Some problems in nonlinear elasticity

Two separate problems are discussed: axisymmetric equilibrium configurations of a circular membrane under pressure and subject to thrust along its edge, and the buckling of a circular cylindrical shell.

An ordinary differential equation governing the circular membrane is imbedded in a family of n-dimensional nonlinear equations. Phase plane methods are used to examine the number of solutions corresponding to a parameter which generalizes the thrust, as well as other parameters determining the shape of the nonlinearity and the undeformed shape of the membrane. It is found that in any number of dimensions there exists a value of the generalized thrust for which a countable infinity of solutions exist if some of the remaining parameters are made sufficiently large. Criteria describing the number of solutions in other cases are also given.

Donnell-type equations are used to model a circular cylindrical shell. The static problem of bifurcation of buckled modes from Poisson expansion is analyzed using an iteration scheme and pertubation methods. Analysis shows that although buckling loads are usually simple eigenvalues, they may have arbitrarily large but finite multiplicity when the ratio of the shell's length and circumference is rational. A numerical study of the critical buckling load for simple eigenvalues indicates that the number of waves along the axis of the deformed shell is roughly proportional to the length of the shell, suggesting the possibility of a "characteristic length." Further numerical work indicates that initial post-buckling curves are typically steep, although the load may increase or decrease. It is shown that either a sheet of solutions or two distinct branches bifurcate from a double eigenvalue. Furthermore, a shell may be subject to a uniform torque, even though one is not prescribed at the ends of the shell, through the interaction of two modes with the same number of circumferential waves. Finally, multiple time scale techniques are used to study the dynamic buckling of a rectangular plate as well as a circular cylindrical shell; transition to a new steady state amplitude determined by the nonlinearity is shown. The importance of damping in determining equilibrium configurations independent of initial conditions is illustrated.

Studies of ambient and chamber aerosol composition using the aerosol mass spectrometer

This thesis presents composition measurements for atmospherically relevant inorganic and organic aerosol from laboratory and ambient measurements using the Aerodyne aerosol mass spectrometer. Studies include the oxidation of dodecane in the Caltech environmental chambers, and several aircraft- and ground-based field studies, which include the quantification of wildfire emissions off the coast of California, and Los Angeles urban emissions.

The oxidation of dodecane by OH under low NO conditions and the formation of secondary organic aerosol (SOA) was explored using a gas-phase chemical model, gas-phase CIMS measurements, and high molecular weight ion traces from particle- phase HR-TOF-AMS mass spectra. The combination of these measurements support the hypothesis that particle-phase chemistry leading to peroxyhemiacetal formation is important. Positive matrix factorization (PMF) was applied to the AMS mass spectra which revealed three factors representing a combination of gas-particle partitioning, chemical conversion in the aerosol, and wall deposition.

Airborne measurements of biomass burning emissions from a chaparral fire on the central Californian coast were carried out in November 2009. Physical and chemical changes were reported for smoke ages 0 – 4 h old. CO₂ normalized ammonium, nitrate, and sulfate increased, whereas the normalized OA decreased sharply in the first 1.5 - 2 h, and then slowly increased for the remaining 2 h (net decrease in normalized OA). Comparison to wildfire samples from the Yucatan revealed that factors such as relative humidity, incident UV radiation, age of smoke, and concentration of emissions are important for wildfire evolution.

Ground-based aerosol composition is reported for Pasadena, CA during the summer of 2009. The OA component, which dominated the submicron aerosol mass, was deconvolved into hydrocarbon-like organic aerosol (HOA), semi-volatile oxidized organic aerosol (SVOOA), and low-volatility oxidized organic aerosol (LVOOA). The HOA/OA was only 0.08–0.23, indicating that most of Pasadena OA in the summer months is dominated by oxidized OA resulting from transported emissions that have undergone photochemistry and/or moisture-influenced processing, as apposed to only primary organic aerosol emissions. Airborne measurements and model predictions of aerosol composition are reported for the 2010 CalNex field campaign.

