Events & Teaching

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Tuesday, 26.08.2014, 10.15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. A. Litvinenko, King Abdullah University of Science and Technology, Saudi Arabia:
Computation of the response surface in the tensor train data
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the polynomial chaos expansion: sparse and full polynomial (multi-index) sets. In the full set, the polynomial orders are chosen independently in each variable, which provides higher flexibility and accuracy. However, the total amount of degrees of freedom grows exponentially with the number of stochastic coordinates. To cope with this curse of dimensionality, the data is kept compressed in the TT decomposition, a recurrent low-rank factorization. PCE computations on sparse grids sets are extensively studied, but the TT representation for PCE is a novel approach that is investigated in this paper. We outline how to deduce the PCE from the covariance matrix, assemble the Galerkin operator, and evaluate some post-processing (mean, variance, Sobol indices), staying within the low-rank framework. The most demanding are two stages. First, we interpolate PCE coefficients in the TT format using a few number of samples, which is performed via the block cross approximation method. Second, we solve the discretized equation (large linear system) via the alternating minimal energy algorithm. In the numerical experiments we demonstrate that the full expansion set encapsulated in the TT format is indeed preferable in cases when high accuracy and high polynomial orders are required.

(joint with Sergey Dolgov, Boris N. Khoromskij and Hermann G. Matthies)

Host
WIAS Berlin

Thursday, 16.10.2014, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. U. Leonhardt, The Weizmann Institute of Science, Israel:
Transformation optics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Science Magazine listed transformation optics among the top 10 science insights of the decade 2000-2010. The lecture gives an introduction into this subject that may, literally, transform optics. Transformation optics grew out of ideas for invisibility cloaking devices and exploits connections between electromagnetism in media and in geometries. Within a short time it grew into a lively research area with applications ranging from invisibility and perfect imaging to the quantum physics of black holes. Invisibility has been a subject of fiction for millennia, from myths of the ancient Greeks and Germans to modern novels and films. In 2006 invisibility turned from fiction into science, primarily initiated by the publication of first ideas for cloaking devices and the subsequent demonstration of cloaking for microwaves. Perfect imaging is the ability to optically transfer images with a resolution not limited by the wave nature of light. Advances in imaging are of significant importance to modern electronics, because the structures of microchips are made by photolithography; in order to make smaller structures, light with increasingly smaller wavelength is used, which is increasingly difficult. Black holes are surrounded by horizons that create quantum particles from the virtual particles of the quantum vacuum, Hawking radiation. Understanding and testing this mysterious phenomenon will shed light on connections between quantum physics and general relativity.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 21.10.2014, 15.15 Uhr (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Prof. E. Tobisch, Universität Linz, Institut für Analysis, Austria:
Nonlinear resonances in bounded domains
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Oberseminar Nonlinear Dynamics

Host
WIAS Berlin
Freie Universität Berlin
Thursday, 23.10.2014, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. E. Tobisch, Universität Linz, Institut für Analysis, Austria:
Energy cascades in physical systems with small and moderate nonlinearity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 27.11.2014, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Dr. R. Martin, Leibniz-Institut für Astrophysik Potsdam (AIP):
Highly stable mode-locked diode laser system for precision comparisons in microgravity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The contemporary term ?Astrophotonics? has already been in use since about a decade, but it is still a relatively new discipline to most physicists and astronomers. Adopting the definition of ?manipulation of light by materials? for photonics, quite analogous to the term ?electronics?, we understand astrophotonics as a subdiscipline of physics research and engineering, that utilizes optical effects of advanced materials for novel applications in observational astronomy and instrumentation. Historically, the field of photonics has emerged from optoelectronics with revolutionary innovations for the telecommunication sector. In a broader sense, there exist today a growing number of applications in other fields, such as industrial process technologies, sensor and illumination technologies, life science (biophotonics), etc. Astrophotonics seems to be a logical evolution in the area of astronomy, with promising applications for a future generation of instrumentation. I shall present a review of the evolution of astrophotonics with some remarks about the impact on the advance of astrophysics to date, and then focus on selected examples of current research like OH suppression fibre bragg gratings, miniaturized spectrographs ?on-the-chip?, and laser frequency combs for wavelength calibration in spectroscopy. I shall conclude with a somewhat speculative vision of future directions.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
March 11 – 13, 2015 (WIAS-ESH)
Workshop/Konferenz: Applied Mathematics and Simulation for Semiconductors
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin