Clustering of branching Brownian motions in confined geometries

Zoia, Andrea; Dumonteil, Éric; Mazzolo, Alain; Mulatier, Clélia de; Rosso, Alberto

doi:10.1103/physreve.90.042118

Cited by 22 publications

(36 citation statements)

References 43 publications

(99 reference statements)

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“…For the simple reactor model detailed above, the pair correlation function h f (x i , x j , t) for the free critical system has been derived in a previous work [30] and is briefly recalled in Eq. 11 in Section 4.…”

Section: Physical Observables and Main Findingsmentioning

confidence: 99%

The critical catastrophe revisited

Mulatier¹,

Dumonteil²,

Rosso³

et al. 2015

J. Stat. Mech.

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The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time. PACS numbers: 05.40.-a, 05.40.Fb, 02.50.-r

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Section: Physical Observables and Main Findingsmentioning

confidence: 99%

The critical catastrophe revisited

Mulatier¹,

Dumonteil²,

Rosso³

et al. 2015

J. Stat. Mech.

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show abstract

“…for an exactly critical system [27,28]. By inspection, observing that the term ν m (A + 2B + C ) is dominated by ν (2) n and that D D, we finally have…”

Section: B Spatial Correlation Functionsmentioning

confidence: 99%

“…in the critical regime [28]. By direct inspection, observing that the term ν m (A + 2B + C) is dominated by ν…”

Section: B Equations For the Second Momentsmentioning

confidence: 99%

“…If the neutron and precursor populations were fully decoupled, and the reactor were to be run based on prompt neutrons alone ( i P i,j = δ j,0 , so that ν m = 0, and λ = 0 for any m 0 ), the net reactivity would be ρ p = α(ν n − 1) − µ, and we would have n(t) p = n 0 e ωpt (12) with ω p = ρ p [28]. We have used the subscript p to denote quantities related to purely prompt systems.…”

Section: Statistical Analysis Of the Total Populationsmentioning

confidence: 99%

“…1), with particles closely packed together and empty spaces nearby [10,[21][22][23]. Spatial clustering phenomena have been first identified in connection with mathematical models of ecological communities [24,25], and since then have been thoroughly investigated for both infinite and finite collections of individuals [21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Neutron fluctuations: The importance of being delayed

et al. 2015

Self Cite

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The neutron population in a nuclear reactor is subject to fluctuations in time and in space due to the competition of diffusion by scattering, births by fission events, and deaths by absorptions. As such, fission chains provide a prototype model for the study of spatial clustering phenomena. In order for the reactor to be operated in stationary conditions at the critical point, the population of prompt neutrons instantaneously emitted at fission must be in equilibrium with the much smaller population of delayed neutrons, emitted after a Poissonian time by nuclear decay of the fissioned nuclei. In this work, we will show that the delayed neutrons, although representing a tiny fraction of the total number of neutrons in the reactor, have actually a key impact on the fluctuations, and their contribution is very effective in quenching the spatial clustering.

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Monte Carlo power iteration: Entropy and spatial correlations

Nowak

Miao

Dumonteil

et al. 2016

Annals of Nuclear Energy

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The behaviour of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. We will support our analysis by examining the higher-order moments of the entropy function and the center of mass of the neutron population. Within the framework of a simplified model based on branching processes, we will relate the behaviour of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.

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Clustering of branching Brownian motions in confined geometries

Cited by 22 publications

References 43 publications

The critical catastrophe revisited

The critical catastrophe revisited

Neutron fluctuations: The importance of being delayed

Monte Carlo power iteration: Entropy and spatial correlations

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