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 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...

We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni,...

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