Collective behavior of asperities as a model for friction and adhesion

Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one. In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials. We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.

Logarithmic Potential Theory on Riemann Surfaces

We develop a logarithmic potential theory on Riemann surfaces which generalizes logarithmic potential theory on the complex plane. We show the existence of an equilibrium measure and examine its structure. This leads to a formula for the structure of the equilibrium measure which is new even in the plane. We then use our results to study quadrature domains, Laplacian growth, and Coulomb gas ensembles on Riemann surfaces. We prove that the complement of the support of the equilibrium measure satisfies a quadrature identity. Furthermore, our setup allows us to naturally realize weak solutions of Laplacian growth (for a general time-dependent source) as an evolution of the support of equilibrium measures. When applied to the Riemann sphere this approach unifies the known methods for generating interior and exterior Laplacian growth. We later narrow our focus to a special class of quadrature domains which we call Algebraic Quadrature Domains. We show that many of the properties of quadrature domains generalize to this setting. In particular, the boundary of an Algebraic Quadrature Domain is the inverse image of a planar algebraic curve under a meromorphic function. This makes the study of the topology of Algebraic Quadrature Domains an interesting problem. We briefly investigate this problem and then narrow our focus to the study of the topology of classical quadrature domains. We extend the results of Lee and Makarov and prove (for n ≥ 3) c ≤ 5n-5, where c and n denote the connectivity and degree of a (classical) quadrature domain. At the same time we obtain a new upper bound on the number of isolated points of the algebraic curve corresponding to the boundary and thus a new upper bound on the number of special points. In the final chapter we study Coulomb gas ensembles on Riemann surfaces.

Exploring the Kinetics of Domain Switching in Ferroelectrics for Structural Applications

The complex domain structure in ferroelectrics gives rise to electromechanical coupling, and its evolution (via domain switching) results in a time-dependent (i.e. viscoelastic) response. Although ferroelectrics are used in many technological applications, most do not attempt to exploit the viscoelastic response of ferroelectrics, mainly due to a lack of understanding and accurate models for their description and prediction. Thus, the aim of this thesis research is to gain better understanding of the influence of domain evolution in ferroelectrics on their dynamic mechanical response. There have been few studies on the viscoelastic properties of ferroelectrics, mainly due to a lack of experimental methods. Therefore, an apparatus and method called Broadband Electromechanical Spectroscopy (BES) was designed and built. BES allows for the simultaneous application of dynamic mechanical and electrical loading in a vacuum environment. Using BES, the dynamic stiffness and loss tangent in bending and torsion of a particular ferroelectric, viz. lead zirconate titanate (PZT), was characterized for different combinations of electrical and mechanical loading frequencies throughout the entire electric displacement hysteresis. Experimental results showed significant increases in loss tangent (by nearly an order of magnitude) and compliance during domain switching, which shows promise as a new approach to structural damping. A continuum model of the viscoelasticity of ferroelectrics was developed, which incorporates microstructural evolution via internal variables and associated kinetic relations. For the first time, through a new linearization process, the incremental dynamic stiffness and loss tangent of materials were computed throughout the entire electric displacement hysteresis for different combinations of mechanical and electrical loading frequencies. The model accurately captured experimental results. Using the understanding gained from the characterization and modeling of PZT, two applications of domain switching kinetics were explored by using Micro Fiber Composites (MFCs). Proofs of concept of set-and-hold actuation and structural damping using MFCs were demonstrated.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

Pulsed neutron measurements in two adjacent finite media

The pulsed neutron technique has been used to investigate the decay of thermal neutrons in two adjacent water-borated water finite media. Experiments were performed with a 6x6x6 inches cubic assembly divided in two halves by a thin membrane and filled with pure distilled water on one side and borated water on the other side.

The fundamental decay constant was measured versus the boric acid concentration in the poisoned medium. The experimental results showed good agreement with the predictions of the time dependent diffusion model. It was assumed that the addition of boric acid increases the absorption cross section of the poisoned medium without affecting its diffusion properties: In these conditions, space-energy separability and the concept of an “effective” buckling as derived from diffusion theory were introduced. Their validity was supported by the experimental results.

