Simulations of Relaxation, Pinning, and Melting in Flux Lattices

Abstract

Fundamental aspects of the physics of an elastic medium in a static random background potential are discussed by use of one -and two dimensional computer simulations. The role of non-linear elastic instabilities and plastic deformations are treated in detail. Elastic instabilities are needed for the existence of a pinning force. In the limit of infinite system size plastic deformations always occur.

Transitions between phyllotactic lattice states in curved geometries

“…We use Molecular dynamics (MD) methods throughout this investigation and additionally use Monte Carlo (MC) techniques to verify that we have indeed found the ground states. MD is performed by numerically solving the over-damped Langevin equation for the motion of each vortex 40 , 41 up to the imposed cut-off radius , where is the lattice parameter. We control temperature through implementation of a thermostat 40 , 42 and slowly anneal a pseudo-randomly generated initial configuration from a high temperature into the zero-temperature ground state.…”

“…MD is performed by numerically solving the over-damped Langevin equation for the motion of each vortex 40 , 41 up to the imposed cut-off radius , where is the lattice parameter. We control temperature through implementation of a thermostat 40 , 42 and slowly anneal a pseudo-randomly generated initial configuration from a high temperature into the zero-temperature ground state. We simulate the flattened system with length , and as the typical values.…”

Extruding the vortex lattice: Two reacting populations of dislocations

“…is the velocity of the ith vortex with η an effective viscosity due to the normal fluid. Temperature is included via F T i , a thermostat [26,28] with F T i = 0 and F T i (t)F T j (t ) = 2k B ηT δ ij δ(t − t ). Finally, the vortices interact via the standard [29] repulsive force:…”

“…The motion of the N two-dimensional vortices is represented via molecular dynamics, describing the vortices as particles with repulsive interactions and following the diffusion dynamics of Jensen et al [22,23]:…”

“…v i is the velocity of the i-th vortex with η an effective viscosity due to the normal fluid. Temperature is included via F T i , a thermostat [22,24] with…”