From noise on the sites to noise on the links: discretizing the conserved Kardar-Parisi-Zhang equation in real space
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929225159671808 |
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| author | Cavagna, Andrea Cristín, Javier Giardina, Irene Veca, Mario |
| author_facet | Cavagna, Andrea Cristín, Javier Giardina, Irene Veca, Mario |
| contents | Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work, we present a novel method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents $α$, $β$, and $z$ in $d=1$ and in $d=2$. To illustrate the potentiality of the method, we further consider the cKPZ equation on different kinds of non-standard lattices and on the random Euclidean graph. This is the first numerical study of conserved field dynamics on an irregular topology, paving the way to a broad spectrum of possible applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13065 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From noise on the sites to noise on the links: discretizing the conserved Kardar-Parisi-Zhang equation in real space Cavagna, Andrea Cristín, Javier Giardina, Irene Veca, Mario Statistical Mechanics Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work, we present a novel method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents $α$, $β$, and $z$ in $d=1$ and in $d=2$. To illustrate the potentiality of the method, we further consider the cKPZ equation on different kinds of non-standard lattices and on the random Euclidean graph. This is the first numerical study of conserved field dynamics on an irregular topology, paving the way to a broad spectrum of possible applications. |
| title | From noise on the sites to noise on the links: discretizing the conserved Kardar-Parisi-Zhang equation in real space |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2312.13065 |