Quantum dynamics in ultracold atomic physics

We review recent developments in the theory of quantum dynamics in ultracold atomic physics, including exact techniques and methods based on phase-space mappings that are applicable when the complexity becomes exponentially large. Phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum Einstein-Podolsky-Rosen (EPR) entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorption, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.     

Residual Stress Measurement in Composite Laminates Using Incremental Hole-Drilling with Power Series

Current methods for incremental hole-drilling in composite laminates have not been successfully applied in laminates of arbitrary construction or where significant variation of residual stress exists within a single ply. This work presents a method to overcome these limitations. Series expansion is applied to each ply orientation separately so that the discontinuities in the residual stresses at ply interfaces can be correctly captured. Temperature variations described by power series are used to set up eigenstrains and consequent stresses which vary in the through-thickness direction. The calibration coefficients at each incremental hole depth are calculated through the use of finite element modelling. The inverse solution employs a least-squares approach which makes the resulting solution insensitive to measurement uncertainty. Robust uncertainties in the residual stress distributions are determined using Monte Carlo simulation. The residual stress distribution is found from that combination of series orders in the different ply orientations that has the lowest RMS uncertainty, selected only from those combinations that have converged. The method is demonstrated on a GFRP laminate of [0₂/+45/?45]_s construction where it is found that transverse cracking of the plies at the inner surface of the hole may have impacted on the accuracy of the results.     

Measurement of the Distribution of Residual Stresses in Layered Thick-Walled GFRP Pipes

The objective of this study is to measure the axial, circumferential, shear and radial residual stress distributions in three thick-walled glass fibre reinforced plastic (GFRP) filament-wound pipes, two of which are layered. The measurement of residual stresses was carried out using a recently published layer removal method which overcomes the limitations of previous techniques and can be applied to layered anisotropic pipes of any wall thickness. Layers of approximately 0.3 mm thickness were incrementally ground from the outer surface of the pipes. The resulting strains were measured on the inner surfaces. A least-squares polynomial was fitted to each measured data set, and used to calculate the corresponding stress distributions. All of the resulting axial, hoop and shear stress distributions adhere to the requirement of self-equilibrium and the radial stress distributions all vanish to zero at the inner and outer surfaces. The radial stresses of the layered pipes showed a tendency to have two peaks, one for each layer, a consequence of the two-stage manufacturing process of these pipes. The measured axial and hoop stresses of all three pipes were similar at the inner surfaces despite significant differences in the stiffnesses in the principal directions arising from different wind angles.     

An efficient and scalable process to produce morpholine-d8

Incorporation of isotopes has long been used as a research tool to label carbons and elucidate biochemical pathways. More recently, H→D exchange has led to analogs of therapeutic agents with improved metabolic stability and properties. Such compounds also have the potential for an improved drug/drug interaction profile and may even avoid the formation of toxic metabolites. Hence, a clear need for an efficient access to deuterated intermediates on large scale has emerged. In the context of an ongoing drug discovery program, we required large quantities of morpholine-d₈. We herein report the successful optimization of a one-pot process allowing a near complete exchange of all methylene hydrogens in morpholine to deuterium atoms using D₂O as the sole source of deuterium and Raney Nickel as catalyst. This facile and safe protocol will be used to scale up the synthesis of morpholine-d₈ in due course.     

Iridium-Catalyzed Formyl-Selective Deuteration of Aldehydes

We report the first direct catalytic method for formyl-selective deuterium labeling of aromatic aldehydes under mild conditions, using an iridium-based catalyst designed to favor formyl over aromatic C−H activation. A good range of aromatic aldehydes is selectively labeled, and a one-pot labeling/olefination method is also described. Computational studies support kinetic product control over competing aromatic labeling and decarbonylation pathways.     

Pulse compression and gain enhancement in a degenerate optical parametric amplifier based on aperiodically poled crystals

We describe theoretically a method of obtaining pulse compression and simultaneously improving amplification in a degenerate optical parametric amplifier by use of quasi-phase-matched engineered crystals. The scheme combines the possibility of increasing the signal spectral bandwidth that is offered by a degenerate parametric amplifier with the ability of engineered aperiodically poled crystals to compensate for group-velocity mismatch.     

Solubility of solid mixtures in supercritical fluids

Kurnik, R.T. and Reid, R.C., 1982. Solubility of solid mixtures in supercritical fluids. Fluid Phase Equilibria, 8: 93-105Supercritical fluids are receiving widespread attention as possible extraction agents for relatively non-volatile solids and liquids. Previous studies of the solubility of solids in supercritical fluids have been limited to pure solids. These pure-component data are interesting and indicate novel properties of supercritical fluids in this respect. The more general problem, however, lies in determining the solubility of multicomponent solids in supercritical fluids. Experimental data have now been obtained on the solubilities of binary, solid hydrocarbon mixtures in both supercritical carbon dioxide and supercritical ethylene. Most of the behavior exhibited by pure solids in supercritical fluids still exists for multicomponent solid solute systems (e.g., retrograde solidification, solubility extrema), but new phenomena were also found. The most interesting finding is that the solubility of a solid component when in a multicomponent solute system can be as much as 300% higher than the component solubility in a pure solid system at the same operating conditions. The multicomponent-solid-fluid data usually correlate well with thermodynamic theory.     

Degree frequencies in digraphs and tournaments

The number of vertices in a digraph G having a particular outdegree (indegree) is called the frequency of the outdegree (indegree). A set F of distinct positive integers {f₁, f₂, …, f_n} is the frequency set of the digraph G if every outdegree and indegree occurs with frequency f_j∈F and for each f_j∈F there is a least one outdegree and at least one indegree with frequency f_j. We prove that each nonempty set F of positive integers is the frequency set of some tournament, and we determine the smallest possible order for such a tournament. Similar results for asymmetric digraphs are also given. The results and techniques for frequency sets are used to derive corresponding results for vertex frequency partitions.     

Measurement of the transition strength of the 00o2 9.4 μm sequence band in CO2 using a tunable diode laser

We report the first accurate measurements of the transition strengths and linewidths of the 00^o2 9.4 μm sequence lines of CO₂. This sequence band is found to be very similar to the regular 00^o1 laser band, except for an experimentally determined factor of 1.89±0.12 increase in transition strength (if the CO₂ molecule is treated as a simple harmonic oscillator the theoretical increase in transition strength is 2.0). The laser absorption spectrometer used for these measurements can detect absorption coefficients in CO₂ of ≈10⁻⁷ m⁻¹, and we discuss the feasibility of using this sensitivity to monitor rare isotopic forms of CO₂. Work supported by the Department of National Health and Welfare, Environment Canada, Ontario Ministry of the Environment, and Atmospheric Environment Service, Environment Canada.