UCT-Kirchberg algebras have nuclear dimension one

We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial _K0$K_0$ and finite _K1$K_1$ have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.     

Considerations in the determination of orientational order parameters from X-ray scattering experiments

An assessment of the data processing and analysis methods used to obtain the second- and fourth-rank orientational order parameters of liquid crystals from X-ray scattering experiments has been carried out, using experimental data from four extensively studied alkyl-cyanobiphenyls and calculated data generated from two general types of theoretical orientational distribution function. The application of a background subtraction and two different baseline correction methods to the scattering profiles is assessed, along with three different methods to analyse the processed data. The choice of baseline correction method is shown to have a significant effect: an offset to zero overestimates the order parameters from the experimental and calculated data sets, particularly for lower order parameters arising from broad distributions, whereas an offset to a value estimated from regions of low scattering intensity provides experimental values close to those reported from other experimental techniques. By contrast, the three different analysis methods are shown generally to result in relatively small absolute differences between the order parameters. We outline a straightforward general approach to experimental X-ray scattering data processing and analysis for uniaxial phases that results in order parameters that match well with those reported using other experimental techniques.     

Dynamics of the Douglas-Rachford Method for Ellipses and <Emphasis Type="Italic">p</Emphasis>-Spheres

We expand upon previous work that examined the behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations:that of a line and an ellipse and that of a line together with a p-sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and—seeking a better understanding of the behavior—we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases.     

Simplicity of <Emphasis Type="Italic">C</Emphasis>*-algebras associated to row-finite locally convex higher-rank graphs

In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing’s “removing sources” construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.     

Energy harvesting from the nonlinear oscillations of magnetic levitation

This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to investigate the energy harvesting potential of this prototypical nonlinear system. Theoretical investigations are followed by a series of experimental tests that validate the response predictions. The motivating hypothesis for the current work was that nonlinear phenomenon could be exploited to improve the effectiveness of energy harvesting devices.     

Experimental investigation of two-phase discharge from a stratified region through a small branch mounted on an inclined wall

Experimental data are presented for the mass flow rate and quality of two-phase discharge through a small branch of diameter d (=6.35 mm) attached normally to an inclined flat plane. The flat plane was situated in a large tank containing a stratified mixture of air and water under pressure (316 kPa) and at room temperature. The plane was inclined through various angles (θ) in increments of 30°, from the outlet-branch orientation being vertically upward through the horizontal to vertically downward. The bulk of the data correspond to seven inclination angles and two test-section-to-separator pressure differences (ΔP) of 11.0 and 115.5 kPa, and for each combination of θ and ΔP, the mass flow rate and quality were measured at different values of the interface level (h) between the onsets of gas and liquid entrainment. Four additional data sets were generated for other values of ΔP in order to confirm certain trends. Influences of these independent variables on the mass flow rate and quality are discussed and normalized plots are presented showing that the data can be collapsed for a wide range of conditions. Comparisons are made between the present data and previous correlations/models and new empirical correlations are formulated and shown to be capable of predicting the present data with good accuracy.     

Chirped pulse amplification in single mode Tm:fiber using a chirped Bragg grating

We report femtosecond pulse generation and chirped pulse amplification in Tm:fiber. A mode-locked oscillator operating in the soliton regime produced 800 fs pulses with 5 nm spectral bandwidth, at 40 pJ pulse energy. This oscillator seeded a pre-amplifier that utilizes a Raman soliton self-frequency shift to produce wavelength tunable pulses with 3 nJ energy, reduced pulse duration of 150 fs, and increased bandwidth of 30 nm. For further amplification, the pulses were stretched up to 160 ps using a chirped Bragg grating (CBG). Stretched pulses were amplified to 85 nJ after compression in single-mode Tm:fiber and recompressed with the CBG as short as 400 fs. Compressed pulses were coupled into a highly nonlinear tellurite fiber to investigate the potential of this ultrashort pulse 2-μm fiber source as a pump for mid-IR supercontinuum generation.