The process of mixing tracks for a live stage performance or studio session is both time consuming and expensive with assistance of professionals. It is also difficult for individuals to remain competitive against established companies, since multiple tracks must be properly mixed in order to achieve well-enhanced elements -- generally, a poor mix makes it difficult for the listener to distinguish the different elements of the mix. The developed method during this thesis work aims at facilitating the mixing work for live performances and studio sessions. The implemented system analyzes the energy spectrum of the tracks included in the mix. By unmasking spectral components, the spectral overlap of the tracks is minimized. The system filters non-characteristic frequencies, leaving significant frequencies undisturbed. Five tracks have been used from the final mix of a successful radio song. These tracks have been analyzed and used to illustrate and validate the developed method. The system was successfully implemented in MATLAB with promising results and conclusions. The processed mix unmasks frequency content and is perceived to sound clearer compared to the unprocessed mix by a number of test individuals. The method reminds of a multi-band compressor that analyzes the spectral information between tracks. Thus, by use of inter-spectral dependencies, the thesis investigates the possibility to control the amplitudes in time by filtration in frequency domain. The compression rate in time domain is reflected in regard to a trade-off between conservation of characteristic frequencies and reduction of spectral overlaps.

This thesis concentrates on stochastic programming problems based on empirical and theoretical distributions and their relationship. Firstly, it focuses on the case where the empirical distribution is an independent random sample. The basic properties are shown followed by the convergence between the problem based on the empirical distribution and the same problem applied to the theoretical distribution. The thesis continues with an overview of some types of dependence - m-dependence, mixing, and also more general weak dependence. For sequences with some of these types of dependence, properties are shown to be similar to those holding for independent sequences. In the last section, the theory is demonstrated using numerical examples, and dependent and independent sequences, including sequences with different types of dependence, are compared.

L'étude porte sur une couche de mélange plane horizontale générée par la rencontre de deux écoulements parallèles à vitesse et température différentes. Le mélange turbulent est analysé pour différentes conditions initiales en termes de gradients de vitesse et de température. On distingue en particulier des configurations en régime de stratification stable et instable sous l'effet des forces de flottabilité. L'analyse des corrélations entre les fluctuations de vitesse et de température s'appuie sur la technique expérimentale d'anémométrie à température de fil variable (PCTA), qui permet la mesure instantanée de la vitesse et de la température en un même point grâce à la variation périodique et par palier du coefficient de surchauffe du fil chaud utilisé. Un premier travail a consisté à étendre la technique PCTA à l'utilisation de fils croisés pour la mesure simultanée de la température et de deux composantes de la vitesse. Dans un premier temps, les statistiques en un point permettent d'identifier les caractéristiques de l'écoulement dans la région de similitude et d'y établir les équations de bilan pour l'énergie cinétique turbulente, l'intensité des fluctuations de température et les flux de quantité de mouvement et de chaleur. Il apparaît, vu les faibles nombres de Richardson en jeu (Rif<0,03), que les forces de flottabilité sont quasi-négligeables devant les moteurs principaux du mouvement. Pourtant, ce forçage thermique peu énergétique est suffisant, en configuration instable, pour augmenter significativement le taux d'expansion et la contrainte de cisaillement, ce qui correspond de fait à une augmentation de la production de turbulence. L'analyse des densités de probabilité jointes permet ensuite de mettre en évidence les mécanismes et évènements qui contribuent significativement aux flux transversaux de quantité de mouvement et de chaleur. Ces différentes contributions sont différenciées et quantifiées par une analyse en quadrants qui fait ressortir la prépondérance des mouvements d'entraînement et d'éjection. On examine enfin les statistiques en deux points associées aux incréments de vitesse et de température. Le comportement de ces incréments est étudié à travers leurs densités de probabilité et leurs coefficients de dissymétrie et d'aplatissement. Les exposants des fonctions de structure confirment l'intermittence plus grande de la température par rapport à celle de la vitesse. Les différents termes des équations de Kolmogorov et de Yaglom sont mesurés. L'équilibre de ces bilans par échelle permet de quantifier le terme qui intègre les différents forçages proposés dans la littérature. / The turbulent mixing is studied in a plane mixing layer for a range of initial conditions applied in terms of velocity and temperature gradients between the two parallel inlet flows. A particular attention is paid to the effect of buoyancy forces, especially in the difference between the so-called stable and unstable configurations, in relation to the sign of the vertical temperature gradient applied. In this study, the novel experimental technique called PCTA, for Parameterizable Constant Temperature Anemometry, is used to enable the analysis of correlations between the velocity and temperature fluctuations. In a preliminary work, the PCTA technique, based on the implementation of repetitive multiple-overheat patterns to a hot wire, is extended and adapted for the instantaneous measurement of temperature and two components of velocity with X-wire probes. In a first stage, one point statistics are analysed. They provide a description of the flow features in the similarity region, where the balance equations for turbulent kinetic energy, temperature variance and the momentum and heat fluxes are established. Considering the low Richardson numbers at stake (Rif <0.03), the buoyancy forces appear logically to be quantitatively negligible compared to the main driving forces, but such a low energy forcing mechanism is in fact sufficient, in unstable configuration, to significantly increase the shear stress and the expansion rate of the mixing layer, both phenomena being associated to an enhanced production of turbulence. In a second stage, a joint probability density function analysis highlights the mechanisms and events that significantly contribute to the transverse momentum and heat fluxes. These contributions are differentiated and quantified through a quadrant analysis which emphasizes the dominance of the local movements of entrainment and ejection associated to the Kelvin-Helmholtz structures. Finally, the study focuses on the two points statistics associated with velocity and temperature increments. The behaviour of these increments is studied through their probability densities, examined along with the skewness and kurtosis coefficients. The structure function exponents confirm the stronger intermittency of temperature compared to that of the velocity. The different terms of the Kolmogorov and Yaglom equations are estimated. The balance of these scale budgets allows the quantification of the forcing term that has been introduced in the literature.

