12 citations · 14 across the 5 of their papers we have counts for
7 papers
Discrete Dislocations Dynamics with annihilation as the limit of the Peierls-Nabarro model in one dimension
Patrick van Meurs, Stefania Patrizi
Plasticity of metals is the emergent phenomenon of many crystal defects (dislocations) which interact and move on microscopic time and length scales. Two of the commonly used model…
Boundary-layer analysis of repelling particles pushed to an impenetrable barrier
Patrick van Meurs
This paper considers the equilibrium positions of particles in one dimension. Two forces act on the particles; a nonlocal repulsive particle-interaction force and an external f…
Quantitative estimate of the continuum approximations of interacting particle systems in one dimension
Masato Kimura, Patrick van Meurs
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in part…
Atomistic origins of continuum dislocation dynamics
Thomas Hudson, Patrick van Meurs, Mark A. Peletier
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocati…
Discrete-to-continuum limits of particles with an annihilation rule
Patrick van Meurs, Marco Morandotti
In the recent trend of extending discrete-to-continuum limit passages for gradient flows of single-species particle systems with singular and nonlocal interactions to particles of…
Asymptotic analysis of boundary layers in a repulsive particle system
Cameron Hall, Thomas Hudson, Patrick van Meurs
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsi…