Mathematics from China to Virginia by Way of Singapore

Our article follows from an interesting concurrence of mathematical and educational lines. At least the concurrence seems so to us and we hope that those who read on will agree. The lines or streams are a joint minimester program at St. Catherine’s and St. Christopher‘s Schools, an interest in problem solving, and a Singapore connection. We shall describe the lines first and then describe the mathematics that we found at their intersection

A simple method for estimation of coagulation efficiency in mixed aerosols

Aerosols of KBr and AgNO3 were mixed, exposed to light in a glass tube and collected in the dark. About 15% of the collected material was reduced to silver upon development. Thus, two aerosols of particles that react to form a photo-reducible compound can be used to measure coagulation efficiency

Raman gain against a background of non-thermal ion fluctuations in a plasma

A complex stimulated Raman scattering event against a background of non-thermal ion acoustic waves in an inhomogeneous plasma is described. We obtain analytic forms for the Raman gain due to a five-wave interaction consisting of conventional three-wave Raman scattering followed by the decay of the Raman Langmuir wave into a second Langmuir wave (or a second scattered light wave) and an ion acoustic wave. Very modest levels of ion waves produce a. significant effect on Raman convective gain. A combination of plasma inhomogeneity and suprathermal ion fluctuations may offer a means for the control of Raman gain

Wire tomography in the H-1NF heliac for investigation of fine structure of magnetic islands

Electron beam wire tomography in the H-1NF heliac enables high resolution mapping of vacuum flux surfaces with minimal disruption of the plasma operations schedule. Recent experimental results have proven this technique to be a highly accurate and high resolution method for mapping vacuum magnetic islands. Islands of width as small as delta approximately 8 mm have been measured, providing estimates of the internal rotational transform of the island. Point-to-point comparison of the mapping results with computer tracing, in conjunction with an image warping technique, enables systematic exploration of magnetic islands and surfaces of interest. Recent development of a fast mapping technique significantly reduced the mapping time and made this technique suitable for mapping at higher magnetic fields. This article presents recent experimental results and associated techniques.with support from the Australian Research Council Grant No. DP0344361

Mixed perturbative expansion: the validity of a model for the cascading

A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized pulses, fundamental and second harmonic, propagating together in a bulk uniaxial crystal with non-vanishing second order susceptibility $\chi^(2)$ and interacting through the nonlinear effect known as ``cascading'' in nonlinear optics. The perturbative method mixes a multi-scale expansion with a power series expansion of the susceptibility, and must be carefully adapted to the physical situation. It allows the determination of the physical conditions under which the model is valid: the order of magnitude of the walk-off, phase-mismatch,and anisotropy must have determined values.Comment: arxiv version is already officia

Polarization squeezing of light by single passage through an atomic vapor

We have studied relative-intensity fluctuations for a variable set of orthogonal elliptic polarization components of a linearly polarized laser beam traversing a resonant $^{87}$Rb vapor cell. Significant polarization squeezing at the threshold level (-3dB) required for the implementation of several continuous variables quantum protocols was observed. The extreme simplicity of the setup, based on standard polarization components, makes it particularly convenient for quantum information applications.Comment: Revised version. Minor changes. four pages, three figure

Capacity of nonlinear bosonic systems

We analyze the role of nonlinear Hamiltonians in bosonic channels. We show that the information capacity as a function of the channel energy is increased with respect to the corresponding linear case, although only when the energy used for driving the nonlinearity is not considered as part of the energetic cost and when dispersive effects are negligible.Comment: 6 pages, 3 figure