Prospects for ultracold carbon via charge exchange reactions and laser cooled carbides

Strategies to produce an ultracold sample of carbon atoms are explored and assessed with the help of quantum chemistry. After a brief discussion of the experimental difficulties using conventional methods, two strategies are investigated. The first attempts to exploit charge exchange reactions between ultracold metal atoms and sympathetically cooled C(+) ions. Ab initio calculations including electron correlation have been conducted on the molecular ions [LiC](+) and [BeC](+) to determine whether alkali or alkaline earth metals are a suitable buffer gas for the formation of C atoms but strong spontaneous radiative charge exchange ensure they are not ideal. The second technique involves the stimulated production of ultracold C atoms from a gas of laser cooled carbides. Calculations on LiC suggest that the alkali carbides are not suitable but the CH radical is a possible laser cooling candidate thanks to very favourable Frank-Condon factors. A scheme based on a four pulse STIRAP excitation pathway to a Feshbach resonance is outlined for the production of atomic fragments with near zero centre of mass velocity.     

Job selection and sequencing on a single machine in a random environment

We examine a single machine scheduling problem with random processing times and deadline. Given a set of independent jobs having specified initiation costs and terminal revenues, the objective is to select a subset of the jobs and sequence the selected jobs such that the expected profit is maximized. The job selection aspect considered by us marks a clear departure from the pure sequencing focus found in the traditional scheduling literature. In this paper, we assume an exponentially distributed deadline and do not allow preemption. Even under these conditions, the selection and sequencing problem remains quite difficult (unlike its pure sequencing counterpart); we in fact conjecture that the problem is NP-hard. However, we show that the problem can be efficiently solved as long as the cost parameter is agreeable or an approximate solution is acceptable. To this end, we describe several solution properties, present dynamic programming algorithms (one of which exhibits a pseudo-polynomial time worst-case complexity), and propose a fully-polynomial time approximation scheme. In addition, we study a number of special cases which can be solved in polynomial time. Finally, we summarize our work and discuss an extension where the jobs are precedence related.     

Noise processes in large ring lasers

Large ring lasers with a cavity Q well above 10¹² are characterized by extremely narrow line-widths and high coherence. At this point, active Sagnac interferometers do not quite reach the quantum limit. In this paper, we will explore the current status of this technology and look at the various noise processes involved with large ring lasers rigidly mounted to the Earth crust.     

Fracture control: Past,present and future

The treatment of this topic is selective; it concentrates initially on the recognition of fracture problems and the experimental investigations that developed in response to them, including fracture-propagation studies in plates and pipelines. Attention is then given to several criteria for crack extension that have been investigated, and to the methods used. Although an understanding of stationary crack stress fields has been established, it is concluded that the position with just-moving cracks is less satisfactory, so that further progress is impeded for lack of a sufficient basis of comparison. Many of the practical problems most in need of fracture-analysis techniques involve complex shapes, and it is suggested that theoretical stress analysis even using numerical methods is unlikely to provide complete solutions in the near future. In helping to resolve the remaining uncertainties with fracture criteria, and in handling complex shapes of component there should be more scope for experimental methods in fracture mechanics than ever before.     

Anisotropic multiple scattering of collimated irradiance

Spherical harmonics are often used to solve multi-scatter transport problems. For a collimated incident beam, we describe a technique similar to the familiar P_N approximation except that we manage the infinite set of coupled equations in a novel way that permits the use of hundreds of harmonics to represent very pointed angular distributions. We split some equations into two approximate ones that depend on the angle of incidence. For plane slab geometry, the harmonics of low degree are solved in a coordinate system aligned to the boundary while the high harmonics use coordinates pointed at the source. We illustrate the technique with an extreme example: a scattering function having an integrable singularity in the forward direction. We give a time-dependent example along with several time-independent ones.     

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.     

p-adic Proofs of congruences for the Bernoulli numbers

Many of the classical theorems for the Bernoulli numbers, particularly those congruences needed in the study of irregular primes, follow easily from the existence of the (p ? 1)st roots of unity in the ring of p-adic integers. Proofs are given for the von Staudt-Clausen theorem, the theorem of J. C. Adams, the Friedmann-Tamarkine congruence, a theorem of Vandiver, special cases of the congruences of Voronoi, Kummer, and Carlitz, and the congruences of E. Lehmer.