Amplitude equations for the electrohydrodynamic instability in nematic liquid crystals.
Amplitude equations for the electrohydrodynamic instability in nematic liquid crystals.
复制标题
向列液晶电流体动力学不稳定性的振幅方程。
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
Pesch
中科院分区：
文献类型：
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作者：
Kaiser;Pesch
我们研究了平面取向向列相液晶在(低频)导电区的电流体动力对流(EHC)的近阈值行为。这些研究是建立在对标准流体动力学方程进行严格而系统的弱非线性分析的基础上的，从而简化了序参数方程的描述。在控制参数和波数空间中，识别了正常滚转在阈值附近的典型实验稳定性区域。特别强调了均流效应在触发典型的二次之字形不稳定导致斜滚中的决定性作用。随后，从基本方程直接导出了一组耦合的振幅方程，其中包含了平均流效应和至少在EHC中重要的高阶梯度项。对振幅方程的模拟表明，在锯齿形失稳线之外可能存在不止一个吸引子，这可能解释了有时相互矛盾的实验结果。该理论很好地解释了“弱湍流”(有时称为“缺陷湍流”)的情景。
We study the near-threshold behavior of electrohydrodynamic convection (EHC) in planarly aligned nematic liquid crystals in the (low-frequency) conduction regime. The investigations are based on a rigorous and systematic weakly nonlinear analysis of the standard hydrodynamic equations leading to a reduced description in terms of order-parameter equations. The typical experimental stability regimes in control parameter and wave-number space are identified for normal rolls near threshold. In particular, the decisive role of mean-flow effects in triggering the typical secondary zigzag instability leading to oblique rolls is emphasized. Subsequently, a set of coupled amplitude equations is derived directly from the basic equations that includes the mean-flow effects and higher-order gradient terms important at least in EHC. Simulations of the amplitude equations point to the possible existence of more than one attractor beyond the zigzag destabilization line, which might explain the sometimes conflicting experimental results. The scenario of ``weak turbulence' (sometimes called ``defect turbulence') is well accounted for by the theory.