Abstract
We investigate numerically the effect of an applied electric field on the physics of cholesteric cubic blue phases. The full hydrodynamic equations of motion are solved via a lattice Boltzmann algorithm which leads to an exact minimisation of the Landau-de Gennes free energy in steady state. This technique is able to reproduce all the main experimental findings including the anomalous electrostriction of blue phase I and the field induced transition to blue phase X. The dynamics of switching is also captured by our simulations and we identify the deformation of double twist cylinders and disclination lines at low field strength as well as the pathway by which the network rearranges during transitions.