Scalar and its dissipation in the near field of turbulent lifted jet flame

In this study various scalar dissipation rates and their modelling in the context of partially premixed flame are investigated. A DNS dataset of the near field of a turbulent hydrogen lifted jet flame is processed to analyse the mixture fraction and progress variable dissipation rates and their cross dissipation rate at several axial positions. It is found that the classical model for the passive scalar dissipation rate ε{lunate}̃ZZ gives good agreement with the DNS, while models developed based on premixed flames for the reactive scalar dissipation rate ε{lunate}̃cc only qualitatively capture the correct trend. The cross dissipation rate ε{lunate}̃cZ is mostly negative and can be reasonably approximated at downstream positions once ε{lunate}̃ZZ and ε{lunate}̃cc are known, although the sign cannot be determined. This approach gives better results than one employing a constant ratio of turbulent timescale and the scalar covariance c'Z'̃. The statistics of scalar gradients are further examined and lognormal distributions are shown to be very good approximations for the passive scalar and acceptable for the reactive scalar. The correlation between the two gradients increases downstream as the partially premixed flame in the near field evolves ultimately to a diffusion flame in the far field. A bivariate lognormal distribution is tested and found to be a reasonable approximation for the joint PDF of the two scalar gradients. © 2011 The Combustion Institute.

A variational perspective on noise-robust speech recognition

Model compensation methods for noise-robust speech recognition have shown good performance. Predictive linear transformations can approximate these methods to balance computational complexity and compensation accuracy. This paper examines both of these approaches from a variational perspective. Using a matched-pair approximation at the component level yields a number of standard forms of model compensation and predictive linear transformations. However, a tighter bound can be obtained by using variational approximations at the state level. Both model-based and predictive linear transform schemes can be implemented in this framework. Preliminary results show that the tighter bound obtained from the state-level variational approach can yield improved performance over standard schemes. © 2011 IEEE.

Surface tension-induced global instability of planar jets and wakes

The effect of surface tension on global stability of co-flow jets and wakes at a moderate Reynolds number is studied. The linear temporal two-dimensional global modes are computed without approximations. All but one of the flow cases under study are globally stable without surface tension. It is found that surface tension can cause the flow to be globally unstable if the inlet shear (or equivalently, the inlet velocity ratio) is strong enough. For even stronger surface tension, the flow is re-stabilized. As long as there is no change of the most unstable mode, increasing surface tension decreases the oscillation frequency. Short waves appear in the high-shear region close to the nozzle, and their wavelength increases with increasing surface tension. The critical shear (the weakest inlet shear at which a global instability is found) gives rise to antisymmetric disturbances for the wakes and symmetric disturbances for the jets. However, at stronger shear, the opposite symmetry can be the most unstable one, in particular for wakes at high surface tension. The results show strong effects of surface tension that should be possible to reproduce experimentally as well as numerically.

Occlusive Components Analysis

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the object parameters can be learnt from an unlabelled set of images in which objects occlude one another. Exact maximum-likelihood learning is intractable. However, we show that tractable approximations to Expectation Maximization (EM) can be found if the training images each contain only a small number of objects on average. In numerical experiments it is shown that these approximations recover the correct set of object parameters. Experiments on a novel version of the bars test using colored bars, and experiments on more realistic data, show that the algorithm performs well in extracting the generating causes. Experiments based on the standard bars benchmark test for object learning show that the algorithm performs well in comparison to other recent component extraction approaches. The model and the learning algorithm thus connect research on occlusion with the research field of multiple-causes component extraction methods.

Two problems with variational expectation maximisation for time-series models

Variational methods are a key component of the approximate inference and learning toolbox. These methods fill an important middle ground, retaining distributional information about uncertainty in latent variables, unlike maximum a posteriori methods (MAP), and yet generally requiring less computational time than Monte Carlo Markov Chain methods. In particular the variational Expectation Maximisation (vEM) and variational Bayes algorithms, both involving variational optimisation of a free-energy, are widely used in time-series modelling. Here, we investigate the success of vEM in simple probabilistic time-series models. First we consider the inference step of vEM, and show that a consequence of the well-known compactness property of variational inference is a failure to propagate uncertainty in time, thus limiting the usefulness of the retained distributional information. In particular, the uncertainty may appear to be smallest precisely when the approximation is poorest. Second, we consider parameter learning and analytically reveal systematic biases in the parameters found by vEM. Surprisingly, simpler variational approximations (such a mean-field) can lead to less bias than more complicated structured approximations.

First-principles energetics of water: a many-body analysis

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for solid, liquid and cluster forms of water. We use a many-body separation of the total energy into its 1-body, 2-body (2B) and beyond-2-body (B2B) components to analyze the deficiencies of two popular DFT approximations. We show how machine-learning methods make this analysis possible for ice structures as well as for water clusters. We find that the crucial energy balance between compact and extended geometries can be distorted by 2B and B2B errors, and that both types of first-principles error are important.

