Interfacial wave theory of dendrite growth: global mode solution and quantum condition

Abstract

This paper is concerned with the global mode solutions of dendritic crystal growth. In this paper, we investigate the signal feed-back process at the leading edge of the dendrite tip and derive the global instability mechanism of the system on the basis of the previous results (Phys. Rev. A, 40, 1599 (1989); 40, 1609 (1989)). A global wave diagram of the system is explored, which we call WEASR (Wave emission at the turning point and signal reflections between the turning point and the leading edge of the tip). This WEASR mechanism determines a discrete set of unstable global modes for the system. The asymptotic solutions for these modes and the quantum condition for the corresponding eigenvalues are obtained. The discovery of the WEASR mechanism is quite a significant step leading to the understanding of instability phenomena in dendrite growth.