A Brief Description
We have studied the Vibrational dynamics of an infinite Vicsek fractal using the Real Space Green's Function method and the decimation technique. The vibrational properties of a Vicsek fractal reveals interesting features which arise from an interplay of self-similarity, 4-fold local symmetry, and the tree-like nature of the Vicsek fractal. The most intriguing feature is the side-by-side occurence of localized and extended states. This feature is very different from a truly disordered system in 3D, where exists a clear demarcation between extended and localized states.
Recent Publications in Fractals
- S.Y. Wu, J.A. Cocks and C.S. Jayanthi, A Real Space Green's Function Approach to the Dynamics of a Vicsek Fractal, Physical Review Letters, 69, 1955 (1992).
- C.S. Jayanthi and S.Y. Wu, Frequency Spectrum of a General Vicsek Fractal, Physical Review B 48, 10188 (1993).
- C.S. Jayanthi and S.Y. Wu, Exact Calculation of the Dynamics of a General Vicsek Fractal, Physical Review B 48 10199 (1993).
- C.S. Jayanthi and S.Y. Wu, Effects of Free-End Boundary Condition on the Frequency Spectrum of a Vicsek Fractal, S.Y. Wu and C.S. Jayanthi, Fractals, 1, 922, (1993).
- C.S. Jayanthi and S.Y. Wu, Dynamics of a Vicsek Fractal: The Boundary Effect and the Interplay among the Local Symmetry, the Self-Similarity, and the Structure of the Fractal, Phys. Rev. B 50, 897 (1994).