Nonlinear Dynamics at the Free University Berlin

Summer 2019

Seminar Advanced Topics in Nonlinear Dynamics

Dr. Isabelle Schneider


Thursday, April 11th Nicola Vassena (Freie Universität Berlin) Kernel and cokernels in chemical reaction networks
In the frame of a signed sensitivity analysis of chemical reaction networks, in this talk I will focus on the crucial role played by one-dimensional kernels and cokernels of certain minor of the stoichiometric matrix.
Thursday, April 18th Alejandro López Nieto (Freie Universität Berlin) Pattern formation in differential delay equations with monotone feedback
Thursday, April 26th Maximilian Bee (Freie Universität Berlin) Zeta and circles - how to and how not to do it.
I treat the partial sums of the zeta function with the trapezoid and the Euler summation formulae. The latter gives the desired result, the former does not.
Dennis Chemnitz (Freie Universität Berlin) An algebraic approach to proving Sharkovskii's theorem.
Prof. Dr. Bernold Fiedler (Freie Universität Berlin) Absolute Truth - a toxic chimera?
The universal prerogative of religion over ethical education is much contested today as old-fashioned, outdated and obsolete, private and subjective, unscientific, sectarian, our outright abusive. Natural Science, in contrast, is considered beyond dispute, even though her ethical record is equally dubious, at best. In education, science is mostly taught, and misunderstood, as a fixed canon of known facts. Science is presented as established Laws of Nature, carved in stone in the unfortunately inscrutable symbolism of mathematics. Both equally beyond the doubt of mortals, religion and mathematics come gilded with the value of truth - for seemingly diametrically opposite reasons. Be their concepts based on pure logic or pure faith: both appear as last vestiges of Absolute Truth, in an otherwise pluralistic mind set. Both appear enshrouded with the mystique of the unfathomable. And neither is thought of as subject to majority vote - quite contrary to the pacifying relativism of "everyone has their own truth". How come we still dare teach the undemocratic absolutes of mathematics? and religion? Our provocative apologetics mostly explores the mathematical side, seeking complementary feedback, critique, and further education.
Thursday, May 2nd Phillipo Lappicy (Universidade de Sao Paulo; Universidade de Lisboa) Non-autonomous Chafee-Infante attractors: a connection matrix approach
The goal of this talk is to present the construction of the global attractor for a genuine nonautonomous variant of the Chafee-Infante parabolic equation in one spatial dimension. In particular, the attractor consists of asymptotic profiles (which correspond to the equilibria in the autonomous counterpart) and heteroclinic solutions between those profiles. We prove the existence of heteroclinic connections between such asymptotic profiles, yielding the same connection structure as the well-known Chafee-Infante attractor. This work is still an ongoing project with Alexandre N. Carvalho (ICMC - Universidade de Sao Paulo).
Jeffrey Guhin (Assistant Professor of Sociology, UCLA) Sociological Equilibrium
Thursday, May 9th Babette de Wolff (Freie Universität Berlin) The pseudospectral approximation method for delay differential equations
C. Güdücü (Technische Universität Berlin) and R. Morandin (Technische Universität Berlin) Introduction and Numerical Methods for Port-Hamiltonian Systems
Part I. In this talk we introduce port-Hamiltonian (pH) systems and their underlying Dirac structures. Then, we proceed to show some properties and a coordinate-based representation of pH systems, together with a toy example. Finally, we present the Lanczos method for the solution of linear systems with nonsymmetric coefficient matrices and its application to pH systems. Part II. In this part we introduce a larger class of pH systems, that include implicit algebraic constraints, known as port-Hamiltonian descriptor systems or pHDAEs. We exhibit some properties of pHDAEs and present some ideas on how to control a pH system through an example. Assuming that we still have time, we conclude by illustrating collocation methods for the numerical solution of pHDAEs.
Friday, May 17th SFB910 Symposium Symposium's Programme
Thursday, May 23rd Hannes Stuke (Freie Universität Berlin) An Introduction to Bayes Optimal Active Learning
Thursday, June 6th Nicola Vassena (Freie Universität Berlin) Good children and bad children
