色晶液晶中的奇异阻尼扭转波
Singular Damped Twist Waves in Chromonic Liquid Crystals
AI总结：
针对色晶液晶四次弹性理论中有耗散的扭转指向矢弛豫问题，本文给出有限时间形成冲击波的充分判据及临界时间估计，并通过扭结初值数值解验证其准确性。
摘要：
色晶是一类特殊的向列相液晶，对其而言，四次弹性理论似乎比经典的二次 Oseen-Frank 理论更合适。已知在忽略耗散的无黏情形中，扭曲指向矢分布的弛豫动力学会在有限时间内形成冲击波。本文研究有耗散的情形。我们给出了在存在耗散时形成冲击波的一个充分判据，并估计了这些奇异性发展形成的临界时间。该判据和估计都依赖于初始指向矢分布。我们在一类初始扭结分布上检验了所提出的理论，并通过将估计结果与数值解的结果进行比较，展示了估计的准确程度。
英文摘要：
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.
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