Prof. Dr. Mark Ainsworth (Brown University)

Despite the recent surge in interest in fractional order PDEs, there are still relatively few application areas where fractional order models have been shown to provide superior predictions than their integer order counterparts. In this talk, we attempt to address this issue in the context of Phase Field Crystal models for crystalline structures which have gained signifcant traction in the physics community. We consider a fractional phase-field crystal model in which the classical Swift-Hohenberg equation is replaced by a fractional order Swift-Hohenberg equation that reduces to the classical case when the fractional order ß=1. It is found that choosing the value of ß appropriately leads to FSHE giving a markedly superior fit to experimental measurements of the structure factor than obtained using the SHE (ß=1) for a number of crystalline materials. The improved fit to the data provided by the fractional partial differential equation prompts our investigation of a FPFC model based on the fractional free energy functional. The talk will outline the main predictions of the fractional phase field crystal model compared with the classical integer order model, and compare with physical measurements for specific crystals.

If you wish to attend one (or more) of the talks please send to request for the zoom link to anapde_mathematik.tu-darmstadt.de (please replace  _ by @ ). Please include in your mail your full name, status (teacher, professor, student,...) and institution.

Wenn Sie als Zuhörer*in an den Kolloquien teilnehmen möchten, schicken Sie bitte eine Anfrage per Mail an anapde_mathematik.tu-darmstadt.de (ersetzen Sie dabei bitte _ durch @ ). Ihre Mail sollte Ihren vollständigen Namen, Ihren Status (Lehrer*in, Professor*in, Student*in, Doktorand*in , ...) und Ihre Institution enthalten.


10. November 2021, 17:15-19:00




FB Mathematik, AG Numerik und wissenschaftliches Rechnen


Prof. Dr. Jan Giesselmann




Mathematisches Kolloquium, Mathematik, Numerik