Together with Alex Ventisei and Victor Pacheco-Pena, we recently published a paper that for the first time connects the world of electromagnetic waves with the graphical modelling language of Petri nets. https://onlinelibrary.wiley.com/doi/10.1002/adts.202100429

Petri nets are known to capture in a very natural for comprehension form ideas of causality, concurrency and choice. The way how the Petri nets primitives – transitions (bars or boxes), places (circles), flow relation between them (arcs between places and transitions and between transitions and places), and marking of places (tokens) – can ‘speak’ in the languages of EM pulses propagating in transmission lines and interacting in their cross-points is quite interesting. For example, firstly, due to the fact that EM or to be precise TEM pulses cannot wait for each other in the points of crossing, is expressed in the corresponding Petri nets by the fact that we have not multiple incidence of flows on the same transition. In other words, we cannot have AND causality in TEM switching structures. On the other hand, secondly, due to the physical superposition of TEM pulses travelling from different sources, we have a pure effect of OR causality, manifested itself in the Petri nets having multiple incidence of flows of tokens on the same place. Thirdly, the fact that pulses are propagated and reflected in the points of crossing according to the proportions dictated by the impedance rations, represented by the scattering matrices, is manifested in the Petri net model by the corresponding fractioning and additions of tokens in places standing for these pulse interactions.

The type of Petri nets characterising TEM pulse interaction is fairly unique and is worthy separate investigation. For example, the EM nature of information flow in such structures has the property of reciprocity, i.e. the ‘execution runs’ in these processes can be played back to the original states, and hence the modelling Petri nets possess a certain notion of reversibility. In his PhD study, Alex Ventisei, is planning to advance this modelling work further to capture more complex structures of TEM pulse interactions, and complement the existing methods of modelling based on scattering matrices with graphical models using such Petri nets, as well as develop some simulation and analysis tools.