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Weierstrass Institute for Applied Analysis and Stochastics 2 Weierstrass Institute for Applied Analysis and Stochastics 2 Cover figure: Calculation of a stress- and temperature-induced morphology on the µm scale of a tin-lead solder joint Edited by Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) Mohrenstraße 39 D – 10117 Berlin Germany ISSN 1437-7489 Berlin 2005 Fax: + 49 30 2044975 E-Mail: [email protected] World Wide Web: http://www.wias-berlin.de/ Annual Research Report 2005 Foreword 3 The Weierstrass Institute for Applied Analysis and Stochastics (WIAS, member of the Leibniz Asso- ciation) presents its Annual Report in its new design for the first time. It gives a general overview of the scientific life, as well as an account of the scientific progress made in 2005. Following a more general introduction in part one, in its second part seven selected scientific contributions, written for a broader public, highlight some results of outstanding importance. Finally, the third part presents the essential results of the research groups. In contrast to the previous two years, which were marked by the very successful external evalua- tion of WIAS by the Senate of the Leibniz Association and by structural changes, 2005 has been a “normal” year. Scientifically, it has again been successful. The work in the Research Program 2004–2006 is in good progress, and despite funding cuts and increasing competition, WIAS has consolidated its leading position in the mathematical community as a center of excellence in the treatment of complex applied problems. Several scientific breakthroughs were achieved, some of which will be detailed later in this report, and WIAS has even expanded its scope into new ap- Prof. Dr. Jürgen Sprekels, plied problems from medicine, economy, science, and engineering, especially in its main fields of Director competence: – Nano-, and optoelectronics – Optimization and control of technological processes – Phase transitions and multifunctional materials – Stochastics in science and economics – Flow and transport processes in continua – Numerical methods of analysis and stochastics The positive development is reflected by an increased acquisition of grants, by the number of international workshops organized by the institute, by numerous invited lectures held by WIAS members at international meetings and research institutions, and by the many renowned foreign visitors hosted by the institute last year. The number of refereed journal publications was the same as in 2004. In addition to this, no less than five excellent monographs authored by WIAS members appeared in renowned scientific series of top-selling publishing companies. Each one of these monographs marks a milestone and culmi- nation point of long-standing research at WIAS, and is visible evidence for the scientific excellence of its collaborators. As a special highlight, Dr. John Schoenmakers’s book Robust Libor Modelling and Pricing of Derivative Products was chosen by RISKBOOK.com into the “Top Ten Finance Books” of 2005. As another highlight of 2005, Prof. Anton Bovier, the second Deputy Director of WIAS, was invited to deliver a lecture at the International Congress of Mathematicians 2006 in Madrid; he will be one of only eight German speakers at this World Congress. The high rank of WIAS in the mathematical community is also witnessed by the fact that the year- long success story of “Transfer of knowledge via brains” through the institute’s members contin- ued also in 2005: Dr. Markus Reiß was appointed W3 Professor for Statistics at the University of Annual Research Report 2005 4 Foreword Heidelberg. Since the institute’s foundation in 1992, a total of 31 calls (including 16 to full pro- fessorships in Germany and nine to professorships abroad) have been received by WIAS members; given the fact that presently there are 54 scientists on the budget of WIAS, this is a truly remarkable output of which we are proud. 2005 has also been a “year of workshops” at WIAS. No less than 12 international workshops or- ganized by WIAS, the largest number ever, evidenced the institute’s reputation and its role as an attractive meeting place for international scientific exchange and cooperation. In addition to this, WIAS members (co-) organized numerous scientific meetings throughout the world; in particular, the WIAS Director Prof. Jürgen Sprekels was one of the organizers of a meeting at the Mathemati- sches Forschungsinstitut Oberwolfach (MFO). One of the workshops held at WIAS, the MATHEON Workshop “Mathematics in Industry: Process Engineering of Thin Liquid Films” co-organized by the WIAS member PD Dr. Barbara Wagner, de- serves special recognition, since it followed a novel concept. On the first day of this workshop, rep- resentatives from industry introduced concrete industrial problems; these were tackled by small interdisciplinary teams that during the following two days developed mathematical models and so- lution ideas. On the final day of the workshop, the results obtained by the teams have then been presented to the industrial partners. This workshop concept turned out to be a very promising line of approach toward the mathematical treatment of problems from industry. The year 2005 was also marked by the introduction of the “WIAS Postdoctoral Fellowships”. These fellowships, which are granted for visits at WIAS for up to one year, give their holders the opportu- nity to participate in the applied research projects of WIAS. We are hoping that this new instrument of international exchange and cooperation will attract outstanding junior researchers from all over the world. In addition to these “global” activities, WIAS has on the “local” scale intensified its well-establish- ed cooperation with the other mathematical institutions in Berlin, with the main attention directed toward the three Berlin universities. This is witnessed by the fact that as of today five leading members of WIAS, including the director and his two deputies, hold special chairs funded by WIAS at the Berlin universities. Another such appointment is under way, and we are hoping that by the end of 2006 six WIAS members will hold chairs funded by WIAS at the Berlin universities. Besides these activities, and besides the cooperation with the universities through the manifold teaching activities of its members, WIAS initiated and participated in successful applications for Collaborative Research Centers, Priority Programs, and Graduate Colleges of the German Science Foundation (DFG). For example, the institute contributes considerably to the DFG Graduate College “Analysis, Numerics, and Optimization of Multiphase Problems” at the Humboldt-Universität zu Berlin. The highlight of cooperation with the mathematical institutions in Berlin, however, was also in 2005 the joint operation of the DFG Research Center MATHEON “Mathematics for key technologies” located at the Technical University of Berlin. Annually, DFG funds exceeding 5.5 million euros flow into Berlin for MATHEON to become an international beacon of applied mathematics. WIAS is com- mitted to the success of the Center by providing considerable financial and personal resources: Annual Research Report 2005 Foreword 5 the Director of WIAS is a member of MATHEON’s Executive Board, both his deputies are “Scientists in Charge” of mathematical fields in the center, and members of WIAS participate in the manage- ment of 13 of its subprojects. In turn, in 2005 up to ten scientific collaborators and several student assistants employed at WIAS were funded by MATHEON. Presently, all efforts are directed towards winning a second funding period for MATHEON for the years 2006–2010. Our primary aim remains unchanged: to join fundamental research with application-oriented re- search, and, by new scientific insights, to contribute to the advancement of innovative technolo- gies. Owing to the continued effective reduction in our basic funding during the past years, it has become more and more difficult to meet all expectations; however, thus far WIAS has been able not only to keep up its scientific output on a high level, but even to increase it by an optimal use of its resources and its capacities. But now a limit has been reached: A sufficient basic funding is imperative for the institute to main- tain its success in the scientific competition, particularly for grants and industrial cooperation partners, but also for qualified collaborators. Therefore, the institute views with much concern the continuing erosion of its budget. As in the past years, we hope that funding agencies, colleagues and partners from industry, econ- omy, and sciences will find this report informative and will be encouraged to cooperate with us. Berlin, in January 2006 J. Sprekels Annual Research Report 2005 6 Scientific Board Chairman: Prof. Dr. D. Kröner Albert-Ludwigs-Universität Freiburg Institut für Angewandte Mathematik Hermann-Herder-Straße 10, 79104 Freiburg Vice Chairman: Prof. Dr. U. Langer Johan Radon Institute for Computational and Applied Mathematics Österreichische Akademie der Wissenschaften Altenberger Straße 69, 4040 Linz, Austria Prof. Dr. A. Gilg Siemens AG, CTPP2 Otto-Hahn-Ring 6, 81739 München Prof. Dr. F. R. Götze Universität Bielefeld, Fakultät für Mathematik Postfach 10 01 31, 33501 Bielefeld Prof. Dr. W. Th. F. den Hollander Leiden University, Mathematical Institute P.O.Box 9512, 2300 RA Leiden, The Netherlands Prof. DI. Dr. K. Kunisch Karl-Franzens-Universität Graz Institut für Mathematik und Wissenschaftliches Rechnen Heinrichstraße 36, 8010 Graz, Austria Prof. Dr. L. Overbeck Justus-Liebig-Universität Gießen, Mathematisches
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