New variational principles for systems of partial differential equations

The question of finding variational principles for coupled systems of first order partial differential equations is considered. Using a potential representation for solutions of the first order system a higher order system is obtained. Existence of a variational principle follows if the original system can be transformed to a self-adjoint higher order system. Existence of variational principles for all linear wave equations with constant coefficients having real dispersion relations is established. The method of adjoining some of the equations of the original system to a suitable Lagrangian function by the method of Lagrange multipliers is used to construct new variational principles for a class of linear systems. The equations used as side conditions must satisfy highly-restrictive integrability conditions. In the more difficult nonlinear case the system of two equations in two independent variables can be analyzed completely. For systems determined by two conservation laws the side condition must be a conservation law in addition to satisfying the integrability conditions.

Part I. On the breaking of nonlinear dispersive waves. Part II. Variational principles in continuum mechanics

A model equation for water waves has been suggested by Whitham to study, qualitatively at least, the different kinds of breaking. This is an integro-differential equation which combines a typical nonlinear convection term with an integral for the dispersive effects and is of independent mathematical interest. For an approximate kernel of the form e^(-b|x|) it is shown first that solitary waves have a maximum height with sharp crests and secondly that waves which are sufficiently asymmetric break into "bores." The second part applies to a wide class of bounded kernels, but the kernel giving the correct dispersion effects of water waves has a square root singularity and the present argument does not go through. Nevertheless the possibility of the two kinds of breaking in such integro-differential equations is demonstrated.

Difficulties arise in finding variational principles for continuum mechanics problems in the Eulerian (field) description. The reason is found to be that continuum equations in the original field variables lack a mathematical "self-adjointness" property which is necessary for Euler equations. This is a feature of the Eulerian description and occurs in non-dissipative problems which have variational principles for their Lagrangian description. To overcome this difficulty a "potential representation" approach is used which consists of transforming to new (Eulerian) variables whose equations are self-adjoint. The transformations to the velocity potential or stream function in fluids or the scaler and vector potentials in electromagnetism often lead to variational principles in this way. As yet no general procedure is available for finding suitable transformations. Existing variational principles for the inviscid fluid equations in the Eulerian description are reviewed and some ideas on the form of the appropriate transformations and Lagrangians for fluid problems are obtained. These ideas are developed in a series of examples which include finding variational principles for Rossby waves and for the internal waves of a stratified fluid.

Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly

Algorithmic DNA tiles systems are fascinating. From a theoretical perspective, they can result in simple systems that assemble themselves into beautiful, complex structures through fundamental interactions and logical rules. As an experimental technique, they provide a promising method for programmably assembling complex, precise crystals that can grow to considerable size while retaining nanoscale resolution. In the journey from theoretical abstractions to experimental demonstrations, however, lie numerous challenges and complications.

In this thesis, to examine these challenges, we consider the physical principles behind DNA tile self-assembly. We survey recent progress in experimental algorithmic self-assembly, and explain the simple physical models behind this progress. Using direct observation of individual tile attachments and detachments with an atomic force microscope, we test some of the fundamental assumptions of the widely-used kinetic Tile Assembly Model, obtaining results that fit the model to within error. We then depart from the simplest form of that model, examining the effects of DNA sticky end sequence energetics on tile system behavior. We develop theoretical models, sequence assignment algorithms, and a software package, StickyDesign, for sticky end sequence design.

As a demonstration of a specific tile system, we design a binary counting ribbon that can accurately count from a programmable starting value and stop growing after overflowing, resulting in a single system that can construct ribbons of precise and programmable length. In the process of designing the system, we explain numerous considerations that provide insight into more general tile system design, particularly with regards to tile concentrations, facet nucleation, the construction of finite assemblies, and design beyond the abstract Tile Assembly Model.

Finally, we present our crystals that count: experimental results with our binary counting system that represent a significant improvement in the accuracy of experimental algorithmic self-assembly, including crystals that count perfectly with 5 bits from 0 to 31. We show some preliminary experimental results on the construction of our capping system to stop growth after counters overflow, and offer some speculation on potential future directions of the field.

