A reduced-order model of diffusive effects on the dynamics of bubbles

We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity

A Numerical Investigation of Unsteady Bubbly Cavitating Nozzle Flows

The effects of unsteady bubbly dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady-state solutions exist, and those where steady-state solutions diverge at the so-called flashing instability. these latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical backpressure for choked flow. The results agree with previous barotropic models for those flows where bubbly dynamics are not important, but show that in many instances the neglect of bubbly dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubbly raidal motion is restricted to a simple "effective" viscosity, but many features of the flow are shown to be independent of the specific damping mechanism

A Reduced-Order Model of Heat Transfer Effects on the Dynamics of Bubbles

The Rayleigh-Plesset equation has been used extensively to model spherical bubble dynamics, yet it has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Radial diffusion equations may be solved for a single bubble, but these are too computationally expensive to implement into a continuum model for bubbly cavitating flows since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive reduced-order models that account for thermal and mass diffusion. We present a model that can capture the damping effects of the diffusion processes in two ODE's, and gives better results than previous models

Reduced-Order Modeling of Diffusive Effects on the Dynamics of Bubbles

The Rayleigh-Plesset equation and its extensions have been used extensively to model spherical bubble dynamics, yet radial diffusion equations must be solved to correctly capture damping effects due to mass and thermal diffusion. The latter are too computationally intensive to implement into a continuum model for bubbly cavitating flows, since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive a reduced-order model that accounts for thermal and mass diffusion. Motivated by results of applying the Proper Orthogonal Decomposition to data from full radial computations, we derive a model based upon estimates of the average heat transfer coefficients. The model captures the damping effects of the diffusion processes in two ordinary differential equations, and gives better results than previous models

A data-based power transformation for compositional data

Compositional data analysis is carried out either by neglecting the compositional constraint and applying standard multivariate data analysis, or by transforming the data using the logs of the ratios of the components. In this work we examine a more general transformation which includes both approaches as special cases. It is a power transformation and involves a single parameter, {\alpha}. The transformation has two equivalent versions. The first is the stay-in-the-simplex version, which is the power transformation as defined by Aitchison in 1986. The second version, which is a linear transformation of the power transformation, is a Box-Cox type transformation. We discuss a parametric way of estimating the value of {\alpha}, which is maximization of its profile likelihood (assuming multivariate normality of the transformed data) and the equivalence between the two versions is exhibited. Other ways include maximization of the correct classification probability in discriminant analysis and maximization of the pseudo R-squared (as defined by Aitchison in 1986) in linear regression. We examine the relationship between the {\alpha}-transformation, the raw data approach and the isometric log-ratio transformation. Furthermore, we also define a suitable family of metrics corresponding to the family of {\alpha}-transformation and consider the corresponding family of Frechet means.Comment: Published in the proceddings of the 4th international workshop on Compositional Data Analysis. http://congress.cimne.com/codawork11/frontal/default.as

Improved classification for compositional data using the α\alpha-transformation

In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of proportions that sum to one. Data of this type arise in many areas including geology, archaeology, biology, economics and political science. In this paper we investigate methods for classification of compositional data. Our approach centres on the idea of using the $\alpha$-transformation to transform the data and then to classify the transformed data via regularised discriminant analysis and the k-nearest neighbours algorithm. Using the $\alpha$-transformation generalises two rival approaches in compositional data analysis, one (when $\alpha=1$) that treats the data as though they were Euclidean, ignoring the compositional constraint, and another (when $\alpha=0$) that employs Aitchison's centred log-ratio transformation. A numerical study with several real datasets shows that whether using $\alpha=1$ or $\alpha=0$ gives better classification performance depends on the dataset, and moreover that using an intermediate value of $\alpha$ can sometimes give better performance than using either 1 or 0.Comment: This is a 17-page preprint and has been accepted for publication at the Journal of Classificatio

Quantitative detection of atropine-delayed gastric emptying in the horse by the ¹³C-octanoic acid breath test

The <sup>13</sup>C-octanoic acid breath test has been correlated significantly to radioscintigraphy for measurement of gastric emptying indices in healthy horses. The objective of this study was to investigate the validity of the test for measurement of equine delayed gastric emptying, prior to its potential clinical application for this purpose. A model of atropine- induced gastroparesis was used. Gastric emptying rate was measured twice in 8 horses using concurrent radioscintigraphy and/or breath test after treatment i.v. with either atropine (0.035 mg/kg bwt) or saline in randomised order. Analysis of both data sets demonstrated that the atropine treatment had caused a significant delay in gastric emptying rate. Paired breath test data showed an atropine-induced delay in gastric half-emptying time t(1/2)), with no overlap in the 99% Cl range (P<0.001). Significant correlations were found between scintigraphy and <sup>13</sup>C-octanoic acid breath test for calculation of both t(1/2) (P<0.01) and lag phase duration (P<0.05) in the atropine-delayed emptying results. The mean (s.d.) bias in breath test t(1/2) when compared with scintigraphy was 1.78 (0.58) h. The results demonstrated that the <sup>13</sup>C-octanoic acid breath test was an effective diagnostic modality for the measurement of equine delayed gastric emptying. The technique offers advantages to existing methods for clinical investigation, as it is noninvasive, not radioactive, quantitative and requires minimal equipment or training to perform

The Stac Fada “impact ejecta” layer: not what it seems

The Stac Fada Member (SFM) forms part of the Stoer Group of the Torridonian of NW Scotland. The SFM is unique in the Torridonian, being characterized by the presence of greenish altered glass clasts. Its origin has been debated for decades with several hypotheses being proposed but all invoking some connection with volcanic activity in the region. More recently, Amor et al. suggested that the SFM represents “a chord section through the continuous ejecta blanket surrounding an impact crater”. Here, we confirm the presence of shocked material within the SFM and then discuss its origin

The Chimera of Competitiveness: Varieties of Capitalism and the Economic Crisis

In this paper we assess the different definitions and theories of economic competitiveness at the firm and national levels. First we contrast the theories of classical liberal economists with those of the German historical school of national economics, noting the importance of the historical school for theories of national economic competitiveness. Drawing on the comparative political economy literature on ‘varieties of capitalism’, we then discuss the factors underlying competitiveness in social market economies, social democratic economies, and liberal economies. These models of capitalism are compared under six headings: labour markets and labour market institutions; financial markets; corporate funding and governance; inter-firm relations; the role of the state; and economic culture and history. In the penultimate section of the paper we discuss how the different models of capitalism have responded to the economic crisis and the impact of the crisis on their economic competitiveness. The paper concludes with a summary of the key points to emerge from the analysis and looks to how the scene may evolve as national economies begin to adapt