Fractional Order Analysis of Sephadex Gel Structures: NMR Measurements Reflecting Anomalous Diffusion

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-(bD)(α)], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4,000 s-mm(-2)). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.     

Novel techniques for the prepartion of synthetic diamond

Abstract

The objectives of this work are two fold: (1) to study the effect of using oxygen-acetylene flame grown synthetic diamond as seed crystals for the high pressure-high temperature conversion of graphite into diamond and (2) to demonstrate the ability to produce small crystallites of diamond by a simple, electron beam evaporation technique. In each case, the production of diamond from graphite was confirmed.     

Error-rate measurements on an all-optically regenerated signal

Error-rate measurements have been performed on an experimental all-optical regenerator at 140 Mbit s⁻¹ for a range of input wavelengths in the 1.5-μm band. The best sensitivity was −40 dB m and the maximum gain 31.5 dB from facet to facet. Wavelength translations from −11 to +24 nm were obtained for a penalty of less than 5 dB. The regenerator used the interaction of the input signal with an optical clock waveform in a bistable laser amplifier to re-time the signal and restore the data levels. Future applications may include use in a repeater, as an interface in a wavelength-multiplexed network or as a logic element.

     

Wavelength-Resolved 3-Dimensional Fluorescence Lifetime Imaging

We have developed a compact system for wide-field fluorescence imaging, resolved in three spatial dimensions, lifetime and wavelength, that is based on a gated optical intensifier and an all-solid-state diode pumped Cr:LiSAF oscillator-amplifier system. Exploiting spectral separation, the system has been applied to human teeth, obtaining good lifetime contrast between enamel, dentin and caries. Exploiting spectral separation combined with depth resolution, the study of fluorescent microspheres led to an enhancement in both lifetime contrast and lateral resolution.     

A note on the instability of Gaussian elimination

It is well-known that Gaussian elimination is very sensitive to round-off errors if row interchanges are not performed. In this note we make precise and prove the fact that there exist sets of data for which that algorithm leads to improper results regardless of how many digits are carried in the computation.Our research was supported in part by NSF grant GJ-797.     

Evidence for non-thermal excitation of energy levels in active biological systems

The ratio R of the intensities of anti Stokes and Stokes Raman shift lines of 124 cm^-1 and of 118 cm^-1 of active E. coli B was measured. For an oscillating system in therm equilibrium R ≈ 0.55 is expected whereas we find R ≈ 1.0. This shows that this system is excited strongly above thermal excitation in agreement with a previous theoretical conjecture [2–5].     

Tumour detection by ultrasonic Doppler blood-flow signals

Ultrasonic Doppler blood-flow signals which seem to be associated with malignant tumour neovascularization have been detected in the female breast. No such signals have been detected from cysts. This discovery may lead to the development of a high-speed ultrasonic Doppler scanner which might make breast screening for cancer practicable.