A phase-field model for fractures in incompressible solids

Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable. Corresponding function spaces have to be chosen properly. On the discrete level, stable Taylor-Hood elements are employed for the displacement-pressure system. Two additional variables describe the phase-field solution and the crack irreversibility constraint. Therefore, the final system contains four variables: displacements, pressure, phase-field, and a Lagrange multiplier. The resulting discrete system is nonlinear and solved monolithically with a Newton-type method. Our proposed model is demonstrated by means of several numerical studies based on two numerical tests. First, different finite element choices are compared in order to investigate the influence of higher-order elements in the proposed settings. Further, numerical results including spatial mesh refinement studies and variations in Poisson's ratio approaching the incompressible limit, are presented

A Stochastic Gradient Method with Mesh Refinement for PDE Constrained Optimization under Uncertainty

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth tracking-type functional subject to a linear partial differential equation with random coefficients and box constraints. The approach we take is based on stochastic approximation where, in place of a true gradient, a stochastic gradient is chosen using one sample from a known probability distribution. Feasibility is maintained by performing a projection at each iteration. In the application of this method to PDE-constrained optimization under uncertainty, new challenges arise. We observe the discretization error made by approximating the stochastic gradient using finite elements. Analyzing the interplay between PDE discretization and stochastic error, we develop a mesh refinement strategy coupled with decreasing step sizes. Additionally, we develop a mesh refinement strategy for the modified algorithm using iterate averaging and larger step sizes. The effectiveness of the approach is demonstrated numerically for different random field choices

Huntingtons Kampf der Kulturen im geschichtsphilosophischen Kontext

In dieser Seminararbeit untersuche ich Huntingtons These vom »Kampf der Kulturen« und stelle sie in einen geschichtsphilosophischen Kontext. Mit Spenglers Idee vom »Untergang des Abendlandes« und Toynbees »Gang der Weltgeschichte« stelle ich zwei solche Ansätze vor, auf die Huntington ganz explizit zurückgreift. Vor allem auf ihren Kulturbegriff greift er zurück, indem er die Kulturen für die Konfliktlinien von morgen hält. Dass er weniger das zyklische Denken berücksichtigt und keine historische Perspektive einnimmt, lässt mich schließen, dass Huntingtons These zwar auf viele geschichtsphilosophische Elemente aufbaut, selbst jedoch keine eigene geschichtsphilosophische Position darstellt. Dies illustrieren auch die von mir angeführten ausgewählten Reaktionen auf Huntington aus unterschiedlichen Perspektiven

Planning Preservation In Pompeii: Revising Wall Painting Conservation Method And Management

The management of Pompeii’s focus on excavation and tourism has caused its wall art to fall into disrepair, but a new focus on efficiency and sustainable practice has the potential to relieve the emergency of Pompeii’s restoration work. Hasty excavations, intermittent and piecemeal conservation, and financial mismanagement have all contributed to the state of decay that has consumed wall painting in this UNESCO World Heritage Site. This article reviews past practices of conservation and management and proposes a step-by-step approach for lasting restoration work on wall paintings

Periodic Atlas of the Metroscape: The Face of Density, Diversity, and Disparity in 20th Century Portland

We of the 21st century often congratulate ourselves on policies that have led to greater density and diversity in our urban settings, as remedies to the sprawl, ghettoization, and poverty that became the bane of planners and activists during the last half of the previous one hundred years. But the maps on this and following pages, generated by the Teaching American History Project of the Institute of Portland Metropolitan Studies, suggest that there was plenty of density in various parts of the city at times in the twentieth century and a lot of diversity in certain neighborhoods. Often, these outcomes were the result of intentional policies of the city government and its business allies, especially those in real estate, transportation, and finance. Frequently, these policies perpetuated or accelerated poverty and decline in the neighborhoods--although those who made them said they were designed to ensure the greater good, or to conform to consensus values, or that they were promulgated because there were more pressing matters to address. Today, we have replaced these policies with different and (we think) more humane, forward looking ones where urban planning is concerned. But perhaps we have only proved that, as the proverb has it, \u27There is nothing new under the sun,\u27 or maybe that as the great historian Arthur Schlesinger, Jr. put it, we have yet to learn what is necessary and what is merely the product of our contingent arrangements

Aktive Arbeitsmarktpolitik im Brennpunkt IV: Evaluierung der Lehrstellenförderung in Wien

Es ist nicht das erste Mal, daß abzwien bzw. einzelne Maßnahmen der Einrichtung einer Evaluation unterzogen wurden. Die Ergebnisse einer ersten - eher qualitativ orientierten - Evaluation, die den Charakter einer wissenschaftlichen Begleitung hat, erschien 1995 als Nr. 2 der Wiener Reihe des AMS Wien.1 Weiterhin gab es in den 90er Jahren eine Overhead-Evaluation. Ganz aktuell liegt die Evaluation einer sehr neuen Maßnahme von abzwien vor, nämlich Karenz Plus. Die Besonderheiten der vorliegenden Studie liegen zum einen darin, daß der Versuch unternommen wird, das gesamte abzwien mit seinen inzwischen sehr vielen und vielfältigen Maßnahmen zu untersuchen. Zum zweiten sind im Design der Studie sowohl qualitative als auch quantitative Methoden integriert

On the Dependence of the Pressure on the Time Step in Incompressible Flow Simulations on Varying Spatial Meshes

Subject of this paper is an analysis of the behavior of the pressure on dynamically changing spatial meshes during the computation of nonstationary incompressible flows. In particular, we are concerned with discontinuous Galerkin finite element discretizations in time. Here it is observed that whenever the spatial mesh is changed between two time steps the pressure in the next time step will diverge with order $k^{-1}$. We will proof that this behavior is due to the fact, that discrete solenoidal fields lose this property under changes of the spatial discretization. In addition we will numerically study the fractional-step-$theta$ scheme, and discuss why the divergence is not observed when using this time discretization. Finally we will derive a possible way to circumvent this problem

Metropolitan Briefing Book, 1997

The Metropolitan briefing book was developed to provide elected and appointed leaders in the six counties with information about issues and trends common to all corners of the region

Relative humidity and its effect on aerosol optical depth in the vicinity of convective clouds

The hygroscopic growth of aerosols is controlled by the relative humidity (RH) and changes the aerosols' physical and hence optical properties. Observational studies of aerosol–cloud interactions evaluate the aerosol concentration using optical parameters, such as the aerosol optical depth (AOD), which can be affected by aerosol humidification. In this study we evaluate the RH background and variance values, in the lower cloudy atmosphere, an additional source of variance in AOD values beside the natural changes in aerosol concentration. In addition, we estimate the bias in RH and AOD, related to cloud thickness. This provides the much needed range of RH-related biases in studies of aerosol–cloud interaction. Twelve years of radiosonde measurements (June–August) in thirteen globally distributed stations are analyzed. The estimated non-biased AOD variance due to day-to-day changes in RH is found to be around 20% and the biases linked to cloud development around 10%. Such an effect is important and should be considered in direct and indirect aerosol effect estimations but it is inadequate to account for most of the AOD trend found in observational studies of aerosol–cloud interactions

First sequence-confirmed case of infection with the new influenza A(H1N1) strain in Germany

Here, we report on the first sequence-confirmed case of infection with the new influenza A(H1N1) virus in Germany. Two direct contacts of the patient were laboratory-confirmed as cases and demonstrate a chain of direct human-to-human transmission