On Isoconcentration Surfaces of Three Dimensional Turing Patterns

We consider three-dimensional Turing patterns and their isoconcentration surfaces corresponding to the equilibrium concentration of the reaction kinetics. We call these surfaces equilibrium concentration surfaces (EC surfaces). They are the interfaces between the regions of high and low concentrations in Turing patterns. We give alternate characterizations of EC surfaces by means of two variational principles, one of them being that they are optimal for diffusive transport. Several examples of EC surfaces are considered. Remarkably, they are often very well approximated by certain minimal surfaces. We give a dynamical explanation for the emergence of Scherk\u27s surface in certain cases, a structure that has been observed numerically previously in [De Wit et al., 1997]

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.Comment: 22 pages, 3 figures, 2 table

Computational studies of pattern formation in Turing systems

This thesis is an analytical and computational treatment of Turing models, which are coupled partial differential equations describing the reaction and diffusion behavior of chemicals. Under particular conditions, such systems are capable of generating stationary chemical patterns of finite characteristic wave lengths even if the system starts from an arbitrary initial configuration. The characteristics of the resulting dissipative patterns are determined intrinsically by the reaction and diffusion rates of the chemicals, not by external constraints. Turing patterns have been shown to have counterparts in natural systems and thus Turing systems could provide a plausible way to model the mechanisms of biological growth. Turing patterns grow due to diffusion-driven instability as a result of infinitesimal perturbations around the stationary state of the model and exist only under non-equilibrium conditions. Turing systems have been studied using chemical experiments, mathematical tools and numerical simulations. In this thesis a Turing model called the Barrio-Varea-Aragon-Maini (BVAM) model is studied by employing both analytical and numerical methods. In addition to the pattern formation in two-dimensional domains, also the formation of three-dimensional structures is studied extensively. The scaled form of the BVAM model is derived from first principles. The model is then studied using the standard linear stability analysis, which reveals the parameter sets corresponding to a Turing instability and the resulting unstable wave modes. Then nonlinear bifurcation analysis is carried out to find out the stability of morphologies induced by two-dimensional hexagonal symmetry and various three-dimensional symmetries (SC, BCC, FCC). This is realized by employing the center manifold reduction technique to obtain the amplitude equations describing the reduced chemical dynamics on the center manifold. The main numerical results presented in this thesis include the study of the Turing pattern selection in the presence of bistability, and the study of the structure selection in three-dimensional Turing systems depending on the initial configuration. Also, the work on the effect of numerous constraints, such as random noise, changes in the system parameters, thickening domain and multistability on Turing pattern formation brings new insight concerning the state selection problem of non-equilibrium physics.reviewe

Microengineering The Neural Tube

Early embryonic development is a complex and highly regulated orchestra of instructive cues that collectively guide naïve stem cells towards progressively more specialized fates. In the neural tube, the precursor structure to the brain and spinal cord, these signals emanate from ‘organizing centers’ surrounding the neural tube. These organizing centers send out soluble cues or morphogens that diffuse tens to hundreds of microns to recipient cells residing in the neural tube. Re-creating this dynamic landscape of cues in vitro is impossible using standard cell culture tools and techniques. However, microfluidics is perfectly suited to fill this gap, allowing precise control over the microenvironment on the same length scale as the developing embryo. A microfluidic device is presented that is able to re-create some of the spatial patterning events that occur during the early development of the neural tube. This platform enables developmental biologists to reverse engineer development from the ground up, enabling researchers to pose radically new experiments to help answer some of the most relevant questions regarding fate specification in the developing neural tube. Here the device is used to guide mouse embryonic stem cells into motor neurons. Importantly, these motor neurons are able to be directed to differentiate in a defined region of the microdevice, a spatial patterning event that is the hallmark of the developing neural tube. For the first time it is now possible to study the effect of development cues on live populations of stem cells. The characterization of these fundamental developmental processes will prove invaluable in understanding how humans acquire both form and function. One day, it may allow researchers to harness these developmental techniques, which have been refined over thousands of years of evolution, to guide patient derived cells into any user defined cell fate