Measurements were performed with the absorption cross section of the poisoned medium increasing gradually up to 16 times its initial value. Extensive use of the IBM 7090-7094 Computing facility was made to analyze properly the decay data (Frantic Code). Attention was given to the count loss correction scheme and the handling of the statistics involved. Fitting of the experimental results into the analytical form predicted by the diffusion model led to

Ʃ_av = 4721 sec^-1 (±150)

D_o = 35972 cm²sec^-1 (±800) for water at 21˚C

C (given) = 3420 cm⁴sec^-1

These values, when compared with published data, show that the diffusion model is adequate in describing the experiment.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Solubility and Diffusivity of Water in Lunar Basalt, and Chemical Zonation in Olivine-Hosted Melt Inclusions

I report the solubility and diffusivity of water in lunar basalt and an iron-free basaltic analogue at 1 atm and 1350 °C. Such parameters are critical for understanding the degassing histories of lunar pyroclastic glasses. Solubility experiments have been conducted over a range of fO₂ conditions from three log units below to five log units above the iron-wüstite buffer (IW) and over a range of pH₂/pH₂O from 0.03 to 24. Quenched experimental glasses were analyzed by Fourier transform infrared spectroscopy (FTIR) and secondary ionization mass spectrometry (SIMS) and were found to contain up to ~420 ppm water. Results demonstrate that, under the conditions of our experiments: (1) hydroxyl is the only H-bearing species detected by FTIR; (2) the solubility of water is proportional to the square root of pH₂O in the furnace atmosphere and is independent of fO₂ and pH₂/pH₂O; (3) the solubility of water is very similar in both melt compositions; (4) the concentration of H₂ in our iron-free experiments is <3 ppm, even at oxygen fugacities as low as IW-2.3 and pH₂/pH₂O as high as 24; and (5) SIMS analyses of water in iron-rich glasses equilibrated under variable fO₂ conditions can be strongly influenced by matrix effects, even when the concentrations of water in the glasses are low. Our results can be used to constrain the entrapment pressure of the lunar melt inclusions of Hauri et al. (2011).

Diffusion experiments were conducted over a range of fO₂ conditions from IW-2.2 to IW+6.7 and over a range of pH₂/pH₂O from nominally zero to ~10. The water concentrations measured in our quenched experimental glasses by SIMS and FTIR vary from a few ppm to ~430 ppm. Water concentration gradients are well described by models in which the diffusivity of water (D^*_water) is assumed to be constant. The relationship between D^*_water and water concentration is well described by a modified speciation model (Ni et al. 2012) in which both molecular water and hydroxyl are allowed to diffuse. The success of this modified speciation model for describing our results suggests that we have resolved the diffusivity of hydroxyl in basaltic melt for the first time. Best-fit values of D^*_water for our experiments on lunar basalt vary within a factor of ~2 over a range of pH₂/pH₂O from 0.007 to 9.7, a range of fO₂ from IW-2.2 to IW+4.9, and a water concentration range from ~80 ppm to ~280 ppm. The relative insensitivity of our best-fit values of D^*_water to variations in pH₂ suggests that H₂ diffusion was not significant during degassing of the lunar glasses of Saal et al. (2008). D^*_water during dehydration and hydration in H₂/CO₂ gas mixtures are approximately the same, which supports an equilibrium boundary condition for these experiments. However, dehydration experiments into CO₂ and CO/CO₂ gas mixtures leave some scope for the importance of kinetics during dehydration into H-free environments. The value of D^*_water chosen by Saal et al. (2008) for modeling the diffusive degassing of the lunar volcanic glasses is within a factor of three of our measured value in our lunar basaltic melt at 1350 °C.

In Chapter 4 of this thesis, I document significant zonation in major, minor, trace, and volatile elements in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (MgO, FeO, Cr₂O₃, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H₂O, and F, components with a lower concentration in the host olivine than in the melt (Al₂O₃, SiO₂, Na₂O, K₂O, TiO₂, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions concurrent with diffusive propagation of the boundary layer toward the inclusion center.

Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na₂O, K₂O) by coupling to slow diffusing components such as SiO₂ and Al₂O₃. Concentrations of H2O and F decrease towards the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects.

A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C hr^-1 from the liquidus down to ~1000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1000 °C is 40 s to just over one hour.

Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization.

All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.