On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

Conformal geometry processing

This thesis introduces fundamental equations and numerical methods for manipulating surfaces in three dimensions via conformal transformations. Conformal transformations are valuable in applications because they naturally preserve the integrity of geometric data. To date, however, there has been no clearly stated and consistent theory of conformal transformations that can be used to develop general-purpose geometry processing algorithms: previous methods for computing conformal maps have been restricted to the flat two-dimensional plane, or other spaces of constant curvature. In contrast, our formulation can be used to produce---for the first time---general surface deformations that are perfectly conformal in the limit of refinement. It is for this reason that we commandeer the title Conformal Geometry Processing.

The main contribution of this thesis is analysis and discretization of a certain time-independent Dirac equation, which plays a central role in our theory. Given an immersed surface, we wish to construct new immersions that (i) induce a conformally equivalent metric and (ii) exhibit a prescribed change in extrinsic curvature. Curvature determines the potential in the Dirac equation; the solution of this equation determines the geometry of the new surface. We derive the precise conditions under which curvature is allowed to evolve, and develop efficient numerical algorithms for solving the Dirac equation on triangulated surfaces.

From a practical perspective, this theory has a variety of benefits: conformal maps are desirable in geometry processing because they do not exhibit shear, and therefore preserve textures as well as the quality of the mesh itself. Our discretization yields a sparse linear system that is simple to build and can be used to efficiently edit surfaces by manipulating curvature and boundary data, as demonstrated via several mesh processing applications. We also present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces.

Optimal scaling in ductile fracture

This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. We also put forth a physical argument that identifies the intrinsic length and suggests a linear growth of the nonlocal energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, i.e., it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material. Next, we present an experimental assessment of the optimal scaling laws. We show that when the specific fracture energy is renormalized in a manner suggested by the optimal scaling laws, the data falls within the bounds predicted by the analysis and, moreover, they ostensibly collapse---with allowances made for experimental scatter---on a master curve dependent on the hardening exponent, but otherwise material independent.

Chemical-scale studies of G protein-coupled receptors and ligand-gated ion channels

This dissertation describes studies of G protein-coupled receptors (GPCRs) and ligand-gated ion channels (LGICs) using unnatural amino acid mutagenesis to gain high precision insights into the function of these important membrane proteins.

Chapter 2 considers the functional role of highly conserved proline residues within the transmembrane helices of the D2 dopamine GPCR. Through mutagenesis employing unnatural α-hydroxy acids, proline analogs, and N-methyl amino acids, we find that lack of backbone hydrogen bond donor ability is important to proline function. At one proline site we additionally find that a substituent on the proline backbone N is important to receptor function.

In Chapter 3, side chain conformation is probed by mutagenesis of GPCRs and the muscle-type nAChR. Specific side chain rearrangements of highly conserved residues have been proposed to accompany activation of these receptors. These rearrangements were probed using conformationally-biased β-substituted analogs of Trp and Phe and unnatural stereoisomers of Thr and Ile. We also modeled the conformational bias of the unnatural Trp and Phe analogs employed.

Chapters 4 and 5 examine details of ligand binding to nAChRs. Chapter 4 describes a study investigating the importance of hydrogen bonds between ligands and the complementary face of muscle-type and α4β4 nAChRs. A hydrogen bond involving the agonist appears to be important for ligand binding in the muscle-type receptor but not the α4β4 receptor.

Chapter 5 describes a study characterizing the binding of varenicline, an actively prescribed smoking cessation therapeutic, to the α7 nAChR. Additionally, binding interactions to the complementary face of the α7 binding site were examined for a small panel of agonists. We identified side chains important for binding large agonists such as varenicline, but dispensable for binding the small agonist ACh.

Chapter 6 describes efforts to image nAChRs site-specifically modified with a fluorophore by unnatural amino acid mutagenesis. While progress was hampered by high levels of fluorescent background, improvements to sample preparation and alternative strategies for fluorophore incorporation are described.

Chapter 7 describes efforts toward a fluorescence assay for G protein association with a GPCR, with the ultimate goal of probing key protein-protein interactions along the G protein/receptor interface. A wide range of fluorescent protein fusions were generated, expressed in Xenopus oocytes, and evaluated for their ability to associate with each other.

