Singular Damped Twist Waves in Chromonic Liquid Crystals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913834153803776 |
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| author | Paparini, Silvia Virga, Epifanio G. |
| author_facet | Paparini, Silvia Virga, Epifanio G. |
| contents | Chromonics are special classes of nematic liquid crystals, for which a quartic elastic theory seems to be more appropriate than the classical quadratic Oseen-Frank theory. The relaxation dynamics of twist director profiles are known to develop a shock wave in finite time in the inviscid case, where dissipation is neglected. This paper studies the dissipative case. We give a sufficient criterion for the formation of shocks in the presence of dissipation and we estimate the critical time at which these singularities develop. Both criterion and estimate depend on the initial director profile. We put our theory to the test on a class of initial kink profiles and we show how accurate our estimates are by comparing them to the outcomes of numerical solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_08023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular Damped Twist Waves in Chromonic Liquid Crystals Paparini, Silvia Virga, Epifanio G. Analysis of PDEs Soft Condensed Matter Mathematical Physics Chromonics are special classes of nematic liquid crystals, for which a quartic elastic theory seems to be more appropriate than the classical quadratic Oseen-Frank theory. The relaxation dynamics of twist director profiles are known to develop a shock wave in finite time in the inviscid case, where dissipation is neglected. This paper studies the dissipative case. We give a sufficient criterion for the formation of shocks in the presence of dissipation and we estimate the critical time at which these singularities develop. Both criterion and estimate depend on the initial director profile. We put our theory to the test on a class of initial kink profiles and we show how accurate our estimates are by comparing them to the outcomes of numerical solutions. |
| title | Singular Damped Twist Waves in Chromonic Liquid Crystals |
| topic | Analysis of PDEs Soft Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2505.08023 |