Conservation Laws and Lumped System Dynamics

12/2008; DOI:10.1007/978-1-4419-0895-7_3

ABSTRACT Physical systems modeling, aimed at network modeling of complex multi-physics systems, has especially flourished in the fifties
and sixties of the 20-th century, see e.g. [11, 12] and references provided therein. With the reinforcement of the ’systems’
legacy in Systems & Control, the growing recognition that ’control’ is not confined to developing algorithms for processing
the measurements of the system into control signals (but instead is concerned with the design of the total controlled system),
and facing the complexity of modern technological and natural systems, systematic methods for physical systems modeling of
large-scale lumpedand distributed-parameter systems capturing their basic physical characteristics are needed more than ever.

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    ABSTRACT: This paper discusses the geometric formulation of the dynamics of chemical reaction networks within the port-Hamiltonian formalism [10, 9, 6]. The basic idea dates back to the innovative work of Oster, Perselson and Katchalsky [8, 7]. The main contribution concerns the formulation of a Dirac structure based on the stoichiometric matrix, which is underlying the port-Hamiltonian formulation. Interaction with the environment is modelled through the boundary metabolites and their boundary fluxes and affinities. This allows a compositional view on chemical reaction network dynamics.
    10/2010: pages 339-348;

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