An experimental investigation has been undertaken to study the depth of cut in multipass abrasive waterjet (AWJ) cutting of an 87% alumina ceramic with controlled nozzle oscillation. The experimental data have been statistically analysed to study the trends of the depth of cut with respect to the process parameters. It has been found that multipass cutting with controlled nozzle oscillation can significantly increase the depth of cut. Within the same cutting time and using the same cutting parameters other than the jet traverse speed, it has been found that multipass cutting with nozzle oscillation can increase the depth of cut by an average of 74.6% as compared to single pass cutting without nozzle oscillation. Furthermore, a multipass cutting with higher nozzle traverse speeds can achieve a larger depth of cut than a single pass cutting at a low traverse speed within the same cutting time. A recommendation has been made for the selection of appropriate process parameters for multipass cutting with nozzle oscillation. In order to estimate the depth of cut on a mathematical basis, predictive models for the depth of cut in multipass cutting with and without nozzle oscillation have been developed using a dimensional analysis technique. The model development starts with the models for single pass cutting which are then extended to multipass cutting where considerations are given to the change of the actual standoff distance after each pass and the variation of kerf width. These predictive models has been numerically studied for their plausibility by assessing their predicted trends with respect to the various process variables, and verified qualitatively and quantitatively based on the experimental data. The model assessment reveals that the developed models correlate very well with the experimental results and can give adequate predictions of this cutting performance measure in process planning.

This thesis addresses three topics in the area of statistics and probability, with applications in risk management. First, for the testing problems in the high-dimensional (HD) data analysis, we present a novel method to formulate empirical likelihood tests and jackknife empirical likelihood tests by splitting the sample into subgroups. New tests are constructed to test the equality of two HD means, the coefficient in the HD linear models and the HD covariance matrices. Second, we propose jackknife empirical likelihood methods to formulate interval estimations for important quantities in actuarial science and risk management, such as the risk-distortion measures, Spearman's rho and parametric copulas. Lastly, we introduce the theory of completely mixable (CM) distributions. We give properties of the CM distributions, show that a few classes of distributions are CM and use the new technique to find the bounds for the sum of individual risks with given marginal distributions but unspecific dependence structure. The result partially solves a problem that had been a challenge for decades, and directly leads to the bounds on quantities of interest in risk management, such as the variance, the stop-loss premium, the price of the European options and the Value-at-Risk associated with a joint portfolio.