Recent progress in femtosecond holography

The recent advancements of femtosecond (fs) holography are introduced. The experimental requirements and the time resolution are presented. Applications of femtosecond holography to signal processing, and other femtosecond holographic techniques such as femtosecond holographic imaging and microprocessing are detailed. A potential alternative of femtosecond holography is proposed, based on the sectional interference of reference pulse with the time stretched signal pulse. (c) 2005 Elsevier B.V. All rights reserved.

Optimization of positions and currents of tokamak poloidal field coils using genetic algorithms

Plasma equilibrium geometry has a great influence on the confinement and magnetohydrodynamic stability in tokamaks. The poloidal field (PF) system of a tokamak should be optimized to support the prescribed plasma equilibrium geometry. In this paper, a genetic algorithm-based method is applied to solve the optimization of the positions and currents of tokamak PF coils. To achieve this goal, we first describe the free-boundary code EQT Based on the EQT code, a genetic algorithm-based method is introduced to the optimization. We apply this new method to the PF system design of the fusion-driven subcritical system and plasma equilibrium geometry optimization of the Experimental Advanced Superconducting Tokamak (EAST). The results indicate that the optimization of the plasma equilibrium geometry can be improved by using this method.

O agravamento do risco no contrato de seguro

Este trabalho objetivou demonstrar o que é e quais os requisitos adotados pela doutrina e pela jurisprudência para que seja aplicado o instituto do agravamento do risco (previsto nos artigos 768 e 769 do Código Civil) nos contratos de seguro, e quais os seus efeitos jurídicos. Para tanto, examinou-se o contrato de seguro buscando revelar a dimensão coletiva que este tipo negocial possui por excelência, em detrimento de parte da doutrina ainda restrita a uma leitura atomística e individualista deste contrato. Partiu-se, ainda, da premissa de que a boa-fé (seja na sua acepção objetiva ou subjetiva) é qualificada no contrato de seguro, eis que este tipo contratual é todo sob ela estruturado. O princípio da boa-fé é uma via de mão dupla que cria deveres para ambas as partes, cujas declarações e comportamentos serão fundamentais para a delimitação do objeto do seguro e para o alcance da função social desse tipo contratual. A boa-fé estará, ainda, incisivamente presente e modelando a relação obrigacional do seguro em todas as fases contratuais: antes da conclusão do contrato, na apresentação da proposta do contrato; durante a relação obrigacional, nas declarações necessárias sobre eventuais alterações no risco (tais como o seu agravamento), e, ainda, na fase pós-contratual, sempre considerando a natureza comunitária do seguro. Passou-se, também, por algumas questões polêmicas envolvendo a utilização de determinadas cláusulas no seguro, tidas como contrárias à boa-fé, a exemplo da cláusula perfil, cuja validade deve ser avaliada no caso concreto, e possui íntima relação com o agravamento do risco.

Combustion of CS₂/O₂ in a laminar mixing layer and processes in the CO chemical laser

The combustion of CS₂ and O₂ in a free burning laminar mixing layer at low pressure was investigated using emission spectroscopy. The temperature fields, CO vibrational distributions, and CO concentrations were measured. The data indicate that vibration ally excited CO was produced in the mixing layer flames, but that there were no vibrational population inversions. In comparison with the CS₂/O₂ premixed flames, the mixing layer flames favored greater production of COS and CO₂. Computer modeling was used to study the mechanisms responsible for the production of COS and CO₂, and to study how the branching chain mechanism responsible for production of CO affects the behavior of the mixing layer flame. The influences of the gas additives, N₂O, COS, and CNBr, were also investigated.