I will rehearse for a talk, which I am giving in a workshop on Chemical Reaction Networks at Politecnico of Torino and (up to small modifications) in a SIAM Conference on Applied Algebraic Geometry in Bern. I have already presented in the past winter semester the mathematical content.
Babette de Wolff (Freie Universität Berlin) Pseudospectral approximation for bifurcation problems in delay equations
Pseudospectral approximation of delay equations was introduced in 2005 by Breda et al. as a numerical method to approximate eigenvalues of delay equations by eigenvalues of ordinary differential equations. The pseudospectral approximation has a natural interpretation as a discretisation of the delay equation in the sun-star-framework. Therefore, the approximating ordinary differential equations `inherit' the structure from the delay equation. Because of this, it has been conjectured that the pseudospectral method can be used as a numerical method for bifurcation problems in delay equations. In this talk, this topic will be adressed in the context of the Hopf bifurcation. In particular, we will discuss the way in which `direction of bifurcation' (i.e. the sign of the Lyapunov coefficient) is preserved in the pseudospectral approximation. This is joint work with Odo Diekmann, Francesca Scarabel and Sjoerd Verduyn Lunel.
Alejandro López Nieto (Freie Universität Berlin) Characterization of periodic solutions for scalar delay equations with monotone feedback and even-odd symmetry
A standard technique in the study of periodic solutions to a delay differential equation (DDE) is the reduction to an ordinary differential equation (ODE) whose periodic solutions happen to solve the original DDE via a symmetry assumption. In such a way one can at least prove the existence of some periodic solutions, but not necessarily all of them. In the talk I will present sufficient conditions that allow to fully characterize the periodic solutions of a DDE in terms of an underlying ODE system.
Thursday, June 13th SFB910 internal project discussion with guest Si Mohamed Sah (Technical University of Denmark)
Thursday, June 27th Gentaro Masuda (Freie Universität Berlin) Hamiltonian Delay Equations
We extend the concept of Hamiltonian delay equations to symplectic manifolds. As an application, we will see a certain class of Hamiltonian delay equations to which Arnold’s conjecture applies.
David Hering (Technische Universität Berlin) Application of Equivariant Pyragas Control on Networks of Chemical Oscillators
Thursday, July 4th Angel Crespo Blanco (Technische Universität Berlin) Ergodic theory and statistical mechanics
Ergodic theory is a branch of mathematics which was born in the late nineteenth century in the wake of a problem posed in the foundation of statistical mechanics: ergodic hypothesis. Verification of this hypothesis would justify the microcanonical ensemble only from the microscopic dynamics of the system. In this talk elementary ergodic theory results will be introduced in order to comprehend this problem. Using this tools ergodic hypothesis will be posed, in addition to comparing it with other classical approaches to the microcanonical ensemble. Finally, current situation of the problem will be presented, which is still an open problem in spite of huge efforts that have been made by many authors.
Tilman Glorius (Freie Universität Berlin) Non-Standard Orbits in a Pyragas-Controlled System
Friday, July 12th Yuya Tokuta (Freie Universität Berlin), Disputation Irreversible processes and the Jarzynski equality
In the real world, phenomena we observe often involve irreversible processes due to friction, viscosity, heat conduction, and so on, resulting in some energy loss as heat waste. Phenomena that involve irreversible processes are called nonequilibrium phenomena and statistical mechanics has been trying to explain such phenomena from a microscopic point of view. In 1997, Christopher Jarzynski discovered an equation between the nonequilibrium work and the Helmholtz free energy, which is called the Jarzynski equality. In this talk, we will prove the Jarzynski equality without assuming familiarity with thermodynamics or statistical mechanics.

Time and Place

Talks usually take place on Thursday at 2:15 p.m.
at the Free University Berlin
Room 130, Arnimallee 7 (rear building), 14195 Berlin.

Guests are always welcome!


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