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  • 1
    Electronic Resource
    Electronic Resource
    Spontaneous pattern on the corroded surface of metal: Phenomenon and theory (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 68 (1990), S. 3625-3629 
    Details
    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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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Maximum principle, dynamic programming, and their connection in deterministic control (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 363-373 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01102352
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Hierarchical controls in stochastic manufacturing systems with convex costs (1994)
    Springer
    Journal of optimization theory and applications 80 (1994), S. 299-317 
    Details
    ISSN: 1573-2878
    Keywords: Stochastic manufacturing systems ; convex production planning ; hierarchical control ; dynamic programming ; viscosity solutions ; convergence rates ; error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents an extension of earlier research on heirarchical control of stochastic manufacturing systems with linear production costs. A new method is introduced to construct asymptotically optimal open-loop and feedback controls for manufacturing systems in which the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of cost. This new approach allows us to carry out an asymptotic analysis on manufacturing systems with convex inventory/backlog and production costs as well as obtain error bound estimates for constructed open loop controls. Under appropriate conditions, an asymptotically optimal Lipschitz feedback control law is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192938
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    Paper (German National Licenses)
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