IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v506y2018icp75-87.html
   My bibliography  Save this article

On the Prony series representation of stretched exponential relaxation

Author

Listed:
  • Mauro, John C.
  • Mauro, Yihong Z.

Abstract

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its “fat tail” at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

Suggested Citation

  • Mauro, John C. & Mauro, Yihong Z., 2018. "On the Prony series representation of stretched exponential relaxation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 75-87.
  • Handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:75-87
    DOI: 10.1016/j.physa.2018.04.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118304795
    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/j.physa.2018.04.047?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. Mauro, John C. & Smedskjaer, Morten M., 2012. "Minimalist landscape model of glass relaxation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3446-3459.
    2. Alvarez-Martinez, R. & Martinez-Mekler, G. & Cocho, G., 2011. "Order–disorder transition in conflicting dynamics leading to rank–frequency generalized beta distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 120-130.
    3. Mauro, John C. & Smedskjaer, Morten M., 2012. "Unified physics of stretched exponential relaxation and Weibull fracture statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6121-6127.
    4. Naumis, G.G. & Phillips, J.C., 2012. "Diffusion of knowledge and globalization in the web of twentieth century science," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3995-4003.
    Full references (including those not matched with items on IDEAS)

    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. Sarabia, José María & Prieto, Faustino & Trueba, Carmen & Jordá, Vanesa, 2013. "About the modified Gaussian family of income distributions with applications to individual incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1398-1408.
    2. Alvarez-Martínez, R. & Cocho, G. & Rodríguez, R.F. & Martínez-Mekler, G., 2014. "Birth and death master equation for the evolution of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 198-208.
    3. Phillips, J.C., 2015. "Similarity is not enough: Tipping points of Ebola Zaire mortalities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 277-281.
    4. Lyu, Haihua & Bu, Yi & Zhao, Zhenyue & Zhang, Jiarong & Li, Jiang, 2022. "Citation bias in measuring knowledge flow: Evidence from the web of science at the discipline level," Journal of Informetrics, Elsevier, vol. 16(4).
    5. Phillips, J.C., 2014. "Fractals and self-organized criticality in proteins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 440-448.
    6. Phillips, J.C., 2015. "Phase transitions in the web of science," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 173-177.

    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:506:y:2018:i:c:p:75-87. 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.