IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v111y1982i1p139-160.html
   My bibliography  Save this article

On the stochastic theory of polymerization reactions

Author

Listed:
  • Moreau, M.
  • Vicente, L.

Abstract

We present a stochastic study of a polymerization reaction model. Using the WKB approximation and the method of factorial cumulants it is shown that the relaxation time of the second factorial cumulant is half the macroscopic relaxation time. Furthermore the system exhibits a globally non-Poissonian and locally Poissonian behavior in agreement with other results. The application of the model is illustrated for the particular case of dimer and trimer formation.

Suggested Citation

  • Moreau, M. & Vicente, L., 1982. "On the stochastic theory of polymerization reactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 111(1), pages 139-160.
  • Handle: RePEc:eee:phsmap:v:111:y:1982:i:1:p:139-160
    DOI: 10.1016/0378-4371(82)90086-3
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437182900863
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/0378-4371(82)90086-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rodríguez, R.F. & Van Kampen, N.G., 1976. "Systematic treatment of fluctuations in a nonlinear oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 347-362.
    2. Van den Broeck, C. & Houard, J. & Malek Mansour, M., 1980. "Chapman-Enskog development of the multivariate master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 101(1), pages 167-184.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Moreau, M. & Vicente, L., 1982. "Influence of an external field on the stochastic theory of polymerization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(3), pages 543-559.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohanty, U. & Shuler, K.E. & Oppenheim, I., 1982. "On the exact and phenomenological Langevin equations for a harmonic oscillator in a fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(1), pages 1-20.
    2. Frankowicz, M. & Gudowska-Nowak, E., 1982. "Stochastic simulation of a bistable chemical system: The two-box model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 331-344.
    3. Chvosta, Petr, 1991. "Exact solution of a stochastic dimer problem with single-site energy modulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 168-194.
    4. Kondepudi, D.K. & Nelson, G.W., 1984. "Chiral-symmetry-breaking states and their sensitivity in nonequilibrium chemical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 465-496.
    5. Garcia, Alejandro L. & van den Broeck, Christian & Aertsens, Marc & Serneels, Roger, 1987. "A Monte Carlo simulation of coagulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 143(3), pages 535-546.
    6. Chechetkin, V.R. & Lutovinov, V.S. & Samokhin, A.A., 1991. "On the diffusion of passive impurities in random flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 87-113.
    7. West, B.J. & Bulsara, A.R. & Lindenberg, K. & Seshadri, V. & Shuler, K.E., 1979. "Stochastic processes with non-additive fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 97(2), pages 211-233.
    8. Belyi, V.V. & Klimontovich, Yu.L., 1979. "On the kinetic theory of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 97(3), pages 577-588.
    9. Stewart, Glen R., 1982. "Long-time behavior of a non-Markovian Brownian oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 519-530.
    10. Papież, Lech, 1983. "The limit diffusion mechanism of relaxation for spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 413-430.
    11. Williams, M.M.R., 1984. "The influence of random fluctuations on the behaviour of an aerosol," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(1), pages 105-123.
    12. Gang, Hu, 1985. "Master equation without strict detailed balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 586-592.
    13. Henery, R.J., 1982. "The short-time evolution of a non-linear oscillator driven by white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 321-330.
    14. Gorini, Vittorio & Verri, Maurizio & Frigerio, Alberto, 1989. "Non-markovian behavior in low-temperature damping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 161(2), pages 357-384.
    15. Garrido, L. & Sancho, J.M., 1982. "Ordered cumulant technique and differential equations for probability density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 479-489.
    16. Dekker, H., 1980. "On the path integral for diffusion in curved spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(3), pages 586-596.
    17. Shapiro, V.E. & Loginov, V.M., 1978. "“Formulae of differentiation” and their use for solving stochastic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 563-574.
    18. Borgis, D. & Moreau, M., 1984. "On the stochastic theory of a bistable chemical reaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(1), pages 109-130.
    19. Boissonade, J., 1982. "Molecular dynamics studies of metastability and nucleation in a non-equilibrium chemical system with multiple steady states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(3), pages 607-618.
    20. Lindenberg, Katja & West, Bruce J., 1984. "Finite correlation time effects in nonequilibrium phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 25-47.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:111:y:1982:i:1:p:139-160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.