Determination of the symmetry classes of orientational ordering tensors
The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical rea...
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| Autor*in: |
Turzi, Stefano S [verfasserIn] |
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| Format: |
Artikel |
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| Erschienen: |
2016 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinearity - Bristol : IOP Publ. Ltd., 1988, (2016) |
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| Übergeordnetes Werk: |
year:2016 |
| Links: |
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| DOI / URN: |
10.1088/1361-6544/aa8713 |
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| 520 | |a The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of \mathbb{S}, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of \mathbb{S} for each class. The nearest tensor of the assigned symmetry is determined by group-projection. In order to test our procedure, we generate uniaxial and biaxial phases in a system of interacting particles, endowed with D_{\infty h} or D_{2h}, which mimic the outcome of Monte-Carlo simulations. The actual symmetry of the phases is correctly identified, along with the optimal choice of laboratory frame. | ||
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10.1088/1361-6544/aa8713 doi PQ20171228 (DE-627)OLC1999407199 (DE-599)GBVOLC1999407199 (PRQ)a742-53bea61aab41c5b4ab1b02c7eafb7ce2033dbcdb835d810a3589130d00523bc20 (KEY)0165812320160000000000000000determinationofthesymmetryclassesoforientationalor DE-627 ger DE-627 rakwb 530 510 DE-600 Turzi, Stefano S verfasserin aut Determination of the symmetry classes of orientational ordering tensors 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of \mathbb{S}, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of \mathbb{S} for each class. The nearest tensor of the assigned symmetry is determined by group-projection. In order to test our procedure, we generate uniaxial and biaxial phases in a system of interacting particles, endowed with D_{\infty h} or D_{2h}, which mimic the outcome of Monte-Carlo simulations. The actual symmetry of the phases is correctly identified, along with the optimal choice of laboratory frame. Condensed Matter Soft Condensed Matter Bisi, Fulvio oth Enthalten in Nonlinearity Bristol : IOP Publ. Ltd., 1988 (2016) (DE-627)130416231 (DE-600)626428-1 (DE-576)018245684 0951-7715 nnns year:2016 http://dx.doi.org/10.1088/1361-6544/aa8713 Volltext http://arxiv.org/abs/1602.06413 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2192 GBV_ILN_2409 AR 2016 |
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10.1088/1361-6544/aa8713 doi PQ20171228 (DE-627)OLC1999407199 (DE-599)GBVOLC1999407199 (PRQ)a742-53bea61aab41c5b4ab1b02c7eafb7ce2033dbcdb835d810a3589130d00523bc20 (KEY)0165812320160000000000000000determinationofthesymmetryclassesoforientationalor DE-627 ger DE-627 rakwb 530 510 DE-600 Turzi, Stefano S verfasserin aut Determination of the symmetry classes of orientational ordering tensors 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of \mathbb{S}, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of \mathbb{S} for each class. The nearest tensor of the assigned symmetry is determined by group-projection. In order to test our procedure, we generate uniaxial and biaxial phases in a system of interacting particles, endowed with D_{\infty h} or D_{2h}, which mimic the outcome of Monte-Carlo simulations. The actual symmetry of the phases is correctly identified, along with the optimal choice of laboratory frame. Condensed Matter Soft Condensed Matter Bisi, Fulvio oth Enthalten in Nonlinearity Bristol : IOP Publ. Ltd., 1988 (2016) (DE-627)130416231 (DE-600)626428-1 (DE-576)018245684 0951-7715 nnns year:2016 http://dx.doi.org/10.1088/1361-6544/aa8713 Volltext http://arxiv.org/abs/1602.06413 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2192 GBV_ILN_2409 AR 2016 |
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Determination of the symmetry classes of orientational ordering tensors |
| abstract |
The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of \mathbb{S}, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of \mathbb{S} for each class. The nearest tensor of the assigned symmetry is determined by group-projection. In order to test our procedure, we generate uniaxial and biaxial phases in a system of interacting particles, endowed with D_{\infty h} or D_{2h}, which mimic the outcome of Monte-Carlo simulations. The actual symmetry of the phases is correctly identified, along with the optimal choice of laboratory frame. |
| abstractGer |
The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of \mathbb{S}, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of \mathbb{S} for each class. The nearest tensor of the assigned symmetry is determined by group-projection. In order to test our procedure, we generate uniaxial and biaxial phases in a system of interacting particles, endowed with D_{\infty h} or D_{2h}, which mimic the outcome of Monte-Carlo simulations. The actual symmetry of the phases is correctly identified, along with the optimal choice of laboratory frame. |
| abstract_unstemmed |
The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor \mathbb{S}. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of \mathbb{S}, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of \mathbb{S} for each class. The nearest tensor of the assigned symmetry is determined by group-projection. In order to test our procedure, we generate uniaxial and biaxial phases in a system of interacting particles, endowed with D_{\infty h} or D_{2h}, which mimic the outcome of Monte-Carlo simulations. The actual symmetry of the phases is correctly identified, along with the optimal choice of laboratory frame. |
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| title_short |
Determination of the symmetry classes of orientational ordering tensors |
| url |
http://dx.doi.org/10.1088/1361-6544/aa8713 http://arxiv.org/abs/1602.06413 |
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| author2 |
Bisi, Fulvio |
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10.1088/1361-6544/aa8713 |
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2024-07-03T14:08:18.145Z |
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