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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
    A central limit theorem for the Fourth Wick power of the free lattice field (1996)
    Springer
    Communications in mathematical physics 181 (1996), S. 1-10 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract LetG a be the free lattice field measure of massm 0 onaZ d , and: φ x 4 : be the corresponding fourth Wick power of the lattice field φ x . Letg∈C 0 (R d ),g≧0, be a given function anda′=a′(a)≧a satisfy: lim a→0+a′=0 anda′Z d ⊂aZ d . We prove that ifd≧3, ord=2 and lim a→0+ a′|loga|2=∞, then $$\left\{ {a'^d \Sigma _{x \in a'Z^d } g_x :\phi _x^4 :} \right\}$$ satisfies the central limit theorem: there isV(a, a′) with lim a→0+ V(a, a′)=∞ such that the distribution of $$V(a,a')^{ - 1} a'^d \Sigma _{x \in a'Z^d } g_x :\phi _x^4 :$$ underG a is convergent to the standard normal distribution, asa→0+.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101671
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  • 3
    Electronic Resource
    Electronic Resource
    Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)
    Springer
    Applied mathematics & optimization 42 (2000), S. 19-33 
    Details
    ISSN: 1432-0606
    Keywords: Key words. Continuous time, Mean-variance, Portfolio, Efficient frontier, Linear-quadratic control. AMS Classification. Primary 90A09, Secondary 93E20.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be ``embedded'' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002450010003
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  • 4
    Electronic Resource
    Electronic Resource
    Stochastic Quantization of the Two-Dimensional Polymer Measure (1999)
    Springer
    Applied mathematics & optimization 40 (1999), S. 341-354 
    Details
    ISSN: 1432-0606
    Keywords: Key words. Two-dimensional polymer measure, Closability, Dirichlet forms, Diffusion processes, Ergodicity, Quasi-invariance. AMS Classification. Primary 60J65, Secondary 60H30.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We prove that there exists a diffusion process whose invariant measure is the two-dimensional polymer measure ν g . The diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. We prove the closability of the appropriate pre-Dirichlet form which is of gradient type, using a general closability result by two of the authors. This result does not require an integration by parts formula (which does not hold for the two-dimensional polymer measure ν g ) but requires the quasi-invariance of ν g along a basis of vectors in the classical Cameron—Martin space such that the Radon—Nikodym derivatives (have versions which) form a continuous process. We also show the Dirichlet form to be irreducible or equivalently that the diffusion process is ergodic under time translations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002459900129
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  • 5
    Electronic Resource
    Electronic Resource
    Hierarchical production policies in stochastic two-machine flowshops with finite buffers (1996)
    Springer
    Journal of optimization theory and applications 89 (1996), S. 681-712 
    Details
    ISSN: 1573-2878
    Keywords: Two-machine flowshops ; unreliable machines ; hierarchical production policy ; weak Lipschitz continuity ; constraint domain approximation ; asymptotic optimal control ; convergence rates ; error estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns production planning in manufacturing systems with two unreliable machines in tandem. The problem is formulated as a stochastic control problem in which the objective is to minimize the expected total cost of production, inventories, and backlogs. Since the sizes of the internal and external buffers are finite, the problem is one with state constraints. As the optimal solutions to this problem are extremely difficult to obtain due to the uncertainty in machine capacities as well as the presence of state constraints, a deterministic limting problem in which the stochastic machine capacities are replaced by their mean capacities is considered instead. The weak Lipschitz property of the value functions for the original and limiting problems is introduced and proved; a constraint domain approximation approach is developed to show that the value function of the original problem converges to that of the limiting problem as the rate of change in machine states approaches infinity. Asymptotic optimal production policies for the orginal problem are constructed explicity from the near-optimal policies of the limiting problem, and the error estimate for the policies constructed is obtained. Algorithms for constructing these policies are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02275355
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Deterministic near-optimal control, part 1: Necessary and sufficient conditions for near-optimality (1995)
    Springer
    Journal of optimization theory and applications 85 (1995), S. 473-488 
    Details
    ISSN: 1573-2878
    Keywords: Near-optimal control ; necessary and sufficient conditions ; Hamiltonian ; adjoint functions ; Ekeland's principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns dynamic near-optimization, or near-optimal control, for systems governed by deterministic ordinary differential equations. Necessary and sufficient conditions for near-optima control are studied. It is shown that any near-optimal control nearly maximizes the Hamiltonian in some integral sense, and vice versa, if some additional concavity conditions are imposed. Error estimates for both the near-optimality of the controls and the near-maximality of the Hamiltonian are obtained. A number of examples are presented to illustrate these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192237
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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Comparison of four combustion models for simulating the premixed combustion in inert porous media (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Fire and Materials 22 (1998), S. 187-197 
    Details
    ISSN: 0308-0501
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This work reports one-dimensional predictions of methane/air fuel combustion in inert porous media using four combustion models: full mechanism (FM, 49 species and 227 elemental reactions), skeletal mechanism (SM, 26 species and 77 elemental reactions), 4-step reduced mechanism (4RM, 9 species) and 1-step global mechanism (1GM). The effects of these models on temperature, species, burning speeds and pollutant emissions are examined. The calculations are compared with available experimental data. It is concluded that the already known limitation of the 1-step global mechanism can be partially eliminated by the present 4-step reduced mechanism. This 4RM model compares very satisfactorily with the full mechanism in the simulation of combustion in porous media. This conclusion is encouraging for the simulation of practical porous media burners because the 4RM model improves the stability of the calculation process and can be used with reduced computational resources and cost. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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