Oberseminar Analysis Summer 2022

Organizers: S. Conti, H. Koch, S. Müller, B. Niethammer, M. Rumpf, C. Thiele, J.J.L. Velázquez, I. Cristian

  • Thursday, May 12 at 14:15 in SemR 0.011
    Arianna Giunti (Imperial College London)
    Quantitative homogenization for interacting particle systems
    We are interested in the bulk diffusion matrix $\bar a$ associated to a class of interacting particle systems in $\mathbb R^{d}$. The models that we consider are reversible with respect to the Poisson measures and are of non-gradient type.
    The matrix $\bar a$ may be thought as the effective diffusion of a cloud of interacting particles. Relying on the recent progress in quantitative stochastic homogenization for elliptic PDEs, we prove that finite-volume approximations of $\bar a$ converge at an algebraic rate. Furthermore, we show that $\bar a$ is smooth in the density of particles and we characterise its derivatives.
    This talk is based on joint works with C. Gu (NYU Shanghai), J.-C. Mourrat (ENS Lyon) and M. Nitzschner (NYU Courant).

  • Thursday, June 02 at 14:15 in Lipschitz Saal
    Anna Lagemann (RWTH Aachen University)
    Variational approach to the Arnold invariants and an application of the principle of symmetric criticality
    Planar closed immersed curves can be classified by the Whitney-Graustein theorem which states that the space of immersions of the circle into the plane with the same winding number is connected. Arnold defined three invariants that are locally constant on generic immersions, i.e. curves where all self-intersections are transverse double points.
    We prove existence of minimizers of a truncated version of the tangent-point energy for curves with fixed Arnold invariants and fixed winding number. By sending the truncation parameter to zero, we obtain a $C^{1}$-curve as the limit of a sequence of minimizers, and we investigate properties of that limit curve.
    An application of the principle of symmetric criticality by Palais yields the existence of point symmetric curves in the class of figure-eight shaped curves as critical points of the considered energy.

  • Thursday, June 23 at 15:00 in Lipschitz Saal
    Richard Höfer (Université Paris Cité)
    On the derivation of viscoelastic models for Brownian suspensions
    We consider effective properties of suspensions of inertialess, rigid, anisotropic, Brownian particles in Stokes flows. Recent years have seen tremendous progress regarding the rigorous justification of effective fluid equations for non-Brownian suspensions, where the complex fluid can be described in terms of an effective viscosity. In contrast to this (quasi-)Newtonian behavior, anisotropic Brownian particles cause an additional elastic stress on the fluid. A rigorous derivation of such visco-elastic systems starting from particle models is completely missing so far. In this talk I will present first results in this direction starting from simplified microscopic models where the particles evolve only due to rotational Brownian motion and cause a Brownian torque on the fluid. In the limit of infinitely many small particles with vanishing particle volume fraction, we rigorously obtain an elastic stress on the fluid in terms of the particle density that is given as the solution to an (in-)stationary Fokker-Planck equation.
    Joint work with Marta Leocata (LUISS Rome) and Amina Mecherbet (Université Paris Cité)


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News

Florian Schweiger erhielt den Hausdorff-Gedächtnispreis 2021 der Fachgruppe Mathematik für die beste Dissertation. Er fertigte die Dissertation unter der Betreuung von Prof. Stefan Müller an. Unter anderen wurde Vanessa Ryborz mit einem Preis der Bonner Mathematischen Gesellschaft für ihre von Prof. Sergio Conti betreute Bachelorarbeit ausgezeichnet. (18.01.2022)

Prof. Dr. Sergio Albeverio has been elected into the Academia Europaea and the Accademia Nazionale dei Lincei (more; 02.12.2021).

Der SFB 1060 Die Mathematik der emergenten Effekte hat eine dritte Förderperiode erhalten. (26.11.20)

Prof. Dr. Andreas Eberle erhält den diesjährigen Lehrpreis der Universität Bonn. (22.07.2020)

Herr Dr. Richard Höfer erhielt den Hausdorff-Gedächtnispreis 2019 der Fachgruppe Mathematik für die beste Disseration. Betreut wurde die Arbeit von Prof. J. Velázquez (29.01.2020).

Contact

Managing Director: Prof. Dr. Massimiliano Gubinelli
Chief Administrator: Dr. B. Doerffel
geschaeftsfuehrung@iam.uni-bonn.de
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