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Donnerstag, 30.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. J.H.M. ten Thije Boonkkamp, Eindhoven University of Technology, Netherlands:
Complete flux schemes fOR conservation laws of advection-diffusion-reaction typ
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Complete flux schemes are recently developed numerical flux approximation schemes for conservation laws of advection-diffusion-reaction type; see e.g. [1, 2]. The basic complete flux scheme is derived from a local one-dimensional boundary value problem for the entire equation, including the source term. Consequently, the integral representation of the flux contains a homogeneous and an inhomogeneous part, corresponding to the advection-diffusion operator and the source term, respectively. Suitable quadrature rules give the numerical flux. For time-dependent problems, the time derivative is considered a source term and is included in the inhomogeneous flux, resulting in an implicit semi-discretisation. The implicit system proves to have much smaller dissipation and dispersion errors than the standard semidiscrete system, especially for dominant advection. Just as for scalar equations, for coupled systems of conservation laws, the complete flux approximation is derived from a local system boundary value problem, this way incorporating the coupling between the constituent equations in the discretization. Also in the system case, the numerical flux (vector) is the superpostion of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term vector, respectively. The scheme is applied to multispecies diffusion and satisfies the mass constraint exactly.
References:
[1] J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen, ``The finite volume-complete flux scheme for advection-diffusion-reaction equations'', J. Sci. Comput., 46, 47--70, (2011).
[2] J.H.M. ten Thije Boonkkamp, J. van Dijk, L. Liu and K.S.C. Peerenboom, ``Extension of the complete flux scheme to systems of comservation laws'', J. Sci. Comput., 53, 552?568, (2012).

Veranstalter
WIAS Berlin
Dienstag, 04.04.2017, 15.15 Uhr (WIAS-ESH)
Seminar Laserdynamik
Prof. E. Knobloch, University of California, USA:
Geostrophic turbulence and the formation of large scale structure
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Low Rossby number convection is studied using an asymptotically reduced system of equations valid in the limit of strong rotation. The equations describe four regimes as the Rayleigh number $Ra$ increases: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger $Ra$, followed for yet larger $Ra$ by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced heat transport efficiency, and finally by geostrophic turbulence. The Nusselt number--Rayleigh number scaling in the ültimate" regime of geostrophic turbulence is predicted and confirmed using direct numerical simulations of the reduced equations. These simulations reveal that geostrophic turbulence is unstable to the formation of large scale barotropic vortices, via a process known as spectral condensation. The details of this process are quantified and its implications explored.

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Seminar Laserdynamik

Veranstalter
WIAS Berlin
Donnerstag, 06.04.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. D. Silvester, University of Manchester, GB:
Accurate time-integration strategies for modelling incompressible flow bifurcations
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbations. In this study, we show that an approach similar to pseudo-spectral analysis can be performed inexpensively using stochastic collocation methods and the results can be used to provide quantitive information about the nature and probability of instability.

Veranstalter
WIAS Berlin
Dienstag, 11.04.2017, 14.00 Uhr (WIAS-406)
Seminar Materialmodellierung
Prof. L. Heltai, SISSA mathLab, Triest, Italien:
A numerical framework for optimal locomotion at low Reynolds numbers
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Swimming (advancing in a fluid in the absence of external propulsive forces by performing cyclic shape changes) is particularly demanding at low Reynolds numbers. This is the regime of interest for microorganisms and micro- or nano-robots, where hydrodynamics is governed by Stokes equations, and swimming is complicated by the fact that viscosity dominates over all participating forces. We exploit a formulation of the swimming problem in the context of Control Theory, and we present a numerical approximation scheme based on Boundary Element Methods (BEM) and reduced space Successive Quadratic Programming (rSQP) that is capable of computing efficiently optimal strokes for a variety of micro swimmers, both biological and artificial. We apply this framework to the study of the locomotion of euglenids (one of the best-known groups of flagellates). These organisms exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). We identify previously unnoticed features of metaboly, and we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.

Veranstalter
WIAS Berlin
Mittwoch, 19.04.2017, 18.15 Uhr (WIAS-ESH)
Berliner Kolloquium Wahrscheinlichkeitstheorie/GK ''Stochastische Analysis''
Prof. Dr. F. den Hollander, Leiden University, Niederlande:
Random walks on dynamic random graphs
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The mixing time of a Markov chain is the time it needs to approach its stationary distribution. For random walks on graphs, the characterisation of the mixing time has been the subject of intensive study. One of the motivations is the fact that the mixing time gives information about the geometry of the graph. In the last few years, much attention has been devoted to the analysis of mixing times for random walks on emphrandom graphs, which poses interesting challenges. Many real-world networks are dynamic in nature. It is therefore natural to study random walks on emphdynamic random graphs. In this talk we consider a random walk on the configuration model, i.e., a random graph with prescribed degrees. We investigate what happens when at each unit of time a fraction $alpha_n$ of the edges is randomly relocated, where $n$ is the number of nodes. We identify emphthree regimes for the mixing time in the limit as $n to infty$, depending on the choice of $alpha_n$. These regimes exhibit surprising behaviour. Joint work with Luca Avena (Leiden), Hakan Guldas (Leiden) and Remco van der Hofstad (Eindhoven)

Veranstalter
Humboldt-Universität zu Berlin
Technische Universität Berlin
Universität Potsdam
WIAS Berlin
Dienstag, 25.04.2017, 15.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
N. Zhivotovskiy, IITP RAS, SkolTech:
Towards minimax optimal rates in classification and regression
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
In this talk, we consider two approaches that allow (in some cases) to obtain minimax rates of the prediction risk up to absolute constants. Classification problems will be considered under small noise conditions for an arbitrary distribution of objects, as well as cases of certain special distributions. In contrast to several standard results in the learning theory, our bounds are simultaneously optimal for entire families of classes.

Veranstalter
WIAS Berlin
Mittwoch, 26.04.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
J. Weed, Massachusetts Institute of Technology, USA:
Optimal rates of estimation for the multi-reference alignment problem
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal.. These bounds show a striking dependence on the signal-to-noise ratio of the problem. Joint work with Afonso Bandeira and Philippe Rigollet.

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Forschungsseminar ``Mathematische Statistik''

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
International Research Training Group 1792
Mittwoch, 14.06.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. J.-M. Loubes, Université Toulouse Paul Sabatier, Frankreich:
Kantorovich distance based kernel for Gaussian processes : Estimation and forecast
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. Here, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling

Veranstalter
WIAS Berlin
Humboldt-Universität zu Berlin
Universität Potsdam