The principles involved in a factory cost system

Successful management has been defined as the art of spending money wisely and well. Profits may not be the end and all of business but they are certainly the test of practicality. Everything worth while should pay for itself. One proposal is no better than another, except as in the working-out it yields better results.

First principles based multiparadigm modeling of electronic structures and dynamics

Electronic structures and dynamics are the key to linking the material composition and structure to functionality and performance.

An essential issue in developing semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band levels. Approximate DFT methods have been justified to predict band gaps from KS/GKS eigenvalues, but the accuracy is decisively dependent on the choice of XC functionals. We show here for CuInSe₂ and CuGaSe₂, the parent compounds of the promising CIGS solar cells, conventional LDA and GGA obtain gaps of 0.0-0.01 and 0.02-0.24 eV (versus experimental values of 1.04 and 1.67 eV), while the historically first global hybrid functional, B3PW91, is surprisingly the best, with band gaps of 1.07 and 1.58 eV. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a MAD of only 0.09 eV, which is substantially better than all modern hybrid functionals, including B3LYP (MAD of 0.19 eV) and screened hybrid functional HSE06 (MAD of 0.18 eV).

The laboratory performance of CIGS solar cells (> 20% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use the B3PW91 hybrid functional of DFT with the AEP method that we validate to provide very accurate descriptions of both band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the CBO of perfect CuInSe₂/CdS interface is large, 0.79 eV, which would dramatically degrade performance. Moreover we show that band gap widening induced by Ga adjusts only the VBO, and we find that Cd impurities do not significantly affect the CBO. Thus we show that Cu vacancies at the interface play the key role in enabling the tunability of CBO. We predict that Na further improves the CBO through electrostatically elevating the valence levels to decrease the CBO, explaining the observed essential role of Na for high performance. Moreover we find that K leads to a dramatic decrease in the CBO to 0.05 eV, much better than Na. We suggest that the efficiency of CIGS devices might be improved substantially by tuning the ratio of Na to K, with the improved phase stability of Na balancing phase instability from K. All these defects reduce interfacial stability slightly, but not significantly.

A number of exotic structures have been formed through high pressure chemistry, but applications have been hindered by difficulties in recovering the high pressure phase to ambient conditions (i.e., one atmosphere and room temperature). Here we use dispersion-corrected DFT (PBE-ulg flavor) to predict that above 60 GPa the most stable form of N₂O (the laughing gas in its molecular form) is a 1D polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03-0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions both polymers relax below 14 GPa to the same stable non-planar trans-polymer, accompanied by possible electronic structure transitions. The predicted phonon spectrum and dissociation kinetics validate the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a new type of conducting polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions.

Modeling non-adiabatic electron dynamics has been a long-standing challenge for computational chemistry and materials science, and the eFF method presents a cost-efficient alternative. However, due to the deficiency of FSG representation, eFF is limited to low-Z elements with electrons of predominant s-character. To overcome this, we introduce a formal set of ECP extensions that enable accurate description of p-block elements. The extensions consist of a model representing the core electrons with the nucleus as a single pseudo particle represented by FSG, interacting with valence electrons through ECPs. We demonstrate and validate the ECP extensions for complex bonding structures, geometries, and energetics of systems with p-block character (C, O, Al, Si) and apply them to study materials under extreme mechanical loading conditions.

Despite its success, the eFF framework has some limitations, originated from both the design of Pauli potentials and the FSG representation. To overcome these, we develop a new framework of two-level hierarchy that is a more rigorous and accurate successor to the eFF method. The fundamental level, GHA-QM, is based on a new set of Pauli potentials that renders exact QM level of accuracy for any FSG represented electron systems. To achieve this, we start with using exactly derived energy expressions for the same spin electron pair, and fitting a simple functional form, inspired by DFT, against open singlet electron pair curves (H₂ systems). Symmetric and asymmetric scaling factors are then introduced at this level to recover the QM total energies of multiple electron pair systems from the sum of local interactions. To complement the imperfect FSG representation, the AMPERE extension is implemented, and aims at embedding the interactions associated with both the cusp condition and explicit nodal structures. The whole GHA-QM+AMPERE framework is tested on H element, and the preliminary results are promising.

