LMP Seminar: Motion of singularities out of equilibrium: anisotropic defects and driven interfaces

Most systems, when studied over large scales, display singularities whose nature varies depending on the symmetries. Magnetic materials show the formation of domain walls, binary mixtures exhibit interfaces, and liquid crystals point defects. Understanding the mechanisms that govern the dynamics of these singularities out of equilibrium is a challenging theoretical problem in both passive and active systems. In this talk, I will present a unified framework allowing to derive the equation of motion describing their dynamics from the underlying field theory. For liquid crystals, we use this approach to solve the long-standing problem of describing the effect of elastic anisotropy on the motion of topological defects. We show that anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. For phase-separating binary mixtures, similar ideas can be used to determine the equation of motion ruling the dynamics of interfaces in the presence of spatially-dependent material properties. The application of these equations to study the influence of the presence of a temperature profile reveals unexpected features in the thermophoresis of droplets. Due to its generality, our method can shed light on the motion of singularities in a wide variety of systems, both driven and active.