Realizable response matrices of multiterminal electrical, acoustic, and elastodynamic networks at a given frequency

TL;DR

This paper provides a comprehensive characterization of the response matrices for multiterminal electrical, acoustic, and elastodynamic networks at a fixed frequency, including construction methods for networks realizing any compatible response matrix.

Contribution

It offers a complete mathematical characterization and construction of response matrices for various physical networks, extending to acoustic networks via mathematical equivalence.

Findings

Any response matrix compatible with symmetry and thermodynamic constraints can be realized.

Constructive methods for networks realizing arbitrary compatible response matrices.

Unified characterization across electrical, acoustic, and elastodynamic networks.

Abstract

We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in the three-dimensional case and in the two-dimensional case. Specifically we construct networks which realize any response matrix which is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Due to a mathematical equivalence we also obtain a characterization of the response matrices of discrete acoustic networks.