1,721,010 research outputs found
A first order projection-based time-splitting scheme for computing chemically reacting flows
No full textProhl, Andreas; Prohl, Andreas. (1998). A first order projection-based time-splitting scheme for computing chemically reacting flows. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3189
A second order projection based time-splitting scheme for computing chemically reacting flows
No full textProhl, Andreas. (1998). A second order projection based time-splitting scheme for computing chemically reacting flows. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3190
Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting
No full textFeng, Xiaobing; Prohl, Andreas. (2003). Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3911
Multiscale resolution in the computation of crystalline microstructure
No full textThis paper addresses the numerical approximation of microstructures in crystalline phase transitions without surface energy. It is shown that branching of different variants near interfaces of twinned martensite and simple austenite phases leads to reduced energies in finite element approximations. Such behavior of minimizing deformations is understood for an extended model that involves surface energies. Moreover, the closely related question of the role of different growth conditions of the employed bulk energy is discussed. By explicit construction of discrete deformations in lowest order finite element spaces we prove upper bounds for the energy and thereby clarify the question of the dependence of the convergence rate upon growth conditions and lamination orders. For first order laminates the estimates are optimal.Bartels, Soren; Prohl, Andreas. (2002). Multiscale resolution in the computation of crystalline microstructure. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3723
Numerical analysis of the Cahn-Hilliard equation and approximation for the Hele-Shaw problem, Part I: Error analysis under minimum regularities
No full textIn this first part of a series, we propose and analyze, under minimum regularity assumptions, a semi-discrete (in time) scheme and a fully discrete mixed finite element scheme for the Cahn-Hilliard equation arising from phase transition in materials science, where \vepsi is a small parameter known as an ``interaction length". The primary goal of this paper is to establish some useful a priori error estimates for the proposed numerical methods, in particular, by focusing on the dependence of the error bounds on . Quasi-optimal order error bounds are shown for the semi-discrete and fully discrete schemes under different constraints on the mesh size and the local time step size of the stretched time grid, and minimum regularity assumptions on the initial function and domain . In particular, all our error bounds depend on only in some lower polynomial order for small . The cruxes of the analysis are to establish stability estimates for the discrete solutions, to use a spectrum estimate result of Alikakos and Fusco [3] and Chen [15], and to establish a discrete counterpart of it for a linearized Cahn-Hilliard operator to handle the nonlinear term on the stretched time grid. It is this polynomial dependency of the error bounds that paves the way for us to establish convergence of the numerical solution to the solution of the Hele-Shaw (Mullins-Sekerka) problem (as ) in Part II \cite{XA3} of the series.Feng, Xiaobing; Prohl, Andreas. (2001). Numerical analysis of the Cahn-Hilliard equation and approximation for the Hele-Shaw problem, Part I: Error analysis under minimum regularities. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3659
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Multi-parameter regularization arising in optimal control of fluid flows
Full text linkThe objective of this thesis is to study optimal control problems subject to equations arising in the field of fluid dynamics. This thesis is split into two essential parts. Each of them deals with an important partial differential equation, that are of interest in various applications and are widely considered in current research: The density dependent Navier--Stokes equation and the thin-film equation.
These optimal control problems are motivated in many ways: First, the equations are mathematically interesting due to strong nonlinear effects occurring additionally as coupling effects in the context of optimization. Also, it is not immediate that properties (such as convergence of numerical approximations) are inherited by the optimal control problem. The literature on optimal control subject to nonlinear partial differential equation is rare, while the knowledge on those problems subject to the mentioned equations is even more rare: Only very few works are known, and the content of this thesis is a big contribution to this topic. Finally, for both control problems, there are industrial applications requiring the optimal control of fluid flows (which will also be addressed within the this thesis) such as the control of the interface in aluminum production, or the control of thin liquid layer on a silicon wafer.
In both parts, the use of regularization parameters is vital in order to overcome analytical issues. The coupling of these parameters is specified, and (in the second part) a limiting problem is solved for these parameters tending to zero.
In the first part of this thesis, we consider an optimal control problem for the interface in a two-dimensional two-phase fluid problem. The minimization functional consists of two parts: The -distance to a given density profile and the interfacial length. We show existence of an optimal control and derive necessary first order optimality conditions for a corresponding phase field approximation. An unconditionally stable fully discrete scheme which is based on low order finite element discretization is proposed, and convergence of corresponding iterates to solutions of the continuous optimality conditions for vanishing discretization parameters is shown.
The second part consists of an optimal control problem subject to the thin-film equation which is deduced from the Navier--Stokes equation. The thin-film equation lacks well-posedness for general controls due to possible degeneracies; state constraints are used to circumvent this problematic issue, and ensure well-posedness of the optimal control problem as well as the rigorous derivation of necessary first order optimality conditions for the optimal control problem. A multi-parameter regularization addressing both, the possibly degenerate term in the equation and the state constraint, is considered, and convergence is shown for vanishing regularization parameters by decoupling both effects.
