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Zeyer KP, Mangold M, Obertopp T, Gilles ED. The Iron(III)-Catalyzed Oxidation of Ethanol by Hydrogen Peroxide: A Thermokinetic Oscillator. J Phys Chem A 1999. [DOI: 10.1021/jp990710v] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- K.-P. Zeyer
- Max-Planck-Institut für Dynamik komplexer technischer Systeme, Leipziger Strasse 44, 39120 Magdeburg, Germany and Institut für Systemdynamik und Regelungstechnik Universität Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany
| | - M. Mangold
- Max-Planck-Institut für Dynamik komplexer technischer Systeme, Leipziger Strasse 44, 39120 Magdeburg, Germany and Institut für Systemdynamik und Regelungstechnik Universität Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany
| | - T. Obertopp
- Max-Planck-Institut für Dynamik komplexer technischer Systeme, Leipziger Strasse 44, 39120 Magdeburg, Germany and Institut für Systemdynamik und Regelungstechnik Universität Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany
| | - E. D. Gilles
- Max-Planck-Institut für Dynamik komplexer technischer Systeme, Leipziger Strasse 44, 39120 Magdeburg, Germany and Institut für Systemdynamik und Regelungstechnik Universität Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany
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Balakotaiah V, Dommeti SMS, Gupta N. Bifurcation analysis of chemical reactors and reacting flows. CHAOS (WOODBURY, N.Y.) 1999; 9:13-35. [PMID: 12779798 DOI: 10.1063/1.166377] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In this work we review the local bifurcation techniques for analyzing and classifying the steady-state and dynamic behavior of chemical reactor models described by partial differential equations (PDEs). First, we summarize the formulas for determining the derivatives of the branching equation and the coefficients in the amplitude equations for the most common singularities. We also illustrate the procedure for the numerical computation of these coefficients. Next, the application of these local results to various reactor models described by PDEs is discussed. Specifically, we review the recent literature on the bifurcation features of convection-reaction and convection-diffusion-reaction models in one and more spatial dimensions, with emphasis on the features introduced due to coupling between the flow, heat and mass diffusion and chemical reaction. Finally, we illustrate the use of dynamical systems concepts in developing low dimensional (effective or pseudohomogeneous) models of reactors and reacting flows, and discuss some problems of current interest. (c) 1999 American Institute of Physics.
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Affiliation(s)
- Vemuri Balakotaiah
- Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4792
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53
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Panfilov V, Sheintuch M. Using weighted global control for stabilizing patterned states. CHAOS (WOODBURY, N.Y.) 1999; 9:78-87. [PMID: 12779803 DOI: 10.1063/1.166381] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
A general method to control a desired patterned state in reaction-diffusion processes is presented. Weighted global control is aimed to keep weighted spatially averaged properties of state variable at preset values. It is shown that weighted global control creates a stable direction in the global space of system states and affects system dynamics globally. We apply it for a specific two-component reaction-diffusion system and show that the desired pattern is attainable for a wide range of the control parameters. (c) 1999 American Institute of Physics.
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Affiliation(s)
- Vadim Panfilov
- Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Bennett CO. Experiments and Processes in the Transient Regime for Heterogeneous Catalysis. ADVANCES IN CATALYSIS 1999. [DOI: 10.1016/s0360-0564(08)60515-5] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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Mohl KD, Kienle A, Gilles ED. Multiple Steady States in a Reactive Distillation Column for the Production of the Fuel Ether TAME I. Theoretical Analysis. Chem Eng Technol 1998. [DOI: 10.1002/(sici)1521-4125(199802)21:2<133::aid-ceat133>3.0.co;2-g] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Russo LP, Bequette B. Operability of chemical reactors: multiplicity behavior of a jacketed styrene polymerization reactor. Chem Eng Sci 1998. [DOI: 10.1016/s0009-2509(97)00281-9] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Cannestra AF, Nett LC, Herz RK. Measurement of Gas Composition at the Center of a Porous Pellet during Adsorption and Catalytic Reaction under Dynamic Conditions. J Catal 1997. [DOI: 10.1006/jcat.1997.1875] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Batigün A, Harris KR, Palazoğlu A. Studies on the analysis of nonlinear processes via functional expansions—I. Solution of nonlinear ODEs. Chem Eng Sci 1997. [DOI: 10.1016/s0009-2509(97)00117-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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61
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Li HY. The determination of possibility of multiple steady states for complex catalytic reactions in an isothermal CSTR. CAN J CHEM ENG 1997. [DOI: 10.1002/cjce.5450750410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Hsuen HKD. Effects of spatial discretization errors on the steady-state multiplicity of a one-dimensional tubular reactor model with intraparticle transport. Chem Eng Sci 1996. [DOI: 10.1016/0009-2509(96)00256-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Jelemensky L, Kuster B, Marin G. Kinetic modelling of multiple steady-states for the oxidation of aqueous ethanol with oxygen on a carbon supported platinum catalyst. Chem Eng Sci 1996. [DOI: 10.1016/0009-2509(96)00035-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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67
