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users:shapira:index [2019/05/10 14:45]
shapira [Publications]
users:shapira:index [2019/07/02 14:46] (current)
shapira [Publications]
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 ====Publications==== ====Publications====
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 +==Time Scales of the Fredrickson-Andersen Model on the Polluted Lattice==
 +With [[https://​sites.google.com/​view/​eslivken|Erik Slivken]]. //arXiv preprint [[https://​arxiv.org/​abs/​1906.09949|arXiv:​1906.09949]]//​ (2019).
 +
 +In this work we studied the Fredrickson-Andersen model on the polluted lattice (i.e. when removing some of the vertices at random). This model is a part of a large family of models called kinetically constrained models, that try to explain certain aspects of glasses and granular materials. We wanted to understand how typical time scales diverge when the density is very high. It's a question that has been studied before for many kinetically constrained models in homogeneous systems, and different models show some behavior that could also be seen experimentally.
 +
 +But physical systems are not always homogeneous (e.g. a granular material with two grain types). In these cases, it could be more appropriate to take a dynamics in random environment. The random environment that we've taken is the polluted lattice, ​ that's already been analyzed in a closely related model called the bootstrap percolation.
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 +Many of the tools used in order to understand kinetically constrained models in homogeneous environments stop working when the system is not homogeneous (e.g. the spectral gap). The reason is that in random systems remote regions that are not really typical influence the quantities that we study, even though they shouldn'​t effect the actual dynamics. We needed to find a way to analyze time scales of the model in a way which ignores these untypical regions. We managed to do that by looking at hitting time of events that depend only on the state near the origin (or any arbitrary vertex). ​
  
 ==Diffusive Scaling of the Kob-Andersen Model on the Integer Lattice== ==Diffusive Scaling of the Kob-Andersen Model on the Integer Lattice==
 
users/shapira/index.1557492348.txt.gz · Last modified: 2019/05/10 14:45 by shapira
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