Two UQ Science researchers have proved two famous physical laws that have been widely used for the past 25 years do not always work.
Dr Tony Roberts and PhD student Christophe P. Haynes, from the School of Maths and Physics, showed the fractal-Einstein and Alexander-Orbach laws can fail in some instances, and have derived a new law to replace them.
Dr Roberts said this new discovery had implications for predicting material properties; how disease spreads through society; mapping how wild animals forage for food; and improving the internet.
“We demonstrated unequivocally that two ‘exact’ foundational laws of fractal science, which have been cited over 2000 times in the scientific literature, can fail for a class of fractals,” he said.
“These are the first definitive counter examples to these laws.
“Given that our key equation solves a number of old and new problems, we believe we have discovered a ‘missing’ equation from fractal physics that will have important implications.”
Dr Roberts said the laws in question were used to describe how particles diffuse in complex environments, which lies at the heart of range of big scientific questions.
“Imagine you have an animal that can search for food in one of two valleys, one narrow, with many side branches, and the other wide, with only a few side tracks,” he said.
“Under the old laws, the probability of the animal locating food in either valley was equal, regardless of which was easier. Intuitively we can see that this just isn’t the case.
“But our new law takes into account the differences in the valleys, predicting the time it takes for the animal to find food is significantly longer in the difficult valley.”
(Mad Lib Quip:) Ah, the well known fractal-Einstein law … I was kind of hoping they’d break the law of ________ .