First passage times in homogeneous nucleation: Dependence on the total number of particles

Yvinec, Romain; Bernard, Samuel; Pujo-Menjouet, Laurent; Hingant, Erwan

doi:10.1063/1.4940033

Title: First passage times in homogeneous nucleation: Dependence on the total number of particles

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Abstract

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.

Authors:

Yvinec, Romain ^[1]; Bernard, Samuel; Pujo-Menjouet, Laurent ^[2]; Hingant, Erwan ^[3]

PRC INRA UMR85, CNRS UMR7247, Université François Rabelais de Tours, IFCE, F-37380 Nouzilly (France)
Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan UMR5208, 69622 Villeurbanne (France)
Departamento de Matemática, Universidad Federal de Campina Grande, Campina Grande, PB (Brazil)

Publication Date:: Thu Jan 21 00:00:00 EST 2016

OSTI Identifier:: 22493657

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 144; Journal Issue: 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AGGLOMERATION; CONFIGURATION; FRAGMENTATION; FUNCTIONS; MEAN-FIELD THEORY; NUCLEATION; PARTICLES; PHASE TRANSFORMATIONS; STATISTICS; STOCHASTIC PROCESSES

Citation Formats


                    Yvinec, Romain, Bernard, Samuel, Pujo-Menjouet, Laurent, INRIA Team Dracula, Inria Center Grenoble Rhône-Alpes, Grenoble, and Hingant, Erwan. First passage times in homogeneous nucleation: Dependence on the total number of particles.  United States: N. p., 2016. 
        Web.  doi:10.1063/1.4940033.

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                    Yvinec, Romain, Bernard, Samuel, Pujo-Menjouet, Laurent, INRIA Team Dracula, Inria Center Grenoble Rhône-Alpes, Grenoble, & Hingant, Erwan. First passage times in homogeneous nucleation: Dependence on the total number of particles.  United States.  https://doi.org/10.1063/1.4940033

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                    Yvinec, Romain, Bernard, Samuel, Pujo-Menjouet, Laurent, INRIA Team Dracula, Inria Center Grenoble Rhône-Alpes, Grenoble, and Hingant, Erwan. 2016.  
        "First passage times in homogeneous nucleation: Dependence on the total number of particles".  United States.  https://doi.org/10.1063/1.4940033.

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@article{osti_22493657,

  title        = {First passage times in homogeneous nucleation: Dependence on the total number of particles},

  author       = {Yvinec, Romain and Bernard, Samuel and Pujo-Menjouet, Laurent and INRIA Team Dracula, Inria Center Grenoble Rhône-Alpes, Grenoble and Hingant, Erwan},

  abstractNote = {Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.},

  doi          = {10.1063/1.4940033},

  url          = {https://www.osti.gov/biblio/22493657},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 3,

  volume       = 144,

  place        = {United States},

  year         = {Thu Jan 21 00:00:00 EST 2016},

  month        = {Thu Jan 21 00:00:00 EST 2016}

}

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