Plasma inverse scattering theory

The object of this report is to calculate the electron density profile of plane stratified inhomogeneous plasmas. The electron density profile is obtained through a numerical solution of the inverse scattering algorithm.

The inverse scattering algorithm connects the time dependent reflected field resulting from a δ-function field incident normally on the plasma to the inhomogeneous plasma density.

Examples show that the method produces uniquely the electron density on or behind maxima of the plasma frequency.

It is shown that the δ-function incident field used in the inverse scattering algorithm can be replaced by a thin square pulse.

掺镱双包层光纤放大器高功率脉冲放大特性

从放大器速率方程出发，分析了掺镱双包层光纤放大器的放大特性。模拟计算了无信号输入时放大器上能级粒子数、泵浦功率和放大自发辐射（ASE）在放大器中的稳态分布。分析了前向和后向泵浦时，高功率高斯脉冲放大时的脉冲波形畸变、上能级粒子数的时间特性、放大器存储能量和脉冲能量演化等动态特性。讨论了掺镱双包层光纤放大器输出脉冲能量随不同输入脉冲峰值功率和泵浦功率的关系。该模型和结论对高功率脉冲放大器的设计和优化具有一定的理论指导意义。

Optimisation of the first principle code Octopus for massive parallel architectures: application to light harvesting complexes

150 p.

Participação do estresse oxidativo na lesão pulmonar induzida por lipopolissacarídeo: repercussões inflamatórias estruturais e funcionais

O objetivo do presente estudo foi investigar o envolvimento do estresse oxidativo na lesão pulmonar aguda (LPA) induzida por lipopolissacarídeo (LPS) e as repercussões inflamatórias, estruturais e funcionais, através de análises bioquímicas de estresse oxidativo, prova de função pulmonar, análise histológica e RT-PCR para citocinas e fatores de transcrição pró-inflamatórios. Na primeira etapa foram utilizados camundongos machos C57BL6 foram divididos em sete grupos: Grupo controle (CTR) (50 μL de solução fisiológica) administrados via intratraqueal [it], LPS 6 horas (10 μL de LPS) [it], LPS 12 horas (10 μL de LPS) [it], LPS 24 horas (10 μL de LPS) [i], LPS 48 horas (10 μL de LPS). Para verificar que as alterações observadas eram estresse oxidativo dependentes camundongos machos C57BL6 foram pré-tratados com N-acetilcisteína (NAC) 1 hora antes do estímulo com LPS e sacrifícados 24 horas depois do estímulo com LPS. Os animais foram divididos da seguinte forma: Grupo LPS 24 horas (10 μL) [it], grupo NAC 40 mg/kg (gavagem) + LPS (10 μL) [it] e grupo NAC 100 mg/kg (gavagem) + LPS (10 μL) [it]. O sistema antioxidante enzimático protegeu o pulmão do estresse oxidativo nas primeiras 12 horas. O estresse oxidativo foi caracterizado em 24 horas e em 48 horas observou-se falência do sistema antioxidante enzimático. Parâmetros de função pulmonar se mostraram alterados nos grupo estimulados com LPS principalmente no grupo LPS. A elastância (p<0,001), resistência de via aérea periférica (ΔP2) (p<0,001), resistência de via aérea central (ΔP1) (p<0,001) e resistência de via aérea total (ΔPtot) (p<0,001) se mostraram principlamente alteradas no grupo LPS 24 horas. O pré-tratamento com NAC impediu o aumento dos parâmetros de elastância (p<0,001), resistência de via aérea periférica (ΔP2) (p<0,001) resistência de via aérea central (ΔP1) (p<0,05) e resistência de via aérea total (ΔPtot) (p<0,001) comparado com o grupo LPS 24 horas. As alterações histológicas como espessamento de septo alveolar, influxo de células inflamatórias e hemorragia mostraram-se tempo dependentes. O pré-tratamento NAC impediu as alterações observadas nos grupo estimulados com LPS. Alterações inflamatórias foram observadas no grupo estimulado com LPS como IL-6 (p<0,001), iNOS (p<0,001), COX2 (p<0,05), TNF-α (p<0,001) e NFκB (p<0,001) quando comparados ao grupo controle. O pré-tratamento com NAC impediu o aumento desses parâmetros como IL-6 (p<0,001), iNOS (p<0,001), COX2 (p<0,05), TNF-α (p<0,05) e NFκB (p<0,001) quando comparados ao grupo LPS 24 horas. Nossos resultados sugerem que o estresse oxidativo desempenha um papel importante nas respostas inflamatórios, estruturais e funcionais no modelo de LPA induzido por LPS e que essas alterações são estresse oxidativo dependentes.

