Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

Erbium and ytterbium co-doped SiO2 : GeO2 planar waveguide prepared by the sol-gel route using an alternative precursor

The sol-gel method combined with a spin-coating technique has been successfully applied for the preparation of rare-earth doped silica:germania films used for the fabrication of erbium-doped waveguide amplifiers (EDWA), presenting several advantages over other methods for the preparation of thin films. As with other methods, the sol-gel route also shows some drawbacks, such as cracks related to the thickness of silica films and high hydrolysis rate of certain precursors such as germanium alkoxides. This article describes the preparation and optical characterization of erbium and ytterbium co-doped SiO2:GeO2 crack-free thick films prepared by the sol-gel route combined with a spin-coating technique using a chemically stable non-aqueous germanium oxide solution as an alternative precursor. The non-crystalline films obtained are planar waveguides exhibiting a single mode at 1,550 nm with an average thickness of 3.9 mu m presenting low percentages of porosity evaluated by the Lorentz-Lorenz Effective Medium Approximation, and low stress, according to the refractive index values measured in both transversal electric and magnetic polarizations. Weakly confining core layers (0.3% < Delta n < 0.75%) were obtained according to the refractive index difference between the core and buffer layers, suggesting that low-loss coupling EDWA may be obtained. The life time of the erbium I-4(13/2) metastable state was measured as a function of erbium concentration in different systems and based on these values it is possible to infer that the hydroxyl group was reduced and the formation of rare-earth clusters was avoided.

NIR luminescent Er3+/Yb3+ co-doped SiO2-ZrO2 nanostructured planar and channel waveguides: Optical and structural properties

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

NIR luminescent Er3+/Yb3+ co-doped SiO2-ZrO2 nanostructured planar and channel waveguides: Optical and structural properties

Optical and structural properties of planar and channel waveguides based on sol gel Er3+ and Yb3+ co-doped SiO2-ZrO2 are reported. Microstructured channels with high homogeneous surface profile were written onto the surface of multilayered densified films deposited on SiO2/Si substrates by a femtosecond laser etching technique. The densification of the planar waveguides was evaluated from changes in the refractive index and thickness, with full densification being achieved at 900 degrees C after annealing from 23 up to 500 min, depending on the ZrO2 content Crystal nucleation and growth took place together with densification, thereby producing transparent glass ceramic planar waveguides containing rare earth-doped ZrO2 nanocrystals dispersed in a silica-based glassy host Low roughness and crack-free surface as well as high confinement coefficient were achieved for all the compositions. Enhanced NIR luminescence of the Er3+ ions was observed for the Yb3+- codoped planar waveguides, denoting an efficient energy transfer from the Yb3+ to the Er3+ ion. (C) 2012 Elsevier B.V. All rights reserved.

The influence of ageing on fatigue crack growth in SiC-particulate reinforced 8090

A study of the influence of SiC-particulate reinforcement on ageing and subsequent fatigue crack growth resistance in a powder metallurgy 8090 aluminium alloy-SiC composite has been made. Macroscopic hardness measurements revealed that ageing at 170°C in the composite is accelerated with respect to the unreinforced alloy, though TEM studies indicate that this is not due to the enhanced precipitation of S′. Fatigue crack growth rates in the naturally aged condition of the composite and unreinforced matrix are similar at low to medium values of ΔK, but diverge above ≈ 8 MPa√m owing to the lower fracture toughness of the composite. As a result of the presence of the reinforcement, planar slip in the composite is suppressed and facetted crack growth is not observed. Ageing at or above 170°C has a deleterious effect on fatigue crack growth. Increased ageing time decreases the roughness of the fracture path at higher growth rates. These effect are though to be due to microstructural changes occurring at or near to the SiC/matrix interfaces, providing sites for static mode failure mechanisms to operate. This suggestion is supported by the observation that as ΔK increases, crack growth rates become Kmax dependent, implying the crack growth rate is strongly influenced by static modes.

