Entropie‐dominierte Selbstorganisationsprozesse birnenförmiger Teilchensysteme

The ambition to recreate highly complex and functional nanostructures found in living organisms marks one of the pillars of today‘s research in bio- and soft matter physics. Here, self-assembly has evolved into a prominent strategy in nanostructure formation and has proven to be a useful tool for many complex structures. However, it is still a challenge to design and realise particle properties such that they self-organise into a desired target configuration. One of the key design parameters is the shape of the constituent particles. This thesis focuses in particular on the shape sensitivity of liquid crystal phases by addressing the entropically driven colloidal self-assembly of tapered ellipsoids, reminiscent of „pear-shaped“ particles. Therefore, we analyse the formation of the gyroid and of the accompanying bilayer architecture, reported earlier in the so-called pear hard Gaussian overlap (PHGO) approximation, by applying various geometrical tools like Set-Voronoi tessellation and clustering algorithms. Using computational simulations, we also indicate a method to stabilise other bicontinuous structures like the diamond phase. Moreover, we investigate both computationally and theoretically(density functional theory) the influence of minor variations in shape on different pearshaped particle systems, including the stability of the PHGO gyroid phase. We show that the formation of the gyroid is due to small non-additive properties of the PHGO potential. This phase does not form in pears with a „true“ hard pear-shaped potential. Overall our results allow for a better general understanding of necessity and sufficiency of particle shape in regards to colloidal self-assembly processes. Furthermore, the pear-shaped particle system sheds light on a unique collective mechanism to generate bicontinuous phases. It suggests a new alternative pathway which might help us to solve still unknown characteristics and properties of naturally occurring gyroid-like nano- and microstructures.Ein wichtiger Bestandteil der heutigen Forschung in Bio- und Soft Matter Physik besteht daraus, Technologien zu entwickeln, um hoch komplexe und funktionelle Strukturen, die uns aus der Natur bekannt sind, nachzubilden. Hinsichtlich dessen ist vor allem die Methode der Selbstorganisation von Mikro- und Nanoteilchen hervorzuheben, durch die eine Vielzahl verschiedener Strukturen erzeugt werden konnten. Jedoch stehen wir bei diesem Verfahren noch immer vor der Herausforderung, Teilchen mit bestimmten Eigenschaften zu entwerfen, welche die spontane Anordnung der Teilchen in eine gewünschte Struktur bewirken. Einer der wichtigsten Designparameter ist dabei die Form der Bausteinteilchen. In dieser Dissertation konzentrieren wir uns besonders auf die Anfälligkeit von Flüssigkristallphasen bezüglich kleiner Änderungen der Teilchenform und nutzen dabei das Beispiel der Selbstorganisation von Entropie-dominierter Kolloide, die dem Umriss nach verjüngten Ellipsoiden oder "Birnen" ähneln. Mit Hilfe von geometrischen Werkzeugen wie z.B. Set-Voronoi Tessellation oder Cluster-Algorithmen analysieren wir insbesondere die Entstehung der Gyroidphase und der dazugehörigen Bilagenformation, welche bereits in Systemen von harten Birnen, die durch das pear hard Gaussian overlap (PHGO) Potential angenähert werden, entdeckt wurden. Des Weiteren zeigen wir durch Computersimulationen eine Strategie auf, um andere bikontinuierliche Strukturen, wie die Diamentenphase, zu stabilisieren. Schlussendlich betrachten wir sowohl rechnerisch (durch Simulationen) als auch theoretisch (durch Dichtefunktionaltheorie) die Auswirkungen kleiner Abweichungen der Teilchenform auf das Verhalten des kolloiden, birnenförmigen Teilchensystems, inklusive der Stabilität der PHGO Gyroidphase. Wir zeigen, dass die Entstehung des Gyroids auf kleinen nicht-additiven Eigenschaften des PHGO Birnenmodells beruhen. In ''echten'' harten Teilchensystemen entwickelt sich diese Struktur nicht. Insgesamt ermöglichen unsere Ergebnisse einen besseren Einblick auf das Konzept von notwendiger und hinreichender Teilchenform in Selbstorganistationsprozessen. Die birnenförmigen Teilchensysteme geben außerdem Aufschluss über einen ungewöhnlichen, kollektiven Mechanismus, um bikontinuierliche Phasen zu erzeugen. Dies deutet auf einen neuen, alternativen Konstruktionsweg hin, der uns möglicherweise hilft, noch unbekannte Eigenschaften natürlich vorkommender, gyroidähnlicher Nano- und Mikrostrukturen zu erklären

