Professor Muhammad Sahimi at the University of Southern California introduces his new publication as follow:
“A fifty year problem was solved
Fifty one years ago it was proposed that the conductivity of composites that are mixtures of conducting and non-conducting elements follow a power law near the conductivity threshold, i.e., the volume fraction of the conducting elements below which the composite as a whole will not conduct electricity. The question was, is the exponent that characterizes the power law related to those that characterize the morphology of the composites? A conjecture in 1982 relating these came very close to solve the problem, but turned out to be an approximation, albeit an excellent one.
My collaborator, Dr. Carl Berg of Norwegian University of Science and Technology,, and I finally solved the problem, deriving an exact relation between the conductivity exponent and those that characterize the morphology. The form of the relation is not what many had suspected or proposed! The paper was published today: Physical Review E Letters 110, L042104 (2024).”
The publication is here