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.

The political econmoy of state government debt : an analysis of constitutional limitations (1961-1990)

Over the past decade, scholarly interest concerning the use of limitations to constrain government spending and taxing has noticeably increased. The call for constitutional restrictions can be credited, in part, to Washington's apparent inability to legislate any significant reductions in government expenditures or in the size of the national debt. At the present time, the federal government is far from instituting any constitutional limitations on spending or borrowing; however, the states have incorporated many controls on revenues and expenditures, the oldest being strictures on full faith and credit borrowing. This dissertations examines the efficacy of these restrictions on borrowing across the states (excluding Alaska) for the period dating from 1961 to 1990 and also studies the limitations on taxing and spending synonymous with the Tax Revolt.

We include socio-economic information in our calculations to control for factors other than the institutional variables that affect state borrowing levels. Our results show that certain constitutional restrictions (in particular, the referendum requirement and the dollar debt limit) are more effective than others. The apparent ineffectiveness of other limitations, such as the flexible debt limit, seem related to the bindingness of the limitations in at least half of the cases. Other variables, such as crime rates, number of schoolage children, and state personal income do affect the levels of full faith and credit debt, but not as strongly as the limitations. While some degree of circumvention can be detected (the amount of full faith and credit debt does inversely affect the levels of nonguaranteed debt), it is so small when compared to the effectiveness of the constitutional restrictions that it is almost negligible. The examination of the tax revolt era limitations yielded quite similar conclusions, with the additional fact that constitutional restrictions appear more binding than statutory ones. Our research demonstrates that constitutional limitations on borrowing can be applied effectively to constrain excessive borrowing, but caution must be used. The efficacy of these restrictions decrease dramatically as the number of loopholes increase.

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.

Contribuição para o planejamento brasileiro de exploração de petróleo e gás natural através da formulação de uma política nacional de uso sustentável das reservas de petróleo e gás natural

Petróleo e gás natural são recursos naturais não renováveis que possuem grande participação na matriz energética mundial e tendência de crescimento na matriz nacional, cujo marco regulatório limita-se a definir critérios técnicos e procedimentais sem incorporar o modelo de sustentabilidade instituído pela Constituição Federal de 1988. A natureza finita dos recursos não renováveis, como o petróleo e o gás natural, exige uma visão do planejamento de sua exploração de longo prazo na definição dos objetivos e metas. Essa perspectiva de longo prazo traduz uma das preocupações do desenvolvimento sustentável: a garantia de direitos para as futuras gerações. Assim, ao procurar fornecer elementos para a tradução do modelo de desenvolvimento sustentável no arcabouço institucional e legal da indústria petrolífera vigente no Brasil, o presente trabalho busca contribuir para o aprimoramento da regulação petrolífera nacional e a qualidade de vida das gerações presentes e futuras. E, mais do que propor a elaboração de um projeto de lei, como modalidade de implantação de uma política pública, queremos contribuir para o fortalecimento das práticas e ações governamentais voltadas para a aplicação do desenvolvimento sustentável, consoante apregoa a Constituição Federal brasileira. Trata-se aqui de demonstrar, através de metodologia quali-quantitativa, a tese de que é possível incorporar o princípio constitucional de desenvolvimento sustentável na atividade de exploração e produção de petróleo e gás natural, formulando uma política pública que incorpore, no regime de propriedade do petróleo, a variável ambiental e o uso intergeracional que já haviam sido e continuam sendo aplicados a algumas fontes renováveis de energia. Inicialmente, identificamos a composição da matriz energética brasileira desde a inserção do petróleo como uma questão de Estado a partir dos anos 50 do século XX. Em seguida, analisamos a concepção legal e doutrinária para propor, então, a conceituação de um modelo de desenvolvimento energético sustentável, estruturante para a proposição de uma política nacional para a indústria petrolífera. Com base nessa conceituação, analisamos o marco regulatório e os procedimentos institucionais praticados atualmente para identificar as lacunas existentes no ordenamento a serem supridas pela política nacional proposta. A partir da análise dos contextos legal e institucional, e das políticas energética e ambiental, propomos a tradução de conceitos, objetivos, princípios e instrumentos num projeto de lei de Política Nacional de Uso Sustentável das Reservas de Petróleo e Gás Natural. Concluímos tecendo considerações gerais e específicas sobre a proposição aqui formulada com vistas ao aprimoramento do modelo nacional de gestão de recursos energéticos e ao fomento das discussões voltadas para a sustentabilidade das políticas públicas e as práticas privadas enraizadas na exploração irracional de recursos não renováveis

O argumento pragmático ou consequencialista de cunho econômico e a modulação temporal dos efeitos das decisões do Supremo Tribunal Federal em matéria tributária

