Tuesday, September 26, 2017

Concepts in Kron's Later Papers....,


stackexchange |  Gabriel Kron was an important research electrical engineer known for applying differential geometry and algebraic topology to the study of electrical system. Towards the end of his career he published a number of unusual, even by his standards, papers on concepts with names like polyhedral networks, self organizing automata, wave automata, multidimensional space filters and crystal computer, which I think are more or less synonymous. I have obtained a few of these papers and did not understand them at all. If they were not written be Kron, I would be suspicious of them.

I have not been able to find any significant secondary literature on these ideas. The few citations I have tracked down only mention them tangentially, but I have also found no refutations of these papers and no suggestions that Kron had gone off the rails. The papers were published in respectable journals.

I am looking for an understandable exposition or refutation of these ideas, or pointers to such. Also pointers to follow on research by others, possibly using different terminology.

I am not looking for explanations of Kron's other ideas like diakoptics and tensor analysis of networks.

Some of the relevant papers are:
  • G. Kron, Multi-dimensional space filters. Matrix and Tensor Quarterly, 9, 40 - 43 (1958).
  • G. Kron, Basic concepts of multi-dimensional space filters. AIEE Transactions, 78, 554 - 561 (1959).
  • G. Kron, Self-organizing, dynamo-type automata. Matrix and Tensor Quarterly, 11, 42 - 52 (1960).
  • G. Kron, Power-system type self-organizing automata. RAAG Memoirs, III, 392 - 417 (1962).
  • G. Kron, Multi-dimensional curve-fitting with self-organizing automata. Journal of Mathematical Analysis and Applications, 5, 46 - 49 (1962).
I have mainly looked at the last one and material at the end of
  • Diakoptics; the piecewise solution of large-scale systems. MacDonald, London, 1963. 166 pp.