Gabriel Kron and the Negative Resistor
At the time of his death, Gabriel Kron was arguably the greatest non-linear scientist ever produced by the United States.
It appears that the availability of this Heaviside energy component surrounding any portion of the circuit may be the long sought secret to Gabriel Kron's "open path" that enabled him to produce a true negative resistor in the 1930s, as the chief scientist for General Electric on the U.S. Navy contract for the Network Analyzer at Stanford University. Kron was never permitted to release how he made his negative resistor, but did state that, when placed in the Network Analyzer, the generator could be disconnected because the negative resistor would power the circuit. Since a negative resistor converges surrounding energy and diverges it into the circuit, it appears that Kron's negative resistor gathered energy from the Heaviside component of energy flow as an "open path" flow of energy connecting together the local vicinities of any two separated circuit components that had been discarded by previous electrodynamicists following Lorentz. Hence Kron referred to it as the "open path." Particularly see Gabriel Kron, "The frustrating search for a geometrical model of electrodynamic networks," circa 1962. We quote: "...the missing concept of "open-paths" (the dual of "closed-paths") was discovered, in which currents could be made to flow in branches that lie between any set of two nodes. (Previously following Maxwell engineers tied all of their open-paths to a single datum point, the 'ground'). That discovery of open-paths established a second rectangular transformation matrix... which created 'lamellar' currents..." "A network with the simultaneous presence of both closed and open paths was the answer to the author's years-long search."
A true negative resistor appears to have been developed by the renowned Gabriel Kron, who was never permitted to reveal its construction or specifically reveal its development. For an oblique statement of his negative resistor success, see Gabriel Kron, "Numerical solution of ordinary and partial differential equations by means of equivalent circuits," Journal of Applied Physics, Vol. 16, Mar. 1945a, p. 173. Quoting: "When only positive and negative real numbers exist, it is customary to replace a positive resistance by an inductance and a negative resistance by a capacitor (since none or only a few negative resistances exist on practical network analyzers)." Apparently Kron was required to insert the words "none or" in that statement. See also Gabriel Kron, Electric circuit models of the Schrödinger equation, Phys. Rev. 67(1-2), Jan. 1 and 15, 1945, p. 39. We quote: "Although negative resistances are available for use with a network analyzer,". Here the introductory clause states in rather certain terms that negative resistors were available for use on the network analyzer, and Kron slipped this one through the censors. It may be of interest that Kron was a mentor of Sweet, who was his protégé. Sweet worked for the same company, but not on the Network Analyzer project. However, he almost certainly knew the secret of Kron's "open path" discovery and his negative resistor.
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