Hydrodynamics at high order gradient expansion in viscoelastic materials

Supervisor: Dr. Alex Buchel

Project Description (Abstract):

Viscoelastic materials share the properties of both solids and fluids: they can ‘flow’ and also exhibit elastic properties unique to solids (the shear modulus). For fluids, it was recently discovered that the hydrodynamic expansion in the ‘velocity gradients’ of the flow has zero radius of convergence; the asymptotic character of the expansion is governed by the presence of the non-hydrodynamic excitations in a fluid. In the past, it was argued that the all-order in strain theory of the elasticity of the solids also has a zero radius of convergence: here the divergence is due to the (solid) material fracture due to thermal nucleation of cracks. The project aims to understand the hydrodynamics of viscoelastic materials at all orders in the velocity gradients: how the two different physical mechanisms producing zero radius of convergence in fluids and solids are realized in viscoelastic materials? (The methodology is to use the holographic correspondence between relativistic quantum field theory plasma and higher-dimensional gravitational models)