigh-numerical-aperture fiber continuum generation source for optical coherence tomography

The axial resolution of optical coherence tomography images is primarily dependent on the bandwidth of the illumination source. Continuum generation is one way to generate the single-mode, high-bandwidth light needed for point illumination. We present an inexpensive and easy-to-implement augmentation to a Ti:sapphire laser that widens the bandwidth from 20 to over 200 nm with commerically available ultrahigh-numerical-aperture fiber. This technique can provide a readily available broad-bandwidth source for researchers and a practical enhancement to a fiber-optic optical coherence tomography system.