External-feedback effects in high-gain scattering media

We report on experimental studies of external-feedback effects on high-gain scattering media. We explain experimental results for the pump energy required for laser action as a function of the separation between a mirror and the media by use of Monte Carlo simulations and integration of the laser equations.     

The strong influence of small amounts of palladium on the structure of liquid potassium-thallium

Neutron diffraction measurements on liquid KT1 alloys with 0, 1, and 5 at % Pd, respectively, show that the prepeak in the structure factor shifts from wave vector k=8.0 to 7.2 nm⁻¹ with an increasing amount of Pd. This corresponds to a periodicity change from 0.96 to 1.07 nm in real space². The structure of the liquid KT1 alloys is compared to the corresponding crystal structures, and some similarities are observed. Reverse Monte Carlo modelling indicates T1 clustering in the liquid alloy. Also in solid KTl Tl-clusters occur. The distance between the clusters increases with the addition of 5%. Pd. More information is needed to discriminate between various possible structures of the Tl clusters in the liquid alloy and to determine the position of Pd in these clusters.     

On the structure of simple molecular liquids SbCl5 and WCl6

Neutron diffraction measurements on liquid antimony pentachloride and tungsten hexachloride have been carried out using the Studsvik liquids and amorphous diffractometer (SLAD) at the Studsvik Neutron Research Laboratory. The corrected structure factors have been interpreted by means of reverse Monte Carlo modeling which provides large structural models, containing thousands of atoms, that are consistent with the experimental data within their uncertainties. From these models, partial structure factors and pair correlation functions can be calculated. It is demonstrated that the intramolecular structure can be determined on the basis of data extending up to 10 Angstrom (-1). SbCl(5) is found to have a trigonal bipyramidal shape in the liquid, while liquid WCl(6) consists of octahedral molecules. The intermolecular structure of liquid SbCl(5) and WCl(6) seems to be determined largely by steric effects (excluded volume and molecular shape).     

Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

A network problem: Modelling alkali-silicate glasses with RMC

Structural models of four potassium-silicate glasses, (K₂O)_x(SiO₂)_1-x with x=0, 0.15, 0.25 and 0.45, have been created using the reverse Monte Carlo (RMC) method. The current use of RMC for creating topologically constrained models of amorphous materials is described in detail. The models are based on the simultaneous combination of neutron diffraction and ²⁹Si magic angle spinning NMR data, the latter for the first time. We show that the predictions of Modified Random Network theory are consistent with the data. It is found that models whose topology is determined by short-range chemical bonding constraints and the macroscopic density are able to reproduce all details of the structure factor, including its complex form at low momentum transfer. It is not necessary to ‘build in’ specific ring structures or other complex units beforehand; these arise naturally as a consequence of the constraints of density and chemical bonding.