Nonlinear Dynamics at the Free University Berlin

Summer 2018

Oberseminar Nonlinear Dynamics

Organizers


Program

April 17, 2018 Misha Zaks
(Universität Potsdam)
Collective dynamics of globally coupled excitable units
April 24, 2018 Cancelled
May 8, 2018 Marc Timme
(Technische Universität Dresden)
Network dynamics as an inverse problem
May 15, 2018 Alexander Linke
(WIAS Berlin)
On the role of the Helmholtz-Leray projector for a novel pressure-robust discretization theory for the incompressible Navier-Stokes equations
The talk discusses several physical regimes of the incompressible Navier--Stokes equations with respect to the role of the pressure and the role of the Helmholtz--Leray projector in the Navier--Stokes momentum balance. It is emphasized that not the forces in the momentum balance themselves matter for the complexity of the flow field, but their Helmholtz--Leray projector. Since the Helmholtz--Leray projector vanishes for arbitrary gradient fields, a semi norm and a corresponding equivalence class of forces play naturally a major role for the evolution of incompressible flows. Novel pressure-robust mixed finite element methods are designed for an appropriate discrete treatment of this equivalence class of forces. On the contrary, classical, (only) inf-sup stable mixed methods do not care about the existence of such an equivalence class. In order to deliver accurate simulation results, they have to resort to expensive high order ansatz spaces. Finally, the talk will indicate suitable applications for efficient and accurate low-order pressure-robust mixed methods like flows with electrolytes and flows with stagnation points, and it will discuss possible extensions to compressible low-Mach number flows.
May 22, 2018 Felix von Oppen
(Free University Berlin)
Elements of a topological quantum computer
This talk will discuss elements of a topological quantum computer with an emphasis on introducing two paradigmatic models, namely the Kitaev chain and the toric (or surface) code.
The talk will take place at the Free University Berlin, Arnimallee 3, Office 130, 14195 Berlin
May 29, 2018 Dr. Murad Banaji
(Middlesex University, London)
Inheritance of behaviours in bio/chemical networks
Consider the following imprecise questions about dynamical systems with some network structure: If a small network is embedded in a larger one, then must the larger one "inherit" some behaviours of the smaller one? Can the presence of certain "motifs" be sensibly used to make predictions about dynamical behaviours of a network? Once such questions are phrased precisely, the answers turn out to depend on the class of networks studied, the dynamical behaviour of interest and, crucially, the chosen notion of "subnetwork". My talk will focus on some recent results on chemical reaction networks (CRNs), where the behaviours in question are multistationarity and oscillation. Network modifications such as adding or deleting reactions, adding or deleting species from reactions, and inserting intermediates into a reaction are considered for their effects on multistationarity and oscillation. For example, it can be shown that both behaviours are inherited in the induced subnetwork partial ordering on fully open CRNs, but the same does not hold for general CRNs. Under certain mild assumptions, growing a CRN by inserting intermediates into reactions preserves the capacity for multistationarity in a CRN. The theorems are proved using essentially local techniques -- the implicit function theorem and regular and singular perturbation theory -- and hold for various kinetics including (but not exclusively) mass action kinetics. The results on multisationarity are joint with Casian Pantea.
The talk will take place at the Free University Berlin, Arnimallee 3, Office 130, 14195 Berlin

Time and Place

Talks usually take place on Tuesday at 3:15 p.m. at WIAS Berlin, Mohrenstr 39, in Erhard-Schmidt lecture room, 10117 Berlin.

Tea/coffee at 2:45 p.m. at the ground floor.
Guests are always welcome !


Archive

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