93 research outputs found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
A mathematical model for meniscus cartilage regeneration
We propose a continuous model for meniscus cartilage regeneration triggered
by two populations of cells migrating and (de)differentiating within an
artificial scaffold with a known structure. The described biological processes
are influenced by a fluid flow and therewith induced deformations of the
scaffold. Numerical simulations are done for the corresponding dynamics within
a bioreactor which was designed for performing the biological experiments.Comment: GAMM2023, May 2023, Dresden (GERMANY), German
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