Non-linear propagation of directional spherical waves

The method of renormalization is used to determine a uniformly valid expansion for the problem of non-linear waves produced in a fluid by spatially non-uniform simple harmonic motion of the surface of a sphere. The effect of dimensionless quantities upon the acoustic shock-formation distance is examined.     

On a class of approximations for closed queueing networks

This paper presents some analytical results concerning an approximation procedure for closed queueing networks. The procedure is well-known and has been found useful for product-form networks where large numbers of queues, jobs or job classes prohibit an exact analysis, as well as for networks which do not possess product-form. The procedure represents the mean sojourn time at a queue as a function of the throughput of the queue, and derives a set of fixed point equations for the throughputs of the various job classes. We begin by showing that under a mild regularity condition the fixed point equations have a unique solution. Then we show that derivatives of performance measures can be readily calculated, and that their simple form provides an interesting insight into capacity allocation in closed queueing networks.This work was supported in part by the Nuffield Foundation     

Precision spectral sculpting for narrow-band amplification of broadband frequency-modulated pulses

Amplification of broadband frequency-modulated (FM) pulses in high-efficiency materials such as ytterbium-doped strontium fluorapatite results in significant gain narrowing, leading to reduced on-target bandwidths for beam smoothing and to conversion from frequency modulation to amplitude modulation (AM). To compensate for these effects, we have applied precision spectral sculpting, requiring both amplitude and phase shaping, to the amplification of broadband FM pulses in narrow-band gain media. We have demonstrated sculpting for centerline small-signal gains of 10(4), producing amplified pulses that have both sufficient bandwidths for on-target beam smoothing and temporal profiles that have no potentially damaging AM.     

A Fourier analysis approach for capillary polarimetry

A new method of fringe interrogation based on Fourier analysis was implemented and tested for a capillary polarimetry detector. It has significant advantages over the previously employed depth of modulation (DOM) approach, including speed and alignment insensitivity. The new and old methods were compared using a set of interference fringes typically used to facilitate nanoliter volume polarimetric determinations. Polarimetric response was calculated with both methods over the range from 0 degrees to 180 degrees. The results were found to be in good agreement with Malus Law and indicate that an fast Fourier transform (fft) could be used for real-time capillary scale polarimetry in a probe volume of 40 nL.     

Chiral amplification by polypeptides and its relevance to prebiotic catalysis

Polyleucine prepared from scalemic Leu-NCA monomers, shows high chiral amplification in the Julia-Colonna epoxidation of chalcone.     

The isomerisation of (Z)-3-[2H1]-phenylprop-2-enone as a measure of the rate of hydroperoxide addition in Weitz-Scheffer and Julia-Colonna epoxidations

(Z)-3-[2H1]-Phenylprop-2-enone is isomerised by hydroperoxide to an equimolar mixture of the (Z)- and (E)-isomers prior to epoxidation. Poly-(L)-leucine (10 mole %) accelerates the addition of hydroperoxide by an order of magnitude and sequesters hydroperoxide from THF.