167 research outputs found
A Meshfree Splitting Method for Soliton Dynamics in Nonlinear Schroedinger Equations
No full textA new method for the numerical simulation of the so-called solitondynamics arising in a nonlinear Schroedinger equation in the semi-classical regime is proposed. For the time discretization a classical fourth-order splitting method is used. For the spatial discretization, however, a meshfree method is employed in contrast to the usual choice of (pseudo) spectral methods. This approach allows to keep the degrees of freedom almost constant as the semi-classical parameter becomes small. This behavior is confirmed by numerical experiments
Meshfree exponential integrators
No full textFor the numerical solution of time-dependent partial dierential equations, a class ofmeshfree exponential integrators is proposed. These methods are of particular interest in situationswhere the solution of the dierential equation concentrates on a small part of the computationaldomain which may vary in time. For the space discretization, radial basis functions with compactsupport are suggested. The reason for this choice are stability and robustness of the resultinginterpolation procedure. The time integration is performed with an exponential Rosenbrock method.The required matrix functions are computed by Newton interpolation based on Leja points. Theproposed integrators are fully adaptive in space and time. Numerical examples that illustrate therobustness and the good stability properties of the method are included
Electrospinning as a Fascinating Platform for Teaching Applied Polymer Science with Safe and Sustainable Experiments
No full textAbstract
Electrospinning has been widely used as a versatile technique to generate nanofibers of various materials. It is also helpful in teaching topics ranging from macromolecular chemistry to physics, safety, and sustainability at various levels of difficulty and student involvement. Simple and safe hands-on experiments/manual assays can be realized for less than 30 euros to demonstrate polymer viscosity and nanofiber alignment and solubility. Students can further study (super)hydrophobicity and even upcycle packaging waste into useful filter materials but also improve the electrospinning setup from a manual assay to an inexpensive Arduino-based 3D printed research platform. Alternatively, the latter can be used for teacher demonstrations of more challenging experiments that can also be easily done using a commercial syringe-pump
A minimisation approach for computing the ground state of Gross–Pitaevskii systems
No full textIn this paper, we present a minimisation method for computing the ground stateof systems of coupled Gross–Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation
The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential
No full textThe Leja method is a polynomial interpolation procedure that can be used to computematrix functions. In particular, computing the action of the matrix exponential on a given vector isa typical application. This quantity is required, e.g., in exponential integrators.The Leja method essentially depends on three parameters: the scaling parameter, the location ofthe interpolation points, and the degree of interpolation. We present here a backward error analysisthat allows us to determine these three parameters as a function of the prescribed accuracy. Addi-tional aspects that are required for an efficient and reliable implementation are discussed. Numericalexamples illustrating the performance of our Matlab code are included
Comparison of software for computing the action of the matrix exponential
No full textThe implementation of exponential integrators requires the action of the matrix exponential and related functions of a large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with others from the literature. As we are interested in exponential intergrators we choose the test examples from spatial discretization of time dependent partial differential equations in two and three space dimensions. The test matrices thus have large eigenvalues and can be nonnormal
Review of : Carolin Ostermann, 2015, Cognitive Lexicography. A New Approach to Lexicography Making Use of Cognitive Semantics [Lexicographica. Series Mayor 149], Berlin/Boston, Walter De Gruyter. In RESLA, Revista Española de Lingüística Aplicada/Spanish Journal of Applied Linguistics, 2017/1, pp. 1-12.
