Local equilibrium of the Gibbs interface in two-phase systems

We analyze the local equilibrium assumption for interfaces from the perspective of gauge transformations, which are the small displacements of Gibbs' dividing surface. The gauge invariance of thermodynamic properties turns out to be equivalent to conditions for jumps of bulk densities across the interface. This insight strengthens the foundations of the local equilibrium assumption for interfaces and can be used to characterize nonequilibrium interfaces in a compact and consistent way, with a clear focus on gauge-invariant properties. Using the principle of gauge invariance, we show that the validity of Clapeyron equations can be extended to nonequilibrium interfaces, and an additional jump condition for the momentum density is recognized to be of the Clapeyron type. © 2012 Europhysics Letters Association.

Aerodynamic noise from a poroelastic trailing edge with implications for the silent flight of owls

The interaction of a turbulent eddy with a semi-infinite, poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of scattered aerodynamic noise. The scattering problem is solved using the Wiener-Hopf technique for constant plate properties to identify their scaling dependence on the resulting aerodynamic noise, including the dependence on flight velocity, where special attention is paid to the limiting cases of rigid, porous and elastic, impermeable plate conditions. Results from these analyses attempt to address how trailing edge noise may be mitigated by porosity and seek to deepen the understanding of how owls hunt in acoustic stealth. © 2012 by Justin W. Jaworski and Nigel Peake. Published by the American Institute of Aeronautics and Astronautics, Inc.

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.

Parametric guidance for turbulent noise reduction from poroelastic trailing edges and owls

The interaction of a turbulent eddy with a semi-infinite, poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of aerodynamic noise generation. The edge is modelled as a thin plate poroelastic plate, which is known to admit fifth-, sixth-, and seventh-power noise dependences on a characteristic velocity U of the turbulent eddy. The associated acoustic scattering problem is solved using the Wiener-Hopf technique for the case of constant plate properties. For the special cases of porous-rigid and impermeable-elastic plate conditions, asymptotic analysis of the Wiener- Hopf kernel function furnishes the parameter groups and their ranges where U5, U6, and U7 behaviours are expected to occur. Results from this analysis attempt to help guide the search for passive edge treatments to reduce trailing-edge noise that are inspired by the wing features of silently flying owls. Furthermore, the appropriateness of the present model to the owl noise problem is discussed with respect to the acoustic frequencies of interest, wing chord-lengths, and foraging behaviour across a representative set of owl species.

Models for acoustic propagation through turbofan exhaust flows

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of previous solutions is that they do not allow for the jet nozzle to protrude a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). In this paper we use the matrix Wiener-Hopf technique, which will allow precisely the finite nacelle-jet nozzle separation to be included. The crucial step in our work is to factorise a certain matrix as a product of terms analytic and invertible in the upper/lower halves of the complex plane. The way we do this matrix factorisation is quite different in the buried and protruding nozzle cases. In the buried case our solution method is the so-called pole-removal technique. In the technically more demanding protruding case, however, we must first use Pade approximants to generate a uniformly-valid, meromorphic representation of a certain function, before the same pole-removal method can be applied. Sample results are presented, investigating in particular the effects of exit plane stagger. © 2007 by B Veitch and N Peake.

Cognitive Tomography Reveals Complex, Task-Independent Mental Representations

Humans develop rich mental representations that guide their behavior in a variety of everyday tasks. However, it is unknown whether these representations, often formalized as priors in Bayesian inference, are specific for each task or subserve multiple tasks. Current approaches cannot distinguish between these two possibilities because they cannot extract comparable representations across different tasks [1-10]. Here, we develop a novel method, termed cognitive tomography, that can extract complex, multidimensional priors across tasks. We apply this method to human judgments in two qualitatively different tasks, "familiarity" and "odd one out," involving an ecologically relevant set of stimuli, human faces. We show that priors over faces are structurally complex and vary dramatically across subjects, but are invariant across the tasks within each subject. The priors we extract from each task allow us to predict with high precision the behavior of subjects for novel stimuli both in the same task as well as in the other task. Our results provide the first evidence for a single high-dimensional structured representation of a naturalistic stimulus set that guides behavior in multiple tasks. Moreover, the representations estimated by cognitive tomography can provide independent, behavior-based regressors for elucidating the neural correlates of complex naturalistic priors. © 2013 The Authors.

Designing output-feedback predictive controllers by reverse-engineering existing LTI controllers

An approach to designing a constrained output-feedback predictive controller that has the same small-signal properties as a pre-existing output-feedback linear time invariant controller is proposed. Systematic guidelines are proposed to select an appropriate (non-unique) realization of the resulting state observer. A method is proposed to transform a class of offset-free reference tracking controllers into the combination of an observer, steady-state target calculator and predictive controller. The procedure is demonstrated with a numerical example. © 2013 IEEE.

