---
_id: '14661'
abstract:
- lang: eng
  text: 'This paper is concerned with equilibrium configurations of one-dimensional
    particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour
    interactions and its passage to the continuum. The goal is to derive compactness
    results for a Γ-development of the energy with the novelty that external forces
    are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates
    and thus may model dead as well as live loads. Our result is based on a new technique
    for deriving compactness results which are required for calculating the first-order
    Γ-limit in the presence of external forces: instead of comparing a configuration
    of n atoms to a global minimizer of the Γ-limit, we compare the configuration
    to a minimizer in some subclass of functions which in some sense are "close to"
    the configuration. The paper is complemented with the study of the minimizers
    of the Γ-limit.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marcello
  full_name: Carioni, Marcello
  last_name: Carioni
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
- first_name: Anja
  full_name: Schlömerkemper, Anja
  last_name: Schlömerkemper
citation:
  ama: 'Carioni M, Fischer JL, Schlömerkemper A. External forces in the continuum
    limit of discrete systems with non-convex interaction potentials: Compactness
    for a Γ-development. <i>Journal of Convex Analysis</i>. 2023;30(1):217-247.'
  apa: 'Carioni, M., Fischer, J. L., &#38; Schlömerkemper, A. (2023). External forces
    in the continuum limit of discrete systems with non-convex interaction potentials:
    Compactness for a Γ-development. <i>Journal of Convex Analysis</i>. Heldermann
    Verlag.'
  chicago: 'Carioni, Marcello, Julian L Fischer, and Anja Schlömerkemper. “External
    Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction
    Potentials: Compactness for a Γ-Development.” <i>Journal of Convex Analysis</i>.
    Heldermann Verlag, 2023.'
  ieee: 'M. Carioni, J. L. Fischer, and A. Schlömerkemper, “External forces in the
    continuum limit of discrete systems with non-convex interaction potentials: Compactness
    for a Γ-development,” <i>Journal of Convex Analysis</i>, vol. 30, no. 1. Heldermann
    Verlag, pp. 217–247, 2023.'
  ista: 'Carioni M, Fischer JL, Schlömerkemper A. 2023. External forces in the continuum
    limit of discrete systems with non-convex interaction potentials: Compactness
    for a Γ-development. Journal of Convex Analysis. 30(1), 217–247.'
  mla: 'Carioni, Marcello, et al. “External Forces in the Continuum Limit of Discrete
    Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.”
    <i>Journal of Convex Analysis</i>, vol. 30, no. 1, Heldermann Verlag, 2023, pp.
    217–47.'
  short: M. Carioni, J.L. Fischer, A. Schlömerkemper, Journal of Convex Analysis 30
    (2023) 217–247.
date_created: 2023-12-10T23:00:59Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2024-01-16T12:03:05Z
day: '01'
department:
- _id: JuFi
external_id:
  arxiv:
  - '1811.09857'
  isi:
  - '001115503400013'
intvolume: '        30'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1811.09857
month: '01'
oa: 1
oa_version: Preprint
page: 217-247
publication: Journal of Convex Analysis
publication_identifier:
  eissn:
  - 2363-6394
  issn:
  - 0944-6532
publication_status: published
publisher: Heldermann Verlag
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'External forces in the continuum limit of discrete systems with non-convex
  interaction potentials: Compactness for a Γ-development'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2023'
...