A singularly perturbed linear two-point boundary-value problem

We consider the following singularly perturbed linear two-point boundary-value problem:

Ly(x) ≡ Ω(ε)D_xy(x) - A(x,ε)y(x) = f(x,ε) 0≤x≤1 (1a)

By ≡ L(ε)y(0) + R(ε)y(1) = g(ε) ε → 0^+ (1b)

Here Ω(ε) is a diagonal matrix whose first m diagonal elements are 1 and last m elements are ε. Aside from reasonable continuity conditions placed on A, L, R, f, g, we assume the lower right mxm principle submatrix of A has no eigenvalues whose real part is zero. Under these assumptions a constructive technique is used to derive sufficient conditions for the existence of a unique solution of (1). These sufficient conditions are used to define when (1) is a regular problem. It is then shown that as ε → 0^+ the solution of a regular problem exists and converges on every closed subinterval of (0,1) to a solution of the reduced problem. The reduced problem consists of the differential equation obtained by formally setting ε equal to zero in (1a) and initial conditions obtained from the boundary conditions (1b). Several examples of regular problems are also considered.

A similar technique is used to derive the properties of the solution of a particular difference scheme used to approximate (1). Under restrictions on the boundary conditions (1b) it is shown that for the stepsize much larger than ε the solution of the difference scheme, when applied to a regular problem, accurately represents the solution of the reduced problem.

Furthermore, the existence of a similarity transformation which block diagonalizes a matrix is presented as well as exponential bounds on certain fundamental solution matrices associated with the problem (1).

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Intersexual and spatial heterogeneity in trophic attributes of the sleeper, Bostrychus africanus (Eleotridae) in the Qua Iboe Estuary, Nigeria

There was variation in the ingestion of the food objects by the sexes. Despite the similarity in rank-order of the food objects, the ingestion of the objects vary significantly (rg=0.320, P>0.05). Dipterans adult and Hymenoptera were the only food objects not eaten by the males whereas insect remains and unidentified bivalves were absent from the trophics spectrum of the females. There was significant increase in feeding intensity by females than males. There was significant increase in GRI by specimens from Nipa Creek whereas individuals from mangrove creek recorded higher MGF and vice-versa. Dipterans adult. Hymenoptera, insect remains, Neritina glabrata and unid bivalves were absent from dietaries for nipa creek whereas a complete array of the food objects were eaten in the mangrove creek. The present findings highlights the importance of the mangrove ecosystem as the native vegetation encompassing great diversity of food resources and living conditions than the succeeding alien nipa vegetation

Charge symmetry in ^(13)N and ^(13)C a coupled-channel model

A set of coupled-channel differential equations based on a rotationally distorted optical potential is used to calculate the wave functions required to evaluate the gamma ray transition rate from the first excited state to the ground state in ^(13)C and ^(13)N. The bremsstrahlung differential cross section of low energy protons is also calculated and compared with existing data. The marked similarity between the potentials determined at each resonance level in both nuclei supports the hypothesis of the charge symmetry of nuclear forces by explaining the deviation of the ratios of the experimental E1 transition strengths from unity.

Phase control of gain and dispersion in an open V-type system

The control role of the relative phase between the probe and driving fields on gain, dispersion and populations in an open V-type three-level system with spontaneously generated coherence is studied. The result shows that by adjusting the value of the relative phase, the transformation between lasing with inversion and lasing without inversion (LWI) can be realized and high dispersion (refractive index) without absorption can be obtained. The shape and value range of the dispersion curve are similar to those of the gain curve, and this similarity is closely related to the relative phase. The effects of the atomic exit and injection rates and the incoherent pump rate on the control role of the relative phase are also analysed. It is found easier to get LWI by adjusting the value of the relative phase using the open system rather than the closed system, and using an incoherent pump rather than without using the incoherent pump. Moreover the open system can give a larger LWI gain than the closed system.

Functional evaluation of noncovalent interactions in neuroreceptors and progress toward the expansion of unnatural amino acid methodology

This dissertation primarily describes chemical-scale studies of G protein-coupled receptors and Cys-loop ligand-gated ion channels to better understand ligand binding interactions and the mechanism of channel activation using recently published crystal structures as a guide. These studies employ the use of unnatural amino acid mutagenesis and electrophysiology to measure subtle changes in receptor function.

