Münchner Mathematische KalenderKalender mit mathematischen Vorträgen im Raum MünchenMon, 13 Mar 2017 11:21:09 +0100
http://mathcal.ma.tum.de/mc/showtalks?
01.03.2017 11:00 Dr. Patrick van Meurs (Kanazawa University): Discrete-to-continuum limits of edge dislocations in 2D
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=937
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=937The starting point is a 2D model for the dynamics of \(n\) dislocations, which are modelled as point particles with a positive or negative ’charge’. In the celebrated engineering paper by Groma and Balogh in 1999, the limit passage n → ∞ of these dislocation dynamics is performed in a statistical mechanics framework, which relies on a phenomenological closure assumption. In my talk, I present how to pass rigorously to the limit n → ∞ by using the theory of Wasserstein gradient flows and using advanced functional analysis on the weak form of the evolution equation. Interestingly, our conclusion for the limiting dynamics of the dislocation density differs from the conclusion in the paper by Groma and Balogh.
03.03.2017 14:00 Ralph Holz (University of Sydney): Consensus and the network - research directions in blockchain
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=953
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=953Over the last six years, blockchains have developed into a 'mainstream'
technology that entire industry sectors are talking about. The latest
generation even supports smart contracts - programs that are executed by
all participants and that may govern everything from simple transactions
to the setup of organisations. Taking a closer look, however, we find
that there is very little deployment beyond the two most prominent
examples, Bitcoin and Ethereum. In this talk, we are going to look at
some of the reasons: the problem of dependability and abortion of
transactions, which is crucial for enterprises; the influence of the
underlying network structure on transaction execution; and the problem
of exploitable smart contracts. Correspondingly, we discuss some
research directions that could prove fruitful in a number of systems,
blockchains or beyond.
Bio:
Ralph Holz is Lecturer in Networks and Security at the School of IT at
the University of Sydney, where he leads the Node for Cybersecurity and
Usable Security inside the Human-Centred Technologies cluster. He works
closely with Data61|CSIRO, Australia's prime innovation body, and is a
Visiting Fellow at the University of New South Wales. Ralph's research
interest is empirical security, in particular measuring the deployment
properties of critical infrastructure (including blockchains) and the
effects and causes of network and routing incidents. He led the
research efforts that culminated in the world's first large-scale, long-
term analysis of the deployment of the Web Public Key Infrastructure.
Most recently, he has turned his attention to analysing the security and
dependability of blockchain networks. Ralph received his PhD from
Technical University of Munich (TUM) in May 2014.
08.03.2017 16:00 Wolfgang Hackbusch (MPI Leipzig): Global and local defect correction
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=954
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=954The (global) defect correction method combines two discretisation scheme. One may be easy solvable,
the other may be better (e.g. or higher consistency order) but more complicated. Even if the
second discretisation is unstable, the defect correction is a finite process leading to a solution
inheriting the features of the better discretisation.
In a similar way, the local defect correction improves the solution locally. This can be used instead
of local grid refinement.
Different from usual discretisations, the obtained solution is neither the solution of the first nor
of the second discretisation. On the other hand it is much more flexible than usual (finite element)
methods.
16.03.2017 17:00 Piotr Swierczynski (TUM): Applications of energy-corrected finite element to optimal control and parabolic problems
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=952
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=952It is a well-known fact that the presence of re-entrant corners, i.e. corner with angle $\Theta > \pi$, in polygonal domains leads to the loss of regularity of solutions of elliptic problems [Kondratiev 1967]. This, in turn, means that only a suboptimal order of convergence of their standard piecewise linear finite element approximation can be obtained. Recently, an effective method of recovering the full second-order convergence for elliptic equations on domains with re-entrant corners, when measured in locally modified $L_2$ and $H^1$ norms, known as energy-correction, has been proposed [Egger, R\"ude, Wohlmuth 2014]. This method is based on a modification of a fixed number of entries in the system's stiffness matrix. In this talk, we present two applications of the energy-correction method.\\
Firstly, we show how the energy-correction method can be applied to finding an approximation of optimal Dirichlet boundary control problem on non-convex domains. We present the saddle-point structure of the problem and investigate the convergence properties of the method building on the work conducted in [Of, Phan, Steinbach 2015].\\
Secondly, we show how the energy-correction method can be applied to regain optimal convergence in weighted norms for parabolic problems and introduce a post-processing strategy yielding optimal convergence order in standard Sobolev norms. Standard discretization approach involving graded meshes results in a very restrictive form of a CFL condition, making the use of explicit time stepping practically impossible. On the other hand, the energy-correction can be used on uniform meshes, allowing for application of explicit time stepping scheme with relatively large time steps. This, combined with mass-lumping strategy, leads to a very efficient discretization of parabolic problems, where at each time step only one vector multiplication with a scaled stiffness matrix needs to be performed. Finally, we extend this idea to higher-order finite element methods.\\
All theoretical results are confirmed by the numerical tests.
28.03.2017 10:30 Dr. Ilaria Lucardesi: On two functionals involving the maximum of the torsion function
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=959
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=959The two most studied elliptic PDEs are probably the torsion problem, also known as St-Venant problem, and the Dirichlet eigenvalue problem. For these classical problems, many estimates and qualitative properties have been obtained, see for example works by Polya, Szego, Schiffer, Payne, Hersch, Bandle, and many others.
In this seminar I present some recent results about upper and lower bounds of two shape functionals involving the maximum of the torsion function: I consider the ratio \(T(\Omega)\lambda_1(\Omega)/|\Omega|\) and the product \(M(\Omega)\lambda_1(\Omega)\), where \(\Omega\) is bounded open set with finite Lebesgue measure \(|\Omega|\), \(T(\Omega)\) denotes the torsion, and \(\lambda_1(\Omega)\) the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.
30.03.2017 14:00 Diverse Vortragende (s. Abstract oder Webseite): Workshop on "Macroscopic Limits of Quantum Systems"
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=928
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=928The main subject of the workshop is the mathematical investigation of equations describing the behaviour of quantum systems at macroscopic scales, and their rigorous emergence from microscopic dynamics. The workshop also serves as an occasion to celebrate the 70th birthday of Herbert Spohn and to congratulate Herbert on the reception of the Max Planck Medal 2017.
Invited Speakers: Jürg Fröhlich, Marcel Griesemer, Christian Hainzl, Mathieu Lewin, Jani Lukkarinen, Marcin Napiórkowski, Peter Pickl, Alessandro Pizzo, Wojciech De Roeck, Chiara Saffirio, Benjamin Schlein, Stefan Teufel, Juan J.L. Velázquez
More information and registration at https://www-m5.ma.tum.de/Allgemeines/MacroscopicLimitsWorkshop