HYDRODYNAMIC FLUCTUATIONS AT CONVECTIVE INSTABILITY
HYDRODYNAMIC FLUCTUATIONS AT CONVECTIVE INSTABILITY
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DOI：
10.1103/physreva.15.319
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发表时间：
1977-01-01
影响因子：
2.9
通讯作者：
HOHENBERG, PC
中科院分区：
文献类型：
--
作者：
SWIFT, J;HOHENBERG, PC
考虑了热波动对对流不稳定性的影响。结果表明，流体动力学波动的朗之万方程在接近不稳定性时，与平衡状态下流体结晶的模型是等价的。然而，与通常的模型不同，本系统的自由能在阶参数中不具有三次项，因此系统在平均场理论中经历了二阶跃迁。波动对这种模型的影响最近由Brazovskii讨论，他发现了三维中的一阶跃迁。一个类似的论点也导致了对流模式的不连续过渡，在足够大的横向维度下，它表现为二维。然而，由于所考虑的热波动很弱，跳变的幅度小得无法观察到。讨论了本分析与格雷厄姆和普莱纳工作的关系。
The effects of thermal fluctuations on the convective instability are considered. It is shown that the Langevin equations for hydrodynamic fluctuations are equivalent, near the instability, to a model for the crystallization of a fluid in equilibrium. Unlike the usual models, however, the free energy of the present system does not possess terms cubic in the order parameter, and therefore the system undergoes a second-order transition in mean-field theory. The effects of fluctuations on such a model were recently discussed by Brazovskii, who found a first-order transition in three dimensions. A similar argument also leads to a discontinuous transition for the convective model, which behaves two dimensionally for sufficiently large lateral dimensions. The magnitude of the jump is unobservably small, however, because of the weakness of the thermal fluctuations being considered. The relation of the present analysis to the work of Graham and Pleiner is discussed.