No full textReview of : Carolin Ostermann, Cognitive Lexicography. A new approach to lexicography making use of cognitive semantics. (Lexicographica. Series Maior, 149) Berlin/Boston: Walter De Gruyter, 2015, xi + 380 pages, ISBN 978-3-11-042744 8 (HBK); e-ISBN (PDF) 978-3-11-042416-4; e-ISBN (EPUB) 978-3-11-042428-7. The author of this book provides a positive answer to the long-debated question whether or not lexicographers need to know about linguistics (among others, Rundell, 2012). In the same way as lexicography is seen by some as ‘art and craft’ (Landau, 2001), and the ‘poor relation’ of lexicology (Lipka,1995, p. 381), there are arguments—also hard-line—against the potential contributions of linguistics to lexicography (for one, Wierzbicka, 1985, p. 5). Without going all the way to endorsing a theory of lexicography (e.g., Tarp, 2008), arguments on the other side take a positive view of the relationship between linguistics and lexicography. In this context, this book takes as its starting point the premise that lexicography can benefit greatly from neighboring disciplines in linguistics and, more specifically, from Cognitive Linguistics and Cognitive Semantics. This is Cognitive Lexicography. With the title of Chapter 1, it represents “A new approach to lexicography,” in the sense that the full potential of this approach has not been explored yet. With works such as Kövecses and Csábi (2014) and Xu (2015), the author clearly reflects the main developments in applications of cognitive linguistics to lexicography. Whereas the suggested methodology can accommodate new features, it is also hoped that further research takes suggestions on cross-referencing between entries to a further stage, which envisages tailoring dictionary macro-structure and arranging entries and meanings according to the needs of individual users. This may enhance vocabulary learning by focusing on the systematicity of language. To give one example, Kövecses and Csábi (2014, pp. 136-137) point out that “a simply alphabetically arranged dictionary may become a systematically arranged group of entries at a click, if it is made possible that, for instance, we can select words and expressions that describe ANGER or LOVE, in order to see what source domains these use, or words and expressions that contain the word fire in order to see what target domains there may be.” In short, Cognitive Lexicography in the electronic age can adapt dictionaries and dictionary entries specific user needs, goals and profiles, thus playing a major part in making so-called ʽlexicographersʼ dreamsʼ (de Schryver 2003) come true
Efficient coding tools for 360° video
No full text360° video is a relatively new video format. The whole scene around a single point is recorded. During playback the user can choose and change his viewing direction. Interest in 360° video and cameras started growing in mid 2015 and it was of particular interest in the development of the standard Versatile Video Coding (VVC), which was approved in late August 2020. This work was performed in parallel to the development of VVC and focused on the development of coding tools specific to 360° video
Analysis of the correlation rock mass- tunnel boring machine using the example of the headrace tunnel of the power plant Hieflau
No full textDie vorliegende Diplomarbeit ist ein Beitrag zur technisch-wirtschaftlichen Optimierung von Tunnelbauvorhaben, bei welchen ein TBM - Einsatz vorgesehen ist. Sie enthält am Beispiel des Vortriebes für den neuen Triebwasserstollen des Kraftwerks Hieflau eine Analyse von Zusammenhängen zwischen ausgewählten Gebirgsparametern und den automatisch aufgezeichneten Daten der dort eingesetzten Tunnelbohrmaschine. Als Maschinendaten wurden die Nettovortriebsgeschwindigkeit in m/h, die Anpresskraft des Bohrkopfes in kN und das Drehmoment in kNm herangezogen. Als Gebirgsparameter dienten die Gesteinsart und der Zerlegungsgrad.Nach einer Aufbereitung der Daten wurden diese statistisch analysiert, um mögliche Fehler in der Aufzeichnung auszufiltern. Anschließend wurde folgendes untersucht:* Die Korrelation zwischen der Vortriebsgeschwindigkeit und der Anpresskraft, der Vortriebsgeschwindigkeit und dem Drehmoment sowie der Anpresskraft und dem Drehmoment. Diese Korrelationen wurden je nach Gesteinsart einzeln untersucht. Die Einteilung in Gesteinsarten erfolgte gemäß dem vorliegenden geologischen Längenschnitt in fünf verschiedene Bereiche.* Der dreidimensionale Zusammenhang zwischen den drei Maschinenparametern in Abhängigkeit der Gesteinsart. Die dreidimensionale Analyse zeigt den räumlichen Zusammenhang zwischen Vortriebsgeschwindigkeit, Anpresskraft und Drehmoment und gibt Aufschluss über etwaige Maxima. * Die Vortriebsgeschwindigkeit und Anpresskraft in Abhängigkeit der Zerlegungsgrade des Gesteins. Zur Analyse des Zerlegungsgrades wurden drei verschiedene Quellen herangezogen. Als Quellen dienten ein Prognoselängenschnitt, in dem der genaue Kluftabstand prognostiziert wurde sowie ein Längenschnitt, in dem die Bereiche, in denen es zu einer stärkeren Zerlegung des Gebirges kam, aufgezeichnet wurden. Diese Bereiche wurden während des Vortriebs sowohl von den Geologen vor Ort, als auch von der ausführenden Firma in Protokollen festgehalten.<br /
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