Single frequency CW and Q-switched operation of a diode-pumped Nd:YAG 1.3µm ring laser

The use of an acousto-optic modulator in a ring laser to enforce unidirectional and hence single-frequency operation has been extended to the 1.3µm lines in Nd:YAG. We have also been able to obtain stable simultaneous operation on a single frequency in each of the 1.319µm and 1.338µm transitions either CW or Q-switched. The mechanism behind this behaviour is described and implications for other laser systems are discussed. When operated single frequency, up to 155 mW of CW output is produced, and 30 pJ, 40 nsec Q-switched pulses have been obtained

Stable high repetition rate single frequency Q-switched Nd:YAG ring laser

Reliable single-frequency operation of a diode-pumped, Q-switched, Nd:YAG ring laser at high repetition frequencies up to 25kHz has been achieved by active stabilisation of the prelase power. Average powers of 250mW have been obtained for a 1.2 watt diode pump

Current Distribution in the Three-Dimensional Random Resistor Network at the Percolation Threshold

We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth moments of the current distribution, finding {\it e.g.\/} that $t/\nu=2.282(5)$ where $t$ is the conductivity exponent and $\nu$ is the correlation length exponent.Comment: 10 pages, latex, 8 figures in separate uuencoded fil

Polynomial Modular Frobenius Manifolds

The moduli space of Frobenius manifolds carries a natural involutive symmetry, and a distinguished class - so-called modular Frobenius manifolds - lie at the fixed points of this symmetry. In this paper a classification of semi-simple modular Frobenius manifolds which are polynomial in all but one of the variables is begun, and completed for three and four dimensional manifolds. The resulting examples may also be obtained from higher dimensional manifolds by a process of folding. The relationship of these results with orbifold quantum cohomology is also discussed

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result

Light propagation in statistically homogeneous and isotropic dust universes

We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat LambdaCDM model.Comment: 33 pages. v2: Published version. Corrected typo

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website