Abstract
Models of thermal explosion in a closed system are studied at the macroscopic level, where a nonlinear rate equation is solved numerically, at the stochastic level, where the corresponding master equation is solved numerically and also analyzed through a 1/N expansion (N is the number of particles in the system) and at the atomistic level, where molecular dynamics simulations of reacting hard disks are carried out. We find that for 800 particles (N=800) simulation gives sufficient agreement with the macroscopic description of the average concentration. In the region ofN = 50–2000 the stochastic and molecular dynamics results show significant overlap with each other; as expected, the effects of fluctuations decrease with increasingN. Under a low-temperature condition (slow reaction rate), a regime which cannot be realized in molecular dynamics simulation, direct numerical solution of the master equation reveals a bimodal distribution during times comparable to a correlation time. This behavior of transient bifurcation, which had been discussed previously, is shown to be a result of small system size.
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Chou, DP., Lackner, T. & Yip, S. Fluctuation effects in models of adiabatic explosion. J Stat Phys 69, 193–215 (1992). https://doi.org/10.1007/BF01053790
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DOI: https://doi.org/10.1007/BF01053790