<div>Computational studies are performed on a Cambridge Stratified Swirl burner (SwB), a lean premixed stratified flame, by using the Reynolds Averaged Navier Stokes (RANS) model and the transported Probability Density Function (PDF) model. The SwB burner was measured</div><div>by Sweeney et al. (Combustion and Flame, 2012, 159: 2896-2911), and comprehensive data are available for model validation, e.g., the mean and root-mean-square values of velocity, temperature, and species mass fractions. The experimental data are available for sixteen different cases to investigate flames in premixed and stratified regimes, with or without swirl. In this study, we consider only non-swirling, premixed and stratified cases. Different</div><div>turbulence models are examined in the modeling studies, and the Reynolds Stress model with standard model constant values is found to perform well with the transported PDF model. A joint PDF for enthalpy and species mass fractions allows for the highly non-linear reaction term in the transport equation to be completely closed. The mixing term arising from molecular diffusion is not closed and requires modeling which is a significant challenge. For the SwB, we consider a series of mixing models including the Interaction by Exchange with the Mean (IEM) mixing model with different mixing model constants, the Modified Curl model, and two mixing models designed for premixed combustion from the literature. We first examine the models in the non-stratified/premixed case (SwB1) to isolate the effect</div><div>of other conditions from stratification on the model predictions. The stratification is then added in two levels, a moderately stratified case (SwB5) and a highly stratified case (SwB9). The predicted results are compared with the experimental data at various locations, inside and outside the recirculation zone in the burner. In general, good agreement is obtained for the velocity fields inside the recirculation zone. Good agreement is also obtained</div><div>of the predicted and measured results is obtained for the mean values of temperature and species mass fractions. The scalar fluctuations are generally underpredicted. Overall, the employed modeling method is able to capture the mean flame structure reasonably well in lean premixed stratified flames. Some limitations are noticed, e.g., the underprediction of scalar fluctuations, and overprediction of CH4 concentration in the stratified cases. These observations are useful for guiding the future research directions.</div>

<p>Secondary atomization is very important in applications like IC engine and aircraft engine performance, agricultural sprays, and inkjet printing to name a few. In case of IC engines and aircraft engines, a good understanding of the modes of secondary atomization and the resultant drop size can contribute to improving the fuel injection and hence the efficiency of the engine. Similarly, with the help of appropriate secondary atomization desired agro-spray quality, ink usage and print quality can be achieved which would optimize the usage of chemicals and ink respectively and avoid any harmful effects on the environment.</p> <p> </p> <p>One of the reasons for secondary atomization that occurs very often in most of the spray applications is the drop impact on a solid or liquid surface. Especially it is cardinal to understand the impact of a drop on a liquid film since even in case of impact of liquid drops on a solid surface ultimately the drops that are injected at a later time are going have a target surface as a thin liquid film on the solid base due to the accumulation of the previously injected drops. Analysis of drop impact on a liquid film with non-dimensional thickness ranging from 0.1 to 1 has been done thoroughly before (Cossali <i>et al.,</i> 2004, Vander Waal <i>et al.,</i> 2006, Moreira <i>et al.,</i> 2010), however, analysis of drop impact on a liquid film with non-dimensional thickness greater than 1 is still in a rudimentary stage. This work focuses on determining the probability density functions for the secondary drop sizes for drops produced in case of drop impact on a liquid film while varying the h/d ratio beyond 1. The experimental set-up used to study drop impact includes a droplet generator and DIH system as mentioned in, Yao <i>et al.</i> (2017). The DIH set-up includes a CW laser, spatial filter, beam expander and a collimator as adapted from Guildenbecher <i>et al.</i> (2016). The height of drop impact is varied to vary the impact <i>We</i>, by adjusting the syringe height. Three fluids- DI-Water, ethanol and glycerol are tested for examining the effect of viscosity on the resultant drop sizes. Results are plotted with respect to viscosity, impact <i>We</i> and the non-dimensional film thickness, as the fragmentation of drops is directly associated to these parameters. Results indicate that majority of the secondary droplets lie in the size range of 25 µm to 50 µm. It is also observed that the tendency of secondary atomization from crown splashing increases with the increase in <i>We</i> and decreases with increase in <i>Oh.</i></p>

We describe basic notions of functional random elements and the space of functions L2 [0, 1]. We discuss the non-existence of a probability density functional and the re- quirements for integrating in a functional space. In Chapter 2, we define distribution functionals and introduce a goodness-of-fit test which utilises them. The concept of char- acteristic functionals follows in Chapter 3, along with the latest test for Gaussianity of functional random elements. We conclude the chapter with our own new goodness-of- fit test, where we prove the distribution of its test statistic under the alternative, then under the null hypothesis, and lastly the distribution of the bootstrapped test statistic. Finally, we illustrate the theory on a simulation study of the empirical significance level and power of the goodness-of-fit tests. 1

No / This paper outlines the current challenges of driver behaviour modelling for real-world applications and presents the novel method to identify the pattern of usage to predict upcoming journeys in probability sense. The primary aim is to establish similarity between observed behaviour of drivers resulting in the ability to cluster them and deploy control strategies based on contextual intelligence and datadriven approach. The proposed approach uses the probability density function (PDF) driven by kernel density estimation (KDE) as a probabilistic approach to predict the type of the upcoming journey, expressed as duration and distance. Using the proposed method, the mathematical formulation and programming algorithm procedure have been indicated in detail, while the case study examples with the data visualisation are given for algorithm validation in simulation.

