The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Hexagonal Resonant Triad patterns are shown to exist as stable solutions of a particular type of nonlinear field where no cubic field nonlinearity is present. The zero ‘dc’ Fourier mode is shown to stabilize these patterns produced by a pure quadratic field nonlinearity. Closed form solutions and stability results are obtained near the critical point, complimented by numerical studies far from the critical point. These results are obtained using a neural field based on the Helmholtzian operator. Constraints on structure and parameters for a general pure quadratic neural field which supports hexagonal patterns are obtained.

The role of nuclear physics in supernovae and the evolution of neutron stars, Neutrino Opacities, Equation of State, Transport Coefficients, and Dark Matter Production

Thesis (Ph.D.)--University of Washington, 2016-08

Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Purificação, modelagem e simulação da adsorção de bioprodutos por troca iônica em coluna de leito expandido

A produção de proteínas através de microrganismos tornou-se uma técnica muito importante na obtenção de compostos de interesse da indústria farmacêutica e alimentícia. Extratos brutos nos quais as proteínas são obtidas são geralmente complexos, contendo sólidos e células em suspensão. Usualmente, para uso industrial destes compostos, é necessário obtê-los puros, para garantir a sua atuação sem interferência. Um método que vem recebendo destaque especialmente nos últimos 10 anos é o uso da cromatografia de troca iônica em leito expandido, que combina em uma única etapa os passos de clarificação, concentração e purificação da molécula alvo, reduzindo assim o tempo de operação e também os custos com equipamentos para realização de cada etapa em separado. Combinado a este fato, a última década também é marcada por trabalhos que tratam da modelagem matemática do processo de adsorção de proteínas em resinas. Está técnica, além de fornecer informações importantes sobre o processo de adsorção, também é de grande valia na otimização da etapa de adsorção, uma vez que permite que simulações sejam feitas, sem a necessidade de gasto de tempo e material com experimentos em bancada, especialmente se é desejado uma ampliação de escala. Dessa forma, o objetivo desta tese foi realizar a modelagem e simulação do processo de adsorção de bioprodutos em um caldo bruto na presença de células, usando inulinase e C-ficocianina como objeto de estudo e purificar C-ficocianina utilizando resina de troca iônica em leito expandido. A presente tese foi então dividida em quatro artigos. O primeiro artigo teve como objeto de estudo a enzima inulinase, e a otimização da etapa de adsorção desta enzima em resina de troca iônica Streamline SP, em leito expandido, foi feita através da modelagem matemática e simulação das curvas de ruptura em três diferentes graus de expansão (GE). As máximas eficiências foram observadas quando utilizadas maiores concentrações de inulinase (120 a 170 U/mL), e altura de leito entre 20 e 30 cm. O grau de expansão de 3,0 vezes foi considerado o melhor, uma vez que a produtividade foi consideravelmente superior. O segundo artigo apresenta o estudo das condições de adsorção de C-ficocianina em resina de troca iônica, onde foi verificado o efeito do pH e temperatura na adsorção e após construída a isoterma de adsorção. A isoterma de adsorção da C-ficocianina em resina Streamline Q XL feita em pH 7,5 e a 25°C (ambiente), apresentou um bom ajuste ao modelo de Langmuir (R=0,98) e os valores qm (capacidade máxima de adsorção) e Kd (constante de equilíbrio) estimados pela equação linearizada da isoterma, foram de 26,7 mg/mL e 0,067mg/mL. O terceiro artigo aborda a modelagem do processo de adsorção de extrato não clarificado de C-ficocianina em resina de troca iônica Streamline Q XL em coluna de leito expandido. Três curvas de ruptura foram feitas em diferentes graus de expansão (2,0, 2,5 e 3,0). A condição de adsorção de extrato bruto não clarificado de C-ficocianina que se mostrou mais vantajosa, por apresentar maior capacidade de adsorção, é quando se alimenta o extrato até atingir 10% de saturação da resina, em grau de expansão 2,0, com uma altura inicial de leito de 30 cm. O último artigo originado nesta tese foi sobre a purificação de C-ficocianina através da cromatografia de troca iônica em leito expandido. Uma vez que a adsorção já havia sido estudada no artigo 2, o artigo 4 enfoca na otimização das condições de eluição, visando obter um produto com máxima pureza e recuperação. A pureza é dada pela razão entre a absorbância a 620 nm pela absorbância a 280 nm, e dizse que quando C-ficocianina apresenta pureza superior a 0,7 ela pode ser usada em como corante em alimentos. A avaliação das curvas de contorno indicou que a faixa de trabalho deve ser em pH ao redor de 6,5 e volumes de eluição próximos a 150 mL. Tais condições combinadas a uma etapa de pré-eluição com 0,1M de NaCl, permitiu obter C-ficocianina com pureza de 2,9, concentração 3 mg/mL, e recuperação ao redor de 70%.