One the most daunting technical challenges in the realization of biosensors is functionalizing transducing surfaces for the detection of biomolecules. Functionalization is defined as the formation of a bio-compatible interface on the transducing surfaces of bio-chemical sensors for immobilizing and subsequent sensing of biomolecules. The kinetics of functionalization reactions is a particularly important issue, since conventional functionalization protocols are associated with lengthy process times, from hours to days. The objective of this thesis is the improvement of the functionalization protocols and their kinetics for biosensing applications. This objective is realized via modeling and experimental verification of novel functionalization techniques in microfluidic environments. The improved functionalization protocols using microfluidic environments enable in-situ functionalization, which reduces the processing times and the amount of reagents consumed, compared to conventional methods. The functionalization is performed using self-assembled monolayers (SAMs) of thiols. The thiols are organic compounds with a sulphur group that assists in the chemisorption of the thiol to the surface of metals like gold. The two reactions in the functionalization process examined in this thesis are the SAM formation and the SAM/probe molecule conjugation. SAM/probe molecule conjugation is the chemical treatment of the SAM followed by the binding of the probe molecule to the SAM. In general, the probe molecule is selective in binding with a given biomolecule, called the target molecule. Within this thesis, the probe molecule is an antibody and the target molecule is an antigen. The kinetics of the reaction between the probe (antibody) and the target biomolecule (antigen) is also studied. The reaction between an antigen and its antibody is called the immunoreaction. The biosensing technique that utilizes the immunoreaction is immunoassay. A numerical model is constructed using the finite element method (FEM), and is used to study the kinetics of the functionalization reactions. The aim of the kinetic studies is to achieve both minimal process times and reagents consumption. The impact of several important parameters on the kinetics of the reactions is investigated, and the trends observed are explained using kinetic descriptive dimensionless numbers, such as the Damköhler number and the Peclet number. Careful numerical modeling of the reactions contributes to a number of findings. A considerably faster than conventional SAM formation protocol is predicted. This fast-SAM protocol is capable of reducing the process times from the conventional 24-hours to 15 minutes. The numerical simulations also predict that conventional conjugation protocols result in the overexposure of the SAM and the probe molecule to the conjugation reagents. This overexposure consequently lowers conjugation efficiencies. The immunoreaction kinetics of a 70 kilo-Dalton heat shock protein (HSP70) with its antibody in a hypothetical microchannel is also investigated through the FEM simulations. Optimal reaction conditions are determined, including the flow velocity and the surface concentration of the immobilized probes (antibodies). Based on the numerical results and a series of experimental studies, the fast-SAM protocol application is successfully confirmed. Moreover, the optimum reagent concentration for a given one- hour conjugation process time is determined. This functionalization protocol is successfully applied to immobilize the HSP70 antibody on gold surfaces. The use of the fast-SAM protocol and the predicted optimum conjugation conditions result in binding of the HSP70 antibody on gold, with the same or superior immobilization quality, compared to the conventional protocols. Upon implementation of a 70 μm.s^(-1) flow velocity, the reaction is observed to complete in around 30-35 minutes, which is close to the numerically predicted 30 minutes and 16 seconds. This immunoreaction time is considerably less than conventional 4-12 hour processes. The modified in-situ functionalization techniques achieved here are promising for substantially reducing the preparation times and improving the performance of biosensors, in general, and immunoassays, in particular.

Selective laser melting process is an additive manufacturing technique that allows obtaining, from a 3D model, a physical model through a layer-by-layer manufacturing strategy. Several machines are commercially available, known as 3D printers. Recently, technology improvements have allowed the use of metallic materials; however, the amount of materials available is low due to the difficulty to find adequate manufacturing parameters. The thesis proposes a methodology, using an inclined plane, to set the minimum energy density to melt a continuous track, the first step of the melting process. Different process parameters from several commercials machines have been used to evaluate dimensional and mechanical properties. Replicas of traditional products have been fabricated using additive process and they have been compared. Finally, a protocol to use a selective laser melting process to reconstruct a personalized jaw prosthesis has been shown / La fusió selectiva per làser és un procés de fabricació additiva que permet obtenir, d'un disseny en 3D, un model físic de forma ràpida i a través d'una estratègia de fabricació capa a capa. Existeixen diferents màquines comercials anomenades impressores 3D. Actualment, les millores tècniques desenvolupades han permès la utilització de materials metàl·lics, no obstant, la quantitat de materials que es poden utilitzar és baix degut a la dificultat per trobar els paràmetres de fabricació més adequats. La tesis proposa una metodologia, a través d’un pla inclinat, que permet definir la densitat d’energia mínima per fondre un cordó continu, el primer pas del procés de fusió làser. Diferents paràmetres de varies màquina comercials s'han utilitzat per avaluar variables dimensionals i mecàniques. S'han comparat rèpliques fabricades mitjançant processos tradicionals i processos additius. Finalment, s'ha realitzat un protocol per a reconstruir una mandíbula personalitzada utilitzant la fusió selectiva per làser

A numerical model for describing the kinetics of intracellular water transport during cryopreservation was developed. As ice is formed outside the cell, depleting the extracellular liquid of water, the cell will experience an osmotic pressure difference across its membrane, which causes cell dehydration and concomitant shrinkage. Although Mazur (1963) has previously modeled this phenomenon as a two-compartment system with membrane limited transport, the assumption of well-mixed compartments breaks down at large Biot numbers. Therefore, we have developed a numerical solution to this moving-boundary problem, including diffusive transport in the intracellular liquid, in addition to the osmotically driven membrane flux. Our model uses a modified Crank-Nicolson scheme with a non-uniform Eulerian-Lagrangian grid, and is able to reproduce predictions from Mazurs model at low Biot numbers, while generating novel predictions at high Biot numbers. Given that cell damage may result from excessive water loss, our model can be used to predict freezing methods that minimize the probability of cell injury during the cryopreservation process.

