Oberseminar Dynamische Systeme:
Mathematische Grundlagen und Anwendungen

Wintersemester 2015/2016
Montag, 26.10.15, 16 Uhr c.t., Raum MI 03.06.011:
Stud. math. Christian Leitner (TUM)
Hopfverzweigung bei einem verallgemeinerten Konvektionsmodell

Montag, 26.10.15, 17 Uhr c.t., Raum MI 03.06.011:
Stud. math. Matthias Lauber (TUM)
Über den Zusammenhang von Poissonstruktur und symplektischer Struktur am Beispiel des starren Körpers

Montag, 26.10.15, 18 Uhr c.t., Raum MI 03.06.011:
Stud. math. Marvin Fritz (TUM)
Zur Stabilität von relativen Gleichgewichtslösungen in der Wirbeldynamik

Montag, 2.11.15, 16 Uhr c.t., Raum MI 03.06.011:
Prof. Dr. Messoud Efendiev (Helmholtz-Zentrum Muenchen)
Infinite-dimensional attractors for p-Laplacian

Abstract: We give a detailed study on the attractors for the parabolic equations in bounded domains involving p-Laplacian as the principal term. Not only the existence of attractors but also their new properties are presented, which cannot be observed for the non-degenerate parabolic equations.

Montag, 18.1.16, 16 Uhr c.t., Raum MI 03.06.011:
Stud. math. Michael Eder (TUM)
Zur Regularisierung des Keplerproblems

Montag, 25.1.16, 16 Uhr c.t., Raum MI 03.06.011:
Prof. Dr. V. Kovtunenko (University Graz, Austria)
Analysis of nonlinear elasticity models with limiting strain for cracks subject to non-penetration

Abstract: The stationary crack problem subject to non-penetration conditions is considered within nonlinear elasticity with limiting small strain introduced by K.R. Rajagopal. The benefit implies strains bounded uniformly over the solid, while the drawback concerns unbounded even singular stresses. This issue describes the principal difficulty for analysis of such models. We introduce the concept of a non-smooth viscosity solution of this problem, which is described by generalized variational inequalities and coincides with the weak solution in a smooth case. The well-posedness is provided by the construction of an approximation problem using elliptic regularization and penalization techniques.

Montag, 7.3.16, 16 Uhr c.t., Raum MI 03.06.011:
Stud. math. Maximilian Schiller (TUM)
Diskrete-Gradienten-Methoden für Hamiltonsche Systeme: Erhalt von Symmetrien und Anwendung auf das Kirchhoffsche Wirbelmodell

Montag, 14.3.16, 16 Uhr c.t., Raum MI 03.06.011:
Prof. Dr. Mads Sørensen (DTU Copenhagen, Denmark)
Modeling of a micro electrochemical cell by the Poisson-Nernst-Planck equation including singular diffusion

Abstract: A model for a micro electrochemical cell with a flowing electrolyte is derived based on the Poisson-Nernst-Planck equation governing the ion transport due to diffusion, advection and electric fields [1,2]. The electrode kinetics we model by the Butler-Volmer boundary conditions. Specifically we performed simulations as well as experimental studies for cyclic voltammetry of the ferri-ferrocyanide redox couple on a gold plated ECC biosensor encapsulated in a microfluidic system. We have examined the effect of flow rate, scan rate, varying concentration of the supporting electrolyte, exchange current density and the position of electrode on the cyclic voltammetry measurements. The results show that at a relatively high flow (250 μ/L) and low scan rates (50 - 200 mV/s), the current response is limited by the convection due to quick supply of fresh ions at the electrode surface which leads to fading hysteresis of the recorded cyclic voltammetry. However, at high scan rates (250 mV/s) and low flow rates (50 - 200 μ/L), peak currents are recorded, which means that mass transport is dominated by the diffusion mechanism and a quasi-steady state of cyclic voltammetry is recorded. In the case of insufficient supporting electrolyte, the excess charges generated during scan will lead to ohmic distortion of the electrolyte solution and consequently result into a ramping effect of the recorded cyclic voltammetry. However, for sufficient amount of supporting electrolyte (200 mM), the simulation results show good agreement with the experimental data [2].
When charging an electrode in an electrolyte strong ion crowding may appear at the electrodes leading to densely packed ions in the Stern layer of the double layer region. The ion size limits the crowing of ions and in the literature it has been suggested to model this steric effect by a singular diffusion term in the Nernst Planck equation [3]. We consider an arbitrary electrolyte solution that is sandwiched between electrodes and allow for electrochemical reactions at the electrode/electrolyte interface. The result shows a quick build up of boundary layers in the double layer which is counterbalanced by the finite size constraint on the ionic species and prevents overcrowding of the ions. Comparison between model simulations with and without a singular diffusion term will be discussed.

[1] B.J. Adesokan, A. Evgrafov and M.P. Soerensen, Simulating cyclic voltammetry under advection for electrochemical cantilevers, Math. Meth. Appl. Sci. 38 (2015) 3384-3391.
[2] B.J. Adesokan, X. Quan, A. Evgrafov, A. Heiskanen, A. Boisen, M.P. Soerensen, Experimentation and numerical modeling of cyclic voltammetry for electrochemicalmicro-sized sensors under the influence of electrolyte flow. Journal of Electroanalytical Chemistry, 763, (2016) 141-148.
[3] M. S. Kilic, M. Z. Bazant, A. Ajdari, Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations, Phys. Rev. E 75 (2007) 021503.