Smallscale behaviour in deterministic reaction models
Abstract
In a recent paper published in this journal (2009 J. Phys. A: Math. Theor. 42 495004) we studied a onedimensional particles system where nearest particles attract with a force inversely proportional to a power α of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z) ~ z^{β(α)} for small z and β(α) > α. We can now prove analytically that in the strict limit of z → 0, β = α for α > 0, corresponding to the meanfield result, and we compute the length scale where the mean field breaks down. More generally, in that same limit correlations are negligible for any similar reaction model where attractive forces diverge with vanishing distance. The actual meaning of the measured exponent β(α) remains an open question.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2010
 DOI:
 10.1088/17518113/43/40/405002
 arXiv:
 arXiv:1006.0121
 Bibcode:
 2010JPhA...43N5002P
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 Six pages. Section 2 has been rewritten. Accepted for publication in Journal of Physics A: Mathematical and Theoretical