Seja X um alfabeto finito ou infinito enumerável, e considere como X^n o conjunto de todas as sequências de tamanho n. No presente trabalho, nós consideramos a função Tn, definida em X^n e tomando valores entre 1 e infinito. Tn será o primeiro tempo que demora sequência de tamanho n, digamos w, em aparecer de novo sobre uma sequência infinita do processo que começa com w. Este tempo é conhecido como o tempo de retorno. Seja Sn(w) = n - Tn(w) o nosso objeto de estudo, definido também em X^n e tomando valores entre menos infinito e n-1. A função Sn foi colocada em evidência, entre outros casos, na análise estatística da Recorrência de Poincaré, e possui relação explícita com a entropia do processo. Abadi e Lambert, provaram a convergência da distribuição de Sn, quando a sequência é escolhida de acordo com a medida produto de n variáveis aleatórias independentes e identicamente distribuídas no alfabeto e como consequência, mostraram a convergência da esperança de Sn. Nosso trabalho consiste em generalizar o trabalho feito por Abadi e Lambert para processos com uma condição de dependência \\beta-mixing. / We consider the set of finite sequences of length n over a finite or countable alphabet X . We consider the function defined over X^n, Sn = n-\"the first return\". Abadi and Lambert, computed the exact distribution and the limiting distribution of the Sn when the sequence is generated by independent and identically distributed random variables. Our work consists in a generalization of the work done by Abadi and Lambert to processes that verify the \\beta-mixing condition and \\{Xn\\}_{n\\inN} takes values over finite or countable alphabet.

Cópulas tem se tornado uma importante ferramenta para descrever e analisar a estrutura de dependência entre variáveis aleatórias e processos estocásticos. Recentemente, surgiram alguns métodos de estimação não paramétricos, utilizando kernels e ondaletas. Neste contexto, sabendo que cópulas podem ser escritas como expansão em ondaletas, foi proposto um estimador não paramétrico via ondaletas para a função cópula para dados independentes e de séries temporais, considerando processos alfa-mixing. Este estimador tem como característica principal estimar diretamente a função cópula, sem fazer suposição alguma sobre a distribuição dos dados e sem ajustes prévios de modelos ARMA - GARCH, como é feito em ajuste paramétrico para cópulas. Foram calculadas taxas de convergência para o estimador proposto em ambos os casos, mostrando sua consistência. Foram feitos também alguns estudos de simulação, além de aplicações a dados reais. / Copulas are important tools for describing the dependence structure between random variables and stochastic processes. Recently some nonparametric estimation procedures have appeared, using kernels and wavelets. In this context, knowing that a copula function can be expanded in a wavelet basis, we have proposed a nonparametric copula estimation procedure through wavelets for independent data and times series under alpha-mixing condition. The main feature of this estimator is the copula function estimation without assumptions about the data distribution and without ARMA - GARCH modeling, like in parametric copula estimation. Convergence rates for the estimator were computed, showing the estimator consistency. Some simulation studies were made, as well as analysis of real data sets.

