Conservation laws and open systems on higher-dimensional networks

— We discuss a framework for defining physical open systems on higher-dimensional complexes. We start with the formalization of the dynamics of open electrical circuits and the Kirchhoff behavior of the underlying open graph or 1complex. It is discussed how the graph can be closed to an ordinary graph, and how this defines a Dirac structure on the extended graph. Then it is shown how this formalism can be extended to arbitrary k-complexes, which is illustrated by a discrete formulation of heat transfer on a two-dimensional spatial domain.

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Arjan van der Schaft, Bernhard Maschke
• Keywords: CDC 2008, Control Systems, Open Electrical Circuits, Open Graph, Physical Open Systems