The stochastic porous medium equation in one dimension
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914366560927744 |
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| author | Bernard, Maximilien Fedorenko, Andrei A. Doussal, Pierre Le Rosso, Alberto |
| author_facet | Bernard, Maximilien Fedorenko, Andrei A. Doussal, Pierre Le Rosso, Alberto |
| contents | We study the porous medium equation (PME) in one space dimension in presence of additive non-conservative white noise, and interpreted as a stochastic growth equation for the height field of an interface. We predict the values of the two growth exponents $α$ and $β$ using the functional RG. Extensive numerical simulations show agreement with the predicted values for these exponents, however they also show anomalous scaling with an additional "local" exponent $α_{\rm loc}$, as well as multiscaling originating from broad distributions of local height differences. The stationary measure of the stochastic PME is found to be well described by a random walk model, related to a Bessel process. This model allows for several predictions about the multiscaling properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stochastic porous medium equation in one dimension Bernard, Maximilien Fedorenko, Andrei A. Doussal, Pierre Le Rosso, Alberto Statistical Mechanics Disordered Systems and Neural Networks Mathematical Physics Probability We study the porous medium equation (PME) in one space dimension in presence of additive non-conservative white noise, and interpreted as a stochastic growth equation for the height field of an interface. We predict the values of the two growth exponents $α$ and $β$ using the functional RG. Extensive numerical simulations show agreement with the predicted values for these exponents, however they also show anomalous scaling with an additional "local" exponent $α_{\rm loc}$, as well as multiscaling originating from broad distributions of local height differences. The stationary measure of the stochastic PME is found to be well described by a random walk model, related to a Bessel process. This model allows for several predictions about the multiscaling properties. |
| title | The stochastic porous medium equation in one dimension |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Mathematical Physics Probability |
| url | https://arxiv.org/abs/2501.10975 |