Seja X um alfabeto finito ou infinito enumerável, e considere como X^n o conjunto de todas as sequências de tamanho n. No presente trabalho, nós consideramos a função Tn, definida em X^n e tomando valores entre 1 e infinito. Tn será o primeiro tempo que demora sequência de tamanho n, digamos w, em aparecer de novo sobre uma sequência infinita do processo que começa com w. Este tempo é conhecido como o tempo de retorno. Seja Sn(w) = n - Tn(w) o nosso objeto de estudo, definido também em X^n e tomando valores entre menos infinito e n-1. A função Sn foi colocada em evidência, entre outros casos, na análise estatística da Recorrência de Poincaré, e possui relação explícita com a entropia do processo. Abadi e Lambert, provaram a convergência da distribuição de Sn, quando a sequência é escolhida de acordo com a medida produto de n variáveis aleatórias independentes e identicamente distribuídas no alfabeto e como consequência, mostraram a convergência da esperança de Sn. Nosso trabalho consiste em generalizar o trabalho feito por Abadi e Lambert para processos com uma condição de dependência \\beta-mixing. / We consider the set of finite sequences of length n over a finite or countable alphabet X . We consider the function defined over X^n, Sn = n-\"the first return\". Abadi and Lambert, computed the exact distribution and the limiting distribution of the Sn when the sequence is generated by independent and identically distributed random variables. Our work consists in a generalization of the work done by Abadi and Lambert to processes that verify the \\beta-mixing condition and \\{Xn\\}_{n\\inN} takes values over finite or countable alphabet.

Continuous flow reaction using micro-reactors is a valued technology due to its excellent mass and heat transfer performance, reduced reactor volume, handling capacity of hazardous reactions, and many other process intensifications. These intensifications opportunities interest the fine chemicals, pharmaceuticals producers and other multiphase reaction users who currently use batch processes or already use continuous flow. In this thesis, elements of passive and active mixing are investigated for the application of immiscible liquid-liquid systems. In the first study, the effects of geometrical arrangements of a residence time between mixing units on the interphase mass transfer rates are evaluated with four different immiscible liquid-liquid systems. A presentation of an algorithm for the optimal selection of a reactor and its operating conditions is given in order to enable easy and improved use of one’s micro-reactor. In the second study, the impact of a secondary pulse flow on interphase mass transfer is investigated. A coil without internal baffles is used as the oscillatory-flow coil reactor with a continuous active mixing source. The best application for the reactor is determined using a comparison to other complementary continuous flow platforms in the toolbox approach. The novel advancements presented here will help lead new molecular discoveries and connect the laboratory science scale to the process engineering production scale.

The overall goal of this research was to develop an efficient microfluidic system to study signal transduction in stimulation dynamics. This research applied reactive transport fundamentals in concert with biological systems knowledge to completely understand diffusion of soluble signals, fluid and particle flow properties, and dynamics of cellular responses. First, a device capable of parallel multi-time-point cell stimulation and lysis on-chip was developed in collaboration. Second, to understand flow of cells through complex 3-D flow schemes, a Single-field Three-dimensional Epifluorescence Particle (STEP) imaging technique was developed. Using the STEP imaging technique, we were able to determine particle distributions and track individual particles in complex flow geometries. Third, during the design of the stimulation device it was observed that the cells do not distribute across the channel in the same way as the fluids. Based on the observation that geometry and particle size were most influential factors on particle distribution, it was hypothesized that our earlier observation and all observed phenomena in our experimental range were due to the volume exclusion of particles of finite size near the wall of the complex flow geometry. Overall, this work contributed to the realization of microfluidic platforms as powerful tools for probing areas of biology and medicine that are difficult with existing technology. The high-throughput format enabled simple and fast generation of large sets of quantitative data, with consistent sample handling. We demonstrated the necessary first steps to designing efficient unit operations on cells in microfluidic devices. The model can be used for informed design of unit operations in many applications in the future.