Both parts are concluded by corresponding numerical experiments, validating the models, comparing parameters (of the regularization and of the numerical algorithms) and their scaling to each other, and including academic examples of industrial applications.Ziel dieser Arbeit ist es, optimale Steuerungsprobleme mit Gleichungen, die auf dem Gebiet der Fluiddynamik auftauchen, zu studieren. Die vorliegende Doktorarbeit ist in zwei wesentliche Teile aufgespalten. Jeder Teil behandelt eine wichtige partielle Differentialgleichung, die von Interesse in weitreichenden Anwendungen sind und noch immer aktuell erforscht werden: Die dichteabhängige Navier-Stokes Gleichung und die dünne Filme Gleichung.
Diese optimalen Steuerungsprobleme sind vielseitig motiviert: Zunächst sind die Gleichungen aufgrund starker nichtlinearer Effekte, die im Rahmen der Optimierung zusätzlich zu Kopplungseffekten führen, mathematisch interessant. Weiter ist es nicht unmittelbar klar, ob sich Eigenschaften (wie etwa die Konvergenz numerischer Approximationen) innerhalb der Optimalsteuerungsproblems vererben. Die Erkenntnisse in der Literatur über Optimalsteuerungsprobleme bezüglich nichtlinearen partiellen Differentialgleichungen sind rar, während der Kenntnisstand über jene Optimalsteuerungsprobleme, die sich mit den benannten Gleichungen beschäftigten, noch viel unvollständiger ist: Es sind bisher nur sehr wenige Arbeiten darüber bekannt und der Inhalt der vorliegenden Doktorarbeit ist ein großer Beitrag zu diesem Thema. Schließlich gibt es für beide Probleme industrielle Anwendungen, welche die Steuerung von Flüssigkeitsströmungen erforderlich machen (diese werden innerhalb der vorliegenden Arbeit auch thematisiert), wie etwa die Kontrolle von Grenzflächen in der Aluminiumproduktion oder die Kontrolle von dünnen Flüssigkeitsschicht auf Siliziumwafern.
In beiden Teilen dieser Arbeit ist die Verwendung von Regularisierungsparametern unerlässlich, um analytische Probleme zu überwinden. Die Kopplung dieser Parameter wird spezifiziert und (im zweiten Teil) ist ein Grenzproblem für den Fall gelöst, dass die Parameter gegen Null konvergieren.
Im ersten Teil der vorliegenden Doktorarbeit betrachten wir ein Optimierungsproblem, um die Grenzfläche eines zweidimensionalen Zwei-Phasen Problems zu steuern. Das zu minimierende Funktional besteht dabei aus zwei Teilen: Dem Abstand zu einem gegebenen gewünschten Dichteprofil (gemessen in der -Norm) sowie der Länge der Grenzfläche. Wir zeigen Existenz einer optimalen Steuerung und leiten notwendige Optimalitätsbedingungen erster Ordnung für eine zugehörige Phasenfeld-Approximation her. Wir schlagen ein vorbehaltlos stabiles volldiskretes Schema vor, welches auf einer Finite Elemente Diskretisierung niedriger Ordnung beruht, und wir zeigen für verschwindende Diskretisierungsparameter die Konvergenz zugehöriger optimaler Steuerungen gegen Lösungen der kontinuierlichen Optimalitätsbedingungen.
Der zweite Teil besteht aus einem Optimalsteuerungsproblem bezüglich der dünnen Filme Gleichung, welche aus der Navier-Stokes Gleichung hergeleitet wird. Der dünnen Filme Gleichung fehlt für allgemeine Kontrolle die Wohlgestelltheit aufgrund möglicher Degeneriertheit; Zustandsbeschränkungen werden benutzt, um dieses Problem in den Griff zu umgehen und Wohlgestelltheit des Optimalsteuerungsproblems sicherzustellen sowie notwendige Optimalitätsbedingungen erster Ordnung rigoros herzuleiten. Ein Mehrparameteransatz zur Regularisierung, der beide Probleme -- den möglicherweise degenerierten Term in der Gleichung und die Zustandsbeschränkungen -- anspricht, wird betrachtet, und für diesen Ansatz wird Konvergenz für verschwindende Regularisierungsparameter gezeigt, der beide Effekte entkoppelt.
Beide Teile werden werden von entsprechenden numerischen Experimenten abgeschlossen, welche die Modelle prüfen, Parameter und deren Skalierungen miteinander vergleichen (solche, die für die Regularisierung nötig sind, aber auch welche, die in den numerischen Algorithmen vorkommen) und Beispiel der industriellen Anwendungen auf akademischen Niveau beinhalten
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