Application of the chirp z-transform to MRI data

A version of the chirp z-transform (CZT) enabling signal intensity and phase-preserving field-of-view scaling has been programmed. The algorithm is important for all single-point imaging sequences such as SPRITE when used with multiple data acquisition for T2* mapping or signal averaging. CZT has particular utility for SPRITE imaging of nuclei with short relaxation times such as sodium at high field. Here, a complete theory of the properties of CZT is given. This method operates entirely in k-space. It is compared with a conventional interpolation approach that works in image space after the application of a fast Fourier transformation.     

A dynamic nuclear polarization strategy for multi-dimensional Earth's field NMR spectroscopy

Dynamic nuclear polarization (DNP) is introduced as a powerful tool for polarization enhancement in multi-dimensional Earth’s field NMR spectroscopy. Maximum polarization enhancements, relative to thermal equilibrium in the Earth’s magnetic field, are calculated theoretically and compared to the more traditional prepolarization approach for NMR sensitivity enhancement at ultra-low fields. Signal enhancement factors on the order of 3000 are demonstrated experimentally using DNP with a nitroxide free radical, TEMPO, which contains an unpaired electron which is strongly coupled to a neighboring ¹⁴N nucleus via the hyperfine interaction. A high-quality 2D ¹⁹F–¹H COSY spectrum acquired in the Earth’s magnetic field with DNP enhancement is presented and compared to simulation.     

A laser extraction/combustion technique for in situ delta(13)C analysis of organic and inorganic materials

A CO(2) laser extraction system is described for in situ delta(13)C analysis of organic and inorganic materials. Carbonaceous compounds volatilized by the laser are quantitatively converted to CO(2) gas by a combustion furnace mounted after the sample chamber. Gases produced by the laser and combustion processes are swept by helium carrier gas and separated by a packed gas chromatography column prior to their introduction to an isotope ratio monitoring mass spectrometer. A sample of lentil bean was analyzed at a spatial resolution of 200 μm and yielded delta(13)C values with precision of +/- 0.3 per thousand. The accuracy of delta(13)C measurements was better than +/- 0.5 per thousand from NBS 22 (mineral oil), USGS 24 (graphite), and IAEA CO-1 (calcium carbonate). Copyright 1999 John Wiley & Sons, Ltd.     

Rotational viscosity of uniaxial molecules

Non-equilibrium molecular dynamics (NEMD) are used to calculate the vortex or rotational viscosity of fluids composed of uniaxial molecules. It is shown that the NEMD homogeneous spin flow algorithm proposed by Edberg, R., Evans, D. J., and Moriss, G. P., 1987, Molec. Phys., 62, 1357 considerably underestimates the vortex viscosity. A modified version of this algorithm is proposed and applied to liquid chlorine and nitrogen. The results are in good agreement with previous work using equilibrium or other NEMD methods, and also show that at high spin rates the vortex viscosity decreases with increase in magnitude of the external torque used to drive the spin flow.     

THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS

In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementar...     

On the role of the definition of potential models in Gibbs ensemble phase equilibria simulations of the H2S-pentane mixture

The effect of treating explicitly the coulombic and polarization interactions is investigated through the calculation of the coexistence curve of the pentane-H₂S binary mixture. In this work, potential models have been developed for hydrogen sulphide and pentane, which include electrostatic sites—estimated from ab initio calculations—and polarizable sites—estimated from experimental data—in addition to Lennard-Jones sites. Compared to existing models, these new models have the same number of fitting parameters to experimental thermodynamic data. They are shown to correctly describe the coexistence curve of the pure compounds. When applied to the case of mixtures, together with Lorentz-Berthelot combining rules, they allow one to obtain a more accurate prediction of the coexisting compositions of the mixture. Furthermore, it is shown that the interaction energy in this kind of mixture cannot be properly described by using effective potential models usually considered for pure compounds.     

C-bifurcations and period-adding in one-dimensional piecewise-smooth maps

This paper examines the behaviour of piecewise-smooth, continuous, one-dimensional maps that have been derived in the literature as normal forms for grazing and sliding bifurcations. These maps are linear for negative values of the parameter and non-linear for positive values of the parameter. Both C¹ and C² maps of this form are considered. These maps display both period-adding and period-doubling behaviour. For maps with a squared or 3/2 term the stability and existence conditions of fixed points and period-2 orbits in the vicinity of the border-collision are found analytically. These agree with the Feigin classification proposed by di Bernardo et al. [Chaos Solitons and Fractals 10 (1999) 1881]. The period-adding behaviour is examined in these maps, where analytical solutions for the boundaries of periodic solutions are found. Implicit equations for the boundaries of periodic windows for varying power term are also found and plotted. Thus, it is proved that period-adding scenarios are generic in maps of this form.     

A comparison of three SPRITE techniques for the quantitative 3D imaging of the 23Na spin density on a 4T whole-body machine

Sodium density maps acquired with three SPRITE-based methods have been compared in terms of the resulting quantitative information as well as image quality and acquisition times. Consideration of factors relevant for the clinical implementation of SPRITE shows that the Conical-SPRITE variant is preferred because of a 20-fold reduction in acquisition time, slightly improved image quality, and no loss of quantitative information. The acquisition of a 3D data set (32x32x16; FOV=256x256x160 mm) for the quantitative determination of sodium density is demonstrated. In vivo Conical-SPRITE 23Na images of the brain of a healthy volunteer were acquired in 30 min with a resolution of 7.5x7.5x7.5 mm and a signal-to-noise ratio of 23 in cerebrospinal fluid and 17 in brain tissue.     

New Zealand Developments in Earth's Field NMR

We review here two decades of development of Earth's field nuclear magnetic resonance (NMR), starting with the first demonstration of resonant refocusing and the generation of spin echoes, the first measurement of diffusion using Earth's field NMR, and its application to Antarctic research, the adaptation of the apparatus to allow its use indoors, in a conventional laboratory setting, and finally, the construction of a flexible laboratory-based Earth's field NMR system capable of not only a range of relaxation and spectroscopy applications but also the straightforward demonstration of NMR Imaging. Authors' address: Paul T. Callaghan, MacDiarmid Institute, Victoria University of Wellington, PO Box 600, Wellington, New Zealand