Dong Han 2003 J. Phys. A: Math. Gen. 36 7485 doi:10.1088/0305-4470/36/27/302
Dong Han
Show affiliationsIn this paper, the subcritical, near-critical and supercritical asymptotic behaviour of a reversible Markov process as a chemical model for polymerization was studied. We establish the existence of three distinct stages (subcritical, near-critical and supercritical stages) of polymerization (in the thermodynamic limit as N → +∞), depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, Na(1/2 < a < 1) and N, respectively. Especially, a = 2/2σ+1 when the coagulation (reaction) rate constant Rij of the polymers satisfies Rij = iσ jσ with 1/2 < σ < 3/2.
Issue 27 (11 July 2003)
Received 14 January 2003, in final form 28 May 2003
Published 25 June 2003
Dong Han 2003 J. Phys. A: Math. Gen. 36 7485
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