On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

Mass Movement-Induced Tsunami Hazard on Perialpine Lake Lucerne (Switzerland): Scenarios and Numerical Experiments

Previous studies of the sediments of Lake Lucerne have shown that massive subaqueous mass movements affecting unconsolidated sediments on lateral slopes are a common process in this lake, and, in view of historical reports describing damaging waves on the lake, it was suggested that tsunamis generated by mass movements represent a considerable natural hazard on the lakeshores. Newly performed numerical simulations combining two-dimensional, depth-averaged models for mass-movement propagation and for tsunami generation, propagation and inunda- tion reproduce a number of reported tsunami effects. Four analysed mass-movement scenarios—three based on documented slope failures involving volumes of 5.5 to 20.8 9 106 m3—show peak wave heights of several metres and maximum runup of 6 to [10 m in the directly affected basins, while effects in neighbouring basins are less drastic. The tsunamis cause large-scale inundation over distances of several hundred metres on flat alluvial plains close to the mass-movement source areas. Basins at the ends of the lake experience regular water-level oscillations with characteristic periods of several minutes. The vulnerability of potentially affected areas has increased dramatically since the times of the damaging historical events, recommending a thorough evaluation of the hazard.

Ventilation-perfusion ratio in perflubron during partial liquid ventilation

BACKGROUND: Functional magnetic resonance imaging (fMRI) of fluorine-19 allows for the mapping of oxygen partial pressure within perfluorocarbons in the alveolar space (Pao(2)). Theoretically, fMRI-detected Pao(2) can be combined with the Fick principle approach, i.e., a mass balance of oxygen uptake by ventilation and delivery by perfusion, to quantify the ventilation-perfusion ratio (Va/Q) of a lung region: The mixed venous blood and the inspiratory oxygen fraction, which are equal for all lung regions, are measured. In addition, the local expiratory oxygen fraction and the end capillary oxygen content, both of which may differ between the lung regions, are calculated using the fMRI-detected Pao(2). We investigated this approach by numerical simulations and applied it to quantify local Va/Q in the perfluorocarbons during partial liquid ventilation. METHODS: Numerical simulations were performed to analyze the sensitivity of the Va/Q calculation and to compare this approach with another one proposed by Rizi et al. in 2004 (Magn Reson Med 2004;52:65-72). Experimentally, the method was used during partial liquid ventilation in 7 anesthetized pigs. The Pao(2) distribution in intraalveolar perflubron was measured by fluorine-19 MRI. Respiratory gas fractions together with arterial and mixed venous blood samples were taken to quantify oxygen partial pressure and content. Using the Fick principle, the local Va/Q was estimated. The impact of gravity (nondependent versus dependent) of perflubron dose (10 vs 20 mL/kg body weight) and of inspired oxygen fraction (Fio(2)) (0.4-1.0) on Va/Q was examined. RESULTS: In numerical simulations, the Fick principle proved to be appropriate over the Va/Q range from 0.02 to 2.5. Va/Q values were in acceptable agreement with the method published by Rizi et al. In the experimental setting, low mean Va/Q values were found in perflubron (confidence interval [CI] 0.08-0.29 with 20 mL/kg perflubron). At this dose, Va/Q in the nondependent lung was higher (CI 0.18-0.39) than in the dependent lung regions (CI 0.06-0.16; P = 0.006; Student t test). Differences depending on Fio(2) or perflubron dose were, however, small. CONCLUSION: The results show that derivation of Va/Q from local Po(2) measurements using fMRI in perflubron is feasible. The low detected Va/Q suggests that oxygen transport into the perflubron-filled alveolar space is significantly restrained.

A triplet spike-timing–dependent plasticity model generalizes the Bienenstock–Cooper–Munro rule to higher-order spatiotemporal correlations

Synaptic strength depresses for low and potentiates for high activation of the postsynaptic neuron. This feature is a key property of the Bienenstock–Cooper–Munro (BCM) synaptic learning rule, which has been shown to maximize the selectivity of the postsynaptic neuron, and thereby offers a possible explanation for experience-dependent cortical plasticity such as orientation selectivity. However, the BCM framework is rate-based and a significant amount of recent work has shown that synaptic plasticity also depends on the precise timing of presynaptic and postsynaptic spikes. Here we consider a triplet model of spike-timing–dependent plasticity (STDP) that depends on the interactions of three precisely timed spikes. Triplet STDP has been shown to describe plasticity experiments that the classical STDP rule, based on pairs of spikes, has failed to capture. In the case of rate-based patterns, we show a tight correspondence between the triplet STDP rule and the BCM rule. We analytically demonstrate the selectivity property of the triplet STDP rule for orthogonal inputs and perform numerical simulations for nonorthogonal inputs. Moreover, in contrast to BCM, we show that triplet STDP can also induce selectivity for input patterns consisting of higher-order spatiotemporal correlations, which exist in natural stimuli and have been measured in the brain. We show that this sensitivity to higher-order correlations can be used to develop direction and speed selectivity.