Dispersive estimates for the Schrödinger equation

In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We focus particularly on the five and seven dimensional cases. We prove that the solution operator precomposed with projection onto the absolutely continuous spectrum of $H=-\Delta+V$ satisfies the following estimate $\|e^{itH} P_{ac}(H)\|_{L^1\to L^\infty} \lesssim |t|^{-\frac{n}{2}}$ under certain conditions on the potential $V$. Specifically, we prove the dispersive estimate is satisfied with optimal assumptions on smoothness, that is $V\in C^{\frac{n-3}{2}}(\R^n)$ for $n=5,7$ assuming that zero is regular, $|V(x)|\lesssim \langle x\rangle^{-\beta}$ and $|\nabla^j V(x)|\lesssim \langle x\rangle^{-\alpha}$, $1\leq j\leq \frac{n-3}{2}$ for some $\beta>\frac{3n+5}{2}$ and $\alpha>3,8$ in dimensions five and seven respectively. We also show that for the five dimensional result one only needs that $|V(x)|\lesssim \langle x\rangle^{-4-}$ in addition to the assumptions on the derivative and regularity of the potential. This more than cuts in half the required decay rate in the first chapter. Finally we consider a problem involving the non-linear Schr\"{o}dinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, \begin{align*} iu_t+d(t) u_{xx}+|u|^2 u=0. \end{align*} We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in $x$ and in the Fourier transform of $x$.

Remoção de hidrocarbonetos aromáticos policíclicos em águas utilizando subprodutos da indústria da cortiça

Os Hidrocarbonetos Aromáticos Policíclicos (HAPs) são contaminantes persistentes em meio aquoso. Estes compostos são conhecidos pelas suas propriedades carcinogénicas, mutagénicas e genotóxicas. O principal objetivo deste trabalho consistiu na avaliação das potencialidades de subprodutos da indústria corticeira, como adsorventes alternativos para a remoção de cinco HAPs em meio aquoso: benzo(a)pireno, benzo(ghi)perileno, benzo(b)fluoranteno, benzo(k)fluoranteno e indeno(1,2,3-cd)pireno. A metodologia analítica para quantificar os HAPs envolveu a preparação das amostras, através da técnica de extração em fase sólida (SPE), e a quantificação dos compostos analisados por cromatografia líquida com detetor de fluorescência (LC-FLD). O método foi otimizado e validado, obtendo-se limites de quantificação de 0,004 μg/L para todos os HAPs. Os estudos incidiram na utilização de uma amostra de cortiça, pó de aglomerado de cortiça expandida (PACE), obtida por aglutinação de cortiça em condições hidrotérmicas, a qual nos estudos preliminares revelou desempenho semelhante aos carvões ativados. Com exceção do benzo(ghi)perileno, os resultados mostram que o processo de adsorção dos HAPs na amostra PACE segue uma cinética de pseudo-segunda ordem e as isotérmicas ajustam-se ao modelo de Langmuir.

A study of electrochemical transport and diffuse charge dynamics using a Langevin equation

This thesis aims to develop new numerical and computational tools to study electrochemical transport and diffuse charge dynamics at small scales. Previous efforts at modeling electrokinetic phenomena at scales where the noncontinuum effects become significant have included continuum models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a Langevin equation for diffuse charge dynamics in nanofluidic devices, which incorporates features from both continuum and atomistic methods. The model is then extended to include steric effects resulting from finite ion size, and applied to the phenomenon of double layer charging in a symmetric binary electrolyte between parallel-plate blocking electrodes, between which a voltage is applied. Finally, the results of this approach are compared to those of the continuum model based on the Poisson-Nernst-Planck equations.

