Variational evolution of one-dimensional Lennard-Jones systems

Andrea Braides; Anneliese Defranceschi; Enrico Vitali; Andrea Braides; Anneliese Defranceschi; Enrico Vitali

doi:10.3934/nhm.2014.9.217

Networks and Heterogeneous Media

2014, Volume 9, Issue 2: 217-238. doi: 10.3934/nhm.2014.9.217

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Variational evolution of one-dimensional Lennard-Jones systems

1.
Dipartimento di Matematica, Università di Roma 'Tor Vergata', via della Ricerca Scientifica, 00133 Roma
2.
Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38123 Povo
3.
Dipartimento di Matematica 'F. Casorati', Università di Pavia, via Ferrata, 1-27100 Pavia

Received: 01 October 2013 Revised: 01 May 2014
Primary: 35K90, 74A45; Secondary: 49J45, 74R10.

We analyze Lennard-Jones systems from the standpoint of variational principles beyond the static framework. In a one-dimensional setting such systems have already been shown to be equivalent to energies of Fracture Mechanics. Here we show that this equivalence can also be given in dynamical terms using the notion of minimizing movements.
- Lennard-Jones systems,
- variational evolution,
- minimizing movements,
- Fracture Mechanics
Citation: Andrea Braides, Anneliese Defranceschi, Enrico Vitali. Variational evolution of one-dimensional Lennard-Jones systems[J]. Networks and Heterogeneous Media, 2014, 9(2): 217-238. doi: 10.3934/nhm.2014.9.217

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Abstract

We analyze Lennard-Jones systems from the standpoint of variational principles beyond the static framework. In a one-dimensional setting such systems have already been shown to be equivalent to energies of Fracture Mechanics. Here we show that this equivalence can also be given in dynamical terms using the notion of minimizing movements.

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