An Arbitrary Lagrangian Eulerian Method for Three-Phase Flows with Triple Junction Points

We present a moving mesh method suitable for solving two-dimensional and axisymmetric three-liquid flows with triple junction points. This method employs a body-fitted unstructured mesh where the interfaces between liquids are lines of the mesh system, and the triple junction points (if exist) are mesh nodes. To enhance the accuracy and the efficiency of the method, the mesh is constantly adapted to the evolution of the interfaces by refining and coarsening the mesh locally; dynamic boundary conditions on interfaces, in particular the triple points, are therefore incorporated naturally and accurately in a Finite- Element formulation. In order to allow pressure discontinuity across interfaces, double-values of pressure are necessary for interface nodes and triple-values of pressure on triple junction points. The resulting non-linear system of mass and momentum conservation is then solved by an Uzawa method, with the zero resultant condition on triple points reinforced at each time step. The method is used to investigate the rising of a liquid drop with an attached bubble in a lighter liquid.

Autonomous rigid body attitude synchronization

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. 40th IEEE conf. decision and control (pp. 4598-4603); Nair, S., Leonard, N. E. (2007). Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2(4), 595-624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies' attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information. © 2008 Elsevier Ltd.

Cubically convergent iterations for invariant subspace computation

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

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.

How polluted is the Yangtze River? Water quality downstream from the Three Gorges Dam

The concentrations of major anions and cations, nitrogen and phosphorus, dissolved and particulate trace elements, and organic pollutants were determined for the middle and lower reaches of the Yangtze River (Changjiang) from below the Three Gorges Dam (TGD) to the mouth at Shanghai in November 2006. The concentration of dissolved inorganic phosphate (DIP) was constant at a low level of 6-8 mu gP/L, but the concentration of nitrate (NO3-) approximately doubled downstream and was closely correlated with K+. This translated to a daily load of well over 1000 It of dissolved inorganic nitrogen (DIN) at Datong. The average concentrations of dissolved Pb (0.078 +/- 0.023 mu g/L), Cd (0.024 +/- 0.009 mu g/L), Cr(0.57 +/- 0.09 mu g/L), Cu (1.9 +/- 0.7 mu g/L), and Ni (0.50 +/- 0.49 mu g/L) were comparable with those in other major world rivers, while As (3.3 +/- 1.3 mu g/L) and Zn (1.5 +/- 0.6 mu g/L) were higher by factors of 5.5 and 2.5, respectively. The trace element contents of suspended particles of As (31 +/- 28 mu g/g), Pb (83 +/- 34 mu g/g), and Ni (52 +/- 16 mu g/g) were close to maximum concentrations recommended for rivers by the European Community (EC). The average concentrations of Cd (2.6 +/- 1.6 mu g/g), Cr (185 +/- 102 mu g/g), Cu (115 +/- 106 mu g/g), and Zn (500 +/- 300 mu g/g) exceeded the EC standards by a factor of two, and Hg (4.4 +/- 4.7 mu g/g) by a factor of 4 to 5. Locally occurring peak concentrations exceed these values up to fourfold, among them the notorious elements As, Hg, and Tl. All dissolved and particulate trace element concentrations were higher than estimates made twenty years ago [Zhang, J., Geochemistry of trace metals from Chinese river/estuary systems: an overview. Estuar Coast Shelf Sci 1995; 41: 631-658.]. The enormous loads of anthropogenic pollutants disposed to the river were diluted by the large water discharge of the Yangtze even during the lowest flow resulting in the relatively low concentration levels of trace elements and organic pollutants observed. We estimated loads of e.g. As, Pb and Ni to the East China Sea to be about 4600 kg As d(-1), 3000 kg Pb d(-1), and 2000 kg Ni d(-1). About 6000 t d(-1) of dissolved organic carbon (DOC) was delivered into the sea at the time of our cruise. We tested for 236 organic pollutants, and only the most infamous were found to be barely above detection limits. We estimated that the load of chlorinated compounds, aromatic hydrocarbons, phenols, and PAHs were between 500 and 3500 kg d(-1). We also detected eight herbicides entering the estuary with loads of 5-350 kg d(-1). The pollutant load, even when at low concentrations, are considerable and pose an increasing threat to the health of the East China Sea ecosystem. (c) 2008 Elsevier B.V. All rights reserved.

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.