A duality principle for homogeneous vectorfields with applications

A duality transformation principle was proposed for converting a positive order homogeneous vectorfield into a negative order homogeneous vectorfield. The principle also converted a uniformly locally asymptotically stable differential equation into a uniformly bounded differential equation. The duality transformations included the geometric framework for homogeneity and the removal of origin from the state space.

The propagation of acoustic waves in a slowly varying duct with radially sheared axial mean flow

We consider the propagation of acoustic waves along a cylindrical duct carrying radially sheared axial mean flow, in which the duct radius is allowed to vary slowly along the axis. In previous work [A.J. Cooper & N. Peake, Journal of Fluid Mechanics 445 (2001) 207-234.] radially sheared axial mean flow with nonzero swirl in a slowly varying duct was considered, but in this paper we set the swirl to zero, thereby allowing simplification of the calculations of both the mean and unsteady flows. In this approach the acoustic wavenumber and corresponding eigenfunction are determined locally, while the wave amplitude is found by solving an evolution equation along the duct. Sample results are presented, including a case in which, perhaps surprisingly, the number of cut-on modes increases as the duct radius decreases. © 2013 Elsevier Ltd. All rights reserved.

Some remarks about periodic feedback stabilization

Periodic feedback stabilization is a very natural solution to overcome the topological obstructions which may occur when one tries to asymptotically (locally) stabilize a (locally) controllable nonlinear system around an equilibrium point. The object of this paper is to give a simple geometric interpretation of this fact, to show that one obtains a weakened form of those obstructions when periodic feedback is used, and to illustrate the success of periodic feedback stabilization on a representative system which contains a drift.

Vortex migration caused by travelling magnetic wave in a 2 in. diameter YBa2Cu3O7-δ thin film

We provide experimental evidence for a vortex migration phenomenon in YBa2Cu3O7-δ (YBCO) thin film caused by travelling magnetic wave. The experiment is carried out on a 2 in. diameter YBCO thin film with a circular-type magnetic flux pump. We found that the travelling wave helps the vortices migrate into the centre of the sample: after the zero-field cooling process, the increase of the flux density in the centre is four times larger than the amplitude of the travelling wave. The reason for this massive vortex migration is probably due to the magnetic stress variation caused by the travelling wave: the magnetic stress increases locally in the crest region while decreases locally in the trough region, which could help the vortices to move locally. A comparison shows that the magnetization by standing wave can be easily predicted by Bean's model while travelling wave causes vortex migration generally much larger than the prediction of Bean's model. It is possible that travelling magnetic wave can be an effective way to magnetize a type II superconductor in considering this unusual vortex dynamics. © 2013 AIP Publishing LLC.

Low-order modelling of the response of ducted flames in annular geometries

The adoption of lean premixed prevaporised combustion systems can reduce NOx emissions from gas turbines, but unfortunately also increases their susceptibility to thermoacoustic instabilities. Initially, acoustic waves can produce heat release fluctuations by a variety of mechanisms, often by perturbing the equivalence ratio. If correctly phased, heat release fluctuations can subsequently generate more acoustic waves, which at high amplitude can result in significant structural damage to the combustor. The prediction of this phenomenon is of great industrial interest. In previous work, we have coupled a physics based, kinematic model of the flame with a network model to provide the planar acoustic response necessary to close the feedback loop and predict the onset and amplitude of thermoacoustic instabilities in a lab-scale, axisymmetric single burner combustor. The advantage of a time domain approach is that the modal interaction, the influence of harmonics, and flame saturation can be investigated. This paper extends this approach to more realistic, annular geometries, where both planar and circumferential modes must be considered. In lean premixed prevaporised combustors, fluctuations in equivalence ratio have been shown to be a dominant cause of unsteady combustion. These can occur, for example, due to velocity perturbations in the premix ducts, which can lead to equivalence ratio fluctuations at the fuel injectors, which are subsequently convected downstream to the flame surfaces. Here, they can perturb the heat release by locally altering the flame speed, enthalpy of combustion, and, indirectly, the flame surface area. In many gas turbine designs, particularly aeroengines, the geometries are composed of a ring of premix ducts linking a plenum and an annular combustor. The most unstable modes are often circumferential modes. The network model is used to characterise the flow response of the geometry to heat fluctuations at an appropriate location, such as the fuel injectors. The heat release at each flame holder is determined in the time domain using the kinematic flame model derived, as a function of the flow perturbations in the premix duct. This approach is demonstrated for an annular ring of burners on a in a simple geometry. The approach is then extended to an industrial type gas turbine combustor, and used to predict the limit cycle amplitudes. Copyright © 2012 by ASME.

Probability-Matching Predictors for Extreme Extremes

A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the three-parameter {\mu, \sigma, \xi} Generalized Pareto Distribution (GPD). The predictor is designed to provide matching probability exactly for the GPD in both the extreme heavy-tailed limit and the extreme bounded-tail limit, whilst giving a good approximation to probability matching at all intermediate values of the tail parameter \xi. The predictor is valid even for small sample sizes N, even as small as N = 3. The main purpose of this paper is to present the somewhat lengthy derivations which draw heavily on the theory of hypergeometric functions, particularly the Lauricella functions. Whilst the construction is inspired by the Bayesian approach to the prediction problem, it considers the case of vague prior information about both parameters and model, and all derivations are undertaken using sampling theory.

Single sublattice endotaxial phase separation driven by charge frustration in a complex oxide.

