[HTML][HTML] Discrete-to-continuum limits of interacting particle systems in one dimension with collisions

P van Meurs - Journal of Mathematical Analysis and Applications, 2024 - Elsevier
We study a class of interacting particle systems in which n signed particles move on the real
line. This class includes the overdamped dynamics (ie 'velocity= force') of charged particles …

[PDF][PDF] Discrete-to-continuum limits of interacting dislocations

PJP van Meurs - 2015 - research.tue.nl
This thesis studies discrete-to-continuum limits of models for interacting dislocations. This
analysis contributes to the ultimate goal of obtaining a system of equations which accurately …

Many-particle limits and non-convergence of dislocation wall pile-ups

P van Meurs - Nonlinearity, 2017 - iopscience.iop.org
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, repulsive …

Distribution of cracks in a chain of atoms at low temperature

S Jansen, W König, B Schmidt, F Theil - Annales Henri Poincaré, 2021 - Springer
We consider a one-dimensional classical many-body system with interaction potential of
Lennard–Jones type in the thermodynamic limit at low temperature 1/β∈(0,∞). The ground …

Asymptotic analysis of boundary layers in a repulsive particle system

CL Hall, T Hudson, P Van Meurs - Acta Applicandae Mathematicae, 2018 - Springer
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 repulsive …

Surface energies arising in microscopic modeling of martensitic transformations

G Kitavtsev, S Luckhaus, A Rüland - Mathematical Models and …, 2015 - World Scientific
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic lattice. The
two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins …

On a -Convergence Analysis of a Quasicontinuum Method

M Schäffner, A Schlömerkemper - Multiscale Modeling & Simulation, 2015 - SIAM
In this paper, we investigate a quasicontinuum method by means of analytical tools. More
precisely, we compare a discrete-to-continuum analysis of an atomistic one-dimensional …

Multiscale analysis of non-convex discrete systems via -convergence

M Schäffner - 2015 - opus.bibliothek.uni-wuerzburg.de
The subject of this thesis is the rigorous passage from discrete systems to continuum models
via variational methods. The first part of this work studies a discrete model describing a one …

Boundary-layer analysis of repelling particles pushed to an impenetrable barrier

P van Meurs - SIAM Journal on Mathematical Analysis, 2022 - SIAM
This paper considers the equilibrium positions of n particles in one dimension. Two forces
act on the particles; a nonlocal repulsive particle-interaction force and an external force …

Stochastic Homogenization in the Passage from Discrete to Continuous Systems-Fracture in Composite Materials

L Lauerbach - 2020 - opus.bibliothek.uni-wuerzburg.de
The work in this thesis contains three main topics. These are the passage from discrete to
continuous models by means of $\Gamma $-convergence, random as well as periodic …