Solution of transport equations by the Monte Carlo method, taking account of the space-time variation in the interaction cross section

Androsenko, A. A.; Androsenko, P. A.; Pupko, S. V.

doi:10.1007/bf01121847

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“…This method has strongly influenced the plasma culture. − The technique is not exclusively called “null collisions”, and there are several other names: null event, pseudocollisions, fictitious collisions, hole tracking, Woodcock scattering, delta scattering, pseudoscattering, or maximum cross section by Marchuk . On the other hand, in neutronics, some authors , introduced the method in this community, followed by the works of others − who implemented the same method in various simulation codes of neutron transport. Finally, during the same period, other scientists , used fictitious events in semiconductor physics.…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo-Based Strategy to Assess Complex Kinetics: Application of the Null-Reaction Method to DAEM

et al. 2023

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The distributed activation energy model (DAEM) is widely used in chemical kinetics to statistically describe the occurrence of numerous independent parallel reactions. In this article, we suggest a rethink in the context of a Monte Carlo integral formulation to compute the conversion rate at any time without approximation. After the basics of the DAEM are introduced, the considered equations (under isothermal and dynamic conditions) are respectively expressed into expected values, which in turn are transcribed into Monte Carlo algorithms. To describe the temperature dependence of reactions under dynamic conditions, a new concept of null reaction, inspired from null-event Monte Carlo algorithms, has been introduced. However, only the first-order case is addressed for the dynamic mode due to strong nonlinearities. This strategy is then applied to both analytical and experimental density distribution functions of the activation energy. We show that the Monte Carlo integral formulation is efficient in solving the DAEM without approximation and that it is well-adapted due to the possibility of using any experimental distribution function and any temperature profile. Furthermore, this work is motivated by the need for coupling chemical kinetics and heat transfer in a single Monte Carlo algorithm.

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