Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2FCZ______%3A_____%2F23%3AN0000030" target="_blank" >RIV/CZ______:_____/23:N0000030 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.014140" target="_blank" >https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.014140</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevE.107.014140" target="_blank" >10.1103/PhysRevE.107.014140</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees

Popis výsledku v původním jazyce

The "Brownian bees" model describes an ensemble of N = const independent branching Brownian particles. The conservation of N is provided by a modified branching process. When a particle branches into two particles, the particle which is farthest from the origin is eliminated simultaneously. The spatial density of the particles is governed by the solution of a free boundary problem for a reaction-diffusion equation in the limit of N >> 1. At long times, the particle density approaches a spherically symmetric steady-state solution with a compact support of radius (l(0)) over bar. However, at finite N, the radius of this support, L, fluctuates. The variance of these fluctuations appears to exhibit a logarithmic anomaly [Siboni et al., Phys. Rev. E 104, 054131 (2021)]. It is proportional to N-1 lnN at N -> infinity. We investigate here the tails of the probability density function (PDF), P(L), of the swarm radius, when the absolute value of the radius fluctuation Delta L = L - (l(0)) over bar is sufficiently larger than the typical fluctuations' scale determined by the variance. For negative deviations the PDF can be obtained in the framework of the optimal fluctuation method. This part of the PDF displays the scaling behavior ln P proportional to -N Lambda L-2 ln(-1)(Lambda L-2), demonstrating a logarithmic anomaly at small negative Delta L. For the opposite sign of the fluctuation, Delta L > 0, the PDF can be obtained with an approximation of a single particle, running away. We find that ln P proportional to -N-1/2 Delta L. We consider in this paper only the case when vertical bar Delta L vertical bar is much less than the typical radius of the swarm at N >> 1.

Název v anglickém jazyce

Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees

Popis výsledku anglicky

The "Brownian bees" model describes an ensemble of N = const independent branching Brownian particles. The conservation of N is provided by a modified branching process. When a particle branches into two particles, the particle which is farthest from the origin is eliminated simultaneously. The spatial density of the particles is governed by the solution of a free boundary problem for a reaction-diffusion equation in the limit of N >> 1. At long times, the particle density approaches a spherically symmetric steady-state solution with a compact support of radius (l(0)) over bar. However, at finite N, the radius of this support, L, fluctuates. The variance of these fluctuations appears to exhibit a logarithmic anomaly [Siboni et al., Phys. Rev. E 104, 054131 (2021)]. It is proportional to N-1 lnN at N -> infinity. We investigate here the tails of the probability density function (PDF), P(L), of the swarm radius, when the absolute value of the radius fluctuation Delta L = L - (l(0)) over bar is sufficiently larger than the typical fluctuations' scale determined by the variance. For negative deviations the PDF can be obtained in the framework of the optimal fluctuation method. This part of the PDF displays the scaling behavior ln P proportional to -N Lambda L-2 ln(-1)(Lambda L-2), demonstrating a logarithmic anomaly at small negative Delta L. For the opposite sign of the fluctuation, Delta L > 0, the PDF can be obtained with an approximation of a single particle, running away. We find that ln P proportional to -N-1/2 Delta L. We consider in this paper only the case when vertical bar Delta L vertical bar is much less than the typical radius of the swarm at N >> 1.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10305 - Fluids and plasma physics (including surface physics)

Projekt

<a href="/cs/project/EF15_003%2F0000449" target="_blank" >EF15_003/0000449: High Field Initiative (Výzkum velmi intenzivních polí)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physical Review E

ISSN

2470-0045

e-ISSN

2470-0053

Svazek periodika

107

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

14140 (1-15)

Kód UT WoS článku

000926765800005

EID výsledku v databázi Scopus

2-s2.0-85147448531