With the increasing amount of collected data, large-scale high-dimensional data analysis is becoming essential in many areas. These data can be analyzed either by using fully computational methods or by leveraging human capabilities via interactive visualization. However, each method has its drawbacks. While a fully computational method can deal with large amounts of data, it lacks depth in its understanding of the data, which is critical to the analysis. With the interactive visualization method, the user can give a deeper insight on the data but suffers when large amounts of data need to be analyzed. Even with an apparent need for these two approaches to be integrated, little progress has been made. As ways to tackle this problem, computational methods have to be re-designed both theoretically and algorithmically, and the visual analytics system has to expose these computational methods to users so that they can choose the proper algorithms and settings. To achieve an appropriate integration between computational methods and visual analytics, the thesis focuses on essential computational methods for visualization, such as dimension reduction and clustering, and it presents fundamental development of computational methods as well as visual analytic systems involving newly developed methods. The contributions of the thesis include (1) the two-stage dimension reduction framework that better handles significant information loss in visualization of high-dimensional data, (2) efficient parametric updating of computational methods for fast and smooth user interactions, and (3) an iteration-wise integration framework of computational methods in real-time visual analytics. The latter parts of the thesis focus on the development of visual analytics systems involving the presented computational methods, such as (1) Testbed: an interactive visual testbed system for various dimension reduction and clustering methods, (2) iVisClassifier: an interactive visual classification system using supervised dimension reduction, and (3) VisIRR: an interactive visual information retrieval and recommender system for large-scale document data.

One the most daunting technical challenges in the realization of biosensors is functionalizing transducing surfaces for the detection of biomolecules. Functionalization is defined as the formation of a bio-compatible interface on the transducing surfaces of bio-chemical sensors for immobilizing and subsequent sensing of biomolecules. The kinetics of functionalization reactions is a particularly important issue, since conventional functionalization protocols are associated with lengthy process times, from hours to days. The objective of this thesis is the improvement of the functionalization protocols and their kinetics for biosensing applications. This objective is realized via modeling and experimental verification of novel functionalization techniques in microfluidic environments. The improved functionalization protocols using microfluidic environments enable in-situ functionalization, which reduces the processing times and the amount of reagents consumed, compared to conventional methods. The functionalization is performed using self-assembled monolayers (SAMs) of thiols. The thiols are organic compounds with a sulphur group that assists in the chemisorption of the thiol to the surface of metals like gold. The two reactions in the functionalization process examined in this thesis are the SAM formation and the SAM/probe molecule conjugation. SAM/probe molecule conjugation is the chemical treatment of the SAM followed by the binding of the probe molecule to the SAM. In general, the probe molecule is selective in binding with a given biomolecule, called the target molecule. Within this thesis, the probe molecule is an antibody and the target molecule is an antigen. The kinetics of the reaction between the probe (antibody) and the target biomolecule (antigen) is also studied. The reaction between an antigen and its antibody is called the immunoreaction. The biosensing technique that utilizes the immunoreaction is immunoassay. A numerical model is constructed using the finite element method (FEM), and is used to study the kinetics of the functionalization reactions. The aim of the kinetic studies is to achieve both minimal process times and reagents consumption. The impact of several important parameters on the kinetics of the reactions is investigated, and the trends observed are explained using kinetic descriptive dimensionless numbers, such as the Damköhler number and the Peclet number. Careful numerical modeling of the reactions contributes to a number of findings. A considerably faster than conventional SAM formation protocol is predicted. This fast-SAM protocol is capable of reducing the process times from the conventional 24-hours to 15 minutes. The numerical simulations also predict that conventional conjugation protocols result in the overexposure of the SAM and the probe molecule to the conjugation reagents. This overexposure consequently lowers conjugation efficiencies. The immunoreaction kinetics of a 70 kilo-Dalton heat shock protein (HSP70) with its antibody in a hypothetical microchannel is also investigated through the FEM simulations. Optimal reaction conditions are determined, including the flow velocity and the surface concentration of the immobilized probes (antibodies). Based on the numerical results and a series of experimental studies, the fast-SAM protocol application is successfully confirmed. Moreover, the optimum reagent concentration for a given one- hour conjugation process time is determined. This functionalization protocol is successfully applied to immobilize the HSP70 antibody on gold surfaces. The use of the fast-SAM protocol and the predicted optimum conjugation conditions result in binding of the HSP70 antibody on gold, with the same or superior immobilization quality, compared to the conventional protocols. Upon implementation of a 70 μm.s^(-1) flow velocity, the reaction is observed to complete in around 30-35 minutes, which is close to the numerically predicted 30 minutes and 16 seconds. This immunoreaction time is considerably less than conventional 4-12 hour processes. The modified in-situ functionalization techniques achieved here are promising for substantially reducing the preparation times and improving the performance of biosensors, in general, and immunoassays, in particular.