Stress free configuration of the human eye

Numerical simulations of eye globes often rely on topographies that have been measured in vivo using devices such as the Pentacam or OCT. The topographies, which represent the form of the already stressed eye under the existing intraocular pressure, introduce approximations in the analysis. The accuracy of the simulations could be improved if either the stress state of the eye under the effect of intraocular pressure is determined, or the stress-free form of the eye estimated prior to conducting the analysis. This study reviews earlier attempts to address this problem and assesses the performance of an iterative technique proposed by Pandolfi and Holzapfel [1], which is both simple to implement and promises high accuracy in estimating the eye's stress-free form. A parametric study has been conducted and demonstrated reliance of the error level on the level of flexibility of the eye model, especially in the cornea region. However, in all cases considered 3-4 analysis iterations were sufficient to produce a stress-free form with average errors in node location <10(-6)mm and a maximal error <10(-4)mm. This error level, which is similar to what has been achieved with other methods and orders of magnitude lower than the accuracy of current clinical topography systems, justifies the use of the technique as a pre-processing step in ocular numerical simulations.

Hemodynamic Modeling of the Intrarenal Circulation

Three dimensional, time dependent numerical simulations of healthy and pathological conditions in a model kidney were performed. Blood flow in a kidney is not commonly investigated by computational approach, in contrast for example, to the flow in a heart. The flow in a kidney is characterized by relatively small Reynolds number (100 < Re < 0.01-laminar regime). The presented results give insight into the structure of such flow, which is hard to measure in vivo. The simulations have suggested that venous thrombosis is more likely than arterial thrombosis-higher shear rate observed. The obtained maximum velocity, as a result of the simulations, agrees with the observed in vivo measurements. The time dependent simulations show separation regimes present in the vicinity of the maximum pressure value. The pathological constriction introduced to the arterial geometry leads to the changes in separation structures. The constriction of a single vessel affects flow in the whole kidney. Pathology results in different flow rate values in healthy and affected branches, as well as, different pulsate cycle characteristic for the whole system.

Topological lattice actions for the 2d XY model

We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

Prediction of water–rock interaction and porosity evolution in a granitoid-hosted enhanced geothermal system, using constraints from the 5 km Basel-1 well

Numerical simulations based on plans for a deep geothermal system in Basel, Switzerland are used here to understand chemical processes that occur in an initially dry granitoid reservoir during hydraulic stimulation and long-term water circulation to extract heat. An important question regarding the sustainability of such enhanced geothermal systems (EGS), is whether water–rock reactions will eventually lead to clogging of flow paths in the reservoir and thereby reduce or even completely block fluid throughput. A reactive transport model allows the main chemical reactions to be predicted and the resulting evolution of porosity to be tracked over the expected 30-year operational lifetime of the system. The simulations show that injection of surface water to stimulate fracture permeability in the monzogranite reservoir at 190 °C and 5000 m depth induces redox reactions between the oxidised surface water and the reduced wall rock. Although new calcite, chlorite, hematite and other minerals precipitate near the injection well, their volumes are low and more than compensated by those of the dissolving wall-rock minerals. Thus, during stimulation, reduction of injectivity by mineral precipitation is unlikely. During the simulated long-term operation of the system, the main mineral reactions are the hydration and albitization of plagioclase, the alteration of hornblende to an assemblage of smectites and chlorites and of primary K-feldspar to muscovite and microcline. Within a closed-system doublet, the composition of the circulated fluid changes only slightly during its repeated passage through the reservoir, as the wall rock essentially undergoes isochemical recrystallization. Even after 30 years of circulation, the calculations show that porosity is reduced by only ∼0.2%, well below the expected fracture porosity induced by stimulation. This result suggests that permeability reduction owing to water–rock interaction is unlikely to jeopardize the long-term operation of deep, granitoid-hosted EGS systems. A peculiarity at Basel is the presence of anhydrite as fracture coatings at ∼5000 m depth. Simulated exposure of the circulating fluid to anhydrite induces a stronger redox disequilibrium in the reservoir, driving dissolution of ferrous minerals and precipitation of ferric smectites, hematite and pyrite. However, even in this scenario the porosity reduction is at most 0.5%, a value which is unproblematic for sustainable fluid circulation through the reservoir.

Tuning curve of type-0 spontaneous parametric down-conversion

We study the tuning curve of entangled photons generated by type-0 spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal. We demonstrate the X-shaped spatiotemporal structure of the spectrum by means of measurements and numerical simulations. Experiments for different pump waists, crystal temperatures, and crystal lengths are in good agreement with numerical simulations.

Stacking of discontinuous regional palaeoclimate records: Chironomid-based summer temperatures from the Alpine region

Since multi-site reconstructions are less affected by site-specific climatic effects and artefacts, regional palaeotemperature reconstructions based on a number of sites can provide more robust estimates of centennial- to millennial-scale temperature trends than individual, site-specific records. Furthermore, reconstructions based on multiple records are necessary for developing continuous climate records over time scales longer than covered by individual sequences. Here, we present a procedure for developing such reconstructions based on relatively short (centuries to millennia), discontinuously sampled records as are typically developed when using biotic proxies in lake sediments for temperature reconstruction. The approach includes an altitudinal correction of temperatures, an interpolation of individual records to equal time intervals, a stacking procedure for sections of the interval of interest that have the same records available, as well as a splicing procedure to link the individual stacked records into a continuous reconstruction. Variations in the final, stacked and spliced reconstruction are driven by variations in the individual records, whereas the absolute temperature values are determined by the stacked segment based on the largest number of records. With numerical simulations based on the NGRIP δ18O record, we demonstrate that the interpolation and stacking procedure provides an approximation of a smoothed palaeoclimate record if based on a sufficient number of discontinuously sampled records. Finally, we provide an example of a stacked and spliced palaeotemperature reconstruction 15000–90 calibrated 14C yr BP based on six chironomid records from the northern and central Swiss Alps and eastern France to discuss the potential and limitations of this approach.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.