Vorträge

Tumor perfusion and vascular properties are important determinants of a cancer’s
response to therapy. Being able to determine those parameters from patient-specific data
collected at the bedside would allow for better, more individual tumor treatment.
Models describing the transport of contrast agent based on advection-diffusion equations
are commonly used, but lack the ability to derive physically accurate solutions
for the transportation of tracer through an organ. Therefore, Sourbron proposed a
two-compartment model, where the flow of contrast agent is modeled by separating the
arterial and venous flows into a system of transport equations, coupled by a transfer
coefficient function which describes the exchange of the contrast agent from arteries to
veins through capillaries.
In this talk we discuss the parameter identification problem, i.e., how to estimate
flow velocities and the conversion coefficient function, given the concentration of contrast
agent over time, which will be obtained via 3D dynamic contrast-enhanced ultrasound
measurements. We derive adjoint equations for efficient gradient computation, discuss
the discretization of state and adjoint equation and the use of Leray projection within the
optimization algorithm to ensure a divergence free velocity field, and present numerical
results for artificial and ultrasound data.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

The atmosphere, ocean, and sea ice components in Earth system models are coupled at the sea surface via boundary conditions. In essence, this amounts to coupled heat equations with discontinuous material parameters. However, the problem is special in two ways: First of all, the boundary conditions used in practice, so-called bulk interface conditions, allow for a temperature jump across the interface. Secondly, sea ice acts as a partially isolating layer and affects the boundary conditions seen by the atmosphere and ocean.
Theoretical analysis of this problem is missing, even with simplified models. For this reason, we propose a coupled toy model that describes the heat exchange of a partially ice-covered ocean with the atmosphere. This allows us to analytically derive convergence factors of the corresponding coupling iteration. We compare this to a numerical implementation of the same model using an open-source coupling software for climate applications, ClimaCoupler.jl. Our results show that the convergence behavior with bulk interface conditions is fundamentally different from using standard Dirichlet-Neumann or Robin-Robin interface conditions for conjugate heat transfer.

Organic redox polymers such as poly (TEMPO-acrylamide) (PTAM) are being investigated as cathode materials for post-lithium batteries, yet their electrochemical behavior is still not well characterized. For PTAM–Zn cells, internal states and dynamic processes remain unclear. To address this, we adapted the single-particle model with electrolyte (SPMe), originally developed for lithium-ion batteries, by re-deriving the governing equations for this chemistry and parametrizing the framework with experimental data. The model describes solid-state and electrolyte diffusion together with electrolyte potential, overpotential and voltage dynamics and is solved using finite-element discretization in space and Backward Euler time stepping with Newton iteration. Simulations quantitatively reproduce charging curves up to 50 C, capturing both capacity and voltage profiles. These results suggest that the adapted SPMe captures the dominant transport and kinetic behavior while highlighting the need for model refinement, targeted material studies, and improved validation through closer integration with experiments

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09