PORT-BASED ENERGY BALANCE ON COMPACT MANIFOLDS

The purpose of this paper is to introduce a novel energy balance structure based on a port-representation for closed manifolds with potential in terms of the Morse theory. The Morse theory states that the local structure around non-degenerate critical points of Morse functions on manifolds reflects the global structure of the whole manifold. The energy balance is then connected to the topological properties of the manifolds and is defined on a non-uniform boundary characterized by the dimensions of submanifolds with outflows. First, we discuss the non-uniform boundary in relation to a Morse-Smale gradient flow. Next, the dual pair of energy variables in the context of ports is defined by using the Poincaré duality theorem. Finally, we present two specific energy balances on the compact manifolds are presented.