Yes / This paper presents a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-­se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação. / We present two different approaches to obtain a probability density function for the stocks future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-08-28T13:57:07Z No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-06T13:18:03Z (GMT) No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-06T13:18:12Z (GMT) No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Made available in DSpace on 2017-09-06T13:28:02Z (GMT). No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) Previous issue date: 2017-06-01 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / We present two different approaches to obtain a probability density function for the stock?s future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula. / Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação.

Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-­se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação. / We present two different approaches to obtain a probability density function for the stocks future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula.

Daniel Duda Visualization of selected flows of superfluid helium using solid hydrogen tracer particles 5 Thesis title: Visualization of selected flows of superfluid helium using solid hydrogen tracer particles Author: Bc. Daniel Duda Department: Department of Low Temperature Physics, Supervisor: prof. RNDr. Ladislav Skrbek, DrSc, Department of Low Temperature Physics, Faculty of Mathematics and Physics, Charles University in Prague. Consultant: Dr. Marco La Mantia, PhD. Abstract: Quantum turbulence generated in thermal counterflow of He II is studied experimentally by visualization. The statistical properties of the motion of micron size solid deuterium particles are studied by using the particle tracking velocimetry technique at length scales comparable to the mean distance between quantized vorti- ces. The probability density function (PDF) of the longitudinal velocity displays two peaks that correspond to two velocity fields of the two-fluid description of He II. The PDF of the transversal velocity displays a classical-like Gaussian core with non- classical power-law tails, confirming the quantum nature of turbulence in counter- flowing He II. The distribution of the particle acceleration is found to be similar in shape to the classical one, in the range of investigated parameters. The observed de-...

139 leaves printed single pages, preliminary pages i-xi and numbered pages 1-127. Includes bibliography and a list of figures and tables. Digitized at 600 dpi grayscale to pdf format (OCR),using a Bizhub 250 Konica Minolta Scanner. / Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: Probability density functions (PDFs) and cumulative distribution functions (CDFs) play a central role in statistical pattern recognition and verification systems. They allow observations that do not occur according to deterministic rules to be quantified and modelled. An example of such observations would be the voice patterns of a person that is used as input to a biometric security device. In order to model such non-deterministic observations, a density function estimator is employed to estimate a PDF or CDF from sample data. Although numerous density function estimation techniques exist, all the techniques can be classified into one of two groups, parametric and non-parametric, each with its own characteristic advantages and disadvantages. In this research, we introduce a novel approach to density function estimation that attempts to combine some of the advantages of both the parametric and non-parametric estimators. This is done by considering density estimation using an abstract approach in which the density function is modelled entirely in terms of its moments or characteristic function. New density function estimation techniques are first developed in theory, after which a number of practical density function estimators are presented. Experiments are performed in which the performance of the new estimators are compared to two established estimators, namely the Parzen estimator and the Gaussian mixture model (GMM). The comparison is performed in terms of the accuracy, computational requirements and ease of use of the estimators and it is found that the new estimators does combine some of the advantages of the established estimators without the corresponding disadvantages. / AFRIKAANSE OPSOMMING: Waarskynlikheids digtheidsfunksies (WDFs) en Kumulatiewe distribusiefunksies (KDFs) speel 'n sentrale rol in statistiese patroonherkenning en verifikasie stelsels. Hulle maak dit moontlik om nie-deterministiese observasies te kwantifiseer en te modelleer. Die stempatrone van 'n spreker wat as intree tot 'n biometriese sekuriteits stelsel gegee word, is 'n voorbeeld van so 'n observasie. Ten einde sulke observasies te modelleer, word 'n digtheidsfunksie afskatter gebruik om die WDF of KDF vanaf data monsters af te skat. Alhoewel daar talryke digtheidsfunksie afskatters bestaan, kan almal in een van twee katagoriee geplaas word, parametries en nie-parametries, elk met hul eie kenmerkende voordele en nadele. Hierdie werk Ie 'n nuwe benadering tot digtheidsfunksie afskatting voor wat die voordele van beide die parametriese sowel as die nie-parametriese tegnieke probeer kombineer. Dit word gedoen deur digtheidsfunksie afskatting vanuit 'n abstrakte oogpunt te benader waar die digtheidsfunksie uitsluitlik in terme van sy momente en karakteristieke funksie gemodelleer word. Nuwe metodes word eers in teorie ondersoek en ontwikkel waarna praktiese tegnieke voorgele word. Hierdie afskatters het die vermoe om 'n wye verskeidenheid digtheidsfunksies af te skat en is nie net ontwerp om slegs sekere families van digtheidsfunksies optimaal voor te stel nie. Eksperimente is uitgevoer wat die werkverrigting van die nuwe tegnieke met twee gevestigde tegnieke, naamlik die Parzen afskatter en die Gaussiese mengsel model (GMM), te vergelyk. Die werkverrigting word gemeet in terme van akkuraatheid, vereiste numeriese verwerkingsvermoe en die gemak van gebruik. Daar word bevind dat die nuwe afskatters weI voordele van die gevestigde afskatters kombineer sonder die gepaardgaande nadele.