Kick-off 3rd funding period (2023-27)

Only invited and registered guests may attend this event.

Image of the cake for the third funding period

On the occasion of the successful renewal of our CRC we will organize a workshop on Thursday 13th of July, 2023 starting at 15:00 with the scientific program (including a coffee break). Afterwards at 18:30 the joint dinner takes place.

15:00	Welcome
15:15	Limiting behavior of nonlinear and nonlocal wave equations in ultrasonics
	held by Prof. Dr. Vanja Nikolić (Radboud University, The Netherlands)
	Abstract Accurate mathematical modeling of nonlinear sound propagation is important to various applications of ultrasonic waves, ranging from imaging to lithotripsy and cancer therapy. In tissue-like media, additionally nonlocal-in-time attenuation comes into play. In this talk, I will discuss how quasilinear wave equations with dissipation of time-fractional type that arise in ultrasonics can be related in the limit of relevant small parameters, such as the sound diffusivity and thermal relaxation time. In particular, it is of interest to quantify the errors made when replacing (singularly) perturbed acoustic models with the unperturbed ones.
16:00	Coffee break
16:30	Towards global convergence for inverse coefficient problems
	held by Prof. Dr. Bastian von Harrach-Sammet (Univ. Frankfurt, Germany)
	Abstract Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. In this talk we will consider the inverse coefficient problem of electrical impedance tomography (EIT) with finitely many measurements and a finite desired resolution. We will demonstrate how standard reconstruction methods suffer from only local convergence, resp., the problem of local minima. We will then show how to overcome these problems by rewriting the problem as an equivalent uniquely solvable convex non-linear semidefinite optimization problem.

17:15	Bifurcation and asymptotics of nonlinear surface plasmons
	held by Prof. Dr. Tomáš Dohnal (Univ. Halle, Germany)
	Abstract Surface plasmons are electromagnetic waves localized at the interface of a metal and a dielectric, or more generally at the interface of dispersive (frequency dependent) materials. In the time harmonic case the linear Maxwell equations reduce to an operator pencil problem which is non-self-adjoint in the presence of metals. The frequency plays role of a spectral parameter. We consider straight interfaces and analyze the linear spectral problem first. Next, the bifurcation of nonlinear surface plasmons from simple isolated eigenvalues and their asymptotic expansion are proved via a fixed point argument. In a PT-symmetric geometry the frequency remains real in the bifurcation. We consider both the TE and TM-polarizations. In the former case the problem become scalar and supports plasmons only in the case of two or more interfaces. In the latter case a system of two coupled ODEs can be derived. Numerical computations are provided to support the analysis. This work includes collaborations with Malcolm Brown, Runan He, Michael Plum, Giulio Romani, and Ian Wood.
~18:25	Address by Vice-President Oliver Kraft
~18:30	Dinner