Conductance of discrete bifurcated waveguides as three terminal junctions

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An expression for the transmission matrix based conductance is provided for the propagation of scalar waves in certain bifurcated discrete waveguides using the paradigm of a three-terminal Landauer-Buttiker junction. It is found that the conductance across the terminals of bifurcated branches forming a sharp corner, interpreted as a controller of `leakage' flux, can be tuned by manipulating the number of channels and the type of lateral confinement. Natural applications in engineering and science arise in the context of nanoscale transport involving elastic, phononic, or electronic waves. In particular, the paper includes a discussion of temperature dependent thermal conductance, assuming only the contribution of out-of-plane phonons, along with some graphical illustrations.