An experimental investigation has been undertaken to study the depth of cut in multipass abrasive waterjet (AWJ) cutting of an 87% alumina ceramic with controlled nozzle oscillation. The experimental data have been statistically analysed to study the trends of the depth of cut with respect to the process parameters. It has been found that multipass cutting with controlled nozzle oscillation can significantly increase the depth of cut. Within the same cutting time and using the same cutting parameters other than the jet traverse speed, it has been found that multipass cutting with nozzle oscillation can increase the depth of cut by an average of 74.6% as compared to single pass cutting without nozzle oscillation. Furthermore, a multipass cutting with higher nozzle traverse speeds can achieve a larger depth of cut than a single pass cutting at a low traverse speed within the same cutting time. A recommendation has been made for the selection of appropriate process parameters for multipass cutting with nozzle oscillation. In order to estimate the depth of cut on a mathematical basis, predictive models for the depth of cut in multipass cutting with and without nozzle oscillation have been developed using a dimensional analysis technique. The model development starts with the models for single pass cutting which are then extended to multipass cutting where considerations are given to the change of the actual standoff distance after each pass and the variation of kerf width. These predictive models has been numerically studied for their plausibility by assessing their predicted trends with respect to the various process variables, and verified qualitatively and quantitatively based on the experimental data. The model assessment reveals that the developed models correlate very well with the experimental results and can give adequate predictions of this cutting performance measure in process planning.