Balanced realisations of all-pass systems using exact arithmetic with application to the approximation of delay systems

Numerically well-conditioned state-space realisations for all-pass systems, such as Padé approximations to exp(-s), are derived that can be computed using exact integer arithmetic. This is then applied to the a series of functions of exp(-s). It is also shown that the H-infinity norm of the transfer function from the input to the state of a balanced realisation of the Padé approximation of exp(-s) is unity. © 2012 IEEE.

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.

POMDP-based statistical spoken dialog systems: A review

Statistical dialog systems (SDSs) are motivated by the need for a data-driven framework that reduces the cost of laboriously handcrafting complex dialog managers and that provides robustness against the errors created by speech recognizers operating in noisy environments. By including an explicit Bayesian model of uncertainty and by optimizing the policy via a reward-driven process, partially observable Markov decision processes (POMDPs) provide such a framework. However, exact model representation and optimization is computationally intractable. Hence, the practical application of POMDP-based systems requires efficient algorithms and carefully constructed approximations. This review article provides an overview of the current state of the art in the development of POMDP-based spoken dialog systems. © 1963-2012 IEEE.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

CLF based designs with robustness to dynamic input uncertainties

The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. Stabilizing control laws may not be robust to this type of uncertainty, especially if cancellation of nonlinearities is used in the design. By exploiting a connection between robustness and optimality, "domination redesign" of the control Lyapunov function (CLF) based Sontag's formula has been shown to possess robustness to static and dynamic input uncertainties. In this paper we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a CLF which is suitable for domination redesign. © 1999 Elsevier Science B.V. All rights reserved.

Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems. © 2013 Elsevier Ltd. All rights reserved.

Path-following steering control for articulated vehicles

Passive steering systems have been used for some years to control the steering of trailer axles on articulated vehicles. These normally use a 'command steer' control strategy, which is designed to work well in steady-state circles at low speeds, but which generates inappropriate steer angles during transient low-speed maneuvers and at high speeds. In this paper, 'active' steering control strategies are developed for articulated heavy goods vehicles. These aim to achieve accurate path following for tractor and trailer, for all paths and all normal vehicle speeds, in the presence of external disturbances. Controllers are designed to implement the path-following strategies at low and high speeds, whilst taking into account the complexities and practicalities of articulated vehicles. At low speeds, the articulation and steer angles on articulated heavy goods vehicles are large and small-angle approximations are not appropriate. Hence, nonlinear controllers based on kinematics are required. But at high-speeds, the dynamic stability of control system is compromised if the kinematics-based controllers remain active. This is because a key state of the system, the side-slip characteristics of the trailer, exhibits a sign-change with increasing speeds. The low and high speed controllers are blended together using a speed-dependent gain, in the intermediate speed range. Simulations are conducted to compare the performance of the new steering controllers with conventional vehicles (with unsteered drive and trailer axles) and with vehicles with command steer controllers on their trailer axles. The simulations show that active steering has the potential to improve significantly the directional performance of articulated vehicles for a wide range of conditions, throughout the speed range. © VC 2013 by ASME.

Towards robust design of axial compressors with uncertainty quantification

Operational uncertainties such as throttle excursions, varying inlet conditions and geometry changes lead to variability in compressor performance. In this work, the main operational uncertainties inherent in a transonic axial compressor are quantified to deter- mine their effect on performance. These uncertainties include the effects of inlet distortion, metal expansion, ow leakages and blade roughness. A 3D, validated RANS model of the compressor is utilized to simulate these uncertainties and quantify their effect on polytropic efficiency and pressure ratio. To propagate them, stochastic collocation and sparse pseudospectral approximations are used. We demonstrate that lower-order approximations are sufficient as these uncertainties are inherently linear. Results for epistemic uncertainties in the form of meshing methodologies are also presented. Finally, the uncertainties considered are ranked in order of their effect on efficiency loss. © 2012 AIAA.

Nonequilibrium dynamics of photoexcited electrons in graphene: Collinear scattering, Auger processes, and the impact of screening

We present a combined analytical and numerical study of the early stages (sub-100-fs) of the nonequilibrium dynamics of photoexcited electrons in graphene. We employ the semiclassical Boltzmann equation with a collision integral that includes contributions from electron-electron (e-e) and electron-optical phonon interactions. Taking advantage of circular symmetry and employing the massless Dirac fermion (MDF) Hamiltonian, we are able to perform an essentially analytical study of the e-e contribution to the collision integral. This allows us to take particular care of subtle collinear scattering processes - processes in which incoming and outgoing momenta of the scattering particles lie on the same line - including carrier multiplication (CM) and Auger recombination (AR). These processes have a vanishing phase space for two-dimensional MDF bare bands. However, we argue that electron-lifetime effects, seen in experiments based on angle-resolved photoemission spectroscopy, provide a natural pathway to regularize this pathology, yielding a finite contribution due to CM and AR to the Coulomb collision integral. Finally, we discuss in detail the role of physics beyond the Fermi golden rule by including screening in the matrix element of the Coulomb interaction at the level of the random phase approximation (RPA), focusing in particular on the consequences of various approximations including static RPA screening, which maximizes the impact of CM and AR processes, and dynamical RPA screening, which completely suppresses them. © 2013 American Physical Society.