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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2337-2354 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Two-dimensional unsteady flows in complex geometries that are characterized by simple (low-dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low-dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short- and long-term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 3 (1991), S. 179-197 
    ISSN: 1572-9222
    Keywords: Inertial manifold ; dissipation ; Kuramoto-Sivashinsky ; non-linear Galerkin method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts such as spurious turning points and inaccurate solution branches. These shortcomings were attributed to a lack of dissipation in the forms used. We show analytically and verify numerically that with an appropriate adjustment we can eliminate these numerical artifacts. The motivation for this adjustment is to enforce dissipation, while maintaining the same order of approximation. We demonstrate with computations that the most natural remedy, namely, preparation of the equation, can be highly sensitive to assumptions on the size of the absorbing ball. In addition, we show that certain implicit forms are dissipative without any adjustment. As an illustrative example we use here the Kuramoto-Sivashinsky equation.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 33 (1987), S. 1850-1864 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Global bifurcations are frequently encountered in the dynamic behavior of chemically reacting systems and their models. They cause dramatic qualitative changes in the system response, such as the birth and death of oscillations and even the onset of chaos. They involve entire regions of the system phase space, and due to their nature they are in general not predictable by standard local bifurcation methods, analytical or numerical. Special methods and algorithms must therefore be developed to locate and analyze them in parameter space. This paper presents such methods and algorithms and illustrates them through standard chemical engineering examples. Test cases include lumped chemical reactor models (homogeneous and heterogeneous, autonomous and periodically forced), a problem of compressible gas flow in porous media, and a case of two coupled oscillators. The phenomena discussed include infinite-period bifurcations, saddle connections, frequency locking, and the creation and extinction of multifrequency responses through global manifold interactions (homoclinic tangles).
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 605-621 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A macroscopic model of two-phase flow in packed beds, based on the volume-averaged equations of motion for the gas and liquid phases, was analyzed in an attempt to understand the onset and evolution of fully-developed pulsing flow in trickle beds. By assuming that solutions take the form of waves travelling at constant speed, periodic solutions to these equations are found which can be associated with long-time, asymptotic behavior of pulses in a very long bed. Families of one-dimensional waves which exist at a particular set of mass fluxes can be characterized by infinite period bifurcations in the travelling wave frame. We numerically follow these bifurcations as the fluxes are changed, generating bifurcation diagrams for the original model. The results predict that properties of one-dimensional pulses should correlate with the total superficial velocity through the bed. A hysteresis in the trickling-pulsing transition is also predicted.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 39 (1993), S. 89-98 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The occurrence of instabilities in chemically reacting systems, resulting in unsteady and spatially inhomogeneous reaction rates, is a widespread phenomenon. In this article, we use nonlinear signal processing techniques to extract a simple, but accurate, dynamic model from experimental data of a system with spatiotemporal variations. The approach consists of a combination of two steps. The proper orthogonal decomposition [POD or Karhunen-Loève (KL) expansion] allows us to determine active degrees of freedom (important spatial structures) of the system. Projection onto these “modes” reduces the data to a small number of time series. Processing these time series through an artificial neural network (ANN) results in a low-dimensional, nonlinear dynamic model with almost quantitative predictive capabilities.This approach is demonstrated using spatiotemporal data from CO oxidation on a Pt (110) crystal surface. In this special case, the dynamics of the two-dimensional reaction profile can be successfully described by four modes; the ANN-based model not only correctly predicts the spatiotemporal short-term behavior, but also accurately captures the long-term dynamics (the attractor). While this approach does not substitute for fundamental modeling, it provides a systematic framework for processing experimental data from a wide variety of spatiotemporally varying reaction engineering processes.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 35 (1990), S. 224-232 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is known that two microbial species competing for a single rate-limiting nutrient cannot grow together in a chemostat under steady-state operation, but eventually the species with the lower specific growth rate at the particular operating conditions will become extinct. Coexistence of the two populations has been shown obtainable in chemostats under periodic operation. This is possible in cases where the specific growth rate functions of the two species are such that for certain values of the nutrient concentration the first species grows faster than the second, and for other values of the nutrient concentration the second species is the one growing faster. In a previous article it was demonstrated that, even in cases where the specific growth rate functions of the two species are such that one of the species grows faster than the other for all values of the nutrient concentration, extinction of either species is possible provided that time delay in the response of the species to changes in their fermentation environment is accounted for, and that the faster growing species is also faster in its response. Here, we show that coexistence of the two species is also possible in a significant range of the operating parameters. We develop a numerical algorithm with which we trace the boundary of the coexistence region in the entire operating parameter space and construct the operating diagram of the system.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Publication Date: 2010-07-19
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 8
    Publication Date: 2000-08-29
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 9
    Publication Date: 1995-12-01
    Print ISSN: 1063-651X
    Electronic ISSN: 1095-3787
    Topics: Physics
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  • 10
    Publication Date: 1998-08-31
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
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