Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1596, USA.
Phys Rev Lett. 2013 Jul 19;111(3):038101. doi: 10.1103/PhysRevLett.111.038101. Epub 2013 Jul 16.
We present a theory of flexural wave propagation on elastic shells having nontrivial geometry and develop an analogy to geometric optics. The transport of momentum within the shell itself is anisotropic due to the curvature, and as such complex classical effects such as birefringence are generically found. We determine the equations of reflection and refraction of such waves at boundaries between different local geometries, showing that waves are totally internally reflected, especially at boundaries between regions of positive and negative Gaussian curvature. We verify these effects by using finite element simulations and discuss the ramifications of these effects for the statistical mechanics of thin curved materials.
我们提出了一种关于具有非平凡几何形状的弹性壳中弯曲波传播的理论，并发展了一种与几何光学的类比。由于曲率的存在，壳体内的动量输运是各向异性的，因此通常会发现复杂的经典效应，如双折射。我们确定了在不同局部几何之间的边界处这种波的反射和折射方程，表明波是完全内反射的，特别是在正高斯曲率和负高斯曲率区域之间的边界处。我们通过使用有限元模拟来验证这些效应，并讨论了这些效应对薄弯曲材料统计力学的影响。
