# Small-scale behaviour in deterministic reaction models

@article{Politi2010SmallscaleBI,
title={Small-scale behaviour in deterministic reaction models},
author={Paolo Politi and Daniel ben-Avraham},
journal={Journal of Physics A},
year={2010},
volume={43},
pages={405002}
}
• Published 1 June 2010
• Mathematics, Physics
• Journal of Physics A
In a recent paper published in this journal (2009 J. Phys. A: Math. Theor. 42 495004) we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power ? of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z) ~ z?(?) for small z and ?(?) > ?. We can now prove analytically that in the strict limit of z ? 0, ? = ? for ? > 0, corresponding to the…

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