In chapter 2, the role of a conserved aromatic microdomain predicted in the D3 dopamine receptor is probed in the closely related D2 and D4 dopamine receptors. This domain was found to act as a structural unit near the ligand binding site that is important for receptor function. The domain consists of several functionally important noncovalent interactions including hydrogen bond, aromatic-aromatic, and sulfur-π interactions that show strong couplings by mutant cycle analysis. We also assign an alternate interpretation for the linear fluorination plot observed at W6.48, a residue previously thought to participate in a cation-π interaction with dopamine.

Chapter 3 outlines attempts to incorporate chemically synthesized and in vitro acylated unnatural amino acids into mammalian cells. While our attempts were not successful, method optimizations and data for nonsense suppression with an in vivo acylated tRNA are included. This chapter is aimed to aid future researchers attempting unnatural amino acid mutagenesis in mammalian cells.

Chapter 4 identifies a cation-π interaction between glutamate and a tyrosine residue on loop C in the GluClβ receptor. Using the recently published crystal structure of the homologous GluClα receptor, other ligand-binding and protein-protein interactions are probed to determine the similarity between this invertebrate receptor and other more distantly related vertebrate Cys-loop receptors. We find that many of the interactions previously observed are conserved in the GluCl receptors, however care must be taken when extrapolating structural data.

Chapter 5 examines inherent properties of the GluClα receptor that are responsible for the observed glutamate insensitivity of the receptor. Chimera synthesis and mutagenesis reveal the C-terminal portion of the M4 helix and the C-terminus as contributing to formation of the decoupled state, where ligand binding is incapable of triggering channel gating. Receptor mutagenesis was unable to identify single residue mismatches or impaired protein-protein interactions within this domain. We conclude that M4 helix structure and/or membrane dynamics are likely the cause of ligand insensitivity in this receptor and that the M4 helix has an role important in the activation process.

The distribution of Corixidae in relation to the water quality of British lakes: A monitoring model

This article is an attempt to devise a method of using certain species of Corixidae as a basis for the assessment of general water quality in lakes. An empirical graphical representation of the distribution of populations or communities of Corixidae in relation to conductivity, based mainly on English and Welsh lakes, is used as a predictive monitoring model to establish the "expected" normal community at a given conductivity, representing the total ionic concentration of the water body. A test sample from another lake of known conductivity is then compared with "expected" community. The "goodness of fit" is examined visually or by calculation of indices of similarity based on the relative proportions of the constituent species of each community. A computer programme has been devised for this purpose.

The electrical and magnetic properties of amorphous Pd-Cu-P alloys

The amorphous phases of the Pd-Cu-P system has been obtained using the technique of rapidly quenching from the liquid state. Broad maxima in the diffraction pattern were obtained in the X-ray diffraction studies which are indicative of a glass-like structure. The composition range over which the amorphous solid phase is retained for the Pd-Cu-P system is (Pd_100-xCu_x)₈₀P₂₀ with 10 ≤ x ≤ 50 and (Pd₆₅Cu₃₅)_100-yP_y with 15 ≤ y ≤ 24 and (Pd₆₀Cu₄₀)_100-yP_y with 15 ≤ y ≤ 24.

The electrical resistivity for the Pd-Cu-P alloys decreases with temperature as T² at low temperatures and as T at high temperatures up to the crystallization temperature. The structural scattering model of the resistivity proposed by Sinha and the spin-fluctuation resistivity model proposed by Hasegawa are re-examined in the light of the similarity of this result to the Pt-Ni-P and Pd-Ni-P systems. Objections are raised to these interpretations of the resistivity results and an alternate model is proposed consistent with the new results on Pd-Cu-P and the observation of similar effects in crystalline transition metal alloys. The observed negative temperature coefficients of resistivity in these amorphous alloys are thus interpreted as being due to the modification of the density of states with temperature through the electron-phonon interaction. The weak Pauli paramagnetism of the Pd-Cu-P, Pt-Ni-P and Pd-Ni-P alloys is interpreted as being modifications of the transition d-states as a result of the formation of strong transition metal-metalloid bonds rather than a large transfer of electrons from the glass former atoms (P in this case) to the d-band of the transition metal in a rigid band picture.

