Generating dense packings of hard spheres by soft interaction design

Maimbourg, Thibaud; Sellitto, Mauro; Semerjian, Guilhem; Zamponi, Francesco

doi:10.21468/SciPostPhys.4.6.039

SciPost Physics

Generating dense packings of hard spheres by soft interaction design

Thibaud Maimbourg, Mauro Sellitto, Guilhem Semerjian, Francesco Zamponi

SciPost Phys. 4, 039 (2018) · published 26 June 2018

doi: 10.21468/SciPostPhys.4.6.039
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Abstract

Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7\, d\, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.4.6.039
TI  - Generating dense packings of hard spheres by soft interaction design
PY  - 2018/06/26
UR  - https://scipost.org/SciPostPhys.4.6.039
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 4
IS  - 6
SP  - 039
A1  - Maimbourg, Thibaud
AU  - Sellitto, Mauro
AU  - Semerjian, Guilhem
AU  - Zamponi, Francesco
AB  - Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7\, d\, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.
ER  -

@Article{10.21468/SciPostPhys.4.6.039,
	title={{Generating dense packings of hard spheres by soft interaction design}},
	author={Thibaud Maimbourg and Mauro Sellitto and Guilhem Semerjian and Francesco Zamponi},
	journal={SciPost Phys.},
	volume={4},
	pages={039},
	year={2018},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.4.6.039},
	url={https://scipost.org/10.21468/SciPostPhys.4.6.039},
}

Cited by 7

Ontology / Topics

See full Ontology or Topics database.

Glasses Hard spheres Infinite dimension Liquids Packing

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Thibaud Maimbourg,
¹ ² Mauro Sellitto,
³ Guilhem Semerjian,
³ Francesco Zamponi

Funder for the research work leading to this publication

European Research Council [ERC]