United Laws of Physics Make More Accurate Predictions

July 8, 2009 -- Australian researchers have found a way to unite two laws of physics, which will lead to more reliable predictions of everything from disease spread to internet traffic.

Mathematicians Dr. Tony Roberts and PhD student Christophe Haynes from the University of Queensland in Brisbane, will report their work on fractals in the July 17 issue of Physical Review Letters.

"We're showing how complexity can be reintroduced so it can start to match reality more," says Roberts.

Fractal networks are characterised by repeating patterns at smaller and smaller scales.

They model a range of real life situations that involve the movement of something through a random complex network.

This could be messages through the internet, animals foraging in a forest, oil moving through rock, electricity moving through a material or disease transmission within a population.

Roberts says each case can be likened to the movement of "blind ants" moving through a complex maze of pathways, randomly turning at each junction they reach. Collectively, the ants move in a way that can be modelled by mathematical laws.

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In the 1980s, scientists developed the fractal-Einstein and Alexander-Orbach laws to explain movement through fractal networks.

But last year Roberts and Haynes discovered that the laws didn't hold up in one experiment they were doing, which modeled the movement of mass through a material.

"The mass was diffusing in the structure in a way that violated a fundamental law, which was written down 25 years ago," says Roberts.

After many late nights puzzling over the situation, Roberts and Haynes came up with a new law that combines the previous two laws and accurately models what they saw in their experiment.

"The new law has this wonderful property that it unifies the other two laws," says Roberts.