On systems having Poincaré and Galileo symmetry

Using the wave equation in d≥1$d\ge 1$ space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1$d=1$ the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1$d>1$ is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.     

Non-Existence of Toroidal Cohomogeneity-1 Near-Horizon Geometries

We prove that D ≥  5 dimensional stationary, non-static near-horizon geometries with (D?3) commuting rotational symmetries subject to the vacuum Einstein equations including a cosmological constant cannot have toroidal horizon topology. In D =  4 dimensions, the same result is obtained under the assumption of a non-negative cosmological constant.     

Probing site-specific 13C/15N-isotope enrichment of spider silk with liquid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) has been extensively used to elucidate spider silk protein structure and dynamics. In many of these studies, site-specific isotope enrichment is critical for designing particular NMR methods for silk structure determination. The commonly used isotope analysis techniques, isotope-ratio mass spectroscopy and liquid/gas chromatography-mass spectroscopy, are typically not capable of providing the site-specific isotope information for many systems because an appropriate sample derivatization method is not available. In contrast, NMR does not require any sample derivatization or separation prior to analysis. In this article, conventional liquid-state ¹H NMR was implemented to evaluate incorporation of ¹³C/¹⁵N-labeled amino acids in hydrolyzed spider dragline silk. To determine site-specific ¹³C and ¹⁵N isotope enrichments, an analysis method was developed to fit the ¹H–¹³C and ¹H–¹⁵N J-splitting (J _CH and J _NH) ¹H NMR peak patterns of hydrolyzed silk fiber. This is demonstrated for Nephila clavipes spiders, where [U–¹³C₃,¹⁵N]-Ala and [1-¹³C,¹⁵N]-Gly were dissolved in their water supplies. Overall, contents for Ala and Gly isotopomers are extracted for these silk samples. The current methodology can be applied to many fields where site-specific tracking of isotopes is of interest.      

A Bayesian approach to characterising multi-phase flows using magnetic resonance: application to bubble flows

Magnetic Resonance (MR) imaging is difficult to apply to multi-phase flows due to both the inherently short T?* characterising such systems and the relatively long time taken to acquire the data. We develop a Bayesian MR approach for analysing data in k-space that eliminates the need for image acquisition, thereby significantly extending the range of systems that can be studied. We demonstrate the technique by measuring bubble size distributions in gas-liquid flows. The MR approach is compared with an optical technique at a low gas fraction (～2%), before being applied to a system where the gas fraction is too high for optical measurements (～15%).     

Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.     

Implementation of the Jacobian-free Newton–Krylov method for solving the first-order ice sheet momentum balance

We have implemented the Jacobian-free Newton–Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8–3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.     

Determination of neurotransmitters and their metabolites using one- and two-dimensional liquid chromatography with acidic potassium permanganate chemiluminescence detection

High-performance liquid chromatography with chemiluminescence detection based on the reaction with acidic potassium permanganate and formaldehyde was explored for the determination of neurotransmitters and their metabolites. The neurotransmitters norepinephrine and dopamine were quantified in the left and right hemispheres of rat hippocampus, nucleus accumbens and prefrontal cortex, and the metabolites vanillylmandelic acid, 3,4-dihydrophenylacetic acid, 5-hydroxyindole-3-acetic acid and homovanillic acid were identified in human urine. Under optimised chemiluminescence reagent conditions, the limits of detection for these analytes ranged from 2.5?×?10^?8 to 2.5?×?10^?7 M. For the determination of neurotransmitter metabolites in urine, a two-dimensional high-performance liquid chromatography (2D-HPLC) separation operated in heart-cutting mode was developed to overcome the peak capacity limitations of the one-dimensional separation. This approach provided the greater separation power of 2D-HPLC with analysis times comparable to conventional one-dimensional separations. Figure

2D-HPLC separation and permanganate chemiluminescence detection of neurotransmitter metabolites     

The role of Sb in the structure of Sb2O3–B2O3 binary glasses—an NMR and Mössbauer spectroscopy study

Glasses of general formula xSb₂O₃ (1−x)B₂O₃ (0x0.8) have been prepared by conventional melt- quenching. Mössbauer spectroscopy shows that a fraction of the Sb³⁺ is converted to Sb⁵⁺ and this fraction increases with x. High-field ¹¹B MAS NMR gives well-resolved resonances from boron atoms which are 3- and 4-coordinated to oxygen. The fraction of 4-coordinated boron, N₄, goes through a maximum value of 0.12±0.01 at x=0.5. The position of the maximum in N₄ is consistent with the cation potential for Sb³⁺, as observed for other systems. However, the low value of N₄ at this maximum is not so readily explained. The values are similar to those predicted if [BO₄]⁻ were stabilised by [SbO₄]⁺ but the trends with composition are different.     

Glass surface chemistry via gas chromatography

We have developed special methods of inverse gas chromatography for surface characterization that are based on the use of capillary chromatography columns. The methods have adequate sensitivity so that low-surface-area materials such as glasses can be studied directly, rather than indirectly from analogous powdered samples (e.g. fused silica versus silica gels). Any material can be studied that can be drawn into capillary tubing of about 50–500 μm i.d.. When desired, powdered samples can also be examined. This paper describes the methods we have developed and presents examples that illustrate how the inverse chromatograms are interpreted and what types of information can be obtained.