A tese analisa a relação íntima que há entre o pragmatismo ou o conseqüencialismo e a modulação temporal dos efeitos das decisões judiciais. Nesta relação, interessa ressaltar o ponto de interseção que certamente sobressai em várias ocasiões: o argumento de cunho econômico. Tal tipo de argumento pode assumir especial relevo quando do exame da oportunidade e conveniência na tomada das decisões eminentemente políticas. No âmbito jurisdicional, no entanto, o argumento pragmático ou consequencialista de cunho econômico não deve prevalecer como fundamento das decisões judiciais, especialmente cuidando-se de matéria tributária. Os problemas que centralizam o estudo podem ser colocados através das seguintes indagações: é possível que o Supremo Tribunal Federal compute, no julgamento de certa matéria tributária, argumento como o eventual rombo de X bilhões de reais que a decisão contrária ao Fisco possa acarretar para os cofres públicos? A fundamentação de eventual decisão judicial calcada exclusiva ou predominantemente em tal argumento é legítima ou ilegítima? Que importância pode ter na tomada de decisão judicial? Quando aplicada, há parâmetros a serem seguidos? Quais? Demonstramos que a prevalência de tal argumento é inadequada na seara judicial, ou seja, deve ter peso reduzido ou periférico, servindo para corroborar ou reforçar os argumentos jurídicos que centralizam o debate submetido ao exame do Poder Judiciário de modo geral, e do Supremo Tribunal Federal, de maneira particular. Em busca de esclarecer quais os principais limites e possibilidades de tal argumento, especialmente relacionando-o à modulação temporal dos efeitos da decisão judicial, explicitamos algumas regras necessárias para a sua adequada utilização, sob pena de inconcebível subversão de variados princípios e direitos fundamentais assegurados em sede constitucional. No exame das questões submetidas à apreciação da Corte Suprema em matéria tributária, o seu parâmetro consiste na maior efetividade e concretude ao texto constitucional. A modulação temporal dos efeitos se aplica a uma decisão que, declarando a inconstitucionalidade do ato normativo, se afastaria ainda mais da vontade constitucional, caso fosse aplicado o tradicional efeito ex tunc (retroativo até o nascimento da lei). Nestas situações específicas e excepcionais se justifica aplicar a modulação, com vistas a dar maior concretude e emprestar maior eficácia à Constituição. A tese proposta, ao final, consiste na reunião das regras explicitadas no trabalho e em proposta legislativa.

Propriedade rural, posse e meio ambiente: uma ponderação harmoniosa

A presente tese tem por objetivo defender, sob a visão do direito civil-constitucional e da função promocional do direito, a inter-relação entre os direitos de posse, propriedade e do meio ambiente e a possibilidade de uma ponderação harmoniosa em caso de desequilíbrio entre esses direitos. Utiliza-se para tanto a dimensão analítica, empírica e normativa. A dimensão analítica tem por objetivo investigar os conceitos jurídicos envolvidos na pesquisa, especialmente em relação à propriedade e à sua função socioambiental. A relação entre tais conceitos sobressai através da análise da função socioambiental da propriedade, da posse enfatizando-se os aspectos da legislação ambiental. O direito fundamental ao meio ambiente é estudado como direito e dever de todos conforme disposto no art. 225 da Constituição de 1988, e, nesse ponto, diretamente eficaz nas relações interprivadas. Aborda-se, na dimensão empírica e normativa essencialmente aspectos práticos, com foco na jurisprudência, especialmente do Supremo Tribunal Federal (STF) e do Superior Tribunal de Justiça (STJ). A ponderação harmoniosa entre a propriedade, a posse e o meio ambiente, busca o equilíbrio na efetivação desses direitos, inclusive mediante a aplicação dos princípios do direito econômico. Por meio da ponderação, é possível alcançar, de forma mais eficiente do que o modelo tradicional de subsunção, uma resposta adequada e fundamentada para os casos difíceis, especialmente na efetivação e na restauração do equilíbrio entre a posse, a propriedade e o meio ambiente quando esses princípios, no caso concreto, colidem uns com os outros. Sobretudo, pretende-se concretizar os direitos fundamentais segundo exigências do pós-positivismo, por meio da aproximação entre o Direito e a Ética, com o fim de se alcançar a Justiça para o caso concreto.

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.

Aplicação da pena privativa de liberdade e o dever jurídico-constitucional de minimização da afetação individual: uma nova proposta discursiva

Investiga se o atual modelo de aplicação da pena privativa de liberdade se mostra adequado aos parâmetros traçados pela constituição de 1988, atendendo ao fundamento da dignidade da pessoa humana e aos objetivos fundamentais de construção de uma sociedade livre, justa e solidária e de promoção do bem de todos. Analisa a dinâmica histórica da aplicação e das teorias das penas privativas de liberdade no Brasil, abordando os principais critérios e atuais orientações da aplicação penal. Sustenta que a dignidade da pessoa humana constitui fundamento do Estado Republicano e Democrático de Direito brasileiro e que, ao lado do princípio da humanidade das penas, seu correspondente penal, fundamenta a necessidade de se evitar ao máximo que os indivíduos sejam afetados pela intervenção do poder punitivo. Conclui, então, pela existência de um autêntico dever jurídico-constitucional da agência judicial no sentido de minimizar a intensidade de afetação do indivíduo sentenciado. Procura erigir novos princípios quanto à aplicação da pena, dotados de força normativa e que atuem de maneira integrada para a tutela dos direitos fundamentais. Defende que a Constituição de 1988 não incorporou o discurso legitimador da pena, limitando-se à tarefa de contenção de danos e de fixação de limites punitivos. Preconiza novos parâmetros para a fixação da pena-base, sustentando a incompatibilidade constitucional das finalidades de reprovação e prevenção do crime. Debate qual deve ser o adequado sentido constitucional das circunstâncias judiciais da pena. Discute as bases da tendência exasperadora da pena, caracterizada pelas agravantes, qualificadoras e causas de aumento, assim como da tendência mitigadora da pena, representada pelas atenuantes, causas de diminuição, participação de agentes, tentativa, concurso de crimes, crime continuado, unificação e limite de penas. Identifica a existência de crise no dogma da pena mínima, propondo, afinal, a construção de um novo modelo interpretativo de aplicação da pena privativa de liberdade.