Composição florística e estrutura da comunidade arbustivo-arbórea de um trecho de floresta submontana na vertente sudeste do Parque Estadual da Ilha Grande, Angra dos Reis / RJ

O estudo objetivou avaliar a composição florística e estrutural dos componentes arbustivo-arbóreo da Floresta Ombrófila Densa submontana em diferentes estágios de regeneração natural, na vertente sudeste do Parque Estadual da Ilha Grande/RJ. Para o inventário florístico foram realizadas coletas assistemáticas em diferentes trechos nessa vertente. A complementação da lista de espécies foi feita a partir, da consulta às exsicatas dos herbários do Rio de Janeiro (FCAB, GUA, HB, HRJ, R, RB, RBR, RFA, RFFP e RUSU) e do inventário fitossociológico. Foi verificado o status de conservação das espécies inventariadas para a Flora Brasileira. Para o inventário fitossociológico foram estabelecidas 34 parcelas amostrais, totalizando 1,02 ha de área amostrada. Todos os indivíduos arbustivo-arbóreos com DAP ≥ 5 cm foram registrados e, após identificação, foram depositados no Herbário da Universidade do Estado do Rio de Janeiro (HRJ). O pacote estatístico FITOPAC 2.1. foi utilizado para a análise dos dados. A similaridade entre o remanescente investigado neste estudo e as outras quatorze áreas distintas do Rio de Janeiro, da própria Ilha Grande ou não, foi avaliada, utilizando-se o coeficiente de Similaridade de Sorensen; pelo critério de agrupamento por ligação média não ponderada (UPGMA) e pelo método de autorreamostragem para a estrutura de grupos; utilizados os programas PAST v1.34 e Multiv 2.4. A partir do levantamento em herbários e dos inventários florístico e fitossociológico realizados neste trabalho, foram analisados 3.470 registros, sendo 1.778 do levantamento de herbários, 1.536 do levantamento fitossociológico e 156 do inventário florístico. Esses registros corresponderam a 606 espécies ou morfo-espécies de Angiospermas e uma de Pteridófita. Os resultados obtidos revelaram a existência de 22 espécies ameaçadas de extinção para a Flora do Brasil. Dentre, as quais, sete são exclusivas da amostragem fitossociológica: Abarema cochliacarpos (Gomes) Barneby & J.W. Grimes, Chrysophyllum flexuosum Mart., Ficus pulchella Schott ex Spreng., Macrotorus utriculatus Perkins, Myrceugenia myrcioides (Cambess.) O.Berg, Rudgea interrupta Benth e Urbanodendron bahiense (Meisn.) Rohwer. No estudo fitossociológico, inventariou-se 1.536 indivíduos de 217 espécies, subordinadas a 53 famílias. O índice de diversidade de Shannon (H) calculado foi de 4,702 nats/ind e equabilidade (J) de 0,874. As 10 famílias com maior riqueza foram: Myrtaceae (31 spp.), Rubiaceae (21), Fabaceae (17), Lauraceae (12), Euphorbiaceae (11), Monimiaceae (8), Melastomataceae (7), Sapindaceae (7), Sapotaceae (6) e Annonaceae (6). Os 10 maiores Valores de Importância das espécies foram para Chrysophyllum flexuosum (3,43%), Lamanonia ternata Vell. (3,40%), Hyeronima alchorneoides Allemão (2,83%), Actinostemon verticillatus (Klotzsch) Baill. (2,55%), Psychotria brasiliensis Vell. (2,55%), Eriotheca pentaphylla (Vell.) A. Robyns (2,28%), Guatteria australis A. St.-Hil. (2,12%), Mabea brasiliensis Müll. Arg. (2,04%), Miconia prasina (Sw.) DC. (1,89%) e Rustia formosa (Cham. & Schltdl. ex DC.) Klotzsch (1,82%). Amostraram-se 27% de espécies representadas por apenas um indivíduo. As análises florísticas avaliadas a partir do Índice de Similaridade de Sorensen indicaram como principais variáveis para a formação dos blocos, os diferentes valores de diversidade para as áreas e a distribuição fitogeográfica das espécies. Os resultados obtidos junto aos dados dos grupos ecológicos, para os indivíduos da fitossociologia, indicaram maior percentual de indivíduos secundários tardios amostrados. Conclui-se que a área de estudo é uma floresta secundária em estágio intermediário de regeneração, com grande riqueza de espécies, muitas das quais de relevante importância ecológica.

