Combined effect of heterogeneity, anisotropy and saturation on steady state flow and transport: Structure recognition and numerical simulation

1 Natural soil profiles may be interpreted as an arrangement of parts which are characterized by properties like hydraulic conductivity and water retention function. These parts form a complicated structure. Characterizing the soil structure is fundamental in subsurface hydrology because it has a crucial influence on flow and transport and defines the patterns of many ecological processes. We applied an image analysis method for recognition and classification of visual soil attributes in order to model flow and transport through a man-made soil profile. Modeled and measured saturation-dependent effective parameters were compared. We found that characterizing and describing conductivity patterns in soils with sharp conductivity contrasts is feasible. Differently, solving flow and transport on the basis of these conductivity maps is difficult and, in general, requires special care for representation of small-scale processes.

Stabilization of subcritical bypass transition in the leading-edge boundary layer by suction

This work investigates the subcritical spatial transition in the swept Hiemenz boundary layer by means of direct numerical simulations (DNS). A pair of steady co-rotating vortices located at the attachment line is enforced as a primary disturbance leading to streaks which are stable. A small secondary, time-dependent disturbance interacts with these streaks such that instability and breakdown to turbulence may occur. The instability only occurs for a certain band of secondary disturbance frequencies. Positive secondary instability growth rates could be observed for Reynolds numbers as low as , whereas the linear critical Reynolds number is. Uniform wall suction is shown to stabilise this transition mechanism, analogously to results from linear stability theory. The effects of suction on the formation of primary streaks and on the secondary growth rate are decoupled. For streaks of different suction whose amplitude is held constant by adjusting the Reynolds number, the suction is shown to increase the growth rate of the secondary instability. The stabilising influence of wall suction consists in decreasing the streak amplitude only. Depending on the Reynolds number and the suction strength, breakdown may either occur locally and may be convected along the far-field streamlines, or occur globally and cover broad regions in the downstream direction.

Patient-specific finite-element simulation of the human cornea: A clinical validation study on cataract surgery

The planning of refractive surgical interventions is a challenging task. Numerical modeling has been proposed as a solution to support surgical intervention and predict the visual acuity, but validation on patient specific intervention is missing. The purpose of this study was to validate the numerical predictions of the post-operative corneal topography induced by the incisions required for cataract surgery. The corneal topography of 13 patients was assessed preoperatively and postoperatively (1-day and 30-day follow-up) with a Pentacam tomography device. The preoperatively acquired geometric corneal topography – anterior, posterior and pachymetry data – was used to build patient-specific finite element models. For each patient, the effects of the cataract incisions were simulated numerically and the resulting corneal surfaces were compared to the clinical postoperative measurements at one day and at 30-days follow up. Results showed that the model was able to reproduce experimental measurements with an error on the surgically induced sphere of 0.38D one day postoperatively and 0.19D 30 days postoperatively. The standard deviation of the surgically induced cylinder was 0.54D at the first postoperative day and 0.38D 30 days postoperatively. The prediction errors in surface elevation and curvature were below the topography measurement device accuracy of ±5μm and ±0.25D after the 30-day follow-up. The results showed that finite element simulations of corneal biomechanics are able to predict post cataract surgery within topography measurement device accuracy. We can conclude that the numerical simulation can become a valuable tool to plan corneal incisions in cataract surgery and other ophthalmosurgical procedures in order to optimize patients' refractive outcome and visual function.

From transient to steady state deformation and grain size: A thermodynamic approach using elasto-visco-plastic numerical modeling

Numerical simulation experiments give insight into the evolving energy partitioning during high-strain torsion experiments of calcite. Our numerical experiments are designed to derive a generic macroscopic grain size sensitive flow law capable of describing the full evolution from the transient regime to steady state. The transient regime is crucial for understanding the importance of micro structural processes that may lead to strain localization phenomena in deforming materials. This is particularly important in geological and geodynamic applications where the phenomenon of strain localization happens outside the time frame that can be observed under controlled laboratory conditions. Ourmethod is based on an extension of the paleowattmeter approach to the transient regime. We add an empirical hardening law using the Ramberg-Osgood approximation and assess the experiments by an evolution test function of stored over dissipated energy (lambda factor). Parameter studies of, strain hardening, dislocation creep parameter, strain rates, temperature, and lambda factor as well asmesh sensitivity are presented to explore the sensitivity of the newly derived transient/steady state flow law. Our analysis can be seen as one of the first steps in a hybrid computational-laboratory-field modeling workflow. The analysis could be improved through independent verifications by thermographic analysis in physical laboratory experiments to independently assess lambda factor evolution under laboratory conditions.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Tissue fusion, a new opportunity for sutureless bypass surgery

