Veranstaltungen

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Dienstag, 26.09.2017, 13.30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Y. Ren, Dalian University of Technology, China:
On tetrahedralisations containing knotted and linked line segments
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
This talk considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schönhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments?
In this talk, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. When the number of twisted line segments is larger than 3, it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 twisted line segments. We show that the addition of a pair of new interior edges decomposes the original knot (or link) into two links (or knots) with less crossing numbers. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n ≥ 3) twisted line segments. This theorem implies that the family of polyhedra generalised from the Schönhardt polyhedron by Rambau are all indecomposable.

Veranstalter
WIAS Berlin
4. – 6. Oktober 2017 (WIAS-ESH)
Workshop/Konferenz: Homogenization Theory and Applications
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
SFB 1114: Scaling Cascades in Complex Systems
SFB 910 ``Control of self-organizing nonlinear systems: Theoretical methods and concepts of application''
11. – 14. Oktober 2017 (WIAS-ESH)
Workshop/Konferenz: SPP 1962 Autumn School 2017 ``Nonsmooth Structures in Mathematical Models''
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
There will be an autumn school on "Nonsmooth Structures in Mathematical Models" at the Weierstrass Institute in Berlin as part of the DFG SPP 1962. We will have three lecturer courses: 'Splitting algorithms in nonsmooth convex and nonconvex optimization' by Prof. Dr. Bot, 'Systems with rate independence: models, sensitivity, optimization' by Prof. Dr. Brokate, 'Problems with equilibrium constraints: Theory and numerics' by Prof. Dr. Outrata. More details of the program can be found at http://www.wias-berlin.de/workshops/sppsummerschool2017/program.jsp. The autumn school will start at 4pm on the 11th October and end around 12:30pm on the 14th October. This school is primarily intended for the doctoral and postdoctoral students. Interested parties may apply to register; the number of available places is limited so registration is mandatory for all and the deadline for registration is 30th August. There is no registration fee, however travel costs will not be paid. For full details and registration, please see http://www.wias-berlin.de/workshops/sppsummerschool2017/index.jsp.

Veranstalter
WIAS Berlin
DFG Schwerpunktprogramm 1962
Donnerstag, 12.10.2017, 10.30 Uhr (HU Berlin in Adlershof RUD25 Raum 2.417)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. S. Schmidt, Universität Würzburg:
SQP methods for shape optimization based on weak shape Hessians
mehr ... Veranstaltungsort
Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Johann-von-Neumann-Haus, Raum 2.417

Abstrakt
Many PDE constrained optimization problems fall into the category of shape optimization, meaning the geometry of the domain is the unknown to be found. Most natural applications are drag minimization in fluid dynamics, but many tomography and image reconstruction problems also fall into this category. The talk introduces shape optimization as a special sub-class of PDE constraint optimization problems. The main focus here will be on generating Newton-like methods for large scale applications. The key for this endeavor is the derivation of the shape Hessian, that is the second directional derivative of a cost functional with respect to geometry changes in a weak form based on material derivatives instead of classical local shape derivatives. To avoid human errors, a computer aided derivation system is also introduced. The methodologies are tested on problem from fluid dynamics and geometric inverse problems.

Weitere Informationen
Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations

Veranstalter
WIAS Berlin
Humboldt-Universität zu Berlin
Montag, 16.10.2017, 14.00 Uhr (WIAS-ESH)
INSTITUTSKOLLOQUIUM
Dr. S. Amiranashvili, WIAS:
Negative frequency radiation in optical fibers
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
Montag, 30.10.2017, 14.00 Uhr (WIAS-ESH)
INSTITUTSKOLLOQUIUM
Prof. Dr. L. Berlyand, Pennsylvania State University, USA:
Hierarchy of PDE Models of Cell Motility
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We consider mathematical PDE models of motility of eukaryotic cells on a substrate and discuss them in a broader context of active materials. Our goal is to capture mathematically the key biological phenomena such as steady motion with no external stimuli and spontaneous breaking of symmetry. We first describe the hierarchy of PDE models of cell motility and then focus on two specific models: the phase-field model and the free boundary problem model. The phase-field model consists of the Allen-Cahn equation for the scalar phase field function coupled with a vectorial parabolic equation for the orientation of the actin filament network. The key mathematical properties of this system are (i) the presence of gradients in the coupling terms and (ii) the mass (volume) preservation constraints. These properties lead to mathematical challenges that are specific to active (out of equilibrium) systems, e.g., the fact that variational principles do not apply. Therefore, standard techniques based on maximum principle and Gamma-convergence cannot be used, and one has to develop alternative asymptotic techniques. The free boundary problem model consists of an elliptic equation describing the flow of the cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. This PDE system is of Keller-Segel type but in a free boundary setting with nonlocal condition that involves boundary curvature. Analysis of this system allows for a reduction to a Liouville type equation which arises in various applications ranging from geometry to chemotaxis. This equation contains an additional term that presents an additional challenge in analysis. In the analysis of the above models our focus is on establishing the traveling wave solutions that are the signature of the cell motility. We also study breaking of symmetry by proving existence of non-radial steady states. Bifurcation of traveling waves from steady states is established via the Schauder's fixed point theorem for the phase field model and the Leray-Schauder degree theory for the free boundary problem model. These results are obtained in collaboration with Jan Fuhrmann, M. Potomkin, and V. Rybalko.

Veranstalter
WIAS Berlin
Mittwoch, 22.11.2017, 14.00 Uhr (WIAS-406)
FG Stochastische Systeme mit Wechselwirkung
Dr. S. Simonella, Technische Universität München:
Correlations in the mean field dynamics: a random walk expansion
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Veranstalter
WIAS Berlin