Plataforma de investigación en el ámbito de la resucitación cardio-pulmonar basada en un maniquí de entrenamiento sensorizado

[ES]Hoy en día las muertes por parada cardiorrespiratoria superan en número a otras más mediáticas como aquellas que se producen por incendios o en accidentes de tráfico, y sin embargo su repercusión es mucho menor. Este hecho debe ser motivo de preocupación ya que, con una correcta formación de la población en materia de resucitación cardíaca, muchas de estas muertes podrían ser evitadas. Con el objetivo de reducir estas estadísticas han surgido multitud de estudios y proyectos de investigación consistentes en tratar de mejorar las herramientas disponibles tanto para personal sanitario como no sanitario. En este marco se encuadra el proyecto presentado en este documento, consistente en la sensorización de un maniquí de entrenamiento para episodios de parada cardiorrespiratoria, el cual ofrecerá la posibilidad de analizar con detalle el artifact o interferencia generada por el rescatador sobre el paciente en el momento de efectuar la maniobra de resucitación, así como la interferencia causada por el contacto electrodo-piel. Paralelamente podrá ser utilizado como mero instrumento de entrenamiento para posibles situaciones reales. El porqué de la utilización de este tipo de maniquíes reside principalmente en la imposibilidad de emplear personas debido a las posibles lesiones torácicas que pueden ocurrir por las compresiones realizadas. Finalmente debe citarse el hecho de que no es imprescindible tener conocimientos médicos para poder aplicar las técnicas básicas de resucitación cardíaca, acción que incrementa las posibilidades de supervivencia de un paciente de manera excepcional, ya que cada minuto que pasa desde la parada cardiorrespiratoria la probabilidad de supervivencia disminuye en un porcentaje significativamente elevado. Tomando como base lo descrito hasta ahora, en este documento se detalla la solución técnica de la sensorización de un maniquí genérico para la adquisición de las señales de fuerza de compresión, aceleración sufrida por el pecho en tres ejes ortogonales, profundidad de compresión, impedancia entre los dos electrodos colocados sobre el pecho del paciente y señal electrocardiográfica emitida por el corazón; además, se incluye la posibilidad de inyectar una señal electrocardiográfica previamente grabada. La base de registros obtenida de estos ensayos podrá ser utilizada posteriormente para su análisis, ya que su similitud con señales extraídas en un caso real es máxima.

As representações sociais de profissionais de saúde acerca do paciente psiquiátrico: aspectos descritivos e de zona muda

A presença de pacientes crônicos em instituições psiquiátricas tem se constituído como um desafio humano, político e programático para esta área assistencial. Frente a isto, definiu-se como objetivo geral deste estudo analisar a reconstrução sócio-cognitiva do profissional de saúde mental acerca do paciente psiquiátrico crônico, contextualizando com a sua permanência institucional e o processo assistencial. Como objetivos específicos, descrever os conteúdos e a estrutura das representações sociais do paciente psiquiátrico crônico para os profissionais; identificar a existência de conteúdos implícitos nas formações discursivas dos profissionais de saúde referentes ao paciente crônico institucionalizado; e analisar a perspectiva assistencial implementada na atenção a esses indivíduos no contexto institucional a partir das representações sociais do paciente crônico. Trata-se de uma pesquisa qualitativa, desenvolvida com o aporte teórico-metodológico da Teoria das Representações Sociais em sua abordagem estrutural, em dois hospitais colônias localizados na cidade do Rio de Janeiro. Os dados foram coletados através de evocações livres em dois momentos. No primeiro, com 159 profissionais e no segundo utilizou-se a técnica de substituição com 151 profissionais. Os dados gerados foram analisados pelo software EVOC 2003 e organizados pelo quadro de quatro casas. Utilizou-se, ainda, a análise de similitude. Quanto à representação do paciente psiquiátrico, a mesma foi organizada ao redor das dimensões assistencial-institucional (cuidado), imagética (louco) e afetividade positiva (atenção), que se desdobram nos demais quadrantes, com destaque para a primeira e a segunda. A análise de similitude revelou que o léxico cuidado, obteve o maior número de ligações. Quanto à representação do paciente crônico em contexto normativo, a dimensão assistencial-institucional mostrou-se fortemente presente (cuidado, paciência e dependente), seguida da imagética (abandonado) e da de necessidade (carência). No entanto, na análise de similitude, a afetividade positiva (amor) mostra-se central com maior número de ligações de léxicos. Em contextos contra-normativos, a representação revelou-se negativa (louco, não e medo). A análise de similitude demonstrou uma representação estruturada através de uma imagem e de uma afetividade negativas. Conclui-se que os avanços na área de saúde mental, nos últimos 30 anos, não foram capazes de realizar mudanças representacionais sob fenômenos que ancoram em imagens produzidas desde os primórdios da humanidade. Ressalta-se a possível existência de uma zona muda acerca do paciente psiquiátrico crônico.

Nonlinear Effects in Granular Crystals with Broken Periodicity

When studying physical systems, it is common to make approximations: the contact interaction is linear, the crystal is periodic, the variations occurs slowly, the mass of a particle is constant with velocity, or the position of a particle is exactly known are just a few examples. These approximations help us simplify complex systems to make them more comprehensible while still demonstrating interesting physics. But what happens when these assumptions break down? This question becomes particularly interesting in the materials science community in designing new materials structures with exotic properties In this thesis, we study the mechanical response and dynamics in granular crystals, in which the approximation of linearity and infinite size break down. The system is inherently finite, and contact interaction can be tuned to access different nonlinear regimes. When the assumptions of linearity and perfect periodicity are no longer valid, a host of interesting physical phenomena presents itself. The advantage of using a granular crystal is in its experimental feasibility and its similarity to many other materials systems. This allows us to both leverage past experience in the condensed matter physics and materials science communities while also presenting results with implications beyond the narrower granular physics community. In addition, we bring tools from the nonlinear systems community to study the dynamics in finite lattices, where there are inherently more degrees of freedom. This approach leads to the major contributions of this thesis in broken periodic systems. We demonstrate the first defect mode whose spatial profile can be tuned from highly localized to completely delocalized by simply tuning an external parameter. Using the sensitive dynamics near bifurcation points, we present a completely new approach to modifying the incremental stiffness of a lattice to arbitrary values. We show how using nonlinear defect modes, the incremental stiffness can be tuned to anywhere in the force-displacement relation. Other contributions include demonstrating nonlinear breakdown of mechanical filters as a result of finite size, and the presents of frequency attenuation bands in essentially nonlinear materials. We finish by presenting two new energy harvesting systems based on our experience with instabilities in weakly nonlinear systems.

Nanocompósitos de elastômero termoplástico à base de PP/EPDM/argila organofílica

Neste trabalho foram preparados nanocompósitos de elastômeros termoplásticos à base de PP/EPDM/argila organofílica. Foram utilizados como agentes interfaciais polipropileno e terpolímero de etileno-propileno-dieno ambos modificados com grupos anidrido maleico, PP-MA e EPDM-MA, respectivamente. Dois tipos de argila organofílica, que se diferenciam pela estrutura química do surfactante e conseqüentemente pela estabilidade térmica, foram empregados como carga inorgânica. Os nanocompósitos foram preparados pela técnica de intercalação por fusão em câmara interna de mistura e a incorporação da argila foi feita pela adição de masterbatches previamente preparados. Foram investigadas as propriedades de tração, reométricas e ainda a morfologia (cristalinidade e estrutura obtida) dos nanocompósitos a fim de estabelecer a influência do tipo e quantidade de argila organofílica e agente interfacial. Os resultados mostraram que a adição de agente interfacial melhorou a dispersão da argila organofílica na matriz de PP/EPDM, particularmente o PP-MA. Foram obtidos nanocompósitos com estruturas mistas intercaladas e esfoliadas, que resultaram em maiores valores de módulo de elasticidade e manutenção dos valores de deformação. As propriedades reométricas confirmaram o maior grau de dispersão da argila organofílica em nanocompósitos contendo PP-MA. Teores crescentes de argila reduziram a cristalinidade dos nanocompósitos, os quais quando reprocessados, mantiveram as características inerentes ao TPE de origem. Por fim, a estrutura do surfactante presente

Análise comparativa in vivo da detecção de lesões de cárie oclusal e proximal por meio de exame visual (ICDAS), exame radiográfico e transiluminação por fibra ótica (FOTI)