Control of Spiral Waves in Reaction-Diffusion Systems Using Response Function

This thesis is motivated by the desire to understand spiral wave dynamics in reactiondiffusion systems with particular focus on the FitzHugh-Nagumo model. We attempt to control the behaviour of spiral waves using controller dynamics. Response functions characterise the behaviour of spiral waves under perturbations, and so it is natural to use these for control purposes. In this project, we consider perturbations of the FitzHugh-Nagumo equation using control functions with different support. We calculate the response functions using the adjoint linear system of the FitzHugh-Nagumo equation with 1D controller dynamics and also characterise the control functions with the smallest support function which can be used to control the system in periodic and meander regimes. We find the minimum size of the support function that the radius is comparable to the region of the non zero response function

Proceedings of the Flat-plate Solar Array Project Research Forum on High-efficiency Crystalline Silicon Solar Cells

The high-efficiency crystalline silicon solar cells research forum addressed high-efficiency concepts, surface-interface effects, bulk effects, modeling and device processing. The topics were arranged into six interactive sessions, which focused on the state-of-the-art of device structures, identification of barriers to achieve high-efficiency cells and potential ways to overcome these barriers

Geothermal energy : the potential in the United Kingdom

The marked increase in energy prices in the mid-1970s focused attention on the fact that conventional energy sources are finite. This realisation led to an acceleration of investigations into the feasibility of using sources of energy other than fossil fuels and nuclear energy. Of these so called renewable forms of energy only geothermal resources are currently making a significant contribution to the world's energy needs. The United Kingdom is not a region that is immediately associated with geothermal energy. But the geothermal gradient, which is similar to the world average, gives temperatures of 60° to 75°C at depths of 2 km in many areas, sufficient for a wide range of energy demands. Furthermore, geothermal resources are being developed in the Paris and Aquitaine basins in France, as well as in the Pannonian Basin in Hungary, under somewhat similar geological conditions to those that exist in the United Kingdom. In view of this, the Department of Energy, in collaboration with the Commission of the European Communities, invited the British Geological Survey to investigate the geothermal potential of the UK

CE-QUAL-W2: A Two-dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 3.5

This manual documents the two-dimensional, laterally averaged, hydrodynamic and water quality model CE-QUAL-W2. This manual was prepared in the Environmental Laboratory (EL), us Army Engineer Waterways Experiment Station (WES), Vicksburg, MS. Bonita Niel and Dr. William Roper, CERD-C provided funding for Version 3.1 of the manual under the Numerical Model Maintenance Program. The principal investigator for Version 3.2 of CE-QUAL-W2 and the User Manual was Mr. Thomas M. Cole of the Water Quality and Contaminant Modeling Branch (WQCMB), Environmental Processes and Effects Division (EPED), EL. This report supersedes the Version 3.2 manual. Revisions made in this V3.5 manual were made under the direction of Dr. Scott Wells at Portland State University. Dr. Chris Berger at Portland State University contributed significantly to this revision. Dr. Berger\u27s macrophyte algorithm was one ofthe many new features of V3.5. The assistance of Mr. Robert Annear at Portland State University is also acknowledged

Degradation Analysis and Parameter Extraction of Organic Semiconductor Devices : Investigation by means of Complementary Measurement Techniques combined with Numerical Simulation

