Gaussian mixture modeling with Gaussian process latent variable models

Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in a variety of complex data. The GPLVM consists of a set of points in a low dimensional latent space, and a stochastic map to the observed space. We show how it can be interpreted as a density model in the observed space. However, the GPLVM is not trained as a density model and therefore yields bad density estimates. We propose a new training strategy and obtain improved generalisation performance and better density estimates in comparative evaluations on several benchmark data sets. © 2010 Springer-Verlag.

Modeling and electrical measurement of transport AC loss in HTS-based superconducting coils for electric machines

AC loss can be a significant problem for any applications that utilize or produce an AC current or magnetic field, such as an electric machine. The authors are currently investigating the electromagnetic properties of high temperature superconductors with a particular focus on the AC loss in coils made from YBCO superconductors. In this paper, a 2D finite element model based on the H formulation is introduced. The model is then used to calculate the transport AC loss using both a bulk approximation and modeling the individual turns in a racetrack-shaped coil. The coil model is based on the superconducting stator coils used in the University of Cambridge EPEC Superconductivity Group's superconducting permanent magnet synchronous motor design. The transport AC loss of a stator coil is measured using an electrical method based on inductive compensation using a variable mutual inductance. The simulated results are compared with the experimental results, verifying the validity of the model, and ways to improve the accuracy of the model are discussed. © 2010 IEEE.

Effects of soil fabric on behaviors of granular soils: Microscopic modeling

The effects of initial soil fabric on behaviors of granular soils are investigated by using Distinct Element Method (DEM) numerical simulation. Soil specimens are represented by an assembly of non-uniform sized spheres with different initial contact normal distributions. Isotropically consolidated triaxial compression loading and extension unloading in both undrained and drained conditions are simulated for vertically- and horizontally-sheared specimens. The numerical simulation results are compared qualitatively with the published experimental data and the effects of initial soil fabric on resulting soil behaviors are discussed, including the effects of specimen reconstitution methods, effects of large preshearing, and anisotropic characteristics in undrained and drained conditions. The effects of initial soil fabric and mode of shearing on the quasi-steady state line are also investigated. The numerical simulation results can systematically explain that the observed experimental behaviors of granular soils are due principally to their conditions of the initial soil fabric. This outcome provides insights into the observed phenomena in microscopic view. © 2011 Elsevier Ltd.

Modeling evaporation effects in conditional moment closure for spray autoignition

Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in themixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective-reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected. © 2011 Taylor & Francis.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model. © 2011 Elsevier Ltd.

Modular risk modeling and management of water infrastructure disaster incidents

Water supply and wastewater control are critical elements of society's infrastructure. The objective of this study will be to provide a generic risk assessment tool to provide municipalities and the nation as a whole with a quantifiable assessment of their vulnerability to water infrastructure threats. The approach will prioritize countermeasures and identify where research and development is required to further minimize risk. This paper outlines the current context, primary concerns and state-of-the art in critical infrastructure risk management for the water sector and proposes a novel approach to resolve existing questions in the field. The proposed approach is based on a modular framework that derives a quantitative risk index for varied domains of interest. The approach methodology is scaleable and based on formal definitions of event probability and severity. The framework is equally applicable to natural and human-induced hazard types and can be used for analysis of compound risk events.

Improved jet noise modeling using a new time-scale.

To calculate the noise emanating from a turbulent flow using an acoustic analogy knowledge concerning the unsteady characteristics of the turbulence is required. Specifically, the form of the turbulent correlation tensor together with various time and length-scales are needed. However, if a Reynolds Averaged Navier-Stores calculation is used as the starting point then one can only obtain steady characteristics of the flow and it is necessary to model the unsteady behavior in some way. While there has been considerable attention given to the correct way to model the form of the correlation tensor less attention has been given to the underlying physics that dictate the proper choice of time-scale. In this paper the authors recognize that there are several time dependent processes occurring within a turbulent flow and propose a new way of obtaining the time-scale. Isothermal single-stream flow jets with Mach numbers 0.75 and 0.90 have been chosen for the present study. The Mani-Gliebe-Balsa-Khavaran method has been used for prediction of noise at different angles, and there is good agreement between the noise predictions and observations. Furthermore, the new time-scale has an inherent frequency dependency that arises naturally from the underlying physics, thus avoiding supplementary mathematical enhancements needed in previous modeling.

Fem modeling of periodic arrays of multi-walled carbon nanotubes

Multiwalled carbon nanotubes display dielectric properties similar to those of graphite, which can be calculated using the well known Drude-Lorentz model. However, most computational softwares lack the capacity to directly incorporate this model into the simulations. We present the finite element modeling of optical propagation through periodic arrays of multiwalled carbon nanotubes. The dielectric function of nanotubes was incorporated into the model by using polynomial curve fitting technique. The computational analysis revealed interesting metamaterial filtering effects displayed by the highly dense square lattice arrays of carbon nanotubes, having lattice constants of the order few hundred nanometers. The curve fitting results for the dielectric function can also be used for simulating other interesting optical applications based on nanotube arrays.