1,764 research outputs found
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
-colourings and of a graph , is it possible to transform
into by changing the colour of one vertex at a time such that every
intermediate mapping is a -colouring? We show that this problem can be
solved in polynomial time for and is PSPACE-complete for
. 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
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