Veranstaltungen
- Dienstag, 08.07.2025, 13:30 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Abdul Wahab, University of Management and Technology, Lahore:
Modeling and simulation of blood flow in unhealthy elliptic arteries with computational fluid dynamics approach
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
This study investigates the influence of varying degrees of stenosis on blood flow within elliptic arteries, emphasizing the critical role of artery shape in clinical evaluations as opposed to the commonly studied circular arteries. Unlike prior work, this research offers a precise definition of stenosis by incorporating the measured length, height, and position of the narrowing. Employing the non-Newtonian Williamson fluid model, we conducted comprehensive numerical simulations to examine blood flow through four distinct stenosis formations. The novelty of this work lies in its accurate modeling of stenosis and use of advanced mesh generation, combined with commercial software and the finite volume method, to capture detailed hemodynamic behavior. Visualized results, including pressure profiles, velocity line graphs, and streamlines, further underscore the distinctive flow dynamics shaped by the elliptic geometry. Key findings of the obtained results reveal that blood velocity peaks near the stenosis and drops significantly post-stenosis, with notable variations in flow patterns, energy loss, and pressure distribution across different stenosis types. Further, higher velocity of blood flow is observed in elliptic arteries in comparison with circular ones. In the area of the high corners of stenotic segments, the pressure profile reaches high values. As a result of the narrowing of the arterial cross-section, the varied time shows that the post-stenotic segment of the artery has a higher pressure than the pre-stenotic section. The varied time suggests that an axially symmetric profile will eventually be the norm for the flow within the arterial portion. These insights have profound implications for improving clinical diagnosis and treatment strategies for conditions related to stenosed elliptic arteries.
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Numerical mathematics seminars
Veranstalter
WIAS Berlin
- Mittwoch, 09.07.2025, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Johannes Bäumler, UCLA:
tba
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
tba
Veranstalter
WIAS Berlin
- Mittwoch, 09.07.2025, 15:30 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Amru Hussein, Universität Kassel:
The three limits of the hydrostatic approximation
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
The primitive equations are a large scale model for ocean and atmosphere. Formally, they are derived from the 3D-Navier--Stokes equations by the assumption of a hydrostatic balance. This can be formalized by a rescaling procedure on an $varepsilon$-thin domain where one considers anisotropic viscosities with vertical viscosity $varepsilon^gamma$ and $varepsilon$-independent horizontal viscosity. Now, the choice of the order $gamma$ leads to different limit equations:
For $gamma=2$, one obtains the primitive equations with full viscosity term $-Delta$;
For $gamma>2$, one obtains the primitive equations with only horizontal viscosity term $- Delta_H$;
For $gamma <2$, one obtains the 2D Navier-Stokes equations.
Thus, there are three possible limits of the hydrostatic approximation depending on the assumption on the vertical viscosity. Here, we show how maximal regularity methods and quadratic inequalities - reminiscent of the Fujita-Kato methods - can be an efficient approach to prove norm-convergences in all three cases. This is a joint work with Ken Furukawa, Yoshikazu Giga, Matthias Hieber, Takahito Kashiwabara, and Marc Wrona, see https://arxiv.org/abs/2312.03418 for a preprint.
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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Donnerstag, 10.07.2025, 10:00 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Thierry Gallay, Université Grenoble Alpes, Frankreich:
Axisymmetric vortex rings at high Reynolds number
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We consider the unique axisymmetric solution without swirl of the 3D Navier-Stokes equations with singular initial data corresponding to a circular vortex filament. We are interested in the high Reynolds number regime where the kinematic viscosity is small compared to the circulation of the filament. We first construct an approximate solution which can be expanded in powers of a small parameter corresponding to the aspect ratio of the vortex ring. We then show that the exact solution remains close to our approximation over a long time interval, during which the vortex ring moves along its symmetry axis at a speed that was predicted by Kelvin in 1867. To prove this, we introduce self-similar variables located at the (unknown) position of the ring, and we control the evolution of the perturbations using an energy functional related to Arnold's variational characterization of steady states for the 2D Euler equations. This talk is based on joint work with Vladimir Sverak.
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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
Vietnam Institute for Advanced Study in Mathematics
- Donnerstag, 10.07.2025, 11:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Daniel Matthes, Technische Universität München:
A mediocre two-component variant of the famous result on equilibration in scalar Fokker--Planck equations
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
One of the most striking by-now-classical results on Wasserstein gradient flows is the one about exponential equilibration in nonlinear Fokker--Planck equations: if the nonlinearity satisfies McCann's condition, and the potential is lambda-uniformly convex, then any solution tends to the steady state at exponential rate lambda. The proof a la Felix Otto is a remarkable application of uniform displacement convexity. Despite lots of efforts and some progress (particularly by people at WIAS), no result of comparable generality and simplicity has ever been derived for a system of two such Fokker--Planck equations that are coupled by means of cross diffusion. In this talk, we indicate the main difficulty, which is the total break-down of the displacement convexity as soon as coupling is introduced, no matter how tame. Our main result is that for sufficiently weak coupling, equilibration still happens exponentially fast, with a rate lambda, reduced by the coupling strength. The proof is based on the lambda-uniform displacement convexity of the decoupled system, and treats the non-convexity as deformation, using non-standard nonlinear functional inequalities. A central challenge is that the steady state is non-explicit and compactly supported. Some adaptations of the idea are discussed as well: to systems of non-local aggregation equations, to a Keller--Segel system from chemotaxis, and to the second-order destabilized fourth order thin film equation. This is joint work with Lisa Beck (Augsburg), Christian Parsch (TUM), and Martina Zizza (SISSA).
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Dienstag, 15.07.2025, 10:15 Uhr (WIAS-405-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. André Massing, Norwegian University of Science and Technology, Norwegen:
Cut finite element methods for complex multi-physics problems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
Many advanced computational problems in engineering and biology require the numerical solution of multidomain, multidimension, multiphysics and multimaterial problems with interfaces. When the interface geometry is highly complex or evolving in time, the generation of conforming meshes may become prohibitively expensive, thereby severely limiting the scope of conventional discretization methods.In this talk we focus on the so-called cut finite element methods (CutFEM) as one possible remedy. The main idea is to design a discretization method which allows for the embedding of purely surface-based geometry representations into structured and easy-to-generate background meshes. In the first part of the talk, using the Cahn-Hilliard and biharmonic equation as starting points, we explain how the CutFEM framework leads to accurate and optimal convergent discretization schemes for a variety of PDEs posed on complex geometries. Afterwards we show that the CutFEM framework can also be used to discretize surface-bound PDEs as well as mixed-dimensional problems where PDEs are posed on domains of different topological dimensionality. In the second part of the talk, we discuss how the CutFEM approach can be employed when discretizing PDEs on evolving domains, and showcase the methodology by considering fluid flow problem involving moving interfaces including Navier-Stokes on moving domains and two-phase flow problem. We conclude with a short outlook of current activities focusing on complex interface problems.
Veranstalter
WIAS Berlin - Donnerstag, 17.07.2025, 10:00 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Alice Marveggio, Universität Bonn:
Stability of multiphase mean curvature flow beyond circular topology changes
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
The evolution of a network of interfaces by mean curvature flow features the occurrence of topology changes and geometric singularities. As a consequence, classical solution concepts for mean curvature flow are in general limited to a finite time horizon. At the same time, the evolution beyond topology changes can be described only in the framework of weak solution concepts (e.g., Brakke solutions), whose uniqueness may fail. Following the relative energy approach, we prove a quantitative stability estimate holding up to the singular time at which a circular closed curve shrinks to a point. This implies a weak-strong uniqueness principle for weak varifold-BV solutions to planar multiphase mean curvature flow beyond circular topology changes. We expect our method to have further applications to other types of shrinkers. This talk is based on a joint work with Julian Fischer, Sebastian Hensel and Maximilian Moser.
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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Donnerstag, 17.07.2025, 14:00 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Patrick Jaap, WIAS Berlin:
Stochastic Rounding: When 0.1 + 0.2 - 0.3 does equal zero (at least on average)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
In standard floating point arithmetic, the simple expression 0.1 + 0.2 - 0.3 is not zero due to round-off errors. Try it. Stochastic rounding provides a trick: floating point rounding is done stochastically: sometimes up, sometimes down. This allows for numerical simulations on hardware made for machine learning, where very low precision (down to 16 bits) is common. In this talk the explain the concept of stochastic floats, and showcase numerical simulations in ultra low precision.
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Numerical mathematics seminars
Veranstalter
WIAS Berlin
- Montag, 21.07.2025, 14:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Prof. Osinga Hinke M, The University of Auckland, Neuseeland:
Phase resetting in a system of coupled Van der Pol oscillators
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
Coupled nonlinear oscillators are found in many application contexts; specific examples in photonics are coupled optical cavities and ring resonators. Synchronisation properties of such systems can be probed by studying the response to external perturbations: after relaxation back to the stable oscillation, there is generally a phase shift. Important information can be gained by studying such phase resets as a function of when the perturbation is applied during the oscillation. We present a case study of a prototypical example: two coupled 1:1 phase-locked Van der Pol oscillators. In contrast to single oscillators, this system has a phase space of dimension four. In particular, the basin of attraction of the stable synchronised oscillation has a complicated boundary, and we show how this affects the observed phase resetting in unexpected ways.
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Forschungsseminar Mathematische Modelle der Photonik
Veranstalter
WIAS Berlin
- 29. September – 1. Oktober 2025 (WIAS-ESH)
- Workshop/Konferenz: Mathematical Analysis of Fluid Flows by Variational Methods
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
Freie Universität Berlin
Universität Leipzig
WIAS Berlin
- 15. – 17. Oktober 2025 (WIAS-ESH)
- Workshop/Konferenz: Recent Developments in Spatial Interacting Random Systems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
WIAS Berlin
- 3. – 7. November 2025 (WIAS-Library)
- Workshop/Konferenz:
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Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstrakt
The ARISE project (Analysis of Robust Numerical Solvers for Innovative Semiconductors in View of Energy Transition) brings together the RAPSODI team at Inria Lille and the NUMSEMIC team at WIAS Berlin. It focuses on developing advanced mathematical and numerical models for drift-diffusion models for charge transport with mobile ions, with applications for novel semiconductor devices such as perovskite solar cells and memristors, as well as ionic solutions or corrosion phenomena.
Veranstalter
WIAS Berlin