On the nature of the torus in the complex Lorenz equations.

The complex Lorenz equations are a nonlinear fifth-order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus. In this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter) and between zero and nonzero r2(complexity parameter); in so doing, we are able to gain insight on the effect of the rotational invariance of the system, and on how extra weak dispersion (r2 ≠ 0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability)

A delay recruitment model of the cardiovascular control system.

Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.

A Dichotomy Theorem for Circular Colouring Reconfiguration

The "reconfiguration problem" for circular colourings asks, given two $(p,q)$-colourings $f$ and $g$ of a graph $G$, is it possible to transform $f$ into $g$ by changing the colour of one vertex at a time such that every intermediate mapping is a $(p,q)$-colouring? We show that this problem can be solved in polynomial time for $2\leq p/q <4$ and is PSPACE-complete for $p/q\geq 4$. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings.Comment: 22 pages, 5 figure

An investigation into the synthesis, structural characterisation, thermal and polymorphic behaviour of organic crystalline materials

The organic solid state appears in a complex number of forms. The design, synthesis and application of solid state organic materials have a big impact upon society, e.g. pharmaceuticals. Traditionally, the process of selecting active pharmaceutical ingredients (APIs) was limited to free drug or accepted salt formulations. The cocrystallisation of APIs with a former molecule significantly increases the developmental options for APIs. Many pharmaceutical solids are prepared as polycrystalline materials in order to deliver favourable physical properties, i.e. solubility, bioavailability and stability. In such cases, the development and application of structure solution techniques via powder X-ray diffraction (pxrd) has played an ever increasing pivotal role. In this thesis a number of new multi-component materials; oxamic acid:nicotinamide, oxamic acid:isonicotinamide, fumaric acid:nicotinamide, maleic acid:nicotinamide and maleic acid:isonicotinamide, will be synthesised, via a number of synthetic methods, and fully structurally characterised. A direct comparison of structures solved by powder and single crystal diffraction, have been made in order to evaluate the reliability of structure solution from pxrd in these types of materials. The thermal behaviour of molecular materials will be presented as significant structural information can be extracted from the anisotropic expansion of molecular materials. In conjunction with the research into new multi-component materials, the structure solution of oxamic acid via pxrd, single X-ray diffraction and neutron diffraction will be investigated. Small organic molecular materials like oxamic acid provide a challenge to the crystallographer due to the similarities in the electron density surrounding each functional group in the molecule

Nanoscale magnetometry through quantum control of nitrogen-vacancy centres in rotationally diffusing nanodiamonds

The confluence of quantum physics and biology is driving a new generation of quantum-based sensing and imaging technology capable of harnessing the power of quantum effects to provide tools to understand the fundamental processes of life. One of the most promising systems in this area is the nitrogen-vacancy centre in diamond - a natural spin qubit which remarkably has all the right attributes for nanoscale sensing in ambient biological conditions. Typically the nitrogen-vacancy qubits are fixed in tightly controlled/isolated experimental conditions. In this work quantum control principles of nitrogen-vacancy magnetometry are developed for a randomly diffusing diamond nanocrystal. We find that the accumulation of geometric phases, due to the rotation of the nanodiamond plays a crucial role in the application of a diffusing nanodiamond as a bio-label and magnetometer. Specifically, we show that a freely diffusing nanodiamond can offer real-time information about local magnetic fields and its own rotational behaviour, beyond continuous optically detected magnetic resonance monitoring, in parallel with operation as a fluorescent biomarker.Comment: 9 pages, with 5 figure

Quasi-Particle Spectra, Charge-Density-Wave, Superconductivity and Electron-Phonon Coupling in 2H-NbSe2

High-resolution photoemission has been used to study the electronic structure of the charge density wave (CDW) and superconducting (SC) dichalcogenide, 2H- NbSe2. From the extracted self-energies, important components of the quasiparticle (QP) interactions have been identified. In contrast to previously studied TaSe2, the CDW transition does not affect the electronic properties significantly. The electron-phonon coupling is identified as a dominant contribution to the QP self-energy and is shown to be very anisotropic (k-dependent) and much stronger than in TaSe2.Comment: 4 pages, 3 figures, minor changes, to appear in PR

Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber

We study theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in photonic crystal optical fiber. We show that it is possible to engineer two-photon states with specific spectral correlation (``entanglement'') properties suitable for quantum information processing applications. We focus on the case exhibiting no spectral correlations in the two-photon component of the state, which we call factorability, and which allows heralding of single-photon pure-state wave packets without the need for spectral post filtering. We show that spontaneous four wave mixing exhibits a remarkable flexibility, permitting a wider class of two-photon states, including ultra-broadband, highly-anticorrelated states.Comment: 17 pages, 7 figures, submitte