Das Verständnis der elektrischen Eigenschaften von organischen Halbleiter-Materialien ist von enormer Bedeutung, um stabile und effiziente Bauelemente zu erreichen. Während organische Leuchtdioden (OLEDs) bereits industriell hergestellt werden, sind organische Solarzellen (OSCs) noch nicht so weit. Beide Technologien eint jedoch das Potential dass sie kostengünstig in grossen Massen, dabei in flexiblen und leichten Bauformen hergestellt werden könnten, was sie interessant für eine ganze Reihe von Anwendungen macht. Die elektrische Funktionsweise von OLEDs und OSCs ist bestimmt durch die physikalischen Prozesse Ladungsträger-Injektion/Extraktion, Transport, Rekombination, Lichtabsorption und -emission. Die Untersuchung dieser Prozesse erfordert ein gutes Verständnis der damit zusammenhängenden Material- und Bauteil-Parameter. Die Etablierung von zuverlässigen Messmethoden und numerischen Modellen zur Bestimmung dieser Parameter ist für die organische Halbleiterindustrie entscheidend, werden doch auch 30 Jahre nach der Erfindung von OLEDs stetig neue organische Halbleitermaterialien entwickelt und Bauelemente optimiert. In dieser Arbeit präsentieren wir einen neuen synoptischen Ansatz, welcher eine Reihe von elektrischen Charakterisierungs-Methoden im stationären Zustand sowie im transienten und ACModus kombiniert. Die Verwendung von komplementären Messungen und analytischen Methoden sowie die qualitative Analyse von spezifischen Charakteristika in den Messungen lässt Rückschlüsse auf die zugrunde liegenden physikalischen Prozesse zu und erlaubt es einzelne Materialparameter zu bestimmen. Dabei sind die verschiedenen Messungen direkt vergleichbar weil sie mit dem selben Messaufbau in kurzer Zeit und bei konstanten Messbedingungen durchgeführt werden. Indem wir diesen kombinatorischen Prozess mit numerischen Drift-Diffusions-Simulationen zusammenbringen, sind wir erstmalig in der Lage die gesamte Bandbreite der elektrischen Experimente zu modellieren. Dies erlaubt uns die Zuverlässigkeit von gebräuchlichen Parameter- Extraktions-Routinen zu testen und ihre Grenzen zu bestimmen. Es zeigt sich, dass der genaueste und zuverlässigste Weg zur Bestimmung des ganzen Parameter-Satzes eine globale Fit-Routine von Drift-Diffusions-Simulationen über die gesamte Reihe an Experimenten ist. Es kann von Vorteil sein, für die Parameter-Analyse spezielle unipolare Bauteile herzustellen, womit Rekombination und andere bipolare Ladungstransport-Effekte vermieden werden. Hier zeigen wir, dass Zwei-Schicht-OLEDs, welche eine polare Elektronen-Transportschicht enthalten, in einem gewissen Spannungsbereich unipolares Verhalten aufweisen. Solche Bauelemente können daher anstelle von Metall-Isolator-Halbleiter (MIS) Bauteilen verwendet werden, um die Loch- Injektion sowie den Loch-Transport in der Loch-Transportschicht, oder in einem beliebigen Material mit passenden molekularen Energieniveaus, zu untersuchen. Durch Variation der Temperatur können wir die thermische Aktivierungsenergie bestimmen, und in Beiträge für den Transport und die Injektion zerlegen. Wir wenden den synoptischen Ansatz weiter an, um Degradation zu untersuchen. Eine Vielzahl von physikalischen und chemischen Prozessen, ausgelöst durch Licht, Temperatur, Feuchte oder elektrischen Strom, kann die Leistung und Stabilität von organischen Halbleiter-Bauelementen beeinträchtigen. Für unsere Studien führen wir ausführliche Messroutinen zu verschiedenen Zeitpunkten während des Alterns durch. Durch die Kombination mit Simulationen sowie durch die Analyse der Signaturen spezifischer Prozesse ist es uns möglich, zwischen verschiedenen Effekten zu unterscheiden und die dominierenden Alterungsmechanismen zu identifizieren. Hierbei zeigt sich, dass in vielen Fällen der gesamte Schichtaufbau, bestehend aus Verkapselung, funktionellen Schichten und dem aktiven Material, in Stabilitäts-Untersuchungen berücksichtigt werden muss. Zusammenfassend lässt sich sagen, dass die Kombination von verschiedenen Experimenten in Verbindung mit Simulationen es ermöglicht, wertvolle Informationen über die Physik hinter Degradationsprozessen zu erhalten. Dieser Ansatz stellt damit einen gültigen und attraktiven Weg für die weitere Charakterisierung von organischen Halbleiter-Materialien und Bauteilen dar