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 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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Acknowledgements
We acknowledge R. Rajesh for several useful inputs and Chandrashekar Iyer for discussions. M.B. acknowledges support under the DAE Homi Bhabha Chair Professorship of the Department of Atomic Energy, India. This project was funded by intramural funds at TIFR Hyderabad from the Department of Atomic Energy (DAE), India.
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Das, A., Barma, M. Dynamic condensates in aggregation processes with mass injection. Indian J Phys (2023). https://doi.org/10.1007/s12648-023-03030-1
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DOI: https://doi.org/10.1007/s12648-023-03030-1