Efetividade da aplicação semestral de verniz fluoretado no controle da cárie dentária em pré-escolares: resultados após 12 meses de acompanhamento

O presente estudo teve como objetivos avaliar se a aplicação de verniz fluoretado com periodicidade semestral em crianças pré-escolares reduz o número de crianças com lesões de cárie em dentina na dentição decídua, diminui a incidência de lesões de cárie em esmalte e dentina, está inversamente associado à ocorrência de dor e abscesso dentário e produz quaisquer efeitos adversos. A população de estudo consistiu de 200 crianças na faixa etária de 12 a 48 meses, recrutadas em uma unidade de saúde pública da cidade do Rio de Janeiro, as quais foram alocadas aleatoriamente nos grupos teste (verniz fluoretado Duraphat) e controle (verniz placebo). Para o registro da incidência de cárie, as crianças foram examinadas na linha de base e a cada seis meses, durante um ano, por dois odontopediatras previamente treinados e calibrados (Kappa=0,85). A ocorrência de dor, abscesso e efeitos adversos foi verificada a partir de entrevistas com os responsáveis. Os participantes, os seus responsáveis, os operadores e os examinadores desconheciam a qual grupo cada criança pertencia. No final do período de acompanhamento, 71 crianças do grupo teste e 77 do grupo controle foram avaliadas. Constatou-se que, nos grupos teste e controle, o número de crianças com novas lesões de cárie em dentina foi igual a 13 e 20 (teste Qui-quadrado, p=0,34) e que a média do incremento de cárie considerando apenas lesões em dentina (c3eos) foi de 1,1(dp=3,4) e de 1,4(dp=2,8), respectivamente (teste de Mann-Whitney, p=0,29). Uma criança apresentou dor de dente e abscesso dentário e outras duas crianças apresentaram apenas dor de dente. Todas pertenciam ao grupo teste. Com relação aos efeitos adversos, encontrou-se que uma criança pertencente ao grupo controle relatou ardência na cavidade bucal após a aplicação do placebo e que o responsável por um participante do grupo teste sentiu-se incomodado com a coloração amarelada dos dentes da criança após a aplicação do verniz fluoretado. Concluiu-se que a aplicação de verniz fluoretado com periodicidade semestral em crianças pré-escolares é segura e parece contribuir para o controle da progressão de cárie. Contudo, é necessário um período de acompanhamento mais longo para se obter evidência conclusiva a respeito da efetividade dessa intervenção. Não houve associação entre a ocorrência de dor e abscesso dentário e o uso profissional do verniz fluoretado.

A report on increasing the thrust of a turbojet engine by combustion of fuel in the tail pipe

The purpose of this work was to develop a means of increasing the thrust of a turbojet engine by burning kerosene in the tail pipe.

A combustion system was developed which gave the following results:
(l) Maximum thrust increase using a G.E. I-14 engine was 64 per cent over straight tail pipe thrust corresponding to 42 per cent increase over the normal engine thrust. This increase was accomplished at an engine rpm of 12,000.
(2) Increase of maximum thrust obtained was 51 per cent over the straight tail pipe thrust corresponding to 23 per cent over the normal engine thrust. This increase was accomplished at an engine rpm of l6,000.
(3) For the thrust increases mentioned in (1) and (2) above, increases of Specific Fuel Consumption were 66 per cent and 76 per cent respectively over normal engine SFC.

A GIS-based model of soil erosion and transport

Soil erosion is a natural process that occurs when the force of wind, raindrops or running water on the soil surface exceeds the cohesive forces that bind the soil together. In general, vegetation cover protects the soil from the effects of these erosive forces. However, land management activities such as ploughing, burning or heavy grazing may disturb this protective layer, exposing the underlying soil. The decision making process in rural catchment management is often supported by the predictive modelling of soil erosion and sediment transport processes within the catchment, using established techniques such as the Universal Soil Loss Equation [USLE] and the Agricultural Nonpoint Source pollution model [AGNPS]. In this article, the authors examine the range of erosion models currently available and describe the application of one of these to the Burrishoole catchment on the north-west coast of Ireland, which has suffered heavy erosion of blanket peat in recent years.