Entropically driven self-assembly of pear-shaped nanoparticles

This thesis addresses the entropically driven colloidal self-assembly of pear-shaped particle ensembles, including the formation of nanostructures based on triply periodic minimal surfaces, in particular of the Ia3d gyroid. One of the key results is that the formation of the Ia3d gyroid, re-ported earlier in the so-called pear hard Gaussian overlap (PHGO) approximation and confirmed here, is due to a slight non-additivity of that potential; this phase does not form in pears with true hard-core potential. First, we computationally study the PHGO system and present the phase diagram of pears with an aspect ratio of 3 in terms of global density and particle shape (degree of taper), containing gyroid, isotropic, nematic and smectic phases. We confirm that it is adequate to interpret the gyroid as a warped smectic bilayer phase. The collective behaviour to arrange into interdigitated sheets with negative Gauss curvature, from which the gyroid results, is investigated through correlations of (Set-)Voronoi cells and local curvature. This geometric arrangement within the bilayers suggests a fundamentally different stabilisation mechanism of the pear gyroid phase compared to those found in both lipid-water and di-block copolymer systems forming the Ia3d gyroid. The PHGO model is only an approximation for hard-core interactions, and we additionally investigate, by much slower simulations, pear-assemblies with true hard-core interactions (HPR). We find that HPR phase diagram only contains isotropic and nematic phases, but neither gyroid nor smectic phases. To understand this shape sensitivity more profoundly, the depletion interactions of both models are studied in two pear-shaped colloids dissolved in a hard sphere solvent. The HPR particles act as one would expect from a geometric analysis of the excluded-volume minimisation, whereas the PHGO particles show deviations from this expectation. These differences are attributed to the unusual angle dependency of the (non-additive) contact function and, more so, to small overlaps induced by the approximation. For the PHGO model, we further demonstrate that the addition of a small concentration of hard spheres ("solvent") drives the system towards a Pn3m diamond phase. This result is explained by the greater spatial heterogeneity of the diamond geometry compared to the gyroid where additional material is needed to relieve packing frustration. In contrast to copolymer systems, however, the solvent mostly aggregates near the diamond minimal surface, driven by the non-additivity of the PHGO pears. At high solvent concentrations, the mixture phase separates into “inverse” micelle-like structures with the blunt ends at the micellar centres and thin ends pointing out-wards. The micelles themselves spontaneously cluster, indicative of a hierarchical self-assembly process for bicontinuous structures. Finally, we develop a density functional for hard solids of revolution (including pears) within the framework of fundamental measure theory. It is applied to low-density ensembles of pear-shaped particles, where we analyse their response near a hard substrate. A complex orientational ordering close to the wall is predicted, which is directly linked to the particle shape and gives insight into adsorption processes of asymmetric particles. This predicted behaviour and the differences between the PHGO and HPR model are confirmed by MC simulations

