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Spontaneous pattern on the corroded surface of metal: Phenomenon and theory (1990)

Yang, J. J. ; Zhou, X. Y.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 68 (1990), S. 3625-3629

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ISSN: 1089-7550

Source: AIP Digital Archive

Topics: Physics

Notes: A spontaneous pattern was found on the corroded surface of 1Cr18Ni9Ti stainless steel which was subjected to a crude oil containing naphthenic acid at temperature about 330 °C. The high regularity, the periodicity, and SO2 symmetry of the pattern imply that a spontaneous dissipative structure arose in this corrosion system. It was also found that the distribution of chemical elements on the corroded surface was in accordance with the morphologic pattern. A new theory, which is based on the linear perturbation method and in which the shift of boundary is considered, is proposed to characterize the formation of the large-scale spontaneous pattern, reveal the mechanism, and explain this phenomenon in the corrosion system.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.346324

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Maximum principle, dynamic programming, and their connection in deterministic control (1990)

Zhou, X. Y.

Springer

Journal of optimization theory and applications 65 (1990), S. 363-373

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ISSN: 1573-2878

Keywords: Optimal control ; maximum principle ; dynamic programming ; viscosity solutions ; superdifferential ; subdifferential

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Two major tools for studying optimally controlled systems are Pontryagin's maximum principle and Bellman's dynamic programming, which involve the adjoint function, the Hamiltonian function, and the value function. The relationships among these functions are investigated in this work, in the case of deterministic, finite-dimensional systems, by employing the notions of superdifferential and subdifferential introduced by Crandall and Lions. Our results are essentially non-smooth versions of the classical ones. The connection between the maximum principle and the Hamilton-Jacobi-Bellman equation (in the viscosity sense) is thereby explained by virtue of the above relationship.