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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 Hessian of the lattice energy functional becomes negative. When the atomistic energy is approximated by a hybrid energy that couples atomistic and continuum models, the… (More)

- Matthew Dobson, Mitchell Luskin
- SIAM J. Numerical Analysis
- 2009

We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the quasi-nonlocal quasicontinuum approximation. For simplicity, the analysis is restricted to the case of second-neighbor… (More)

Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are popular tools in computational physics. For example, the force-based quasicontinuum (QCF) approximation is the only known pointwise consistent quasicontinuum approximation for coupling a general atomistic model with a finite element continuum model. In this… (More)

A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We formulate a simple one-dimensional model problem and give a detailed analysis of the stability of the force-based quasicontinuum (QCF) method. The focus of the analysis is the… (More)

The quasicontinuum (QC) method is applied to materials possessing a multilattice crystal structure. Cauchy-Born (CB) kinematics, which accounts for the shifts of the crystal basis, is used in continuum regions to relate atomic motions to continuum deformation gradients. To avoid failures of the CB kinematics, QC is augmented with a phonon stability analysis… (More)

- Matthew Dobson, Mitchell Luskin
- J. Sci. Comput.
- 2008

We give an analysis of a continuation algorithm for the numerical solution of the forcebased quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner. The analysis presented in this paper is used to determine an… (More)

- Matthew Dobson, Mitchell Luskin, Christoph Ortner
- Multiscale Modeling & Simulation
- 2010

The accuracy of atomistic-to-continuum hybrid methods can be guaranteed only for deformations where the lattice configuration is stable for both the atomistic energy and the hybrid energy. For this reason, a sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation of… (More)

We propose that sharp stability estimates are essential for evaluating the predictive capability of atomistic-to-continuum coupling methods up to the limit load for atomistic instabilities such as fracture, dislocation movement, or crack tip propagation. Using rigorous analysis, asymptotic methods, and numerical experiments, we obtain such sharp stability… (More)

- Claudio Martella, Matthew Dobson, Aart van Halteren, Maarten van Steen
- 2014 IEEE International Conference on Pervasive…
- 2014

Understanding the social dynamics of a group of people can give new insights into social behavior. Physical proximity between individuals results from the interactions between them. Hence, measuring physical proximity is an important step towards a better understanding of social behavior. We discuss a novel approach to sense proximity from within the social… (More)

- Matthew Dobson, Spyros Voulgaris, Maarten van Steen
- 2011 IEEE/IFIP 41st International Conference on…
- 2011

Energy is the scarcest resource in ad-hoc wireless networks, particularly in wireless sensor networks requiring a long lifetime. Intermittently switching the radio on and off is widely adopted as the most effective way to keep energy consumption low. This, however, prevents the very goal of communication, unless nodes switch their radios on at synchronized… (More)