A influência do fumo sobre a morfologia ovariana de camundongos Swiss

Considerando que nos tempos atuais o hábito de fumar atingiu uma parcela significativa das adolescentes brasileiras e apesar de seus conhecidos efeitos deletérios sobre diversos órgãos, pouco se sabe da sua ação sobre os ovários. Este estudo teve como objetivo avaliar os efeitos da exposição à fumaça de cigarro sobre o ciclo estral e a morfologia ovariana. Para tal, foram utilizados camundongos da linhagem Swiss, cujo estudo teve início com o estudo do perfil das características da maturação sexual. Após o desmame, aos 21 dias de idade, a partir da abertura vaginal, o 1 estro e o início da ciclicidade foram acompanhados através da citologia vaginal. As características do ciclo estral foram determinadas no decorrer de doze semanas. O efeito da exposição à fumaça de cigarro 3R4F utilizou fêmeas Swiss de 35 dias de idade que foram subdivididos em dois grupos expostos à fumaça de cigarro (grupo 15E) e animais controles livres de fumaça (grupo 15C). A exposição ocorreu por 15 dias e ao final deste período, metade dos animais de cada grupo foi sacrificada e ovários direitos foram coletados. A outra metade permaneceu em observação durante 30 dias, sem exposição à fumaça, originando os grupos 45Ex e 45C. A citologia vaginal foi avaliada durante todo o período experimental. Ao final dos 30 dias, sangue e ovários direitos foram coletados. Estes foram pesados e processados por técnica de rotina histológica para análise morfológica. A caracterização dos eventos da puberdade estabeleceu o tempo de abertura vaginal com média de 33,60,24 de idade, o primeiro estro 39,42,58 dias de idade e o início da ciclicidade, com média de 39,51,19 dias de idade, concomitante com o primeiro estro. Além disso, os ciclos estrais apresentaram períodos de cinco dias com freqüência baixa da fase diestro. Com relação à exposição da fumaça de cigarro ocorreu aumento significativo na extensão dos ciclos estrais e uma forte tendência ao aumento de estros nos animais 45Ex, apesar de não ser significativa. O número e o diâmetro de folículos grandes foram maiores no 15E, enquanto o de corpos lúteos foi menor. Em relação ao grupo 45C, o 45Ex não se alterou, porém, mostrou uma discreta redução da massa ovariana, do número de folículos pequenos, do número e do diâmetro dos folículos médios, dos corpos lúteos e aumento de folículos atrésicos. A comparação entre controles, 15C e 45C e expostos, 15E e 45Ex, mostrou uma redução no diâmetro de folículos médios e grandes. O estudo do perfil das características reprodutivas de fêmeas Swiss é indispensável para modelos experimentais em pesquisa que fazem uso desta linhagem. Permitiu verificar que a exposição à fumaça de cigarro promove alteração do ciclo estral, da massa ovariana e antecipa alterações morfológicas tempo dependente que sinaliza a finalização da vida reprodutiva

Acoustic plasmons in extrinsic free-standing graphene

An acoustic plasmon is predicted to occur, in addition to the conventional two-dimensional (2D) plasmon, as the collective motion of a system of two types of electronic carriers coexisting in the same 2D band of extrinsic (doped or gated) graphene. The origin of this novel mode stems from the anisotropy present in the graphene band structure near the Dirac points K and K'. This anisotropy allows for the coexistence of carriers moving with two distinct Fermi velocities along the Gamma K and Gamma K' directions, which leads to two modes of collective oscillation: one mode in which the two types of carriers oscillate in phase with one another (this is the conventional 2D graphene plasmon, which at long wavelengths (q -> 0) has the same dispersion, q(1/2), as the conventional 2D plasmon of a 2D free electron gas), and the other mode found here corresponds to a low-frequency acoustic oscillation (whose energy exhibits at long-wavelengths a linear dependence on the 2D wavenumber q) in which the two types of carriers oscillate out of phase. This prediction represents a realization of acoustic