# Invincibility cloak

Researchers at Liverpool University have shown it is mathematically possible to develop a cloak to protect buildings from earthquakes.

The seismic waves produced by earthquakes include body waves that travel through the earth and surface waves that travel across it. The idea would be to control the path of surface waves, which are the most damaging and responsible for much of the destruction that follows earthquakes.

The technique involves the use of concentric rings of plastic which could be fitted to the Earth’s surface to divert surface waves. By controlling the stiffness and elasticity of the rings, waves travelling through the rings pass into the material and are compressed into small fluctuations in pressure and density. The path of the surface waves could be made into an arc that directs the waves outside the protective cloak. The idea could also be applied to buildings by installing the rings into foundations.

Sebastien Guenneau, from the university’s Department of Mathematics, who developed the technique with Stefan Enoch and Mohamed Farhat from the Fresnel Institute (CNRS) in Marseilles, France, explained: ‘We are able to “tune” the cloak to the differing frequencies of incoming waves, which means we can divert waves of a variety of frequencies. For each small frequency range, there is a pair of rings that do most of the work and these move about a lot – bending up and down – when they are hit by a wave at their frequency.

‘The waves are then directed outside the cloak where they return to their previous size. The cloak does not reflect waves – they continue to travel behind it with the same intensity. At this stage, therefore, we can only transfer the risk from one area to another, rather than eliminate it completely.’

He added: ‘This work has the potential to offer protection for densely populated areas of the world at risk from earthquakes. The challenge now is to turn our theories into real applications that can save lives and small-scale experiments are underway.’

Seismic waves also include coupled pressure and shear body waves, which are less destructive than surface waves. Sebastien Guenneau and Sasha Movchan at Liverpool University, together with Michele Brun at Cagliari University, have designed an ‘elastic’ cloak to protect against these particular seismic waves and the team is currently seeking a suitable material to accommodate the elastic parameters of the cloak.