Experiments and simulations were performed to examine the complex processes that occur in Rayleigh�Taylor driven mixing. A water channel facility was used to examine a buoyancy-driven Rayleigh�Taylor mixing layer. Measurements of �uctuating den- sity statistics and the molecular mixing parameter were made for Pr = 7 (hot/cold water) and Sc 103 (salt/fresh water) cases. For the hot/cold water case, a high- resolution thermocouple was used to measure instantaneous temperature values that were related to the density �eld via an equation of state. For the Sc 103 case, the degree of molecular mixing was measured by monitoring a di�usion-limited chemical reaction between the two �uid streams. The degree of molecular mixing was quanti- �ed by developing a new mathematical relationship between the amount of chemical product formed and the density variance 02. Comparisons between the Sc = 7 and Sc 103 cases are used to elucidate the dependence of on the Schmidt number. To further examine the turbulent mixing processes, a direct numerical simu- lation (DNS) model of the Sc = 7 water channel experiment was constructed to provide statistics that could not be experimentally measured. To determine the key physical mechanisms that in�uence the growth of turbulent Rayleigh�Taylor mixing layers, the budgets of the exact mean mass fraction em1, turbulent kinetic energy fE00, turbulent kinetic energy dissipation rate e 00, mass fraction variance gm002 1 , and mass fraction variance dissipation rate f 00 equations were examined. The budgets of the unclosed turbulent transport equations were used to quantitatively assess the relative magnitudes of di�erent production, dissipation, transport, and mixing processes. Finally, three-equation (fE00-e 00-gm002 1 ) and four-equation (fE00-e 00-gm002 1 -f 00) turbulent mixing models were developed and calibrated to predict the degree of molecular mix- ing within a Rayleigh�Taylor mixing layer. The DNS data sets were used to assess the validity of and calibrate the turbulent viscosity, gradient-di�usion, and scale- similarity closures a priori. The modeled transport equations were implemented in a one-dimensional numerical simulation code and were shown to accurately reproduce the experimental and DNS results a posteriori. The calibrated model parameters from the Sc = 7 case were used as the starting point for determining the appropri- ate model constants for the mass fraction variance gm002 1 transport equation for the Sc 103 case.

<p>The thesis is dealing with mixing processes havingapplication to ground improvement by deep mixing. The mainobjectives of the thesis is to make a contribution to knowledgeof the basic mechanisms in mixing binding agents into soil andimprove the knowledge concerning factors that influence theuniformity of stabilised soil.</p><p>A great part of the work consists of a literature surveywith particular emphasis on literature on the processindustries. This review forms a basis for a profounddescription and discussion of the mixing process and factorsaffecting the process in connection with deep mixingmethods.</p><p>The thesis presents a method for a simple field test for thestudy of influential factors in the mixing process. A number offactors in the installation process of lime-cement columns havebeen studied in two field tests using statistical multifactorexperiment design. The effects of retrieval rate, number ofmixing blades, rotation speed, air pressure in the storagetank, and diameter of the binder outlet on the stabilisationeffect and the coefficient of variation determined byhand-operated penetrometer tests for excavated lime-cementcolumns, were studied.</p><p>The literature review, the description of the mixingprocess, and the results from the field tests provide a morebalanced picture of the mixing process and are expected to beuseful in connection to ground improvement projects and thedevelopment of mixing equipments.</p><p>The concept of sufficient mixture quality, i.e. theinteraction between the mixing process and the mechanicalsystem, is discussed in the last section. By means ofgeostatistical methods, the analysis considers thevolume-variability relationship with reference to strengthproperties. According to the analysis, the design values forstrength properties depends on the mechanical system, the scaleof scrutiny, the spatial correlation structure, and the conceptof safety, i.e. the concept of sufficient mixture quality isproblem specific.</p><p><b>Key words:</b>Deep Mixing, Lime cement columns, Mixingmechanisms, Mixture quality, Field test, ANOVA, Variancereduction.</p>