Boundary effects on the dynamics of chains of coupled oscillators

We study the dynamics of a chain of coupled particles subjected to a restoring force (Klein-Gordon lattice) in the cases of either periodic or Dirichlet boundary conditions. Precisely, we prove that, when the initial data are of small amplitude and have long wavelength, the main part of the solution is interpolated by a solution of the nonlinear Schr\"odinger equation, which in turn has the property that its Fourier coefficients decay exponentially. The first order correction to the solution has Fourier coefficients that decay exponentially in the periodic case, but only as a power in the Dirichlet case. In particular our result allows one to explain the numerical computations of the paper \cite{BMP07}

Vergleich der Bundesländer: Analyse der Erfolgsfaktoren für den Ausbau der Erneuerbaren Energien 2014 - Indikatoren und Ranking

[Einleitung. Bundesländer-Vergleichsstudie 2014] Die vorliegende Bundesländer-Vergleichsstudie 2014 baut auf den Vorgängerstudien auf. Wie in den früheren Studien werden neben energie- und umweltpolitischen Aspekten der Nutzung Erneuerbarer Energien in den Bundesländern auch technologie- und industriepolitische Aspekte der Branche einbezogen. Dabei werden jeweils sowohl politische Ziele und Anstrengungen als auch bisher beobachtbare Erfolge im Indikatorensystem erfasst. Das Ziel der aktuellen Studie besteht vor allem darin, die vergleichenden Analysen der Bundesländer im Bereich Erneuerbarer Energien zu aktualisieren, wobei eine weitgehende Vergleichbarkeit mit den Ergebnissen der Bundesländer-Vergleichsstudie 2012 angestrebt wird. Darüber hinaus werden in der aktuellen Studie explizit Aspekte der Systemintegration Erneuerbarer Energien in das Indikatorensystem einbezogen, da diese vor dem Hintergrund stark wachsender Anteile Erneuerbarer Energien im Stromsektor zunehmende Bedeutung für das Gelingen der Energiewende erlangt. Mit dem Vorhaben soll die Transparenz über den Stand und die Entwicklung Erneuerbarer Energien in der regionalen Struktur nach Bundesländern erhöht werden. Es dient zugleich der Politikberatung im Hinblick auf die Verbesserung der Rahmenbedingungen für den Ausbau Erneuerbarer Energien in den Bundesländern. Hauptadressaten sind insofern die Entscheidungsträger in den Bundesländern. Berührt werden damit zugleich aber auch politische Abstimmungsfragen auf Bundes- und Kommunalebene. Darüber hinaus richtet sich die Studie auch an die interessierte Öffentlichkeit sowie an die energiewirtschaftliche Fachwelt. Die vorliegende Studie wurde von Februar bis September 2014 in Kooperation des Deutschen Instituts für Wirtschaftsforschung (DIW Berlin) mit dem Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW) und der Agentur für Erneuerbare Energien (AEE) erstellt. Die Datenerfassung wurde im Wesentlichen Anfang Juni 2014 abgeschlossen. Zu den Informationsgrundlagen haben dankenswerterweise die zuständigen Landesministerien sowie zahlreiche Vertreter von Fachverbänden Erneuerbarer Energien und von Industrie- und Handelskammern im Rahmen von Befragungen wesentlich beigetragen. In Kapitel 2 werden zunächst konzeptionelle und methodische Aspekte der Indikatorenanalyse sowie Fragen der Datenverfügbarkeit erläutert. Kapitel 3 enthält eine vollständige Darstellung der ermittelten Einzelindikatoren im Ländervergleich. Auf dieser Basis werden in Kapitel 4 die Einzelindikatoren zu Gruppenindikatoren und zu einem Gesamtindikator für ein übergreifendes Ranking der Bundesländer im Bereich Erneuerbare Energien zusammengefasst. Eine Analyse nach Bundesländern im Hinblick auf Best Practice erfolgt in Kapitel 5. Kapitel 6 enthält eine kurze Zusammenfassung der Ergebnisse. Weitere Details werden im Anhang dokumentiert

On the validity of mean-field amplitude equations for counterpropagating wavetrains

We rigorously establish the validity of the equations describing the evolution of one-dimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic model equation, namely the sine-Gordon equation. We consider both periodic amplitude functions and localized wavepackets. For the localized case, the wavetrains are completely decoupled at leading order, while in the periodic case the amplitude equations take the form of mean-field (nonlocal) Schr\"odinger equations rather than locally coupled partial differential equations. The origin of this weakened coupling is traced to a hidden translation symmetry in the linear problem, which is related to the existence of a characteristic frame traveling at the group velocity of each wavetrain. It is proved that solutions to the amplitude equations dominate the dynamics of the governing equations on asymptotically long time scales. While the details of the discussion are restricted to the class of model equations having a leading cubic nonlinearity, the results strongly indicate that mean-field evolution equations are generic for bimodal disturbances in dispersive systems with \O(1) group velocity.Comment: 16 pages, uuencoded, tar-compressed Postscript fil

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Death and the Plowman or, The Bohemian Plowman

This dialogue about death from the year 1400 has no peer in early German Renaissance literature. Ernest Kirrmann presents an English translation of the German classic, as well as a preface by Alois Bernt giving an introduction to the context and significance of the work. The text is accompanied by five woodcuts reproduced from the earliest known printed version of the German original

Fehlertolerante Systeme in der Automatisierungstechnik

The aspects of safety and availability are increasingly joinly treated. This special edition of AT considers different contributions from the praxis, especially industrial automation, automotive electronics, railways

Procedural Creation of Medical Reports with Hierarchical Information Processing in Radiation Oncology

Background: For many years, the oncological doctor's letter has been the pivotal means of information transfer to general practitioners, medical specialists or medical consultants. Yet, both creator and recipient require a high level of abstraction, retentiveness and analysis due to the large number of diagnoses and therapies. In contrast to the commonly used structure of doctor's letters, where all diagnoses and therapies are listed in sequential order with all diagnoses first, it is by no means trivial to establish the important chronological and hierarchical context in the description of oncological cases. Additional aspects of importance are the integration of these letters into existing clinical and departmental information systems (for example via HL7 interface), various export formats (for example PDF, HTML), fax and encrypted email. Moreover these letters need a modern layout that, among others, meets the requirements of corporate design. Methods: The requirements for a doctor's letter system are manifold and can only be represented rudimentarily via a normal word processing system. Due to this deficiency we developed a system that covers all special features and requirements for clinical use. The system is based on a scalable and extensible client-server architecture. We use the programming languages Harbour, C++, PHP and JavaScript, Microsoft SQL database for data storage and the HL7 standard as the interface to other information systems such as hospital information system (HIS). Export formats are PDF, HTML/XML. Layouts are generated with TeX, LaTeX and MikTeX. Results: The aforementioned requirements were resolved with the doctor's letter and finding system IntDok. The hierarchical presentation of diagnoses, histologies and therapies provides the recipient with a first outline of the course of the disease. A strict procedure controls the whole process of document compilation and assists the user with many highly regarded tools such as text blocks, import and export (PDF and HTML/XML including barcodes) functions or HL7 interface to other information systems. The software also provides a sophisticated mail merging. All content from previous letters can easily be inserted into the current document. A TeX-server automatically provides document layout including supreme hyphenation so that uniform and perfect appearance (corporate design) is guaranteed. The documents are saved in a MS-SQL database (almost 230,000 documents since 1991), independent of any proprietary formats such as MS-Word. Conclusion: Creation of documents is fast, simple and well-structured. Sophisticated tools guarantee the optimal use of human resources and time. The system is an important module in our overall digital work environment

The validity of modulation equations for extended systems with cubic nonlinearities

Modulation equations play an essential role in the understanding of complicated systems near the threshold of instability. Here we show that the modulation equation dominates the dynamics of the full problem locally, at least over a long time-scale. For systems wuh no quadratic interaction term, we develop a method which is much simpler than previous ones. It involves a careful bookkeeping of errors and an estimate of Gronwall type. As an example for the dIssipative case. we find that the Ginzburg-Landau equation is the modulation equation for the Swift-Hohenberg problem. Moreover, the method also enables us to handle hyperbolic problems: the nonlinear Schrodinger equatton is shown to describe the modulation of wave packets in the Sine-Gordon equation

A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem

We consider the 2D inviscid incompressible irrotational infinite depth water wave problem neglecting surface tension. Given wave packet initial data, we show that the modulation of the solution is a profile traveling at group velocity and governed by a focusing cubic nonlinear Schrodinger equation, with rigorous error estimates in Sobolev spaces. As a consequence, we establish existence of solutions of the water wave problem in Sobolev spaces for times in the NLS regime provided the initial data is suitably close to a wave packet of sufficiently small amplitude in Sobolev spaces