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Last-passage Monte Carlo Algorithm for Charge Density on a Conducting Spherical Surface

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Abstract

For solving some elliptic boundary value problems, Monte Carlo diffusion algorithms are often the most efficient ones. Among them, last-passage algorithms are good for obtaining charge density at a specific point on a conducting surface. In our previous research, we developed the last-passage Monte Carlo algorithm for charge density on a flat conducting surface. In the research, we used the Laplace Green’s function only on a flat surface. In this paper, we further develop the last-passage algorithm on a spherical surface. We demonstrate the last-passage algorithm by obtaining charge density on a sphere held at unit potential. In addition, using the last-passage algorithm we compute the mutual capacitance and charge distribution of two conducting spheres. We compare them with the analytic results of J. Lekner to find an excellent agreement.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant (No. 2017R1E1A1A03070543) funded by the Korea government (Ministry of Science and Information & Communication Technology (ICT)). In addition, this work was supported by the GIST Research Institute (GRI) grant funded by GIST in 2021.

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Authors and Affiliations

  1. Division of Liberal Arts and Sciences, Gwangju Institute of Science and Technology (GIST), Gwangju, South Korea

    Chi-Ok Hwang

  2. Department of Physics and Photon Science, Gwangju Institute of Science and Technology (GIST), Gwangju, South Korea

    Unjong Yu

  3. Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea

    Young-Min Lee

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  1. Unjong Yu
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  2. Young-Min Lee
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  3. Chi-Ok Hwang
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Correspondence to Chi-Ok Hwang.

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Yu, U., Lee, YM. & Hwang, CO. Last-passage Monte Carlo Algorithm for Charge Density on a Conducting Spherical Surface. J Sci Comput 88, 82 (2021). https://doi.org/10.1007/s10915-021-01594-w

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  • DOI: https://doi.org/10.1007/s10915-021-01594-w

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