A single cell based model for cell divisions with spontaneous topology changes

The development of multicellular organisms is accompanied by the formation of tis- sues of precise shapes, sizes and topologies. Remarkable similarities between tissue topologies, in particular proliferating epithelial topologies, in various species suggest that the mechanisms that govern the formation of tissues are conserved among species. To understand these mechanisms various models have been developed. In this thesis, we present a novel mechanical model for cell divisions and tissue for- mation. The model accounts for cell mechanics and cell-cell adhesion. In our model, each cell is treated individually, thus the changes in cell’s shape and its local rearrange- ments occur naturally as a response to the evolving cellular environment and cell-cell interactions. We introduce the processes of cell growth and divisions and numerically simulate tissue proliferation. As tissue grows starting from few cells, we follow the dynamics of the tissue growth and cell packing topologies. The outcomes are com- pared with experimental observations in Drosophila wing growth. Our model accounts for the exponential decay of the mitotic index and reproduces commonly observed cell packing topologies in proliferating epithelia. Next, we consider two biologically relevant division schemes, namely, division through asymmetric division plane and division by Hertwig’s rule. We study the im- pact of division planes on tissue growth and show that the division plane may affect cell packing topologies. Development of the tissue is accompanied by cellular rearrange- ments. We vary the extent of cellular rearrangements and analyse their effects on tissue topology. We find that when cells are allowed to move freely, more organized packing topologies emerge

Automatic 3D model creation with velocity-based surface deformations

The virtual worlds of Computer Graphics are populated by geometric objects, called models. Researchers have addressed the problem of synthesizing models automatically. Traditional modeling approaches often require a user to guide the synthesis process and to look after the geometry being synthesized, but user attention is expensive, and reducing user interaction is therefore desirable. I present a scheme for the automatic creation of geometry by deforming surfaces. My scheme includes a novel surface representation; it is an explicit representation consisting of points and edges, but it is not a traditional polygonal mesh. The novel surface representation is paired with a resampling policy to control the surface density and its evolution during deformation. The surface deforms with velocities assigned to its points through a set of deformation operators. Deformation operators avoid the manual computation and assignment of velocities, the operators allow a user to interactively assign velocities with minimal effort. Additionally, Petri nets are used to automatically deform a surface by mimicking a user assigning deformation operators. Furthermore, I present an algorithm to translate from the novel surface representations to a polygonal mesh. I demonstrate the utility of my model generation scheme with a gallery of models created automatically. The scheme's surface representation and resampling policy enables a surface to deform without requiring a user to control the deformation; self-intersections and hole creation are automatically prevented. The generated models show that my scheme is well suited to create organic-like models, whose surfaces have smooth transitions between surface features, but can also produce other kinds of models. My scheme allows a user to automatically generate varied instances of richly detailed models with minimal user interaction

