A finite-temperature dynamic coupled atomistic/discrete dislocation method
S. Qu, V. Shastry, W. A. Curtin and R. E. Miller
Modelling and Simulation in Materials Science and Engineering, 13, 1101-1118 (2005).

ABSTRACT
A method for simultaneously thermostatting an atomistic region and absorbing
energetic pulses impinging on the atormstic/continuum interface from the
atomistic region is developed to operate within the framework of the coupled
atomistic/discrete dislocation method. The approach inserts an additional
Langevin damping term and a random force term into the equations of motion for
atoms in a 'stadium' boundary region near the atom/continuum interface, with the
damping coefficient ramped linearly over the width of the region, as suggested
by Holian and Ravelo. The remaining interior atom dynamics are computed using a
standard MD algorithm with no artificial damping or thermostatting. The
continuum region deformations are computed using static FEM updated
stochastically over time scales comparable to the Debye frequency of the atoms
using time-averaged displacements at the atom/continuum interface, thereby
providing an evolution of the continuum region that tracks the atomistic
deformation. The method is evaluated by studying the ability of the coupled
system: (i) to equilibrate the inner atomistic region at a desired temperature
under conditions of no external or internal loading, (ii) to produce the proper
canonical thermal fluctuations and (iii) to absorb deformation pulses initiated
in the interior region and incident upon the atomistic/continuum boundary. With
an optimal maximum damping coefficient of approximately 1/2 of the Debye
frequency, temperature stability is attained at values very close to the target
temperature. The temperature variance agrees well with the canonical expectation
for various temperatures. For the same damping parameters and at low
temperature, high-energy deformation pulses propagate unimpeded up to the
stadium boundary region and then are completely damped out upon approach to the
atomistic/continuum interface with no measurable reflections. At higher
temperatures, thermal fluctuations in the total energy make analyses difficult,
but damping of high-energy deformation pulses is achieved within the limits of
the thermal noise in the system while observation of the time-dependent
displacements shows no observable reflections.