19 citations · 60 across the 11 of their papers we have counts for
8 papers · 1 filter
Discrete-to-continuum limits of interacting particle systems in one dimension with collisions
Patrick van Meurs
We study a class of interacting particle systems in which signed particles move on the real line. At close range particles with the same sign repel and particles with opposite…
Convergence rates for energies of interacting particles whose distribution spreads out as their number increases
Patrick van Meurs, Ken'ichiro Tanaka
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of…
Discrete-to-continuum convergence of charged particles in 1D with annihilation
Patrick van Meurs, Mark A. Peletier, Norbert Pozar
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite ti…
Regularity of the minimiser of one-dimensional interaction energies
M. Kimura, P. van Meurs
We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind…
Many-particle limits and non-convergence of dislocation wall pile-ups
Patrick van Meurs
The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repe…
Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock
Adriana Garroni, Patrick van Meurs, Mark Peletier +1
In this paper we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a cont…
Upscaling of the dynamics of dislocation walls
Patrick van Meurs, Adrian Muntean
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open…
Is adding charcoal to soil a good method for CO2 sequestration? - Modeling a spatially homogeneous soil
David Bourne, Tasnim Fatima, Patrick van Meurs +1
Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a…