arXiv subjects

Eric Dumonteil

Publications and source records attributed to Eric Dumonteil.

At least 19 recordsLinked to original sources

arXiv2026

Branching stochastic mechanics. II. Relative localization and collective poles from Bohm/Fisher feedback

Paper I introduced branching stochastic mechanics (BSM) by lifting the Schr\"odinger-Nagasawa pair to reciprocal forward and backward branching fields. Their centered connected kernel $C_{\rm FB}=\mathbb E_\omega[\psi_F\psi_B]$ carries the organized reciprocal sector, where $\mathbb E_\omega$ denotes expectation over branching-noise realizations, with $\rho_{\rm BSM}=-C_{\rm FB}(x,x)$ on the anticorrelated branch. Here we develop the stochastic field theory of the Bohm/Fisher feedback that acts on this connected sector. Starting from the multiplicative branching covariance of BSM, a Martin-Siggia-Rose-Janssen-de~Dominicis (MSRJD) formulation and a causal two-loop two-particle-irreducible (2PI) closure are used to determine response and correlation functions self-consistently. The free connected theory exhibits secular growth and ultraviolet accumulation, whereas the dressed theory develops a finite relative screening length. A reduced numerical evolution shows bounded formation of this localized sector, and a self-similar Fisher construction defines the saturated information velocity $c_\star$. A Born-Oppenheimer separation then distinguishes internal relative organization from collective propagation. Restoring the complete frequency structure gives two fixed-$q$ pole families: a gapless difference branch and a gapped sum branch. The infrared velocity of the difference branch approaches $c_\star$ at saturation. The common cone and the projected sum-sector gap are then formulated as additional fixed-point matching conditions for the collective theory.

cond-mat.stat-mech↗

arXiv2026

Branching stochastic mechanics. I. Clustering and connected correlations within a branching-process representation of the Schr\"odinger equation

Can finite-range correlations hide in the statistics of an extended quantum state? The Schr\"odinger-Nagasawa transform represents the wave function by positive forward and backward diffusion fields whose product is the Born density. We promote them to branching superprocesses, $\Phi_F$ and $\Phi_B$: diffusion samples stochastic paths, whereas Bohm/Fisher-controlled branching generates genealogies of alternative continuations. With rates evaluated on the prescribed Born density, their means reproduce Schr\"odinger dynamics exactly. The connected sector exhibits supercritical, critical, and subcritical clustering in confinement and has critical dimension $d_c=2$ in free space. Stationary eigenmodes remain extended; subcritical clusters acquire the reduced de~Broglie scale. We then let the branching rate respond to the fluctuating product $\Phi_F\Phi_B$. In the reciprocal basis, the fields equal a smooth reference $R$ plus centered fluctuations $\psi_F,\psi_B$, defining the signed kernel $C_{\rm FB}(x,y)=\mathbb E_\omega[\psi_F(x)\psi_B(y)]$. On the anticorrelated branch, $\rho_{\rm BSM}(x)=-C_{\rm FB}(x,x)$ is the positive paired density. Stationary recovery requires its diagonal to match the Born profile, while off-diagonal decay defines the correlation range. The pair equation splits into collective and relative sectors: spectral cancellation selects the Born collective mode, while suppression of the leading density fluctuation selects the anticorrelated source channel. With relative diffusivity $D_{\rm eff}$ and positive relaxation rate $\mu_{\rm FB}$, correlations have screening length $\xi_{\rm FB}=\sqrt{D_{\rm eff}/\mu_{\rm FB}}$. Thus an extended Born density and a finite correlation range can coexist in one stochastic kernel, suggesting particle-like organization.

cond-mat.stat-mech↗

arXiv2025

A universal property of random trajectories in bounded domains

The celebrated invariance property states that particles entering a bounded domain, with isotropic and uniform incidence, spend on average $\langle \ell \rangle=4V/S$ length inside, no matter how they scatter. We show that this remarkable property is merely the infinite-length limit of an even broader law: for any curves randomly placed and oriented in space -- stochastic or deterministic, generated by ballistic or diffusive dynamics, with possible stopping or branching, in two or more dimensions -- $ \displaystyle \frac{1}{\langle \ell \rangle}= \frac{1}{\langle L\rangle}+ \frac{1}{\langle σ\rangle} $, with $\langle\ell\rangle$ its mean in-domain path, $\langle L\rangle$ its mean total length, and $\langleσ\rangle$ the mean chord of the domain, a known geometric quantity related to the volume-to-surface ratio. Derived solely from the kinematic formula of integral geometry, the result is independent of step-length statistics, memory, absorption, and branching, making it equally relevant to photons in turbid tissue, active bacteria in micro-channels, cosmic rays in molecular clouds, or neutron chains in nuclear reactors. Monte-Carlo simulations spanning straight needles, Y-shapes, and isotropic random walks in 2D and 3D confirm the universality and demonstrate how a local measurement of $\langle \ell \rangle$ yields $\langle L\rangle$ without ever tracking the full trajectory.

math-ph↗

arXiv2024

Limit theorems for the neutron transport equation

Over the last decade, ingenuous developments in Monte Carlo methods have enabled the unbiased estimation of adjoint-weighted reactor parameters expressed as bilinear forms, such as kinetics parameters and sensitivity coefficients. A prominent example is the Iterated Fission Probability method, which relies on the simulation of the fission chains descending from an ancestor neutron: the neutron population at an asymptotic fission generation yields an estimate of the importance function (and hence of the adjoint fundamental eigenmode) at the phase-space coordinates of the ancestor neutron. In this paper we first establish rigorous results concerning the moments of the asymptotic neutron population stemming from a single initial particle, with special focus on the average and the variance. Then, we propose a simple benchmark configuration where exact solutions are derived for these moments, which can be used for the verification of new functionalities of production Monte Carlo codes involving the Iterated Fission Probability method.

physics.comp-ph↗

arXiv2024

Rough neutron fields and nuclear reactor noise

Nuclear reactor cores achieve sustained fission chain reactions through the so-called 'critical state' -a subtle equilibrium between their material properties and their geometries. Observed at macroscopic scales during operations, the resulting stationary neutron field is tainted by a noise term, that hinders various fluctuations occurring at smaller scales. These fluctuations are either of a stochastic nature (whenever the core is operated at low power) or related to various perturbations and vibrations within the core, even operated in its power regime. For reasons that are only partially understood using linear noise theory, incidental events have been reported, characterized by an increase of the power noise. Such events of power noise growth, sometimes up to seemingly unbounded levels, have already led in the past to volontary scramming of reactors. In this paper, we will extend the findings of \cite{percolation_pre} (where a statistical field theory of critical processes was employed to model stochastic neutron noise) by incorporating the effects of power noise. We will show that the evolution of the neutron field in a reactor is intimately connected to the dynamic of surface growths given by the Kardar-Parisi-Zhang equation. Recent numerical results emerging from renormalization group approaches will be used to calculate a threshold in the amplitude of the reactor noise above which the core could enter a new criticality state, and to estimate the critical exponents characterizing this phase transition to rough neutron fields. The phenomenology of this roughening transition will be correlated and compared to data of misunderstood reactor noise levels and reactor instabilities, and will be shown to provide both qualitative and quantitative insights into this long-standing issue of reactor physics.

cond-mat.stat-mech↗

arXiv2023

Generational variance reduction in Monte Carlo criticality simulations as a way of mitigating unwanted correlations

Monte Carlo criticality simulations are widely used in nuclear safety demonstrations, as they offer an arbitrarily precise estimation of global and local tallies while making very few assumptions. However, since the inception of such numerical approaches, it is well known that bias might affect both the estimation of errors on these tallies and the tallies themselves. In particular, stochastic modeling approaches developed in the past decade have shed light on the prominent role played by spatial correlations through a phenomenon called neutron clustering. This effect is particularly of great significance when simulating loosely coupled systems (i.e., with a high dominance ratio). In order to tackle this problem, this paper proposes to recast the power iteration technique of Monte Carlo criticality codes into a variance reduction technique called Adaptative Multilevel Splitting. The central idea is that iterating over neutron generations can be seen as pushing a sub-population of neutrons towards a generational detector (instead of a spatial detector as variance reduction techniques usually do). While both approaches allow for neutron population control, the former blindly removes or splits neutrons. In contrast, the latter optimizes spatial, generational, and spectral attributes of neutrons when they are removed or split through an adjoint flux estimation, hence tempering both generational and spatial correlations. This is illustrated in the present article with a simple case of a bare slab reactor in the one speed theory on which the Adaptive Multilevel Splitting was applied and compared to variations of the Monte Carlo power iteration method used in neutron transport. Besides looking at the resulting efficiency of the methods, this work also aims at highlighting the main mechanisms of the Adaptive Multilevel Splitting in criticality calculations.

cond-mat.stat-mech↗

arXiv2022

Percolation properties of the neutron population in nuclear reactors

Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems however require to define intermediate quantities (e.g. the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined to the analysis of the resulting field equation involving a fractional Laplacian will show that the critical diffusion equation cannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical super-diffusion equation. The analysis of this equation will reveal that non-negligible departure from mean field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.

cond-mat.stat-mech↗

arXiv2021

Improvement of Geant4 Neutron-HP package: from methodology to evaluated nuclear data library

An accurate description of interactions between thermal neutrons (below 4 eV) and materials is key to simulate the transport of neutrons in a wide range of applications such as criticality-safety, reactor physics, compact accelerator-driven neutron sources, radiological shielding or nuclear instrumentation, just to name a few. While the Monte Carlo transport code Geant4 was initially developed to simulate particle physics experiments, %-with a large emphasis given on modeled cross-sections for all known particles at all conceivable energies-, its use has spread to neutronics applications, requiring evaluated cross-sections for neutrons and gammas between $0$ and $20$ MeV (the so-called neutron High Precision -HP- package), as well as a proper offline or on-the-flight treatment of these cross-sections. In this paper we will point out limitations affecting Geant4 (version 10.07.p01) thermal neutron treatment and associated nuclear data libraries, by using comparisons with the reference Monte Carlo neutron transport code \tripoli, version 11, and we will present the results of various modifications of the Geant4 neutron-HP package, required to overcome these limitations. Also, in order to broaden the support of nuclear data libraries compatible with Geant4, a nuclear processing tool has been developed and validated allowing the use of the code together with ENDF-BVIII.0 and JEFF-3.3 libraries for example. These changes should be taken into account in an upcoming Geant4 release.

physics.comp-ph↗

arXiv2020

Patchy nuclear chain reactions

Stochastic fluctuations of the neutron population within a nuclear reactor are typically prevented by operating the core at a sufficient power, since a deterministic behavior of the neutron population is required by automatic safety systems to detect unwanted power excursions. Recent works however pointed out that, under specific circumstances, non-Poissonian patterns could affect neutron spatial distributions. This motivated an international program to experimentally detect and characterize such fluctuations and correlations, which took place in 2017 at the Rensselaer Polytechnic Institute Reactor Critical Facility. The main findings of this program will indeed unveil patchiness in snapshots of neutron spatial distributions -- obtained with a dedicated numerical twin of the reactor -- that support this first experimental characterization of the 'neutron clustering' phenomenon, while a stochastic model based on reaction-diffusion processes and branching random walks will reveal the key role played by the reactor intrinsic sources in understanding neutron spatial correlations.

physics.ins-det↗

arXiv2017

Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in $d$-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning and extended by Brantley: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

cond-mat.stat-mech↗

arXiv2017

Monte Carlo particle transport in random media: the effects of mixing statistics

Particle transport in random media obeying a given mixing statistics is key in several applications in nuclear reactor physics and more generally in diffusion phenomena emerging in optics and life sciences. Exact solutions for the ensemble-averaged physical observables are hardly available, and several approximate models have been thus developed, providing a compromise between the accurate treatment of the disorder-induced spatial correlations and the computational time. In order to validate these models, it is mandatory to resort to reference solutions in benchmark configurations, typically obtained by explicitly generating by Monte Carlo methods several realizations of random media, simulating particle transport in each realization, and finally taking the ensemble averages for the quantities of interest. In this context, intense research efforts have been devoted to Poisson (Markov) mixing statistics, where benchmark solutions have been derived for transport in one-dimensional geometries. In a recent work, we have generalized these solutions to two and three-dimensional configurations, and shown how dimension affects the simulation results. In this paper we will examine the impact of mixing statistics: to this aim, we will compare the reflection and transmission probabilities, as well as the particle flux, for three-dimensional random media obtained by resorting to Poisson, Voronoi and Box stochastic tessellations. For each tessellation, we will furthermore discuss the effects of varying the fragmentation of the stochastic geometry, the material compositions, and the cross sections of the transported particles.

cond-mat.stat-mech↗

arXiv2016

Finite-size effects and percolation properties of Poisson geometries

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of $d$-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case $d=3$. We first analyse the behaviour of the key features of these stochastic geometries as a function of the dimension $d$ and the linear size $L$ of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two `labels' with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster and the average cluster size.

cond-mat.stat-mech↗

arXiv2015

Neutron fluctuations: the importance of being delayed

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.

cond-mat.stat-mech↗

arXiv2015

The critical catastrophe revisited

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.

cond-mat.stat-mech↗

arXiv2014

Clustering of branching Brownian motions in confined geometries

We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behaviour can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.

cond-mat.stat-mech↗

arXiv2013

Spatial extent of an outbreak in animal epidemics

Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are important: then, it is commonly assumed that the susceptible-infected-recovered (SIR) mechanism can be described by a stochastic birth-death process of Galton-Watson type. The displacements of the infected individuals can be modelled by resorting to Brownian motion, which is applicable when long-range movements and complex network interactions can be safely neglected, as in case of animal epidemics. In this context, the spatial extent of an epidemic can be assessed by computing the convex hull enclosing the infected individuals at a given time. We derive the exact evolution equations for the mean perimeter and the mean area of the convex hull, and compare them with Monte Carlo simulations.

q-bio.PE↗

arXiv2012

Properties of branching exponential flights in bounded domains

Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the properties of trajectories starting on the boundary and those starting inside the domain. Within this context, we show that the total length travelled by the walker and the number of performed collisions in bounded volumes can be assessed by resorting to the Feynman-Kac formalism. Other physical observables related to the branching trajectories, such as the survival and escape probability, are derived as well.

cond-mat.stat-mech↗

arXiv2012

Branching exponential flights: travelled lengths and collision statistics

The evolution of several physical and biological systems, ranging from neutron transport in multiplying media to epidemics or population dynamics, can be described in terms of branching exponential flights, a stochastic process which couples a Galton-Watson birth-death mechanism with random spatial displacements. Within this context, one is often called to assess the length $\ell_V$ that the process travels in a given region $V$ of the phase space, or the number of visits $n_V$ to this same region. In this paper, we address this issue by resorting to the Feynman-Kac formalism, which allows characterizing the full distribution of $\ell_V$ and $n_V$ and in particular deriving explicit moment formulas. Some other significant physical observables associated to $\ell_V $ and $n_V$, such as the survival probability, are discussed as well, and results are illustrated by revisiting the classical example of the rod model in nuclear reactor physics.

cond-mat.stat-mech↗