Knowledge about dietary fibres (KADF): development and validation of an evaluation instrument through structural equation modelling (SEM)

Objectives: Because there is scientific evidence that an appropriate intake of dietary fibre should be part of a healthy diet, given its importance in promoting health, the present study aimed to develop and validate an instrument to evaluate the knowledge of the general population about dietary fibres. Study design: The present study was a cross sectional study. Methods: The methodological study of psychometric validation was conducted with 6010 participants, residing in ten countries from 3 continents. The instrument is a questionnaire of self-response, aimed at collecting information on knowledge about food fibres. For exploratory factor analysis (EFA) was chosen the analysis of the main components using varimax orthogonal rotation and eigenvalues greater than 1. In confirmatory factor analysis by structural equation modelling (SEM) was considered the covariance matrix and adopted the Maximum Likelihood Estimation algorithm for parameter estimation. Results: Exploratory factor analysis retained two factors. The first was called Dietary Fibre and Promotion of Health (DFPH) and included 7 questions that explained 33.94 % of total variance ( = 0.852). The second was named Sources of Dietary Fibre (SDF) and included 4 questions that explained 22.46% of total variance ( = 0.786). The model was tested by SEM giving a final solution with four questions in each factor. This model showed a very good fit in practically all the indexes considered, except for the ratio 2/df. The values of average variance extracted (0.458 and 0.483) demonstrate the existence of convergent validity; the results also prove the existence of discriminant validity of the factors (r2 = 0.028) and finally good internal consistency was confirmed by the values of composite reliability (0.854 and 0.787). Conclusions: This study allowed validating the KADF scale, increasing the degree of confidence in the information obtained through this instrument in this and in future studies.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Parameterization of quasigeostrophic eddies in primitive equation ocean models

A parameterization of mesoscale eddy fluxes in the ocean should be consistent with the fact that the ocean interior is nearly adiabatic. Gent and McWilliams have described a framework in which this can be approximated in L-coordinate primitive equation models by incorporating the effects of eddies on the buoyancy field through an eddy-induced velocity. It is also natural to base a parameterization on the simple picture of the mixing of potential vorticity in the interior and the mixing of buoyancy at the surface. The authors discuss the various constraints imposed by these two requirements and attempt to clarify the appropriate boundary conditions on the eddy-induced velocities at the surface. Quasigeostrophic theory is used as a guide to the simplest way of satisfying these constraints.

Sequestering of Fe and Pb ions from Wastewater by Canarium schweinfurthii after carbonization and chemical treatment: Isothermal and Kinetic Modeling

In this paper agricultural waste; Canarium schweinfurthii was explored for the sequestering of Fe and Pb ions from wastewater solution after carbonization and chemical treatment at 400oC. Optimum time of 30 and 150 min with percentage removal of 95 and 98% at optimum pH of 2 and 6 was obtained for Fe and Pb ions. Kinetics model followed pseudofirst order as sum of absolute error (EABS) between Qe and Qc greater than that of pseudo second order. Parameters evaluated from isothermal equation (Freundlich and Langmuir) showed that KL and QO for Fe > Pb and R2 for Langmuir> Freundlich. The study reveals the suitability of the adsorbent for sequestering of Fe and Pb ions from industrial wastewater.

The Cambridge Equation with government activity revisited

Neste artigo faz-se uma análise das características distributivas do processo Kaldor-Pasinetti, assumindo-se que o setor governamental incorre em persistentes déficits que podem ser financiados através de diferentes instrumentos, como a emissão de títulos e de moeda. Através dessa abordagem é possível estudar como a atividade governamental afeta a distribuição de renda entre capitalistas e trabalhadores e assim obter generalizações do Teorema de Cambridge em que versões anteriores como as de Steedman (1972), Pasinetti (1989), Dalziel (1991) e Faria (2000) surgem como casos particulares. _________________________________________________________________________________ ABSTRACT

Removal of BrO3 − from drinking water samples using newly developed agricultural waste-based activated carbon and its determination by ultra-performance liquid chromatography-mass spectrometry

Activated carbon was prepared from date pits via chemical activation with H3PO4. The effects of activating agent concentration and activation temperature on the yield and surface area were studied. The optimal activated carbon was prepared at 450 °C using 55 % H3PO4. The prepared activated carbon was characterized by Fourier transform infrared spectroscopy, scanning electron microscopy, thermogravimetric-differential thermal analysis, and Brunauer, Emmett, and Teller (BET) surface area. The prepared date pit-based activated carbon (DAC) was used for the removal of bromate (BrO3 −). The concentration of BrO3 − was determined by ultra-performance liquid chromatography-mass tandem spectrometry (UPLC-MS/MS). The experimental equilibrium data for BrO3 − adsorption onto DAC was well fitted to the Langmuir isotherm model and showed maximum monolayer adsorption capacity of 25.64 mg g−1. The adsorption kinetics of BrO3 − adsorption was very well represented by the pseudo-first-order equation. The analytical application of DAC for the analysis of real water samples was studied with very promising results.

Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.