Derivation of a macroscopic model for Brownian hard needles
We study the role of anisotropic steric interactions in a system of hard Brownian needles in two dimensions. Despite having no volume, non-overlapping needles exclude a volume in configuration space that influences the macroscopic evolution of the system. Starting from the stochastic particle system...
| Автори: | , , |
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| Формат: | Journal article |
| Мова: | English |
| Опубліковано: |
Royal Society
2023
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| _version_ | 1826310782016552960 |
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| author | Bruna, M Chapman, SJ Schmidtchen, M |
| author_facet | Bruna, M Chapman, SJ Schmidtchen, M |
| author_sort | Bruna, M |
| collection | OXFORD |
| description | We study the role of anisotropic steric interactions in a system of hard Brownian needles in two dimensions. Despite having no volume, non-overlapping needles exclude a volume in configuration space that influences the macroscopic evolution of the system. Starting from the stochastic particle system, we use the method of matched asymptotic expansions and conformal mapping to systematically derive a nonlinear non-local partial differential equation for the evolution of the population density in position and orientation. We consider the regime of high rotational diffusion, resulting in an equation for the spatial density that allows us to compare the effective excluded volume of a hard-needle system with that of a hard-sphere system. We further consider spatially homogeneous solutions and find an isotropic to nematic transition as density increases, consistent with Onsager’s theory. |
| first_indexed | 2024-03-07T07:57:02Z |
| format | Journal article |
| id | oxford-uuid:20f1ae07-d85a-4751-a304-91c652a9d374 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:57:02Z |
| publishDate | 2023 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:20f1ae07-d85a-4751-a304-91c652a9d3742023-09-05T15:39:18ZDerivation of a macroscopic model for Brownian hard needlesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:20f1ae07-d85a-4751-a304-91c652a9d374EnglishSymplectic ElementsRoyal Society2023Bruna, MChapman, SJSchmidtchen, MWe study the role of anisotropic steric interactions in a system of hard Brownian needles in two dimensions. Despite having no volume, non-overlapping needles exclude a volume in configuration space that influences the macroscopic evolution of the system. Starting from the stochastic particle system, we use the method of matched asymptotic expansions and conformal mapping to systematically derive a nonlinear non-local partial differential equation for the evolution of the population density in position and orientation. We consider the regime of high rotational diffusion, resulting in an equation for the spatial density that allows us to compare the effective excluded volume of a hard-needle system with that of a hard-sphere system. We further consider spatially homogeneous solutions and find an isotropic to nematic transition as density increases, consistent with Onsager’s theory. |
| spellingShingle | Bruna, M Chapman, SJ Schmidtchen, M Derivation of a macroscopic model for Brownian hard needles |
| title | Derivation of a macroscopic model for Brownian hard needles |
| title_full | Derivation of a macroscopic model for Brownian hard needles |
| title_fullStr | Derivation of a macroscopic model for Brownian hard needles |
| title_full_unstemmed | Derivation of a macroscopic model for Brownian hard needles |
| title_short | Derivation of a macroscopic model for Brownian hard needles |
| title_sort | derivation of a macroscopic model for brownian hard needles |
| work_keys_str_mv | AT brunam derivationofamacroscopicmodelforbrownianhardneedles AT chapmansj derivationofamacroscopicmodelforbrownianhardneedles AT schmidtchenm derivationofamacroscopicmodelforbrownianhardneedles |