We study the problem of instability in the following a priori unstable Hamiltonian system with a time-periodic perturbationare Morse potentials, and ε is a small nonzero parameter. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbations H 1 . Indeed, the set of admissible H 1 is C ω dense and C 3 open. The proof also works for arbitrarily small V i . Our perturbative technique for the genericity is valid in the C k topology for allIn the present paper we focus on the C ω -genericity of Arnold diffusion in a priori unstable Hamiltonian systems. The a priori unstable Hamiltonian system consists of a rotor-pendulum system plus a time periodic perturbation, and it can be viewed as a scaled approximation on the dynamics near simple resonances of the a priori stable systems [15].

Real-time evolution of pre-textured anodic porous alumina growth during anodization is numerically simulated in two-dimensional cases based on a kinetic model involving the Laplacian electric field potential distribution and a continuity equation for current density within the oxide body. Ion current densities governed by the Cabrera-Mott equation in high electric field theory are formed by ion migration within the oxide as well as across the metal/oxide (m/o) and oxide/electrolyte (o/e) interfaces, and the movements of the m/o and o/e interfaces due to oxidation and electric field assisted

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