Complex transition-metal oxides are important functional materials in areas such as energy and information storage. The cubic ABO3 perovskite is an archetypal example of this class, formed by the occupation of small octahedral B-sites within an AO3 network defined by larger A cations. We show that introduction of chemically mismatched octahedral cations into a cubic perovskite oxide parent phase modifies structure and composition beyond the unit cell length scale on the B sublattice alone. This affords an endotaxial nanocomposite of two cubic perovskite phases with distinct properties. These locally B-site cation-ordered and -disordered phases share a single AO3 network and have enhanced stability against the formation of a competing hexagonal structure over the single-phase parent. Synergic integration of the distinct properties of these phases by the coherent interfaces of the composite produces solid oxide fuel cell cathode performance superior to that expected from the component phases in isolation.

High resolution direct measurement of temperature distribution in silicon nanophotonics devices.

Following the miniaturization of photonic devices and the increase in data rates, the issues of self heating and heat removal in active nanophotonic devices should be considered and studied in more details. In this paper we use the approach of Scanning Thermal Microscopy (SThM) to obtain an image of the temperature field of a silicon micro ring resonator with sub-micron spatial resolution. The temperature rise in the device is a result of self heating which is caused by free carrier absorption in the doped silicon. The temperature is measured locally and directly using a temperature sensitive AFM probe. We show that this local temperature measurement is feasible in the photonic device despite the perturbation that is introduced by the probe. Using the above method we observed a significant self heating of about 10 degrees within the device.

Refining sparse principal components

In this paper, we discuss methods to refine locally optimal solutions of sparse PCA. Starting from a local solution obtained by existing algorithms, these methods take advantage of convex relaxations of the sparse PCA problem to propose a refined solution that is still locally optimal but with a higher objective value. © 2010 Springer -Verlag Berlin Heidelberg.

Picosecond laser patterning of PEDOT:PSS thin films

Picosecond pulsed laser (10.4 ps, 1064 nm, 5 and 50 kHz) patterning studies were performed, of PEDOT:PSS thin films of varying thickness deposited by spin coating on glass substrates, by ablating the films or by changing locally by laser irradiation the optical and electrical properties of the polymer. From a detailed observation of the morphology of single pulse ablated holes on the surfaces of the films, in combination with simple calculations, it is concluded that photomechanical ablation is the likely ablation mechanism of the films. The single pulse ablation thresholds were measured equal to 0.13-0.18 J/cm 2 for films with thicknesses in the region of ∼100-600 nm. The implications on ablation line patterning of the films using different fluences, scanning speeds and pulse repetition rates, were investigated systematically. Laser irradiation of the films before ablation induces a metal-insulator transition of the polymer because of the formation of charge localization due to a possible creation of molecular disorder in the polymer and shortening of its conjugation length. © 2010 Elsevier B.V. All rights reserved.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated "dynamic walking" biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents "transversal" dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. © The Author(s) 2011.

Stable dynamic walking over rough terrain: Theory and experiment

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated "dynamic walking" biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to higher degree-of-freedom robots over arbitrary terrain and other impulsive mechanical systems. © 2011 Springer-Verlag.

Changes in biomechanical properties of the coronary artery wall contribute to maintained contractile responses to endothelin-1 in atherosclerosis.

AIMS: Our aim was to determine whether alterations in biomechanical properties of human diseased compared to normal coronary artery contribute to changes in artery responsiveness to endothelin-1 in atherosclerosis. MAIN METHODS: Concentration-response curves were constructed to endothelin-1 in normal and diseased coronary artery. The passive mechanical properties of arteries were determined using tensile ring tests from which finite element models of passive mechanical properties of both groups were created. Finite element modelling of artery endothelin-1 responses was then performed. KEY FINDINGS: Maximum responses to endothelin-1 were significantly attenuated in diseased (27±3 mN, n=55) compared to normal (38±2 mN, n=68) artery, although this remained over 70% of control. There was no difference in potency (pD2 control=8.03±0.06; pD2 diseased=7.98±0.06). Finite element modelling of tensile ring tests resulted in hyperelastic shear modulus μ=2004±410 Pa and hardening exponent α=22.8±2.2 for normal wall and μ=2464±1075 Pa and α=38.3±6.7 for plaque tissue and distensibility of diseased vessels was decreased. Finite element modelling of active properties of both groups resulted in higher muscle contractile strain (represented by thermal reactivity) of the atherosclerotic artery model than the normal artery model. The models suggest that a change in muscle response to endothelin-1 occurs in atherosclerotic artery to increase its distensibility towards that seen in normal artery. SIGNIFICANCE: Our data suggest that an adaptation occurs in medial smooth muscle of atherosclerotic coronary artery to maintain distensibility of the vessel wall in the presence of endothelin-1. This may contribute to the vasospastic effect of locally increased endothelin-1 production that is reported in this condition.

Characterizing the class of local metal sheet thickening processes

The need to create high-value products for specialist applications, and the search for efficient forming routes that obviate the need for some machining steps, is driving Interest In a novel class of forming processes aiming to create locally thickened features within sheet work- pieces. A number of novel forming processes have been proposed to meet this need, but it is as yet unclear which processes will be most effective in creating local thickening of various geometries, and many process configurations have yet to be tried. This paper aims to provide some basic principles for designing and characterising process behaviour. A simplified generic description of sheet thickening processes is provided, with two tools of variable operating on a sheet workpiece in plane strain, with different tool separations and motions parameterised. A comprehensive numerical study of the behaviour of this class of processes is conducted in Abaqus to predict the main characteristics of the material flow in each configuration. The results are used to classify the different basic behaviours that can be achieved by the sheet-bulk thickening processes and to give guidance on future process development, capability and applicability. © 2011 Wiley-VCH Verlag GmbH & Co. KGaA. Weinheim.