Photonic and Device Design Principles for Ultrahigh-Efficiency (>50%), Spectrum-Splitting Photovoltaics

The sun has the potential to power the Earth's total energy needs, but electricity from solar power still constitutes an extremely small fraction of our power generation because of its high cost relative to traditional energy sources. Therefore, the cost of solar must be reduced to realize a more sustainable future. This can be achieved by significantly increasing the efficiency of modules that convert solar radiation to electricity. In this thesis, we consider several strategies to improve the device and photonic design of solar modules to achieve record, ultrahigh (> 50%) solar module efficiencies. First, we investigate the potential of a new passivation treatment, trioctylphosphine sulfide, to increase the performance of small GaAs solar cells for cheaper and more durable modules. We show that small cells (mm2), which currently have a significant efficiency decrease (~ 5%) compared to larger cells (cm2) because small cells have a higher fraction of recombination-active surface from the sidewalls, can achieve significantly higher efficiencies with effective passivation of the sidewalls. We experimentally validate the passivation qualities of treatment by trioctylphosphine sulfide (TOP:S) through four independent studies and show that this facile treatment can enable efficient small devices. Then, we discuss our efforts toward the design and prototyping of a spectrum-splitting module that employs optical elements to divide the incident spectrum into different color bands, which allows for higher efficiencies than traditional methods. We present a design, the polyhedral specular reflector, that has the potential for > 50% module efficiencies even with realistic losses from combined optics, cell, and electrical models. Prototyping efforts of one of these designs using glass concentrators yields an optical module whose combined spectrum-splitting and concentration should correspond to a record module efficiency of 42%. Finally, we consider how the manipulation of radiatively emitted photons from subcells in multijunction architectures can be used to achieve even higher efficiencies than previously thought, inspiring both optimization of incident and radiatively emitted photons for future high efficiency designs. In this thesis work, we explore novel device and photonic designs that represent a significant departure from current solar cell manufacturing techniques and ultimately show the potential for much higher solar cell efficiencies.

Discurso e ensino: o curso de Letras e a formação docente

Esta tese tem por objetivo discutir a política científico-educacional do curso de Letras, por meio da análise do projeto político-pedagógico (PPP) que norteia a formação do acadêmico e do futuro professor de Língua Portuguesa. A compreensão de que toda esfera da atividade humana elabora os seus gêneros mais ou menos estáveis, segundo os quais os sujeitos se relacionam e interagem socialmente (BAKHTIN, 1997) é significativa, pois permite afirmar que o PPP é um documento norteador de uma política científico-educacional, podendo se manifestar nas práticas discursivas próprias da vida universitária de um curso. No PPP se delineiam, entre outros princípios, concepções filosófico-educacionais e abordagens teóricas e metodológicas que fundamentam o discurso científico-educacional e os saberes instituídos do curso de Letras. Em virtude disso, procurou-se traçar um percurso histórico das referências locais e globais, a partir de concepções sobre ser, tempo, acontecimento e alteridade, advindas do saber literário (BARTHES, 1992 e BAKHTIN, 2010) e da trajetória universitária em foco, articuladas à conjuntura que vem marcando o movimento por mudanças nas ciências e na educação. Investigou-se, em seguida, o PPP do curso de Letras, analisando esse gênero do discurso acadêmico-universitário, consoante a forma e tipo de interação em relação com a situação concreta de enunciação e com o horizonte histórico e social mais amplo (BAKHTIN/VOLOCHINOV, 1992), em que se configuram novos sentidos que convergem e/ou confrontam com discursos e saberes historicamente instituídos do curso. Refletiu-se, pois, se a introdução de novas disciplinas em estudos da linguagem resulta de uma transição consensual de uma Linguística do enunciado para uma Linguística da enunciação ou marca uma crise de paradigma(s) no âmbito da Linguística. Procedeu-se, por fim, a uma análise dos discursos dos acadêmicos de Letras da UFPA-Marabá, a fim de compreender os sentidos que constroem sobre o curso, sobre o projeto político-pedagógico, a imagem que constroem da instituição, de si mesmos, como acadêmicos e futuros professores de Língua Portuguesa. Objetivou-se, com isso, confrontar a política científico-educacional proposta pelo PPP com o discurso desses sujeitos, a fim de compreender seus posicionamentos diante da formação que permeia o projeto, bem como sua avaliação a respeito do discurso de integração curricular. Procurou-se, por fim, focalizar outras referências de cursos de Letras, com o objetivo de cotejar os posicionamentos de diferentes PPP em relação ao perfil que pretendem construir de professor de Língua Portuguesa, consoante o quadro curricular proposto em estudos da linguagem. Toma-se como córpus os PPPs dos Cursos de Letras do Câmpus Universitário de Marabá e de Belém, da Universidade Federal do Pará e, da Universidade Federal de Goiás (Câmpus de Catalão e Câmpus de Goiânia), para então compará-los com depoimentos escritos dos acadêmicos de Letras da UFPA-Marabá

