The DOI matches its Crossref record; 86 of the 86 references it cites were found in a registry or an index.
The bifurcation behavior of tubular reactors
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“By applying first-principle modelling through relevant mass balance relations on an infinitesimally small section of the reactor, the dynamics of the reactant concentration can be described by the PDE given in Equation ( 1), belonging to the class of second order parabolic PDEs commonly used to characterize diffusion-convection-reaction systems [25] in chemical engineering.”
From Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs (2025) · cites this paper as [25]
Citations
Cites
Bifurcation, perturbation of simple eigenvalues, itand linearized stability
Crandall, M. G., & Rabinowitz, P. H. (1973) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00282325 · Cited by 830
On the dynamic behavior of continuous stirred tank reactors
Uppal, A., Ray, W. H., & Poore, A. B. (1974) · Chemical Engineering Science · doi:10.1016/0009-2509(74)80089-8 · Cited by 737
Self-citationThe QR Transformation A Unitary Analogue to the LR Transformation--Part 1
Francis, J. G. F. (1961) · The Computer Journal · doi:10.1093/comjnl/4.3.265 · Cited by 696
Solution of boundary-value problems by orthogonal collocation
Villadsen, J. V., & Stewart, W. E. (1967) · Chemical Engineering Science · doi:10.1016/0009-2509(67)80074-5 · Cited by 673
Francis, J. G. F. (1962) · The Computer Journal · doi:10.1093/comjnl/4.4.332 · Cited by 384
Orthogonal collocation on finite elements
Carey, G. F., & Finlayson, B. A. (1975) · Chemical Engineering Science · doi:10.1016/0009-2509(75)80031-5 · Cited by 338
Uppal, A., Ray, W. H., & Poore, A. B. (1976) · Chemical Engineering Science · doi:10.1016/0009-2509(76)85058-0 · Cited by 284
Self-citationThe Hopf Bifurcation Theorem in infinite dimensions
Crandall, M. G., & Rabinowitz, P. H. (1977) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00280827 · Cited by 181
On the theory and application of the Hopf-Friedrichs bifurcation theory
Poore, A. B. (1976) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00248886 · Cited by 132
Hlaváček, V., & Hofmann, H. (1970) · Chemical Engineering Science · doi:10.1016/0009-2509(70)85030-8 · Cited by 119
Research works printed but not linked: 11
- Gilles, 1976, Proc. 4th Int. Symp. Chem. React. Engng Heidelberg, 459
- Hlaváček, 1978, Advan. Catal., 27, 59
- Butakov, 1973, Dokl. Akad. Nauk. SSSR, 209, 643
- Hlaváček, 1974, Int. J. Chem. Engng, 14, 461
- Butakov, 1978, Dokl. Akad, Nauk SSSR, 238, 166
- Oh, 1978, am. Chem. Soc. Symp. Ser., 65, 461
- Paspek, 1980, A.I.Ch.E.J.
- Vortmeyer, 1961, Z. Electrochem., 65, 282
- McGinnis, 1965, Chem. Engng Prog. Symp. Ser., 55, 2
- Sørensen, 1973, A.I.Ch.E.J., 969, 1286
- Poore, 1980, A.I.Ch.E. Annual Meeting
Cited by
Sorted by citations
Tezduyar, T. E., & Park, Y. J. (1986) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(86)90003-4 · Cited by 269
Olefin/paraffin separations by adsorption: π‐Complexation vs. kinetic separation
Rege, S. U., Padin, J., & Yang, R. T. (1998) · AIChE Journal · doi:10.1002/aic.690440405 · Cited by 225
Multiplicities and instabilities in chemically reacting systems — a review
Razón, L. F., & Schmitz, R. A. (1987) · Chemical Engineering Science · doi:10.1016/0009-2509(87)80055-6 · Cited by 193
Meurer, T., & Kugi, A. (2009) · Automatica · doi:10.1016/j.automatica.2009.01.006 · Cited by 184
Dochain, D., Babary, J. P., & Tali-Maamar, N. (1992) · Automatica · doi:10.1016/0005-1098(92)90141-2 · Cited by 151
Metadata
- Authors
- Jensen, K. F., & Ray, W. H.
- Affiliations
- University of Wisconsin–Madison (US)
- Corresponding author
- Ray, W.Harmon
- ORCID
- Jensen, Klavs F.
- Venue
- Chemical Engineering Science
- Publisher
- Elsevier BV
- Published
- 1982
- Volume
- 37
- Issue
- 2
- Pages
- 199-222
- ISSN
- 0009-2509 (ISSN-L)
- OpenAlex
- W2065214383
- Cited by
- 180
- References
- 86
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 5 · 2022: 3 · 2021: 4 · 2020: 4 · 2019: 5 · 2018: 3 · 2017: 4 · 2016: 3 · 2015: 6 · 2014: 1 · 2013: 7 · 2012: 2
- FWCI
- 5.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Chemical Engineering Science (publishedVersion)
- Defense Technical Information Center (DTIC) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Heat and Mass Transfer in Porous Media
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Keywords
- tubular reactor, bifurcation analysis, Hopf bifurcation, steady-state profiles, axial dispersion, first-order irreversible reaction, multiple steady states, periodic solutions, Lewis number, Peclet number, fixed-bed reactor, reaction-diffusion systems, two-phase model
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