Emergence of particle clusters in a one-dimensional model:  connection to condensation processes

Matthew Burman; Daniel Carpenter; Robert L Jack

doi:10.1088/1751-8121/aa601b

Emergence of particle clusters in a one-dimensional model: connection to condensation processes

Matthew Burman, Daniel Carpenter, Robert L Jack

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Abstract

We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of particles, with large gaps between them. These clusters are correlated in space, and the system has a self-similar (fractal) structure. These results are related to condensation phenomena in mass transport models and to a recent mathematical analysis of the hydrodynamic limit in a related model.

Original language	English
Article number	135002
Number of pages	17
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	50
Issue number	13
Early online date	3 Mar 2017
DOIs	https://doi.org/10.1088/1751-8121/aa601b
Publication status	Published - 31 Mar 2017

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10.1088/1751-8121/aa601b

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This is an author-created, un-copyedited version of an article accepted for publication/published in: Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at: https://doi.org/10.1088/1751-8121/aa601b
Accepted author manuscript, 1.53 MB

https://arxiv.org/abs/1608.04304

Cite this

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abstract = "We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of particles, with large gaps between them. These clusters are correlated in space, and the system has a self-similar (fractal) structure. These results are related to condensation phenomena in mass transport models and to a recent mathematical analysis of the hydrodynamic limit in a related model.",

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AB - We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of particles, with large gaps between them. These clusters are correlated in space, and the system has a self-similar (fractal) structure. These results are related to condensation phenomena in mass transport models and to a recent mathematical analysis of the hydrodynamic limit in a related model.

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Emergence of particle clusters in a one-dimensional model: connection to condensation processes

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