High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems
Abstract The classical problem of determining the density and capacity of arrays of potential sources is studied. This corresponds to a wide variety of physical problems such as electrostatic capacitance, stress in elastostatics and the evaporation of fluid droplets. An asymptotic solution is derive...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-02-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-54377-2 |
| _version_ | 1797274936079810560 |
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| author | Alexander W. Wray Madeleine R. Moore |
| author_facet | Alexander W. Wray Madeleine R. Moore |
| author_sort | Alexander W. Wray |
| collection | DOAJ |
| description | Abstract The classical problem of determining the density and capacity of arrays of potential sources is studied. This corresponds to a wide variety of physical problems such as electrostatic capacitance, stress in elastostatics and the evaporation of fluid droplets. An asymptotic solution is derived that is shown to give excellent accuracy for arbitrary arrays of sources with non-circular footprints, including polygonal footprints. The solution is extensively validated against both experimental and numerical results. We illustrate the power of the solution by showcasing a variety of newly accessible classical problems that may be solved in a rapid, accurate manner. |
| first_indexed | 2024-03-07T15:06:14Z |
| format | Article |
| id | doaj.art-7aea9d3e6ef54bd3bb271c0055fb9473 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-07T15:06:14Z |
| publishDate | 2024-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-7aea9d3e6ef54bd3bb271c0055fb94732024-03-05T18:54:29ZengNature PortfolioScientific Reports2045-23222024-02-0114111110.1038/s41598-024-54377-2High-order asymptotic methods provide accurate, analytic solutions to intractable potential problemsAlexander W. Wray0Madeleine R. Moore1Department of Mathematics and Statistics, University of StrathclydeDepartment of Mathematics, School of Natural Sciences, University of HullAbstract The classical problem of determining the density and capacity of arrays of potential sources is studied. This corresponds to a wide variety of physical problems such as electrostatic capacitance, stress in elastostatics and the evaporation of fluid droplets. An asymptotic solution is derived that is shown to give excellent accuracy for arbitrary arrays of sources with non-circular footprints, including polygonal footprints. The solution is extensively validated against both experimental and numerical results. We illustrate the power of the solution by showcasing a variety of newly accessible classical problems that may be solved in a rapid, accurate manner.https://doi.org/10.1038/s41598-024-54377-2Potential problemsAsymptotic methodsElectrostaticsEvaporation |
| spellingShingle | Alexander W. Wray Madeleine R. Moore High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems Scientific Reports Potential problems Asymptotic methods Electrostatics Evaporation |
| title | High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems |
| title_full | High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems |
| title_fullStr | High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems |
| title_full_unstemmed | High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems |
| title_short | High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems |
| title_sort | high order asymptotic methods provide accurate analytic solutions to intractable potential problems |
| topic | Potential problems Asymptotic methods Electrostatics Evaporation |
| url | https://doi.org/10.1038/s41598-024-54377-2 |
| work_keys_str_mv | AT alexanderwwray highorderasymptoticmethodsprovideaccurateanalyticsolutionstointractablepotentialproblems AT madeleinermoore highorderasymptoticmethodsprovideaccurateanalyticsolutionstointractablepotentialproblems |