Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by...
We give results for the approximation of a laminate with
varying volume fractions for multi-well energy minimization
problems modeling martensitic crystals that
can undergo either an orthorhombic
to monoclinic or a cubic to tetragonal transformation.
We construct energy minimizing sequences of deformations which satisfy
the corresponding boundary condition, and we
establish a series of error bounds in terms of the elastic energy
for the approximation of the limiting macroscopic
deformation and...
We analyze a force-based quasicontinuum approximation to a
one-dimensional system of atoms that interact by a classical
atomistic potential. This force-based quasicontinuum approximation
can be derived as the modification of an energy-based
quasicontinuum approximation by the addition of nonconservative
forces to correct nonphysical “ghost” forces that occur in the
atomistic to continuum interface during constant strain. The algorithmic
simplicity and consistency with the purely atomistic model
at...
The atomistic to continuum interface for quasicontinuum energies
exhibits nonzero forces under uniform strain that have been
called ghost forces.
In this paper,
we prove for a linearization of a one-dimensional quasicontinuum energy
around a uniform strain
that the effect of the ghost forces on the displacement
nearly cancels and has a small effect on the error away from the interface.
We give optimal order error estimates
that show that the quasicontinuum displacement
converges to the atomistic...
We give an analysis of the stability and uniqueness of the simply
laminated microstructure for all three tetragonal to monoclinic
martensitic transformations. The energy density for tetragonal to
monoclinic transformations has four rotationally invariant wells since
the transformation has four variants. One of these tetragonal to
monoclinic martensitic transformations corresponds to the shearing of
the rectangular side, one corresponds to the shearing of the square
base, and one corresponds to...
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
We propose, analyze, and compare several numerical methods for the
computation of the deformation of a pressurized martensitic thin
film. Numerical results have been obtained for the hysteresis of
the deformation as the film transforms reversibly from austenite to
martensite.
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