Visualization of implicit geographic information through map-like graphics

Viele von Web 2.0-Benutzern gesammelte Daten sind ortsbezogen, wobei der Ort meist nur eine Information unter vielen ist und dem Ortsbezug häufig keine besondere Bedeutung zugesprochen wird. Jedoch werden auch mehr und mehr geographische Informationen von Laien gesammelt und im Netz veröffentlicht. Trotz der technischen Möglichkeiten, die im Web-2.0 geboten werden, ist es für Nutzer ohne entsprechendes Expertenwissen meist nicht möglich, gut lesbare und ansprechende Karten zu erzeugen. Dieses Problem besteht, da der Nutzer den darzustellenden Inhalt bestimmt, ohne dass überprüft wird, ob die daraus resultierende Karte den kartographischen Ansprüchen genügt. Des Weiteren hat der Nutzer keinerlei Möglichkeiten, die Standardkartenbilder zu bearbeiten, um beispielsweise für seine Thematik irrelevante Objekte auszublenden oder durch Verdrängung relevante Objekte freizustellen. Besonders bei der Darstellung von POIs treten Überlappungen zwischen Signaturen häufig auf. Trotz des Bedarfs existiert aus verschiedenen Gründen keine etablierte Methode zur Verdrängung von Punktdaten. Daher liegt der Schwerpunkt dieser Arbeit auf der Entwicklung von Verfahren zur Verdrängung von Punktsignaturen. Als Hilfsstrukturen werden dazu Voronoi-Diagramme benutzt und als nutzergenerierte Information werden Sentiments visualisiert. Für den Entwurf der Visualisierungen werden relevante kartographische Bedingungen berücksichtigt und durch zugehörige Qualitätsmaße bewertet. Für die Darstellung von Sentiments werden neben der Verwendung von Punktsignaturen zwei weitere Darstellungsarten erstellt: Anpassung gegebener Signaturen und die Darstellung von Sentiments als Kontinua. Es werden Verdrängungsverfahren für Punktsignaturen entworfen und implementiert. Zur Bestimmung der Verschiebungsrichtung werden zwei verschieden Heuristiken vorgeschlagen und untersucht. Des Weiteren wird eine Möglichkeit zur Steigerung der Effizienz durch Aufteilung der Punktmenge aufgezeigt. Die Bewertung der entworfenen Punktsignaturen erfolgt durch eine Umfrage. Anschließend wird das realisierte Verfahren für gleich große Kreissignaturen in drei Aspekten evaluiert: Grad der Reduzierung der Iterationsschritte durch Zerlegung der Punktmenge, erreichte Verminderung der Überlappungsfläche und Veränderung der relativen Lage der Punkte.A lot of user generated information accumulated in the web is related to a place, with the location usually being just one piece of information among many, which gets no special attention. However, more and more geographic information is collected by laymen and published on the web. Despite the technical possibilities that are offered in Web 2.0, it is usually not possible for users without expert knowledge to produce legible and appealing maps. This problem exists because the user determines the content to be displayed without checking whether the resulting map meets the cartographic requirements. Furthermore, the user has no possibilities to edit the standard map images, for example, hide for his subject irrelevant objects or reducing overlap of relevant objects by displacement. Especially when displaying POIs, overlaps between point symbols often occur. Despite the need, there is no established method for displacing point data for various reasons. Therefore, the focus of this work is the development of methods for the displacement of point signatures. Voronoi diagrams are used as auxiliary structures and sentiment is visualized as user-generated information. For the design of the visualizations relevant cartographic requirements are taken into account and evaluated by quality measures. For the depiction of sentiments, in addition to the use of point symbols, two further types of visualizations are created: adaptation of given map symbols and the representation of sentiments as continua. Displacement techniques for point symbols are designed and implemented. To determine the direction of displacement two different heuristics are proposed and examined. Furthermore, a way to increase the efficiency by dividing the point set is shown. The evaluation of the designed point symbols is done by a survey. Subsequently, the realized method for circular symbols with equal size is evaluated in three aspects: degree of reduction of the iteration steps by decomposition of the point set, achieved reduction of the overlap area and change of the relative position of the points

Advanced Knowledge Application in Practice

The integration and interdependency of the world economy leads towards the creation of a global market that offers more opportunities, but is also more complex and competitive than ever before. Therefore widespread research activity is necessary if one is to remain successful on the market. This book is the result of research and development activities from a number of researchers worldwide, covering concrete fields of research

Stable Topological Structures in Data

Topological data analysis is a relatively new and emerging field - it combines concepts from computational geometry and algebraic topology to analyze data. This thesis builds on the recent result on continuous optimization of point clouds via persistence diagrams by giving further theoretic results on the geometric realization of the gradient on the persistence diagrams in the underlying metric space of point clouds and giving experimental results on two distinct applications where the use of this method yields novel approaches to the problems presented. After introduction of the needed preliminary information about simplicial complexes, (persistent) homology, and neural networks, the key concepts from the three topics are used to describe and define the notions of continuous optimization of point clouds via persistence diagrams. The idea behind it is to use the information about the topology, which is encoded in the persistence diagram, to adjust the coordinates of the points in the point cloud so that the point cloud exhibits some desired topological structures or properties. The algorithm for optimization is described for two different cases: when the coordinates of the point cloud are directly optimized, and when we optimize the coordinates indirectly through some parameters. These two cases serve as basis for two applications we discuss - to optimize the point clouds and to optimize the embedding of a time series. Experimental work on optimization of point clouds revealed strong potential for generation of point clouds with specific requirements on the topological structure - may it be in terms of persistence diagrams or with regards to the distribution of points in the persistence diagram. When optimizing the delay-coordinate embeddings of a time series the method gave good results on finding an appropriate delay to construct informative embeddings with