A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves

Glosarium Matematika

273 p.; 24 cm

DETC2006-99643 MODELING DESIGN SPACES WITH DISCONTINUOUS VARIABLES USING NURBS HYPERMODELS

Abstract The vast majority of metamodeling demonstrations focuses on problems composed of continuous variables. However, important engineering design problems often include one or more discontinuous variables that require special attention. Previous work demonstrated the ability of Non-Uniform Rational B-spline HyPerModels to represent highly nonlinear functions composed of continuous variables. With minor modifications those capabilities can be extended to include functions defined by combinations of discontinuous input and output variables of different types, including discrete integer variables, feasibility variables and membership functions. Examples are used to demonstrate these modeling capabilities including applications developed from real engineering design problems such as the optimal positioning of a construction site crane and the optimal lay-up of a composite material I-beam

Numerical methods for large-scale, time-dependent partial differential equations

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described

Proceedings: Computer Science and Data Systems Technical Symposium, volume 1

Progress reports and technical updates of programs being performed by NASA centers are covered. Presentations in viewgraph form are included for topics in three categories: computer science, data systems and space station applications

Nonlinear dynamics and fluctuations in biological systems

The present habilitation thesis in theoretical biological physics addresses two central dynamical processes in cells and organisms: (i) active motility and motility control and (ii) self-organized pattern formation. The unifying theme is the nonlinear dynamics of biological function and its robustness in the presence of strong fluctuations, structural variations, and external perturbations. We theoretically investigate motility control at the cellular scale, using cilia and flagella as ideal model system. Cilia and flagella are highly conserved slender cell appendages that exhibit spontaneous bending waves. This flagellar beat represents a prime example of a chemo-mechanical oscillator, which is driven by the collective dynamics of molecular motors inside the flagellar axoneme. We study the nonlinear dynamics of flagellar swimming, steering, and synchronization, which encompasses shape control of the flagellar beat by chemical signals and mechanical forces. Mechanical forces can synchronize collections of flagella to beat at a common frequency, despite active motor noise that tends to randomize flagellar synchrony. In Chapter 2, we present a new physical mechanism for flagellar synchronization by mechanical self-stabilization that applies to free-swimming flagellated cells. This new mechanism is independent of direct hydrodynamic interactions between flagella. Comparison with experimental data provided by experimental collaboration partners in the laboratory of J. Howard (Yale, New Haven) confirmed our new mechanism in the model organism of the unicellular green alga Chlamydomonas. Further, we characterize the beating flagellum as a noisy oscillator. Using a minimal model of collective motor dynamics, we argue that measured non-equilibrium fluctuations of the flagellar beat result from stochastic motor dynamics at the molecular scale. Noise and mechanical coupling are antagonists for flagellar synchronization. In addition to the control of the flagellar beat by mechanical forces, we study the control of the flagellar beat by chemical signals in the context of sperm chemotaxis. We characterize a fundamental paradigm for navigation in external concentration gradients that relies on active swimming along helical paths. In this helical chemotaxis, the direction of a spatial concentration gradient becomes encoded in the phase of an oscillatory chemical signal. Helical chemotaxis represents a distinct gradient-sensing strategy, which is different from bacterial chemotaxis. Helical chemotaxis is employed, for example, by sperm cells from marine invertebrates with external fertilization. We present a theory of sensorimotor control, which combines hydrodynamic simulations of chiral flagellar swimming with a dynamic regulation of flagellar beat shape in response to chemical signals perceived by the cell. Our theory is compared to three-dimensional tracking experiments of sperm chemotaxis performed by the laboratory of U. B. Kaupp (CAESAR, Bonn). In addition to motility control, we investigate in Chapter 3 self-organized pattern formation in two selected biological systems at the cell and organism scale, respectively. On the cellular scale, we present a minimal physical mechanism for the spontaneous self-assembly of periodic cytoskeletal patterns, as observed in myofibrils in striated muscle cells. This minimal mechanism relies on the interplay of a passive coarsening process of crosslinked actin clusters and active cytoskeletal forces. This mechanism of cytoskeletal pattern formation exemplifies how local interactions can generate large-scale spatial order in active systems. On the organism scale, we present an extension of Turing’s framework for self-organized pattern formation that is capable of a proportionate scaling of steady-state patterns with system size. This new mechanism does not require any pre-pattering clues and can restore proportional patterns in regeneration scenarios. We analytically derive the hierarchy of steady-state patterns and analyze their stability and basins of attraction. We demonstrate that this scaling mechanism is structurally robust. Applications to the growth and regeneration dynamics in flatworms are discussed (experiments by J. Rink, MPI CBG, Dresden).:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 66Das Thema der vorliegenden Habilitationsschrift in Theoretischer Biologischer Physik ist die nichtlineare Dynamik funktionaler biologischer Systeme und deren Robustheit gegenüber Fluktuationen und äußeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen für zwei grundlegende biologische Prozesse: (i) die zell-autonome Kontrolle aktiver Bewegung, sowie (ii) selbstorganisierte Musterbildung in Zellen und Organismen. In Kapitel 2, untersuchen wir Bewegungskontrolle auf zellulärer Ebene am Modelsystem von Zilien und Geißeln. Spontane Biegewellen dieser dünnen Zellfortsätze ermöglichen es eukaryotischen Zellen, in einer Flüssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus für die Synchronisation zweier schlagender Geißeln, unabhängig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur Verfügung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestätigt diesen neuen Mechanismus im Modellorganismus der einzelligen Grünalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des Geißel-Schlags direkt, wofür wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaßlich durch die stochastische Dynamik molekularen Motoren im Innern der Geißeln, welche auch den Geißelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. Zusätzlich zur Regulation des Geißelschlags durch mechanische Kräfte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus für die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein räumlicher Konzentrationsgradient in der Phase eines oszillierenden chemischen Signals kodiert wird. Dieser Chemotaxis-Mechanismus unterscheidet sich grundlegend vom bekannten Chemotaxis-Mechanismus von Bakterien. Wir entwickeln eine Theorie der senso-motorischen Steuerung des Geißelschlags während der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestätigt. In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewählten biologischen Systemen. Auf zellulärer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor für die spontane Selbstorganisation von periodischen Zellskelett-Strukturen, wie sie sich z.B. in den Myofibrillen gestreifter Muskelzellen finden. Dieser Mechanismus zeigt exemplarisch auf, wie allein durch lokale Wechselwirkungen räumliche Ordnung auf größeren Längenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie für selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der Systemgröße skalieren. Dieser neue Mechanismus erfordert weder eine vorgegebene Kompartimentalisierung des Systems noch spezielle Randbedingungen. Insbesondere kann dieser Mechanismus proportionale Muster wiederherstellen, wenn Teile des Systems amputiert werden. Wir bestimmen analytisch die Hierarchie aller stationären Muster und analysieren deren Stabilität und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezüglich Variationen von Parametern und sogar funktionalen Beziehungen zwischen dynamischen Variablen. Zusammen mit Kollaborationspartnern im Labor von J. Rink (MPI CBG, Dresden) diskutieren wir Anwendungen auf das Wachstum von Plattwürmern und deren Regeneration in Amputations-Experimenten.:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 6