Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale
schemes that combine the accuracy of atomistic models with the efficiency of continuum …

Numerical simulations of crystal defects are necessarily restricted to finite computational
domains, supplying artificial boundary conditions that emulate the effect of embedding the …

Justification of the Cauchy–Born Approximation of Elastodynamics Page 1 Digital Object
Identifier (DOI) 10.1007/s00205-012-0592-6 Arch. Rational Mech. Anal. 207 (2013) 1025–1073 …

We formulate an energy-based atomistic-to-continuum coupling method based on blending
the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results …

Quantitative prediction on mesoscale crystal plasticity via first principle-based methods or
first principle-based multiscale methods is still unreachable, even though several …

We develop and analyze QM/MM (quantum/classic) hybrid methods for crystalline defects
within the context of the tight-binding model. QM/MM methods employ accurate quantum …

The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries,
occurs when the lattice configuration loses stability, that is, when an eigenvalue of the …

We develop a rigorous framework for modeling the geometry equilibration of crystalline
defects. We formulate the equilibration of crystal defects as a variational problem on a …

We present a comprehensive error analysis of two prototypical atomistic-to-continuum
coupling methods of blending type: the energy-based and the force-based quasicontinuum …

Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D
triangular lattice Page 1 MATHEMATICS OF COMPUTATION Volume 82, Number 284, October …