Renormalization group theory of molecular dynamics
Abstract Large scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have...
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Nature Portfolio
2021
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oai:doaj.org-article:228dc87c377048f1b279e160fb55189d2021-12-02T13:18:01ZRenormalization group theory of molecular dynamics10.1038/s41598-021-85286-32045-2322https://doaj.org/article/228dc87c377048f1b279e160fb55189d2021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-85286-3https://doaj.org/toc/2045-2322Abstract Large scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 .Daiji IchishimaYuya MatsumuraNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021) |
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Medicine R Science Q |
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Medicine R Science Q Daiji Ichishima Yuya Matsumura Renormalization group theory of molecular dynamics |
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Abstract Large scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 . |
| format |
article |
| author |
Daiji Ichishima Yuya Matsumura |
| author_facet |
Daiji Ichishima Yuya Matsumura |
| author_sort |
Daiji Ichishima |
| title |
Renormalization group theory of molecular dynamics |
| title_short |
Renormalization group theory of molecular dynamics |
| title_full |
Renormalization group theory of molecular dynamics |
| title_fullStr |
Renormalization group theory of molecular dynamics |
| title_full_unstemmed |
Renormalization group theory of molecular dynamics |
| title_sort |
renormalization group theory of molecular dynamics |
| publisher |
Nature Portfolio |
| publishDate |
2021 |
| url |
https://doaj.org/article/228dc87c377048f1b279e160fb55189d |
| work_keys_str_mv |
AT daijiichishima renormalizationgrouptheoryofmoleculardynamics AT yuyamatsumura renormalizationgrouptheoryofmoleculardynamics |
| _version_ |
1718393320461303808 |