Dynamic condensates in aggregation processes with mass injection

Arghya Das; Mustansir Barma

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arXiv · 2307.16310

Dynamic condensates in aggregation processes with mass injection

Arghya Das·Mustansir Barma

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Abstract

The Takayasu aggregation model is a paradigmatic model of aggregation with mass injection, known to exhibit a power law distribution of mass over a range which grows in time. Working in one dimension we find that the mass profile in addition shows distinctive {\it dynamic condensates} which collectively hold a substantial portion of the mass (approximately $80\%$ when injection and diffusion rates are equal) and lead to a substantial hump in the scaled distribution. To track these, we monitor the largest mass within a growing coarsening length. An interesting outcome of extremal statistics is that the mean of the globally largest mass in a finite system grows as a power law in time, modulated by strong multiplicative logarithms in both time and system size. At very long times in a finite system, the state consists of a power-law-distributed background with a condensate whose mass increases linearly with time.

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Arghya Das, Mustansir Barma. 2023-07-30. Dynamic condensates in aggregation processes with mass injection. https://arxiv.org/abs/2307.16310

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