Variational formulation of active nematic fluids: theory and simulation
The structure and dynamics of important biological quasi-two-dimensional systems, ranging from cytoskeletal gels to tissues, are controlled by nematic order, flow, defects and activity. Continuum hydrodynamic descriptions combined with numerical simulations have been used to understand such complex...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2025-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/adcd93 |
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| author | W Mirza A Torres-Sánchez G Vilanova Marino Arroyo |
| author_facet | W Mirza A Torres-Sánchez G Vilanova Marino Arroyo |
| author_sort | W Mirza |
| collection | DOAJ |
| description | The structure and dynamics of important biological quasi-two-dimensional systems, ranging from cytoskeletal gels to tissues, are controlled by nematic order, flow, defects and activity. Continuum hydrodynamic descriptions combined with numerical simulations have been used to understand such complex systems. The development of thermodynamically consistent theories and numerical methods to model active nemato-hydrodynamics is eased by mathematical formalisms enabling systematic derivations and structured-preserving algorithms. Alternative to classical nonequilibrium thermodynamics and bracket formalisms, here we develop a theoretical and computational framework for active nematics based on Onsager’s variational formalism to irreversible thermodynamics, according to which the dynamics result from the minimization of a Rayleighian functional capturing the competition between free-energy release, dissipation and activity. We show that two standard incompressible models of active nemato-hydrodynamics can be framed in the variational formalism, and develop a new compressible model for density-dependent active nemato-hydrodynamics relevant to model actomyosin gels. We show that the variational principle enables a direct and transparent derivation not only of the governing equations, but also of the finite element numerical scheme. We exercise this model in two representative examples of active nemato-hydrodynamics relevant to the actin cytoskeleton during wound healing and to the dynamics of confined colonies of elongated cells. |
| format | Article |
| id | doaj-art-92123769de5c468d9944ef78dea8d78b |
| institution | OA Journals |
| issn | 1367-2630 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
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| series | New Journal of Physics |
| spelling | doaj-art-92123769de5c468d9944ef78dea8d78b2025-08-20T02:30:06ZengIOP PublishingNew Journal of Physics1367-26302025-01-0127404302510.1088/1367-2630/adcd93Variational formulation of active nematic fluids: theory and simulationW Mirza0https://orcid.org/0000-0002-5197-1371A Torres-Sánchez1https://orcid.org/0000-0002-4275-173XG Vilanova2https://orcid.org/0000-0002-9650-0602Marino Arroyo3LaCàN, Universitat Politècnica de Catalunya BarcelonaTech , Jordi Girona 1-3, 08034 Barcelona, Spain; Barcelona Graduate School of Mathematics (BGSMath), Campus de Bellaterra , Edifici C, 08193 Bellaterra Barcelona, SpainLaCàN, Universitat Politècnica de Catalunya BarcelonaTech , Jordi Girona 1-3, 08034 Barcelona, Spain; Institute for Bioengineering of Catalonia (IBEC) , The Barcelona Institute of Science and Technology (BIST), Baldiri Reixac 10-12, 08028 Barcelona, SpainLaCàN, Universitat Politècnica de Catalunya BarcelonaTech , Jordi Girona 1-3, 08034 Barcelona, SpainLaCàN, Universitat Politècnica de Catalunya BarcelonaTech , Jordi Girona 1-3, 08034 Barcelona, Spain; Institute for Bioengineering of Catalonia (IBEC) , The Barcelona Institute of Science and Technology (BIST), Baldiri Reixac 10-12, 08028 Barcelona, Spain; Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE) , 08034 Barcelona, SpainThe structure and dynamics of important biological quasi-two-dimensional systems, ranging from cytoskeletal gels to tissues, are controlled by nematic order, flow, defects and activity. Continuum hydrodynamic descriptions combined with numerical simulations have been used to understand such complex systems. The development of thermodynamically consistent theories and numerical methods to model active nemato-hydrodynamics is eased by mathematical formalisms enabling systematic derivations and structured-preserving algorithms. Alternative to classical nonequilibrium thermodynamics and bracket formalisms, here we develop a theoretical and computational framework for active nematics based on Onsager’s variational formalism to irreversible thermodynamics, according to which the dynamics result from the minimization of a Rayleighian functional capturing the competition between free-energy release, dissipation and activity. We show that two standard incompressible models of active nemato-hydrodynamics can be framed in the variational formalism, and develop a new compressible model for density-dependent active nemato-hydrodynamics relevant to model actomyosin gels. We show that the variational principle enables a direct and transparent derivation not only of the governing equations, but also of the finite element numerical scheme. We exercise this model in two representative examples of active nemato-hydrodynamics relevant to the actin cytoskeleton during wound healing and to the dynamics of confined colonies of elongated cells.https://doi.org/10.1088/1367-2630/adcd93active nematicsOnsager’s variational formalismwound healingnematic defectsfinite element method |
| spellingShingle | W Mirza A Torres-Sánchez G Vilanova Marino Arroyo Variational formulation of active nematic fluids: theory and simulation New Journal of Physics active nematics Onsager’s variational formalism wound healing nematic defects finite element method |
| title | Variational formulation of active nematic fluids: theory and simulation |
| title_full | Variational formulation of active nematic fluids: theory and simulation |
| title_fullStr | Variational formulation of active nematic fluids: theory and simulation |
| title_full_unstemmed | Variational formulation of active nematic fluids: theory and simulation |
| title_short | Variational formulation of active nematic fluids: theory and simulation |
| title_sort | variational formulation of active nematic fluids theory and simulation |
| topic | active nematics Onsager’s variational formalism wound healing nematic defects finite element method |
| url | https://doi.org/10.1088/1367-2630/adcd93 |
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