Στην παρούσα Διπλωματική Εργασία μελετώνται εφαρμογές της θεωρίας της Διαστατικής Ανάλυσης στην μαθηματική μοντελοποίηση. Πιο συγκεκριμένα, στο πρώτο κεφάλαιο εισάγουμε την έννοια της διαστατικής ανάλυσης καθώς και την χρησιμότητά της κάνοντας ταυτόχρονα μια σύντομη ιστορική αναδρομή. Στο ίδιο κεφάλαιο ακόμα παραθέτουμε το περίφημο παράδειγμα στο οποίο ο G.I. Taylor υπολόγισε, με την βοήθεια της Διαστατικής Ανάλυσης, την ενέργεια που εκλύθηκε από την πρώτη, δοκιμαστική ατομική βόμβα στο New Mexico τον Ιούλιο του 1945. Στο δεύτερο κεφάλαιο αναπτύσσονται το Θεώρημα Π του Buckingham, το οποίο αποτελεί το θεμελιώδες θεωρητικό υπόβαθρο της Διαστατικής Ανάλυσης, καθώς και δύο εφαρμογές που βασίζονται στο παραπάνω θεώρημα. Η πρώτη εξ' αυτών αναφέρεται στην ταχύτητα εξάπλωσης της πετρελαιοκηλίδάς στον Κόλπο του Μεξικού που προκλήθηκε από την έκρηξη σε υποθαλάσσια πλατφόρμα εξόρυξης πετρελαίου την άνοιξη του 2010. Τέλος, στο τρίτο κεφάλαιο αναλύονται οι εξισώσεις Navier-Stokes και συνέχειας της Ρευστοδυναμικης. Ελέγχουμε ότι οι εξισώσεις αυτές είναι διαστατικά ομογενείς και στη συνέχεια περιγράφουμε τη διαδικασία κανονικοποίησής τους. / In this paper, we study applications of the theory of dimensional analysis in mathematical modeling. More specifically, the first chapter introduces the concept of dimensional analysis and the usefulness of simultaneously making a brief historical overview. In the same chapter is describt the famous example in which the G.I. Taylor estimated with the help of dimensional analysis, the energy emitted by the first atomic bomb test in New Mexico in July 1945. In the second chapter, Theorem Π of Buckingham, which is the fundamental theoretical basis of dimensional analysis, as well as two applications based on the above theorem. The first of them refers at the spead of spreading oil slick in the Gulf of Mexico caused by the boom in offshore oil platform in the spring of 2010. Finally, the third chapter analyzes the equations of Navier-Stokes and continuity of fluid dynamics. We check that these equations are dimensional homogeneous and then we describe the process of how we can to normalize them.

Os custos com a implantação de unidades piloto de flotação por ar dissolvido (FAD) requerem estratégias especiais em função da falta de correlações entre a escala laboratorial e a industrial, uma vez que os projetos de FAD têm sido concebidos apenas sob o ponto de vista econômico. Nesse sentido, tem-se realizado esforços significativos para descrever e modelar um scale-up para o processo de FAD, sendo necessário elaborar e validar um modelo de previsão de scale-up para promover a mudança de escala necessária. No presente trabalho foi obtida uma correlação de scale-up como base para o projeto de uma unidade piloto, a partir de um modelo físico em escala de laboratório por meio da análise de correlações de semelhança dinâmica envolvendo grandezas predominantes em uma câmara de FAD usada na separação e recuperação de águas oleosas. Com auxílio da fluidodinâmica computacional e de vídeos dos fluxos de microbolhas e flocos, as forças de inércia e de gravidade foram identificadas como as grandezas predominantes em uma câmara de FAD pela discrepância entre as velocidades médias de ascensão de microbolhas e flocos, de 8,7310-7 m/s e 1,17510-5 m/s, respectivamente. As simulações foram realizadas por meio do software ANSYS e as medidas foram efetuadas com o auxílio de uma câmera fotográfica. A metodologia de trabalho empregada permitiu o desenvolvimento de uma técnica simples e de baixo custo, diminuindo a probabilidade de riscos futuros em um investimento de scale-up. / The implantation costs of dissolved air flotation (DAF) pilot units require special strategies due to the lack of correlations between laboratory and industrial scale, as novel flotation methods have been considered strictly from an economic standpoint. In this sense, significant efforts have been made to describe and model a scale-up to the process of FAD, being necessary to design and validate a scale-up forecasting model to promote a change in the required scale. In this study a scale-up correlation for a pilot unit project was determined based on the analysis of dynamic similarity correlations involving the predominant phenomena of a dissolved air flotation (DAF) chamber used in separating and recovering oily water. With the aid of computational fluid dynamics and videos of microbubble and floc flow, inertia and gravity were identified as the predominant phenomena in a DAF chamber by the discrepancy between the average speeds of rise of microbubbles and flakes of 8.73 10-7 m/s and 1.17510-5 m/s, respectively. The simulations were performed using ANSYS software and measurements were made with the aid of a camera. The strategy described herein is simple and reduces the likelihood of future risks in scale-up investments.