IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v661y2025ics0378437125000287.html
   My bibliography  Save this article

Moving boundary truncated grid method: Application to activated barrier crossing with the Klein–Kramers and Boltzmann–BGK models

Author

Listed:
  • Li, Ming-Yu
  • Lu, Chun-Yaung
  • Chou, Chia-Chun

Abstract

We exploit the moving boundary truncated grid method for the Klein–Kramers and Boltzmann–BGK kinetic equations to approach the problem of thermally activated barrier crossing across non-parabolic barriers with reduced computational effort. The grid truncation algorithm dynamically deactivates the insignificant grid points while the boundary extrapolation procedure explores potentially important portions of phase space. An economized Eulerian framework is established to integrate the kinetic equations in the tailored phase space efficiently. The effects of coupling strength, kinetic model, and potential shape on the escape rate are assessed through direct numerical simulations. Besides, we adapt the Padé approximant approach for non-parabolic barriers by introducing a correction factor into the spatial diffusion asymptote to account for the anharmonicity. The modified Padé approximants are remarkably consistent with the numerical results obtained from the conventional full grid method in underdamped and overdamped regimes, whereas overestimating the rates in the turnover region, even exceeding the upper bound given by the transition-state theory. By contrast, the truncated grid method provides accurate rate estimates in excellent agreement with the full grid benchmarks globally, with negligible relative errors lower than 1.02% for the BGK model and below 0.56% for the Kramers model, while substantially reducing the computational cost. Overall, the truncated grid method has shown great promise as a high-performance scheme for the escape problem.

Suggested Citation

  • Li, Ming-Yu & Lu, Chun-Yaung & Chou, Chia-Chun, 2025. "Moving boundary truncated grid method: Application to activated barrier crossing with the Klein–Kramers and Boltzmann–BGK models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 661(C).
  • Handle: RePEc:eee:phsmap:v:661:y:2025:i:c:s0378437125000287
    DOI: 10.1016/j.physa.2025.130376
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437125000287
    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.2025.130376?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.

    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:661:y:2025:i:c:s0378437125000287. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.