Conservative mixing, competitive mixing and their applications

In many of the models applied to simulations of turbulent transport and turbulent combustion, the mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. Stochastic particles with properties and mixing can be used not only for simulating turbulent combustion, but also for modeling a large spectrum of physical phenomena. Traditional mixing, which is commonly used in the modeling of turbulent reacting flows, is conservative: the total amount of scalar is (or should be) preserved during a mixing event. It is worthwhile, however, to consider a more general mixing that does not possess these conservative properties; hence, our consideration lies beyond traditional mixing. In non-conservative mixing, the particle post-mixing average becomes biased towards one of the particles participating in mixing. The extreme form of non-conservative mixing can be called competitive mixing or competition: after a mixing event, the loser particle simply receives the properties of the winner particle. Particles with non-conservative mixing can be used to emulate various phenomena involving competition. In particular, we investigate cyclic behavior that can be attributed to complex competing systems. We show that the localness and intransitivity of competitive mixing are linked to the cyclic behavior. PACS numbers: 47.27.−i, 47.10.A−