Metamorfose planar via métodos Level Set e Particle Level Set para a reconstrução de superfícies tridimensionais

Evolving interfaces were initially focused on solutions to scientific problems in Fluid Dynamics. With the advent of the more robust modeling provided by Level Set method, their original boundaries of applicability were extended. Specifically to the Geometric Modeling area, works published until then, relating Level Set to tridimensional surface reconstruction, centered themselves on reconstruction from a data cloud dispersed in space; the approach based on parallel planar slices transversal to the object to be reconstructed is still incipient. Based on this fact, the present work proposes to analyse the feasibility of Level Set to tridimensional reconstruction, offering a methodology that simultaneously integrates the proved efficient ideas already published about such approximation and the proposals to process the inherent limitations of the method not satisfactorily treated yet, in particular the excessive smoothing of fine characteristics of contours evolving under Level Set. In relation to this, the application of the variant Particle Level Set is suggested as a solution, for its intrinsic proved capability to preserve mass of dynamic fronts. At the end, synthetic and real data sets are used to evaluate the presented tridimensional surface reconstruction methodology qualitatively.

Metamorfose planar via métodos Level Set e Particle Level Set para a reconstrução de superfícies tridimensionais

Evolving interfaces were initially focused on solutions to scientific problems in Fluid Dynamics. With the advent of the more robust modeling provided by Level Set method, their original boundaries of applicability were extended. Specifically to the Geometric Modeling area, works published until then, relating Level Set to tridimensional surface reconstruction, centered themselves on reconstruction from a data cloud dispersed in space; the approach based on parallel planar slices transversal to the object to be reconstructed is still incipient. Based on this fact, the present work proposes to analyse the feasibility of Level Set to tridimensional reconstruction, offering a methodology that simultaneously integrates the proved efficient ideas already published about such approximation and the proposals to process the inherent limitations of the method not satisfactorily treated yet, in particular the excessive smoothing of fine characteristics of contours evolving under Level Set. In relation to this, the application of the variant Particle Level Set is suggested as a solution, for its intrinsic proved capability to preserve mass of dynamic fronts. At the end, synthetic and real data sets are used to evaluate the presented tridimensional surface reconstruction methodology qualitatively.

Circuitos de uso de crack na região central da cidade de São Paulo (SP, Brasil)

Apesar de o uso de drogas ser uma prática presente desde os primórdios da humanidade, atualmente o seu abuso adquiriu dimensões preocupantes, configurando-se como um problema de saúde pública. O surgimento do crack, droga derivada da pasta de coca, agravou esse quadro ao aumentar os danos sociais e à saúde dos usuários. Visando conhecer o impacto de sua inserção no cotidiano dos usuários, foi realizado um estudo etnográfico em locais de venda e uso de crack na região central da cidade de São Paulo (SP, Brasil). Foi utilizado um diário de campo para registrar as observações e os diálogos informais efetuados com as pessoas que circulavam no local estudado. Os resultados apontaram os circuitos percorridos pelos usuários, suas dinâmicas e as relações que estabelecem com outros atores sociais, as quais são permeadas por permanente tensão, envolvendo a prática de atos violentos nos quais os usuários são tanto agressores quanto vítimas. O estudo também sugere a importância de outros fatores como a história da região pesquisada, as políticas públicas, questões econômicas e ausência de investimentos sociais e em saúde pública. Sugere-se que o alto grau de degradação da região pesquisada não seria consequência apenas das pessoas e atividades exercidas no local, mas principalmente do processo urbano que gerou tal quadro social.

Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum C(l), this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual C(l)'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales l = 7 and l = 8. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.

Absorption of planar waves in a draining bathtub

We present an analysis of the absorption of acoustic waves by a black hole analogue in (2 + 1) dimensions generated by a fluid flow in a draining bathtub. We show that the low-frequency absorption length is equal to the acoustic hole circumference and that the high-frequency absorption length is 4 times the ergoregion radius. For intermediate values of the wave frequency, we compute the absorption length numerically and show that our results are in excellent agreement with the low-and high-frequency limits. We analyze the occurrence of superradiance, manifested as negative partial absorption lengths for corotating modes at low frequencies.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

On the k-restricted structure ratio in planar and outerplanar graphs

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1/2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.

Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. (C) 2009 Elsevier Ltd. All rights reserved.

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris` law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena. (C) 2010 Elsevier Ltd. All rights reserved.