GRK 2326:  Energy, Entropy, and Dissipative Dynamics

• Subject Area: Mathematics
• Term: since 2017
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 320021702

The research training group (RTG) “Energy, entropy, and dissipative dynamics” will train doctoral researchers in analysis, modeling, and numerics in the fields of nonlinear partial differential equations and applied analysis. Carefully selected research projects, many of which are strategically located at the intersection of the established research fields of the participating professors in order to foster interaction and cooperation, and which will always be supervised by two professors of the research training group, will introduce doctoral researchers to interesting and relevant topics at the forefront of current research. The research projects are tied together by the themes of energy/entropy functionals and dissipation mechanisms as tools to understand the properties of the system and the admissible dynamics. Energy minimization and the exploration of energy landscapes play an important role, as does the maximization of energy dissipation or entropy production as a selection criterion in time-dependent situations and in kinetic closure mechanisms. The research topics are concerned with various models from physics, materials science, geometry, and machine learning, such as moment models in gas dynamics, hyperbolic conservation laws, kinetic partial differential equations, network flows, and the Allen-Cahn, Cahn-Hilliard, Mullins-Sekerka, and Landau-Lifshitz-Gilbert equations. The work will require the use of powerful tools from (applied) analysis, such as optimal transport theory, 􀀀-convergence, energy–energy-dissipation estimates, and symplectic geometry, as well as sophisticated numerical methods for constrained optimization problems, asymptotic preserving schemes, and stochastic Galerkin methods. The program will be carried out using numerical and analytical approaches in novel and innovative combinations. The research projects will be augmented by a rich seminar program covering analytical, modeling, and numerical aspects of the field, research stays abroad, and additional offerings to ensure the comprehensive training of the doctoral researchers.

• DFG Programme: Research Training Groups
• Applicant Institution: Rheinisch-Westfälische Technische Hochschule Aachen
• Participating Researchers: Professor Dr. Michael Herty; Professor Dr. Umberto Hryniewicz; Professor Dr. Christof Erich Melcher; Professor Dr. Heiko von der Mosel; Professor Dr. Siegfried Müller; Professor Dr. Manuel Torrilhon; Professor Dr. Michael Westdickenberg
• Spokesperson: Professorin Dr. Maria G. Westdickenberg, since 4/2022