Preface

WILLIAMS, M.M.R.

doi:10.1016/b978-0-08-017920-9.50004-4

Cited by 7 publications

(21 citation statements)

References 0 publications

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“…The stochastic paths of neutrons within multiply-ing media are known to follow position-and velocitydependent random flights [2,33,34]. To begin with, the reactor will be taken to be spatially homogeneous and the random displacements will be approximated by regular ddimensional Brownian motion with a constant diffusion coefficient D. The interaction rates of neutrons with matter can be safely assumed to be Poissonian: a neutron is absorbed and disappears at rate µ, and undergoes fission at rate α.…”

Section: A Prototype Model Of Fission Chains In Nuclear Reactorsmentioning

confidence: 99%

“…In view of the relevance of neutron clustering in the context of nuclear reactor physics, in this paper we will investigate the spatial and temporal behaviour of a collection of neutrons undergoing scattering (random displacements), fission (reproduction) and absorption (death). As illustrated in the following, a prototype model of a nuclear reactor can be described in terms of a multi-type branching process involving an equilibrium between neutrons and a second species of particles, the so-called precursors [1][2][3]. Upon fission, a random number of secondary neutrons (called prompt) are emitted almost instantaneously.…”

Section: Introductionmentioning

confidence: 99%

“…In most of the models cited above, individuals also interact with the surrounding environment and are typi- * Electronic address: andrea.zoia@cea.fr cally subject to random displacements [2,15]. The interplay between the fluctuations stemming from birth-death events and those stemming from diffusion will thus subtly affect the spatial distribution of the particles in such systems [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…In the intermediate regime, the population stays constant on average, and the system is said to be exactly critical. A prominent example of a system operating at (or close to) the critical point is provided by the self-sustaining fission chains of neutrons in nuclear reactors [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…Examples are widespread and encompass neutron multiplication [1][2][3], nuclear collision cascades [3][4][5], epidemics and ecology [6][7][8], bacterial growth [9,10], and genetics [11][12][13]. Neglecting particleparticle correlations and non-linear effects, the evolution of such systems can be effectively explained by the Galton-Watson model [3].…”

Section: Introductionmentioning

confidence: 99%

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Neutron fluctuations: The importance of being delayed

et al. 2015

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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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Section: A Prototype Model Of Fission Chains In Nuclear Reactorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neutron fluctuations: The importance of being delayed

et al. 2015

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Mathematical and computational models for simulating transient nuclear criticality excursions within wetted fissile powder systems

Jones

Winter

Cooling

et al. 2022

Annals of Nuclear Energy

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Time-dependent branching processes: a model of oscillating neuronal avalanches

Pausch

Garcia-Millan

Pruessner

2020

Sci Rep

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Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the coexistence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such timedependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results. In the brain, electrical signals propagate between neurons of the cortical network through action potentials, which are spikes of polarisation in the membrane of the neuron's axon. These spikes have an amplitude of about 100 mV, typically last about 1 ms 1 and can be recorded using micro-electrodes 2,3. In order to study the signaling in larger regions of neurons, multielectrode arrays, comprising about 60 electrodes spread across ≈ 4 mm 2 , are used to capture the collective occurrence of spikes as local field potentials (LFPs). In this setting, the electrodes are extracellular and each is sensitive to electrical signals from several surrounding neurons 4-8. The data of the LFP recordings are processed by putting them into time bins of a few milliseconds duration and by introducing a voltage threshold. In addition, a refractory period is imposed to avoid counting large voltage excursions more than once. The details of processing can differ slightly between experiments 5-9. However, after processing, the data is a time series of two values for each electrode: on (detected signal above threshold) and off (no detected signal or signal below threshold). A neuronal avalanche is then defined as a set of uninterrupted signals detected across the micro-electrode array. Each avalanche is both preceded and succeeded by at least one time bin where none of the electrodes detected a signal, defining the avalanche duration as the number of time bins where the avalanche unfolds. Which and how many electrodes detect a signal varies during the avalanche 5,6. The duration of avalanches typically ranges between a few milliseconds and 30 ms 10. A prominent observable is the avalanche size, which is the total number of recorded signals during the avalanche. If there is only one electrode detecting a signal in each time bin of an avalanche, its size and duration are equal. However, the size of an avalanche is usually larger than its duration due to the simultaneous detection of signals by different electrodes. Histograms of the avalanche size show an apparent power-law distribution of sizes, with common small avalanches and rare large avalanches 5,6 , the fingerprint of scale-free phenomena. The exponent of the power law was observed to be −3/2 in Ref. 5. However, its exac...

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Preface

Cited by 7 publications

References 0 publications

Neutron fluctuations: The importance of being delayed

Neutron fluctuations: The importance of being delayed

Mathematical and computational models for simulating transient nuclear criticality excursions within wetted fissile powder systems

Time-dependent branching processes: a model of oscillating neuronal avalanches

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