As malhas da exclusão no projeto da escola inclusiva: relações de poder

O denominado Projeto Inclusivo nas escolas de Ensino Regular, embora desgastado na atualidade pelo seu uso excessivo sem a contrapartida governamental, bem como a de diversos setores da sociedade de ações efetivas , reflete problemáticas importantes de serem pensadas acerca da precarização e da desigualdade de suas condições. Para polemizar a formação escolar como um conjunto de relações marcadas por certos modos de inclusão/exclusão do educador e do aluno no processo de ensino-aprendizagem, implicados com a organização do trabalho e dos bens produzidos socialmente, este trabalho de pesquisa tentou abordar as condições em que o ensino acontece, circunscrevendo o tempo/espaço da constituição sócio-histórico-política da educação. Pensar as práticas educacionais é abraçar o desafio de deixar-se afetar por suas questões, potencializando acontecimentos. A questão é problematizar o Projeto Inclusivo e seus efeitos como formas de publicizar a vida e a produção dos critérios de organização político-pedagógica. Tornar público significa empoderar o outro de saber e ação, fazer circular as análises, tornar públicas as instituições (valores, critérios, princípios) em jogo para uma produção de conhecimento. O objetivo é fazer entrar nos diversos campos do cotidiano escolar uma nova micropolítica que abra as portas para as trocas, para a avaliação dos efeitos das práticas, potencializando intervenções efetivas.

Movimentos sociais, educação e cidadania: um estudo sobre os Cursos Pré-vestibulares populares

Este estudo, que constitui minha Dissertação de Mestrado em Educação, descreve e analisa a história, as concepções e as práticas político-pedagógicas dos Cursos Pré-Vestibulares Populares, tomando como base os dados colhidos através de análise de documentos, observação e depoimentos das principais lideranças do Movimento Pré-Vestibular para Negros e Carentes (PVNC), movimento criado em 1993 na Baixada Fluminense, Rio de Janeiro. O texto parte da discussão sobre a educação no atual contexto sócio-político, identifica questões a serem aprofundadas sobre a relação entre movimentos sociais, educação e projeto político-pedagógico, examina as idéias de democracia e cidadania, incorporando os conceitos de autonomia, identidade e interculturalismo, descreve a história dos Cursos Pré-Vestibulares Populares no Estado do Rio de Janeiro, os princípios e as práticas presentes no Pré-Vestibular para Negros e Carentes. O objetivo principal do estudo foi analisar a relação entre Movimentos Sociais, Cidadania e Educação, investigando a prática político-pedagógica dos cursos Pré-Vestibulares Populares, especificamente do Pré-Vestibular para Negros e Carentes. Além disso, e estudo tenta verificar as possibilidades dos Cursos Pré-Vestibulares Populares como movimento de construção de relações educacionais democráticas.