Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision
- 作者：S. Villette ; E. Piron ; F. Cointault ; B. Chopinet
- 关键词：Galloping waves ; Hopf bifurcation ; Systems of viscous conservation laws
- 刊名：Biosystems Engineering
- 出版年：2008
- 期刊代码：112_15375110
- 类别：abs
- 出版时间：April 2008
- 卷：99
- 期：4
- 页码：496-507
- 文件大小：612 K
摘要
Motivated by physical and numerical observations of time oscillatory “galloping”, “spinning”, and “cellular” instabilities of detonation waves, we study Poincaré–Hopf bifurcation of traveling-wave solutions of viscous conservation laws. The main difficulty is the absence of a spectral gap between oscillatory modes and essential spectrum, preventing standard reduction to a finite-dimensional center manifold. We overcome this by direct Lyapunov–Schmidt reduction, using detailed pointwise bounds on the linearized solution operator to carry out a nonstandard implicit function construction in the absence of a spectral gap. The key computation is a space-time stability estimate on the transverse linearized solution operator reminiscent of Duhamel estimates carried out on the full solution operator in the study of nonlinear stability of spectrally stable traveling waves.