Network reconstruction using knock-out and over-expression data

This paper outlines necessary and sufficient conditions for network reconstruction of linear, time-invariant systems using data from either knock-out or over-expression experiments. These structural system perturbations, which are common in biological experiments, can be formulated as unknown system inputs, allowing the network topology and dynamics to be found. We assume that only partial state measurements are available and propose an algorithm that can reconstruct the network at the level of the measured states using either time-series or steady-state data. A simulated example illustrates how the algorithm successfully reconstructs a network from data. © 2013 EUCA.

Control limitations from distributed sensing: Theory and Extremely Large Telescope application

We investigate performance bounds for feedback control of distributed plants where the controller can be centralized (i.e. it has access to measurements from the whole plant), but sensors only measure differences between neighboring subsystem outputs. Such "distributed sensing" can be a technological necessity in applications where system size exceeds accuracy requirements by many orders of magnitude. We formulate how distributed sensing generally limits feedback performance robust to measurement noise and to model uncertainty, without assuming any controller restrictions (among others, no "distributed control" restriction). A major practical consequence is the necessity to cut down integral action on some modes. We particularize the results to spatially invariant systems and finally illustrate implications of our developments for stabilizing the segmented primary mirror of the European Extremely Large Telescope. © 2013 Elsevier Ltd. All rights reserved.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Synchronization of user-generated videos through trajectory correspondence and a refinement procedure

Temporal synchronization of multiple video recordings of the same dynamic event is a critical task in many computer vision applications e.g. novel view synthesis and 3D reconstruction. Typically this information is implied through the time-stamp information embedded in the video streams. User-generated videos shot using consumer grade equipment do not contain this information; hence, there is a need to temporally synchronize signals using the visual information itself. Previous work in this area has either assumed good quality data with relatively simple dynamic content or the availability of precise camera geometry. Our first contribution is a synchronization technique which tries to establish correspondence between feature trajectories across views in a novel way, and specifically targets the kind of complex content found in consumer generated sports recordings, without assuming precise knowledge of fundamental matrices or homographies. We evaluate performance using a number of real video recordings and show that our method is able to synchronize to within 1 sec, which is significantly better than previous approaches. Our second contribution is a robust and unsupervised view-invariant activity recognition descriptor that exploits recurrence plot theory on spatial tiles. The descriptor is individually shown to better characterize the activities from different views under occlusions than state-of-the-art approaches. We combine this descriptor with our proposed synchronization method and show that it can further refine the synchronization index. © 2013 ACM.

Sparse recovery of complex phase-encoded velocity images using iterative thresholding

In this paper we propose a new algorithm for reconstructing phase-encoded velocity images of catalytic reactors from undersampled NMR acquisitions. Previous work on this application has employed total variation and nonlinear conjugate gradients which, although promising, yields unsatisfactory, unphysical visual results. Our approach leverages prior knowledge about the piecewise-smoothness of the phase map and physical constraints imposed by the system under study. We show how iteratively regularizing the real and imaginary parts of the acquired complex image separately in a shift-invariant wavelet domain works to produce a piecewise-smooth velocity map, in general. Using appropriately defined metrics we demonstrate higher fidelity to the ground truth and physical system constraints than previous methods for this specific application. © 2013 IEEE.

Scaling arguments for the fluxes in turbulent miscible fountains

For established axisymmetric turbulent miscible Boussinesq fountains in quiescent uniform environments, expressions are developed for the fluxes of volume, momentum and buoyancy at the outflow from the fountain: the outflow referring to the counterflow at the horizontal plane of the source. The fluxes are expressed in terms of the fountain source conditions and two dimensionless functions of the source Froude number, Fr0: a radial function (relating a horizontal scale of the outflow to the source radius) and a volume flux function (relating the outflow and source volume fluxes). The forms taken by these two functions at low Fr0 and high Fr0 are deduced, thereby providing the outflow fluxes and outflow Froude number solely in terms of the source conditions. For high Fr0, the outflow Froude number, Frout, is shown to be invariant, indicating (by analogy with plumes for which the 'far-field' Froude number is invariant with source Froude number) that the outflow may be regarded as 'far-field' since the fluxes within the fountain have adjusted to attain a balance which is independent of the source conditions. Based on Frout, the fluxes in the plume that forms beyond the fountain outflow are deduced. Finally, from the results of previously published studies, we show that the scalings deduced for fountains are valid for 0.0025 ≲ Fr0 ≲ 1.0 for low Fr0 and Fr0≳ 3.0 for high Fr0. © 2014 Cambridge University Press.