Hans J. Herrmann

Roman Vetter, Norbert Stoop, Thomas Jenni et al.

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.

Damian L. Berger, Lucilla de Arcangelis, Hans J. Herrmann

Recent studies have proposed that the diffusion of messenger molecules, such as monoamines, can mediate the plastic adaptation of synapses in supervised learning of neural networks. Based on these findings we developed a model for neural learning, where the signal for plastic adaptation is assumed to propagate through the extracellular space. We investigate the conditions allowing learning of Boolean rules in a neural network. Even fully excitatory networks show very good learning performances. Moreover, the investigation of the plastic adaptation features optimizing the performance suggests that learning is very sensitive to the extent of the plastic adaptation and the spatial range of synaptic connections.