Dia: Dimecres 3 de setembre de 2025

Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.

• Hora: 16h00m

A càrrec de: Kathrin Padberg-Gehle, Leuphana Universitaet Lueneburg

Títol: From trajectories to transport: network-based approaches for coherent sets and scalar mixing in turbulent flows

Resum: Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures, including recent data-based methods that aim to identify such coherent objects directly from simulated or measured tracer trajectories. Among these approaches are Lagrangian flow networks, where trajectories serve as network nodes and the links are weighted according to spatio-temporal distances between trajectories. Spectral clustering as well as simple network measures such as node degrees or clustering coefficients can be used to identify flow regions of different dynamical behavior. In this talk, we propose some extensions to the network-based framework that allow us

1. to study the long-term dynamics of coherent sets in turbulent flows and
2. to describe and quantify the transport and mixing of scalar quantities. We demonstrate our approaches in a number of example systems, including turbulent Rayleigh-Bénard convection flows.

Dia: Dimecres 10 de setembre de 2025

Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.

• Hora: 16h00m

A càrrec de: Dongchen Li, Imperial College

Títol: Symplectic blenders near whiskered tori and persistence of saddle-center homoclinics

Resum: A blender is a hyperbolic basic set such that the projection of its stable/unstable set onto some central subspace has a non-empty interior and thus has a higher topological dimension than the set itself. We show that, for any symplectic C^r-diffeomorphism (where r is sufficiently large and finite, or r=∞,ω) of a 2N-dimensional (N>1) symplectic manifold, symplectic blenders can be obtained by an arbitrarily small symplectic perturbation near any one-dimensional whiskered KAM-torus that has a homoclinic orbit. Using this result, we prove that non-transverse homoclinic intersections between invariant manifolds of a saddle-center periodic point (i.e., it has exactly one pair of complex multipliers on the unit circle) are persistent in the following sense: the original map is in the C^r closure of a C¹ open set in the space of symplectic C^r diffeomorphisms, where maps having such saddle-center homoclinic intersections are dense. These results also hold for Hamiltonian flows in the corresponding settings.

Last updated: Fri Sep 12 19:05:11 2025