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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …