Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.

Approximate analytical description for fundamental-mode fields of graded-index fibers: Beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

TRANSFER OF ANALYTICAL METHODS FOR THE CHARACTERISATION OF NATURAL PRODUCTS TO R&D PROCESSES OF IDOKI

IDOKI SCF Technologies S.L. is a technology-based company, set up on September 2006 in Derio (Biscay) with the main scope of developing extraction and purification processes based on the use of supercritical fluid extraction technology (SFE) in food processing, extraction of natural products and the production of personal care products. IDOKI¿s researchers have been working on many different R&D projects so far, most of them using this technology. However, the optimization of a SFE method for the different matrices cannot be performed unless we have an analytical method for the characterisation of the extracts obtained in each experiment. The analytical methods are also essential for the quality control of the raw materials that are going to be used and also for the final product. This PhD thesis was born to tackle this problem and therefore, it is based on the development of different analytical methods for the characterisation of the extracts and products. The projects that we could include in this thesis were the following: the extraction propolis, the recovery of agroindustrial residues (soy and wine) and the dealcoholisation of wine.On the one hand, for the extraction of propolis, several UV-Vis spectroscopic methods were used in order to measure the antioxidant capacity and the total polyphenol and flavonoid content of the extracts. A SFC method was also developed in order to measure more specific phenolic compounds. On the other hand, for the recovery of agroindustrial residues UV-Vis spectroscopy was used to determine the total polyphenol content and two SFC methods were developed to analyse different phenolic compounds. Extraction methods such as MAE, FUSE and rotary agitation were also evaluated for the characterisation of the raw materials.Finally, for the dealcoholisation of wine, the development of a SBSE-TD-GC-MS and DHS-TD-GC-MS methods for the analysis of aromas and a NIR spectroscopic method for the determination of ethanol content with the help of chemometrics was necessary. Most of these methods are typically used in IDOKI¿s lab as routine analyses apart from others not included in this PhD thesis.

The analytical description and experiments of the optical bottle generated by an axicon and a lens

Based on the interferential theory, we deduce a new type of analytic expression suitable for describing the evolutions of the optical bottle beam generated from the axicon-lens optical system illuminated by the Gaussian beam for the first time. The theory does not use much approximation in the process of mathematical analysis and can better illustrate the optical bottle beam evolutions at any positions. With the derived expression, the three-dimensional (3D) longitudinal and transverse intensity profiles of the optical bottle beam are simulated numerically. The numerical calculations have been confirmed by the experimental results.

Judgmental-analytical procedures for adapting tests: Adaptation to Spanish of the Reasoning Tests Battery

Adapting a test between cultures or languages requires taking into account legal, linguistic, metric, and use-related considerations. Significantly more attention has been paid to the methodological aspects involved in the study of metric equivalence than to judgmental-analytical procedures prior to the empirical confirmation stage. However, considering the latter is crucial in the adaptation process. Along these lines, this paper seeks to describe and focus on the relevance of the previous stages, thereby offering a systematization process that comprises ten sections. This approach contributes to ensuring the construction of a test adapted and equivalent in as much as possible to the original. This process is exemplified by means of a Spanish language adaptation of a cognitive test originally designed in Portuguese for the Portuguese population, the Reasoning Test Battery. Copyright (C) 2013, Konrad Lorenz University Foundation. Published by Elsevier Espana, S.L.U.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation. (c) 2008 Optical Society of America.

Uma abordagem integrativa do conceito de Eco-eficiência: elementos para a concepção de Sistemas de Gestão de Resíduos Sólidos Industriais em Arranjos Produtivos Locais Têxtil-Vestuário

A identificação e avaliação das vulnerabilidades e potencialidades socioambientais e socioecológicas, ao considerar as múltiplas realidades de ecossistemas, territórios e lugares, podem revelar novos caminhos, ações coletivas, solidárias, bem como auxiliar na tomada de decisão estratégica em sistemas de gestão de resíduos sólidos. Tal perspectiva, qualificaria princípios e conceitos metodológicos e técnicos, como aqueles direcionados a responder aos problemas que surgem da interação Humanidade-Sociedade-Natureza, com vistas à sustentabilidade. A Eco-eficiência, ao final do século XX, apresentou-se como solução para os problemas ambientais corporativos. Idealizada para ser aplicada em um empresas isolada, evoluiu para uma categoria central da Ecologia Industrial, ganhou contornos de Princípio e Filosofia para a Gestão Ambiental Empresarial, passando a orientar a geopolítica das nações no trato das questões ambientais supranacionais e políticas públicas das nações. A recente Política Nacional de Resíduos Sólidos apresenta a Eco-eficiência como um de seus princípios que deverão orientar gestores públicos e privados na elaboração de seus sistemas de gestão de resíduos sólidos. Devido aos impactos sociais, ambientais e ecológicos resultantes da geração e destinação inadequada dos resíduos sólidos, estes sistemas de gestão apresentam interfaces com outras políticas e sistemas de gestão públicos e privados nacionais. Estas interações conferem ao sistema de gestão de resíduos sólidos um caráter complexo, aberto, dinâmico e inclusivo, no qual o conceito de Eco-eficiência, baseado na alocação de recursos naturais, pode ser ressignificado em um outro nível de realidade, o nível coletivo, apresentando-se, como um conceito potencial voltado para a criação de recursos. Para corroborar esta hipótese apresenta-se uma abordagem integrativa com base na perspectiva socioecológica e no pensamento e metodologia transdisciplinar, na qual o conceito será contextualizado, problematizado e complexificado em seis níveis de realidade: Nível Genus-Global, Nível Político, Nível Acadêmico, Nível do Ecossistema, Território e Lugares, Nível Operacional e Nível Coletivo. Considera-se nesta abordagem os Arranjos Produtivos (indústrias e a Cadeia de Reciclagem), Arranjos Sociais (Comunidade localizadas e áreas de risco e precárias), Ecossistemas e Territórios, como Teia de Lugares, como Unidade Transdisciplinar perceptiva, cognitiva e analítica. A aplicação desta metodologia no Arranjo Produtivo Local Têxtil- Vestuário de Petrópolis, localizado na Região Serrana Fluminense, que se insere em um Ecossistema de Montanha, permitiu revelar outro Arranjo, invisível ao sistema de gestão público. Neste Arranjo de Retalhos e Estopas, cerca de 240 mulheres, residentes em comunidades precárias e de risco, beneficiam os resíduos sólidos gerados pelas indústrias do arranjo formal, conhecidos como retalhos, com os quais fabricam estopas. Conclui-se que esta abordagem integrativa, como proposta de ressignificação do conceito de Eco-eficiência, permitiu revelar, não somente uma nova realidade conceitual para a sua adoção e prática, como novos aspectos e variáveis para a construção de sistemas de gestão de resíduos sólidos industriais que tenham por foco a inclusão social, produtiva, cientifica e tecnológica de novos atores e recursos ao sistema.

Analytical method development for the uptake study of different organic pollutants by crops cultivated in compost-amended soils

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A relação entre o principio de razão suficiente e o principio da contradição em Leibniz

De acordo com Leibniz, nossos raciocínios estão fundados em dois grandes princípios, o Princípio de Razão Suficiente e o Princípio de Contradição. Apesar da reconhecida relevância de tais princípios para sua filosofia, muitas são as interpretações sobre o real papel que eles desempenham dentro dela e sobre a relação deles entre si. Nosso estudo pauta-se não só pela interpretação de Leibniz como pela visão de alguns de seus comentadores, especialmente três deles: Russell, Couturat e Deleuze. Iremos pesquisar, entre outras coisas, se tais princípios são independentes um do outro; se são aplicáveis a todo tipo de verdade; se o Princípio de Perfeição é uma particularização do Princípio de Razão Suficiente ou se é irredutível a ele; e se as verdades da razão são regidas pelo Princípio de Contradição e as verdades de fato são regidas pelo Princípio de Razão Suficiente. A articulação entre tais princípios remete a um terceiro ponto: a concepção da verdade como inclusão do conceito do predicado no sujeito, tema este que iremos analisar com base nos diferentes pontos de vista acerca das proposições essenciais e existenciais. Em relação a esta última, investigaremos se representam ou não uma exceção ao caráter analítico de todas as proposições verdadeiras.