O objetivo do presente trabalho foi avaliar in vivo a detecção de cárie através do exame visual ICDAS, transiluminação por fibra ótica combinado ao ICDAS e exame radiográfico. Um total de 2.279 superfícies proximais e cicatrículas e fissuras em incisivos superiores, pré-molares e molares permanentes e 272 superfícies em molares decíduos em72 escolares (8 a 18 anos) foram avaliadas por um examinador treinado. Os sete escores para detecção de cárie primária do sistema visual ICDAS foram aplicados. Dois equipamentos de transiluminação por fibra ótica foram avaliados: FOTI Schott (SCH), com ponta de fibra ótica com 0,5mm de diâmetro, e FOTI Microlux (MIC), com diâmetro da ponta 3 mm. Durante o exame combinado FOTI/ICDAS, a fibra ótica era utilizada tanto para iluminar quanto para transiluminar a superfície sob avaliação. O exame radiográfico (RX) consistiu de radiografias interproximais posteriores e periapicais anteriores. Os exames foram realizados em consultório odontológico após escovação supervisionada. No primeiro dia de exame, o exame visual utilizando o ICDAS era realizado e em seguida, o exame combinado ao MIC ou SCH. Logo após era realizado o exame radiográfico. Após uma semana, novamente o ICDAS era realizado, e em seguida o exame combinado com o equipamento de FOTI não utilizado na semana anterior. Os exames foram repetidos em 10 pacientes após intervalo mínimo de uma semana para avaliação da reprodutibilidade intra-examinador, a qual apresentou valores de 0,95 (ICDAS), 0,94 (MIC), 0,95 (SCH) e 0,99 (RX) pelo kappa ponderado. Em cicatrículas e fissuras de permanentes, o RX julgou que um número maior de superfícies apresentava lesão em dentina (53) do que os outros métodos (34 a 36); porém não detectou nenhuma lesão em esmalte, as quais foram identificadas pelo ICDAS (94), SCH (107) e MIC (91). Em proximais permanentes, a transiluminação por fibra ótica identificou maior número de proximais como lesão em esmalte - 150 (SCH) e 139 (MIC) - do que o exame visual (106), enquanto o RX identificou somente 43. Em oclusais de decíduos, os quatro métodos julgaram um número aproximadamente similar de superfícies sem lesão (52 a 59) ou com lesão em dentina (21 a 26), assim como para lesões proximais em dentina (31 a 36). Entretanto um número reduzido de lesões proximais decíduas em esmalte foi julgado pelo exame radiográfico (3) em comparação com os outros métodos (15 a 16). Em decíduos, o ICDAS e o FOTI combinado ao exame visual julgaram maior número de lesões proximais em esmalte que o exame radiográfico, sendo que número similar de lesões em dentina foram classificadas pelos quatro métodos em oclusais e proximais de molares decíduos. Em cicatrículas e fissuras de permanentes, tanto o exame visual ICDAS quanto sua combinação aos dois equipamentos de transiluminação apresentaram maior similaridade de superfícies julgadas como lesão em esmalte ou como lesão em dentina, enquanto o exame radiográfico classificou mais superfícies como lesão em dentina e nenhuma como lesão em esmalte. A adição da transiluminação por fibra ótica ao exame visual aumentou em um terço a detecção das lesões cariosas proximais julgadas em dentina pelo ICDAS isoladamente e aproximadamente quadruplicou o número daquelas assim classificadas pela avaliação radiográfica em permanentes.

偏振模色散和时延抖动对啁啾光纤光栅色散补偿特性的影响

对存在偏振模色散(PMD)和群时延(GD)抖动的非理想线性啁啾光纤光栅的色散补偿特性进行了研究。实验测量了啁啾光纤光栅的群时延谱和偏振模色散光谱，理论分析和实验测量表明，啁啾光纤光栅差分群时延(DGD)抖动与其时延抖动密切相关。通过数值模拟方法，计算了线性啁啾光纤光栅偏振模色散眼图代价与入射到啁啾光纤光栅色散补偿器的光信号的偏振方向的关系，计算结果表明在使用啁啾光纤光栅色散补偿器时应对光信号的偏振方向进行调整，以获得最佳补偿效果。另外结合实验数据，模拟计算并讨论了非理想线性啁啾光纤光栅群时延抖动和偏振模色