In this paper, we investigate additional structure that might be put on bond graphs in order that (1) a bond graph has a physical realization and (2) physical realizations have bond graph within an appropriate physical domain. In particular, restrictions are proposed on the allowed form for the constitutive laws for energy storing and dissipative elements and the allowed form for the modulation of coupling elements. This added structure is proposed to ensure the existence of an energy state function, passivity, unique solutions to the model equations, and to preserve the signal nature of modulation.

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