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- ItemDamage functions for climate-related hazards: Unification and uncertainty analysis(Göttingen : Copernicus GmbH, 2016) Prahl, B.F.; Rybski, D.; Boettle, M.; Kropp, J.P.
- ItemQuantifying the effect of sea level rise and flood defence - A point process perspective on coastal flood damage(Göttingen : Copernicus GmbH, 2016) Boettle, M.; Rybski, D.; Kropp, J.P.
- ItemReply to Comment on 'High-income does not protect against hurricane losses'(Bristol : IOP Publishing, 2017) Geiger, Tobias; Frieler, Katja; Levermann, AndersRecently a multitude of empirically derived damage models have been applied to project future tropical cyclone (TC) losses for the United States. In their study (Geiger et al 2016 Environ. Res. Lett. 11 084012) compared two approaches that differ in the scaling of losses with socio-economic drivers: the commonly-used approach resulting in a sub-linear scaling of historical TC losses with a nation's affected gross domestic product (GDP), and the disentangled approach that shows a sub-linear increase with affected population and a super-linear scaling of relative losses with per capita income. Statistics cannot determine which approach is preferable but since process understanding demands that there is a dependence of the loss on both GDP per capita and population, an approach that accounts for both separately is preferable to one which assumes a specific relation between the two dependencies. In the accompanying comment, Rybski et al argued that there is no rigorous evidence to reach the conclusion that high-income does not protect against hurricane losses. Here we affirm that our conclusion is drawn correctly and reply to further remarks raised in the comment, highlighting the adequateness of our approach but also the potential for future extension of our research.
- ItemHigh-income does not protect against hurricane losses(Bristol : IOP Publishing, 2016) Geiger, Tobias; Frieler, Katja; Levermann, AndersDamage due to tropical cyclones accounts for more than 50% of all meteorologically-induced economic losses worldwide. Their nominal impact is projected to increase substantially as the exposed population grows, per capita income increases, and anthropogenic climate change manifests. So far, historical losses due to tropical cyclones have been found to increase less than linearly with a nation's affected gross domestic product (GDP). Here we show that for the United States this scaling is caused by a sub-linear increase with affected population while relative losses scale super-linearly with per capita income. The finding is robust across a multitude of empirically derived damage models that link the storm's wind speed, exposed population, and per capita GDP to reported losses. The separation of both socio-economic predictors strongly affects the projection of potential future hurricane losses. Separating the effects of growth in population and per-capita income, per hurricane losses with respect to national GDP are projected to triple by the end of the century under unmitigated climate change, while they are estimated to decrease slightly without the separation.
- ItemGlobal higher integrability of minimizers of variational problems with mixed boundary conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Fiaschi, Alice; Knees, Dorothee; Reichelt, SinaWe consider integral functionals with densities of p-growth, with respect to gradients, on a Lipschitz domain with mixed boundary conditions. The aim of this paper is to prove that, under uniform estimates within certain classes of p-growth and coercivity assumptions on the density, the minimizers are of higher integrability order, meaning that they belong to the space of first order Sobolev functions with an integrability of order p+e for a uniform e >0. The results are applied to a model describing damage evolution in a nonlinear elastic body and to a model for shape memory alloys.
- ItemExistence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Heinemann, Christian; Kraus, ChristianeThe Cahn-Hilliard model is a typical phase field approach for describing phase separation and coarsening phenomena in alloys. This model has been generalized to the so-called Cahn-Larché system by combining it with elasticity to capture non-neglecting deformation phenomena, which occurs during phase separation in the material. Evolving microstructures such as phase separation and coarsening processes have a strong influence on damage initiation and propagation in alloys. We develop the existing framework of Cahn-Hilliard and Cahn-Larché systems by coupling these systems with a unidirectional evolution inclusion for an internal variable, describing damage processes. After establishing a weak notion of the corresponding evolutionary system, we prove existence of weak solutions for rate-dependent damage processes under certain growth conditions of the energy functional
- ItemExistence results for diffuse interface models describing phase separation and damage(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Heinemann, Christian; Kraus, ChristianeIn this paper we analytically investigate Cahn-Hilliard and Allen-Cahn systems which are coupled with elasticity and uni-directional damage processes. We are interested in the case where the free energy contains logarithmic terms of the chemical concentration variable and quadratic terms of the gradient of the damage variable. For elastic Cahn-Hilliard and Allen-Cahn systems coupled with uni-directional damage processes, an appropriate notion of weak solutions is presented as well as an existence result based on certain regularization methods and an higher integrability result for the strain Literaturverz.
- ItemFeature Adaptive Sampling for Scanning Electron Microscopy([London] : Macmillan Publishers Limited, part of Springer Nature, 2016) Dahmen, Tim; Engstler, Michael; Pauly, Christoph; Trampert, Patrick; de Jonge, Niels; Mücklich, Frank; Slusallek, PhilippA new method for the image acquisition in scanning electron microscopy (SEM) was introduced. The method used adaptively increased pixel-dwell times to improve the signal-to-noise ratio (SNR) in areas of high detail. In areas of low detail, the electron dose was reduced on a per pixel basis and a-posteriori image processing techniques were applied to remove the resulting noise. The technique was realized by scanning the sample twice. The first, quick scan used small pixel-dwell times to generate a first, noisy image using a low electron dose. This image was analyzed automatically and a software algorithm generated a sparse pattern of regions of the image that require additional sampling. A second scan generated a sparse image of only these regions, but using a highly increased electron dose. By applying a selective low-pass filter and combining both datasets, a single image was generated. The resulting image exhibited a factor of ≈3 better SNR than an image acquired with uniform sampling on a Cartesian grid and the same total acquisition time. This result implies that the required electron dose (or acquisition time) for the adaptive scanning method is a factor of ten lower than for uniform scanning.