Microsurgical suturing is the standard for cerebral bypass surgery, a technique where temporary occlusion is usually necessary. Non-occlusive techniques such as excimer laser-assisted non-occlusive anastomosis (ELANA) have certainly widened the spectrum of treatment of complex cerebrovascular situations, such as giant cerebral aneurysms, that were otherwise non-treatable. Nevertheless, the reduction of surgical risks while widening the spectrum of indications, such as a prophylactic cerebral bypass, is still a main aim, that we would like to pursue with our sutureless tissue fusion research. The primary concern in sutureless tissue fusion- and especially in tissue fusion of cerebral vessels- is the lack of reproducibility, often caused by variations in the thermal damage of the vessel. This has prevented this novel fusion technique from being applicable in daily surgical use. In this overview, we present three ways to further improve the laser tissue soldering technique.In the first section entitled "Laser Tissue Soldering Using a Biodegradable Polymer," a porous polymer scaffold doped with albumin (BSA) and indocyanine green (ICG) is presented, leading to strong and reproducible tensile strengths in tissue soldering. Histologies and future developments are discussed.In the section "Numerical Simulation for Improvement of Laser Tissue Soldering," a powerful theoretical simulation model is used to calculate temperature distribution during soldering. The goal of this research is to have a tool in hand that allows us to determine laser irradiation parameters that guarantee strong vessel fusion without thermally damaging the inner structures such as the intima and endothelium.In a third section, "Nanoparticles in Laser Tissue Soldering," we demonstrate that nanoparticles can be used to produce a stable and well-defined spatial absorption profile in the scaffold, which is an important step towards increasing the reproducibility. The risks of implanting nanoparticles into a biodegradable scaffold are discussed.Step by step, these developments in sutureless tissue fusion have improved the tensile strength and the reproducibility, and are constantly evolving towards a clinically applicable anastomosis technique.

An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Characterization and age determination of Quaternary volcanism in the southern Ankaratra region (central Madagascar) through novel approaches in luminescence dating

This work introduces two novel approaches for the application of luminescence dating techniques to Quaternary volcanic eruptions: crystalline xenoliths from lava flows are demonstrated to be basically suitable for luminescence dating, and a set of phreatic explosion deposits from the Late Quaternary Vakinankaratra volcanic field in central Madagascar is successfully dated with infrared stimulated luminescence (IRSL). Using a numerical model approach and experimental verification, the potential for thermal resetting of luminescence signals of xenoliths in lava flows is demonstrated. As microdosimetry is an important aspect when using sample material extracted from crystalline whole rocks, autoradiography using image plates is introduced to the field of luminescence dating as a method for detection and assessment of spatially resolved radiation inhomogeneities. Determinations of fading rates of feldspar samples have been observed to result in aberrant g-values if the pause between preheat and measurement in the delayed measurements was kept short. A systematic investigation reveals that the phenomenon is caused by the presence of three signal components with differing individual fading behaviour. As this is restricted to short pauses, it is possible to determine a minimal required delay between preheating and measurement after which the aberrant behaviour disappears. This is applied in the measuring of 12 samples from phreatic explosion deposits from the Antsirabe – Betafo region in the Late Quaternary Vakinankaratra volcanic field. The samples were taken from stratigraphically correlatable sections and appear to represent at least three phreatic events, one of which created the Lac Andraikiba maar near Antsirabe. The obtained ages indicate that the eruptive activity in the region started in the Late Pleistocene between 113.9 and 99.6 ka. A second layer in the Betafo area is dated at approximately 73 ka and the Lac Andraikiba deposits give an age between 63.9 and 50.7 ka. The youngest phreatic layer is dated between 33.7 and 20.7 ka. These ages are the first recorded direct ages of such volcanic deposits, as well as the first and only direct ages for the Late Quaternary volcanism in the Vakinankaratra volcanic field. This illustrates the huge potential of this new method for volcanology and geochronology, as it enables direct numerical dating of a type of volcanic deposit which has not been successfully directly dated by any other method so far.

3D Direct Simulation Monte Carlo Modelling of the Inner Gas Coma of Comet 67P/Churyumov-Gerasimenko: A Parameter Study

Direct Simulation Monte Carlo (DSMC) is a powerful numerical method to study rarefied gas flows such as cometary comae and has been used by several authors over the past decade to study cometary outflow. However, the investigation of the parameter space in simulations can be time consuming since 3D DSMC is computationally highly intensive. For the target of ESA's Rosetta mission, comet 67P/Churyumov-Gerasimenko, we have identified to what extent modification of several parameters influence the 3D flow and gas temperature fields and have attempted to establish the reliability of inferences about the initial conditions from in situ and remote sensing measurements. A large number of DSMC runs have been completed with varying input parameters. In this work, we present the simulation results and conclude on the sensitivity of solutions to certain inputs. It is found that among cases of water outgassing, the surface production rate distribution is the most influential variable to the flow field.

Fast Update of Conditional Simulation Ensembles

Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at mini- mal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulae proveto substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.