On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond

Abad, E.

doi:10.1103/physreve.70.031110

Cited by 5 publications

(17 citation statements)

References 46 publications

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“…Setting n = 1, they include explicit expressions for the average particle-densities and their correlators. In the special situation of initially uncorrelated particles of prescribed densities, we reproduce all previously obtained results [36,26,27,44,46,47,48,60,19,2] as special cases.…”

Section: Discussionsupporting

confidence: 72%

“…For the special case of initially uncorrelated particles such that C n (0) = ρ n , we reproduce the well-known form [26,44,2]…”

Section: Densities Of N-strings On Bethe Latticesmentioning

confidence: 98%

“…These models can be solved, for example by the well-established method of empty intervals [8,9,3]. The average particle concentration c(t) ∼ t −1/2 [61] (2). The usual Glauber dynamics corresponds to δ = 0 and the kdh dynamics is given by γ = 2δ (dashed line).…”

Section: Introductionmentioning

confidence: 99%

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Exact correlation functions in particle-reaction models with immobile particles

et al. 2012

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Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pairannihilation where each particle interacts at most once throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating-function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both infinite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

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Section: Discussionsupporting

confidence: 72%

“…For the special case of initially uncorrelated particles such that C n (0) = ρ n , we reproduce the well-known form [26,44,2]…”

Section: Densities Of N-strings On Bethe Latticesmentioning

confidence: 98%

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Exact correlation functions in particle-reaction models with immobile particles

et al. 2012

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“…With the help of these connections, we have been able to compare our own numerical results (Figs. 4 and 5) with analytic predictions [25] for the remaining density of wealth-possessing agents on several networks. A good coincidence is found throughout the entire unstable phase.…”

Section: Discussion Of Resultsmentioning

confidence: 96%

“…In particular, Abad [25] provides explicit expressions for the final density ρ of active agents on 1d and 2d lattices, as well as on Bethe Lattices with coordination γ. If ρ 0 is the initial density of active sites, the final density on a Bethe lattice is…”

Section: Analytical Prediction For ρmentioning

confidence: 99%

Yard-Sale exchange on networks: wealth sharing and wealth appropriation

Bustos-Guajardo¹,

Moukarzel²

2012

J. Stat. Mech.

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Yard Sale (YS) is a stochastic multiplicative wealth exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1D rings, 2D square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allows us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.

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Crossover between diffusion-limited and reaction-limited regimes in the coagulation–diffusion process

Shapoval¹,

Dudka²,

Durang³

et al. 2018

J. Phys. A: Math. Theor.

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The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction–diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation–diffusion process on a chain and on the Bethe lattice. On a chain, this model is exactly solvable through the empty-interval method. This method can be extended to the Bethe lattice, in the ben-Avraham–Glasser approximation. On the Bethe lattice, the analysis of the Laplace-transformed time-dependent particle-density is analogous to the study of the stationary state, if a stochastic reset to a configuration of uncorrelated particles is added. In this stationary state logarithmic corrections to scaling are found, as expected for systems at the upper critical dimension. Analogous results hold true for the time-integrated particle-density. The crossover scaling functions and the associated effective exponents between the chain and the Bethe lattice are derived.

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On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond

Cited by 5 publications

References 46 publications

Exact correlation functions in particle-reaction models with immobile particles

Exact correlation functions in particle-reaction models with immobile particles

Yard-Sale exchange on networks: wealth sharing and wealth appropriation

Crossover between diffusion-limited and reaction-limited regimes in the coagulation–diffusion process

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