Structural anisotropy and internal magnetic fields in trabecular bone: coupling solution and solid dipolar interactions

We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone-water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.     

Forced responses of solid axially polarized piezoelectric ceramic finite cylinders with internal losses

A method is presented to determine the forced responses of piezoelectric cylinders using weighted sums of only certain exact solutions to the equations of motion and the Gauss electrostatic conditions. One infinite set of solutions is chosen such that each field variable is expressed in terms of Bessel functions that form a complete set in the radial direction. Another infinite set of solutions is chosen such that each field variable is expressed in terms of trigonometric functions that form a complete set in the axial direction. Another solution is used to account for the electric field that can exist even when there is no vibration. The weights are determined by using the orthogonal properties of the functions and are used to satisfy specified, arbitrary, axisymmetric boundary conditions on all the surfaces. Special cases including simultaneous mechanical and electrical excitation of cylinders are presented. All numerical results are in excellent agreement with those obtained using the finite element software ATILA. For example, the five lowest frequencies at which the conductance and susceptance of a stress-free cylinder, of length 10 mm and radius 5 mm, reach a local maximum or minimum differ by less than 0.01% from those computed using ATILA.     

The prospects for high resolution optical brain imaging: the magnetic resonance perspective

Various analogs of NMR and MRI are now technically possible in optics; specifically, high-resolution laser-pulse shaping and complex pulse sequence generation with well-defined phase shifts has been demonstrated. Here we summarize this technology and discuss the potential for these methods to enhance optical functional imaging, competing with (and surpassing?) what is possible by functional MRI.     

Aerosol assisted chemical vapour deposition of tungsten oxide films from polyoxotungstate precursors: active photocatalysts

Aerosol assisted chemical vapour deposition of polyoxotungstate precursors [n-Bu4N]2[W6O19] and [n-Bu4N]4H3[PW11O39] produces films of WO(3 - x) and WO3 on glass substrates; the WO3 films show significant photocatalytic decomposition of a test organic pollutant--stearic acid--when irradiated with either 254 or 365 nm radiation.     

Isobutene polymerization using a chelating diborane co-initiator

Lewis acidic diborane 1 (J. Am. Chem. Soc. 1999, 121, 3244-3245) is highly effective for both proton- and cationogen-initiated isobutene polymerization in hydrocarbon media at low temperature. Reactions of diborane 1 with cumyl chloride and cumyl methyl ether were studied by variable-temperature 1H and 19F NMR spectroscopy. At low temperatures stable ion pairs 2a and 2b are formed; at higher temperatures these ion-pairs form phenyl-1,3,3-trimethylindan (3) with concomitant release of HCl to form 1 in the case of 2a or degradation of the anion (2b). Reaction between Ph3C-Cl and diborane 1 resulted in the generation of an ion-pair 4 consisting of the Ph3C cation very weakly associated with the chelated, mu-Cl counteranion as revealed by X-ray crystallography.     

Quadrature spectral interferometric detection and pulse shaping

We introduce a new variant of spectral interferometry, using spectrally dispersed ultrafast laser pulses and quadrature detection to measure optical thickness variations related to surface structure. We can resolve surface features with depths of 3 mm to 25 nm, using a lateral resolution of ~100mum . Quadrature detection gives a larger dynamic range and solves the sign ambiguity problem. This method has potential applications in device manufacture, optical communications, and error compensation in pulse shaping.     

Functional magnetic resonance imaging with intermolecular multiple-quantum coherences

For the first time, we demonstrate here functional magnetic resonance imaging (fMRI) using intermolecular multiple-quantum coherences (iMQCs). iMQCs are normally not observed in liquid-state NMR because dipolar interactions between spins average to zero. If the magnetic isotropy of the sample is broken through the use of magnetic field gradients, dipolar couplings can reappear, and hence iMQCs can be observed. Conventional (BOLD) fMRI measures susceptibility variations averaged over each voxel. In the experiment performed here, the sensitivity of iMQCs to frequency variations over mesoscopic and well-defined distances is exploited. We show that iMQC contrast is qualitatively and quantitatively different from BOLD contrast in a visual stimulation task. While the number of activated pixels is smaller in iMQC contrast, the intensity change in some pixels exceeds that of BOLD contrast severalfold.     

Explicit gradient estimates for minimal Lagrangian surfaces of dimension two

We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two. Y. Yuan is partially supported by an NSF grant.