环形对流中的斑图形成
Pattern formation in annular convection
AI总结：
本研究针对环形对流中的时空斑图形成，以大气对流和薄膜电对流为背景，利用O(2)-等变分岔理论预测稳态及时空斑图动力学。
摘要：
这项对环形区域中时空斑图形成的研究，源于两个尺度迥异的物理问题。第一个是赤道平面上地球温暖表面与寒冷对流层顶之间的大气对流，由二维Boussinesq方程建模。第二个是薄半导体薄膜中的环形电对流，实验揭示随着电场强度增加，平面内会出现类似对流的涡旋的诞生。这由二维Navier-Stokes方程与简化版Maxwell方程耦合建模。这两个模型共享基本的数学性质，并满足应用O(2)-等变分岔理论的前提条件。我们表明，这可以预测有趣的动力学，包括稳态和时空斑图。
英文摘要：
This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold tropopause, modeled by the two dimensional Boussinesq equations. The second is annular electroconvection in a thin semetic film, where experiments reveal the birth of convection-like vortices in the plane as the electric field intensity is increased. This is modeled by two dimensional Navier-Stokes equations coupled with a simplified version of Maxwell's equations. The two models share fundamental mathematical properties and satisfy the prerequisites for application of O(2)-equivariant bifurcation theory. We show this can give predictions of interesting dynamics, including stationary and spatio-temporal patterns.
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