O estresse no trabalho dos Agentes Comunitários de Saúde do Município do Rio de Janeiro

O estudo das dimensões psicossociais do trabalho tem aumentado em importância nas últimas décadas, devido ao novo contexto político e econômico mundial de globalização, que determina mudanças no mundo do trabalho e expõe trabalhadores a fatores de risco ocupacional, entre eles o estresse. A categoria profissional do Agente Comunitário de Saúde (ACS), criada no contexto das reformas sanitárias atravessadas pelo Brasil desde a década de 80, tem como um dos principais propósitos atuar na reorganização do sistema de saúde do país. O ACS tem como especificidade e pré-requisitos a necessidade de ser morador da região atendida pela Equipe de Saúde da Família, fato este responsável por um aspecto único dentro do estudo na área de saúde do trabalhador. Nesse cenário o enfermeiro exerce papel de liderança e possui uma característica marcante, que é a manutenção de constante contato com a comunidade, realizando atividades de grande interação com os ACS, devendo evitar ou minimizar fatores estressores e possíveis agravos à saúde no âmbito da Saúde do Trabalhador. O presente estudo tem como objeto o trabalho do ACS como gerador de estresse ocupacional no Programa de Saúde da Família. Tem como objetivo geral discutir o estresse ocupacional na percepção dos ACS no PSF, numa Área Programática do Município do Rio de Janeiro. Trata-se de um estudo descritivo e de abordagem qualitativa. O cenário do estudo foram Unidades de Saúde da Família do Município do Rio de Janeiro, e os sujeitos 32 ACS inseridos em três módulos do PSF. A coleta de dados foi realizada através de entrevistas individuais semi-estruturadas, organizadas e analisadas utilizando a metodologia da Análise de Conteúdo, a partir da qual foram identificadas as seguintes categorias: frustração, trabalho do ACS, representação do trabalho, processo de trabalho, o estresse e relação trabalho x saúde. Os resultados identificam o baixo reconhecimento interferindo na produtividade e na auto-estima, excessiva intensidade e ritmo empregados no trabalho, valorização da burocracia na execução do trabalho, violência como fator de insegurança e reconhece a interferência do estresse na saúde tanto física quanto psíquica. A análise do trabalho do ACS atuante no PSF aponta aspectos que dificultam sua plena atuação, assim como a prática estende-se para além dos conceitos normatizados contidos nas Portarias e outros instrumentos que regulamentam suas atribuições. O trabalho real representa um universo mais complexo e rico do que o trabalho prescrito, que nesse estudo, apresentou-se como fonte geradora de tensão, adoecimento e mal estar, expresso nas vocalizações de queixas.

Characterization and modeling of premixed turbulent n-heptane flames in the thin reaction zone regime

n-heptane/air premixed turbulent flames in the high-Karlovitz portion of the thin reaction zone regime are characterized and modeled in this thesis using Direct Numerical Simulations (DNS) with detailed chemistry. In order to perform these simulations, a time-integration scheme that can efficiently handle the stiffness of the equations solved is developed first. A first simulation with unity Lewis number is considered in order to assess the effect of turbulence on the flame in the absence of differential diffusion. A second simulation with non-unity Lewis numbers is considered to study how turbulence affects differential diffusion. In the absence of differential diffusion, minimal departure from the 1D unstretched flame structure (species vs. temperature profiles) is observed. In the non-unity Lewis number case, the flame structure lies between that of 1D unstretched flames with "laminar" non-unity Lewis numbers and unity Lewis number. This is attributed to effective Lewis numbers resulting from intense turbulent mixing and a first model is proposed. The reaction zone is shown to be thin for both flames, yet large chemical source term fluctuations are observed. The fuel consumption rate is found to be only weakly correlated with stretch, although local extinctions in the non-unity Lewis number case are well correlated with high curvature. These results explain the apparent turbulent flame speeds. Other variables that better correlate with this fuel burning rate are identified through a coordinate transformation. It is shown that the unity Lewis number turbulent flames can be accurately described by a set of 1D (in progress variable space) flamelet equations parameterized by the dissipation rate of the progress variable. In the non-unity Lewis number flames, the flamelet equations suggest a dependence on a second parameter, the diffusion of the progress variable. A new tabulation approach is proposed for the simulation of such flames with these dimensionally-reduced manifolds.