Topological representations of thermodynamic systems—I. Basic concepts

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Abstract

This paper describes the development of a generalized topological representation for thermodynamic systems. The elements and topology of the representation provide a conceptual reticulation of the real system into elements drawn from a set of ideal, but physically realizable, lumped-parameter components. The representation is in the form of bond-graph notation. This notation leads to a graphical description of a dynamic system (very much resembling a chemical bond diagram in appearance) that can be manipulated in an algorithmic fashion to produce the system differential equations, a computer simulation algorithm or a topological (circuit) graph of the system. There is no restriction to linearity in the representation.

The reticulated structure represents a conceptual separation of the energy storage and dissipative processes within the system and a description of all the energetic interactions of the system. The ideal components used in the model generalize the familiar electric circuit elements—resistors, capacitors, inductors, transformers—but, unlike electrical circuit diagrams, a reticulation into several components does not necessarily imply any physical separation in the actual system. Bond-graph notation is utilized because it was found to be particularly well suited for dealing with systems involving multiple energy domains with identifiable couplings between them.

The thermodynamic systems of general interest comprise ionic flows, fluid flows, chemical reactions, heat flows, etc. with coupling and transduction between all energy modes.

Specific applications dealt with here are electro-chemical phenomena. Case studies are presented for relaxation oscillations and rectification in electrolytic systems with multiple ionic flows, chemical reaction and ion-exchange membranes, coupled with electrical circuitry.

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One of the authors (G.F.O.) wishes to acknowledge the support by the National Institutes of Health—Fellowship 2-FO2-CA41228-02 from the National Cancer Institute—during the course of this work.

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