In this thesis, we study the mathematical modelling of some problems that involve surface effects. These include an optical biosensor, which uses optical principles qualitatively to convert chemical and biochemical concentrations into electrical signals. A typical sensor of this type was constructed in Badley et al., [6], and Jones et al., [18],but diffusion was considered in only one direction in [18] to simulate the reaction between the antigen and the antibody. For realistic applications, we propose the biosensor model in R3. Our theoretical approach is explicitly presented since it is simple and directly applicable to the numerical part of the thesis. In particular, we present existence and uniqueness results based on Maximum Principle and weak solution arguments. These ideas are later applied to systems and to the numerical analysis of the approximate discretized problems.It should be noted that without one dimensional symmetry, the equations can not be decoupled in order to reduce the problem to a single equation. We also show the long time monotonic convergence to the steady state. Next, a finite volume method is applied to the equations, and we obtain existence and uniqueness for the approximate solution as well as the convergence of the the first order temporal norm and the L2 spatial norm. We illustrate the results via some numerical simulations. Finally we consider a mathematically related system motivated by lagoon ecology. We show that under suitable conditions on the coecients, the system has a periodic solution under harvesting conditions. The mathematical techniques now depend on estimates for periodic parabolic problems. / Applied Mathematics

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Silicon nanocrystals (SiNCs) are nanometer-sized semiconducting materials. Their small size endows them with unique photophysical properties. Efficient photoluminescence (PL) from silicon nanocrystal (SiNC) composites has important implications for emerging solar-energy collection technologies, yet a detailed understanding of PL relaxation in non-colloidal SiNCs is still materializing. In this dissertation, we examine the photophysical properties of silicon nanocrystal/off-stoichiometry thiol-ene composites (SiNCs/OSTE hybrids). The dissertation begins with an introduction to the photophysical properties of SiNCs, their photophysical properties, how SiNC/polymer composites are made, the various SiNC preparation techniques, and the most likely application areas for these nanocrystals. A description of experimental methods such as PL spectroscopy and transmission electron microscopy (TEM) follows, and SiNC/OSTE polymer preparation methods are then explained in detail. In the first study, TEM and photophysical characterization were performed on selected polydisperse SiNCs samples. These samples were synthesized in a nonthermal plasma reactor, using Si6H12 as precursor, and functionalized with R (where R is 1-dodecene). These SiNCs were dispersed in mesitylene:1-dodecene (5:1) as a colloid. Optical absorption, quantum efficiency, and PL lifetime of SiNCs were then investigated, as well as the relationship between quantum yield, lifetime, and PL peak. In the second study, we selected samples for size separation via the density gradient ultracentrifugation method (DGU). We successfully applied this technique to separate silicon nanocrystals with sizes from 2 nm to 4 nm from the ensemble samples using an engineered density medium layer stack, and photophysical characterization was performed on the DGU size–separated SiNCs. Lastly, we explored details of PL relaxation in photo-polymerized off-stoichiometric polymer/nanocrystal hybrids. We found time- and air-stable emission from dilute composites with up to 70% QY, and we investigated PL relaxation in the parameter space of nanocrystal size and temperature. In light of previous work, our results reveal similarities between the impacts of crosslinking and cooling to cryogenic temperature, but of which are characterized by a relative reduction in the available of phonons.

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Made available in DSpace on 2015-04-22T22:07:28Z (GMT). No. of bitstreams: 1 VANUSA_ BEZERRA_ PACHECO.pdf: 1062027 bytes, checksum: 0625cb2a00e9f5171bb97d813a81f04d (MD5) Previous issue date: 2006-12-01 / Fundação de Amparo à Pesquisa do Estado do Amazonas / Neste trabalho investigamos o diagrama de fase do modelo de Ising de spin ½ aleatoriamente decorado nos planos de um filme fino de tamanho L. As interações nos planos simula a interação cobre-cobre (Cu-Cu) numa rede cúbica simples antiferromagnética, onde entre os vértices da rede coloca-se um spin decorador aleatoriamente distribuído, que simula o íon de oxigênio no plano de cobre-oxigênio (CuO2) de valor ½ e interagindo ferromagneticamente com os íons de cobre, provocando assim o fenômeno de frustração. Para este estudo, utilizamos a técnica do operador diferencial em aglomerado com um íon em conjunto com a aproximação do campo efetivo. Através dos diagramas de fase (formúla), onde (formúla) , que representa a relação das energias de interação ferromagnética da superfície com o bulk é possível notar um ponto multicrítico (formúla) que corresponde ao caso em que tanto a superfície quanto o bulk estão ordenados a um dado valor de concentração e valores para os parâmetros de frustrações (formúla) (parâmetro de frustração da superfície) e (formúla) (parâmetro de frustração do bulk). Para valores Δ < Δc, o sistema apresenta-se com bulk ordenado e a superfície desordenada, isto significa que a temperatura crítica do bulk ( b ) c T é maior que a temperatura crítica da superfície ( s ) c T , no entanto para Δ >Δc a superfície está ordenada e o bulk desordenado, isto é, . E para (formúla) verificamos que para determinados valores de concentração encontramos para qualquer valor de Δ os mesmos valores de temperaturas críticas.

Thesis (M.Dent.), Faculty of Health Sciences, University of the Witwatersrand, 2009 / This in vitro study compares tooth bleaching and consequences of tooth surface effects of Ozicure Oxygen Activator (O3, RSA) with Opalescence Quick (Ultradent, USA) tooth bleaching. One hundred and thirty six teeth (canines, incisors and premolars), which were caries free, had no surface defects and within the colour range 1M2 and 5M3. Teeth were randomly divided into the three experimental groups: Opalescence Quick, Ozicure Oxygen Activator and control. The three experimental groups received three treatments of one hour each over three consecutive days. Tooth colour was assessed using the VITAPAN 3D MASTER TOOTH GUIDE (VITA, Germany) and VITA Easyshade (VITA, Germany). A randomized block design was used to assess tooth colour change. A General Linear Models test for analysis of variance for a fractional design with significance set at P<0.05 was used. Both bleaching methods significantly lightened the teeth, visually (P<0.0001) and digitally (P= 0.013). Tooth colour change was seen after the first hour of tooth bleaching; thereafter there was little or no benefit. The tooth type played a significant role in tooth colour change (visually P=0.0416 and digitally P=0.004). The quality of the spectrophotometer may account for the different results found compared to the tooth guide. Scanning electron microscopy showed no effect of enamel loss following bleaching. Atomic force microscopy showed a 2.5 rougher enamel surface with Opalescence Quick.

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Early in the ship design process, naval architects must often evaluate and compare multiple hull forms for a specific set of requirements. Analytical tools are useful for quick comparisons, but they usually specialize in a specific hull type and are therefore not adequate for comparing dissimilar hull types. Scale model hydrodynamic testing is the traditional evaluation method, and is applicable to most hull forms. Scale model tests are usually performed on the largest model possible in order to achieve the most accurate performance predictions. However, such testing is very resource intensive, and is therefore not a cost effective method of evaluating multiple hull forms. This thesis explores the testing of small scale models. It is hypothesized that although the data acquired by these tests will not be accurate enough for performance predictions, they will be accurate enough to rank the performance of the multiple hull forms being evaluated.