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Russo L, Bequette B. Effect of process design on the open-loop behavior of a jacketed exothermic CSTR. Comput Chem Eng 1996. [DOI: 10.1016/0098-1354(95)00031-3] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Murzin DY. Computation of reaction rates for catalytic reactions on inhomogeneous surfaces with multicomponent chemisorption. Chem Eng Sci 1996. [DOI: 10.1016/0009-2509(95)00252-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Murzin D, Salmi T. Isothermal multiplicity in catalytic surface reactions with coverage dependent parameters — Case of polyatomic species. Chem Eng Sci 1996. [DOI: 10.1016/0009-2509(95)00157-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Chien YS, Liou CT. Steady-state multiplicity for autocatalytic reactions in a nonideal mixing of CSTR with two unpremixed feeds. Chem Eng Sci 1995. [DOI: 10.1016/0009-2509(95)00194-a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Pinto J. The dynamic behavior of continuous solution polymerization reactors—A full bifurcation analysis of a full scale copolymerization reactor. Chem Eng Sci 1995. [DOI: 10.1016/0009-2509(95)00163-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Kienle A, Lauschke G, Gehrke V, Gilles E. On the dynamics of the Circulation Loop Reactor—Numerical methods and analysis. Chem Eng Sci 1995. [DOI: 10.1016/0009-2509(95)00112-i] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Pinto J, Ray W. The dynamic behavior of continuous solution polymerization reactors—VIII. A full bifurcation analysis of a lab-scale copolymerization reactor. Chem Eng Sci 1995. [DOI: 10.1016/0009-2509(94)00457-3] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Jelemensky L, Kuster BFM, Marin GB. Multiple steady-states for the oxidation of aqueous ethanol with oxygen on a carbon supported platinum catalyst. Catal Letters 1995. [DOI: 10.1007/bf00813693] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Effects of Macromixing on the oregonator model of the belousov — zhabotinsky reaction in a stirred reactor. Chem Eng Sci 1994. [DOI: 10.1016/0009-2509(94)00278-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Hartmann N, Imbihl R, Vogel W. Experimental evidence for an oxidation/reduction mechanism in rate oscillations of catalytic CO oxidation on Pt/SiO2. Catal Letters 1994. [DOI: 10.1007/bf00806068] [Citation(s) in RCA: 56] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Patnaik P. Steady-state multiplicity in enzyme deactivation: Application of a simple graph theoretic method. Enzyme Microb Technol 1993. [DOI: 10.1016/0141-0229(93)90043-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Bos A, Hof E, Kuper W, Westerterp K. The behaviour of a single catalyst pellet for the selective hydrogenation of ethyne in ethene. Chem Eng Sci 1993. [DOI: 10.1016/0009-2509(93)80074-z] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Li RS, Liu QH. Sustained oscillations in isothermal, heterogeneously catalyzed reactions with the simplest Langmuir-type kinetics. Chem Eng Sci 1992. [DOI: 10.1016/0009-2509(92)87019-m] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Sistu PB, Wayne Bequette B. A comparison of nonlinear control techniques for continuous stirred tank reactors. Chem Eng Sci 1992. [DOI: 10.1016/0009-2509(92)87092-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Li R, Wu X. From bistability to temporal oscillations and spatial pattern formation. J Chem Phys 1992. [DOI: 10.1063/1.462023] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Li R, Horsthemke W. Effects of product occupancy on self‐organization in heterogeneous catalysis. II. Spatial pattern formation. J Chem Phys 1992. [DOI: 10.1063/1.462848] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Olsen RJ, Epstein IR. Bifurcation analysis of chemical reaction mechanisms. I. Steady state bifurcation structure. J Chem Phys 1991. [DOI: 10.1063/1.459831] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Experimental studies on limit cycle behaviour of the sulphuric acid catalysed hydrolysis of acetic anhydride in a CSTR. Chem Eng Sci 1991. [DOI: 10.1016/0009-2509(91)85115-e] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Eiswirth RM, Krischer K, Ertl G. Nonlinear dynamics in the CO-oxidation on Pt single crystal surfaces. ACTA ACUST UNITED AC 1990. [DOI: 10.1007/bf00324269] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Sheintuch M, Adjaye J. Excitable waves in a fixed bed reactor: ethylene oxidation on platinum. Chem Eng Sci 1990. [DOI: 10.1016/0009-2509(90)87065-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Comparison of multiplicity patterns of a single catalytic pellet and a fixed catalytic bed for ethylene oxidation. Chem Eng Sci 1990. [DOI: 10.1016/0009-2509(90)87125-c] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Moiola J, Colantonio MC, Desages A, Romagnoli J. Bifurcations and degeneracies in a CSTR with reactions A→B→C: frequency domain analysis. Chem Eng Sci 1990. [DOI: 10.1016/0009-2509(90)87101-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Colantonio MC, Moiola J, Desages A, Romagnoli J. HOPF bifurcation in a CSTR using characteristic LOCI. Chem Eng Sci 1989. [DOI: 10.1016/0009-2509(89)85036-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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