Cited by 180Heat and Mass Transfer in Porous MediaNonlinear Dynamics and Pattern FormationAdvanced Differential Equations and Dynamical Systems

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

Jensen, Klavs F., Ray, W.Harmon·1982·Chemical Engineering Science

DOI 10.1016/0009-2509(82)80155-3

Open this paper in CoChat — free account

Integrity signals

Registry

Crossref · 10.1016/0009-2509(82)80155-3

Cites

86 of 86 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

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-citation
The 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
The QR Transformation--Part 2
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
The classification of the dynamic behavior of continuous stirred tank reactors—influence of reactor residence time
Uppal, A., Ray, W. H., & Poore, A. B. (1976) · Chemical Engineering Science · doi:10.1016/0009-2509(76)85058-0 · Cited by 284
Self-citation
The 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
Modeling of chemical reactors — XVI Steady state axial heat and mass transfer in tubular reactors An analysis of the uniqueness of solutions
Hlaváček, V., & Hofmann, H. (1970) · Chemical Engineering Science · doi:10.1016/0009-2509(70)85030-8 · Cited by 119

Show all 86 references

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

Sorted by citations

Items 101–180 of 180

Trajectory planning and receding horizon tracking control of a quasilinear diffusion-convection-reaction system
Utz, T., Graichen, K., & Kugi, A. (2010) · IFAC Proceedings Volumes · doi:10.3182/20100901-3-it-2016.00215 · Cited by 8
Bifurcation Analysis of a Tubular Reactor for Nitroxide‐Mediated Radical Polymerization of Styrene
Zitlalpopoca‐Soriano, A. G., Vivaldo‐Lima, E., & Flores‐Tlacuahuac, A. (2010) · Macromolecular Reaction Engineering · doi:10.1002/mren.201000003 · Cited by 8
Matrices are forever: On applied mathematics and computing in chemical engineering
Kevrekidis, I. G. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00274-x · Cited by 8
Bifurcation and complex dynamics in fixed-bed catalytic reactors
Wagialla, K. M., & Elnashaie, S. S. E. H. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00042-4 · Cited by 8
Wave phenomena in the packed‐bed reactor: Their relation to the differential‐flow instability
Yakhnin, V. Z., Rovinsky, A. B., & Menzinger, M. (1996) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.5450740514 · Cited by 7
Recent developments in chemical oscillations
Gurel, D., & Gürel, O. (1983) · Topics in current chemistry · doi:10.1007/3-540-12575-2_2 · Cited by 7
Flatness-based feedback tracking control of a distributed parameter tubular reactor model
Meurer, T., Becker, J., & Zeitz, Μ. (2003) · European Control Conference (ECC) · doi:10.23919/ecc.2003.7086479 · Cited by 7
“1Differing from [11] it is assumed, that the outlet cooling temperature is constant such that the normalized state is introduced with respect to instead of the inflow temperature, i.”
Background
Numerical Deterkination of Bifurcation Points in Steady State and Periodic Solutions — Numerical Algorithms and Examples
Kubı́ček, M., & Holodniok, M. (1984) · International series of numerical mathematics · doi:10.1007/978-3-0348-6256-1_17 · Cited by 7
Saturated output-feedback control and state estimation of a class of exothermic tubular reactors
Reyes, H. A. F.-D. L., & Álvarez, J. (2022) · Journal of Process Control · doi:10.1016/j.jprocont.2022.02.005 · Cited by 6
A Simple Feedback Control Approach for Output Modulation of Spatiotemporal Patterns in a Class of Tubular Reactors
Puebla, H., Hernández‐Martínez, E., Hernández-Suárez, R., Ramirez-Muñoz, J., & Álvarez‐Ramírez, J. (2013) · Industrial & Engineering Chemistry Research · doi:10.1021/ie4013562 · Cited by 6
Dynamic simulation and optimal heat management policy of a coupled solar reforming–heat storage process
Pantoleontos, G., Koutsonikolas, D., Lorentzou, S., Karagiannakis, G. P., Lekkos, C. P., & Konstandopoulos, A. G. (2017) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2017.05.024 · Cited by 6
Deactivation avalanches through the interaction of locally deactivated catalyst with traceling hot spots
Yakhnin, V. Z., & Menzinger, M. (1999) · Studies in surface science and catalysis · doi:10.1016/s0167-2991(99)80478-9 · Cited by 6
Bifurcation analysis of dynamic process models using Aspen Dynamics® and Aspen Custom Modeler®
Restrepo, J. B., Olivar, G., & Álzate, C. A. C. (2013) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2013.11.013 · Cited by 6
Stability analysis of steady-state solutions for porous catalytic pellets: influence of the Lewis number
Berezowski, M., & Burghardt, A. (1993) · Chemical Engineering Science · doi:10.1016/0009-2509(93)80056-v · Cited by 6
Multiplicities and periodic behavior in laser direct-write metallization
Price, P. E., & Jensen, K. F. (1989) · Chemical Engineering Science · doi:10.1016/0009-2509(89)85129-2 · Cited by 6
Self-citation
On the dynamical instability of packed-bed reactors in the presence of catalyst deactivation
Jaree, A., Boonsomlanjit, B., & Limtrakul, J. P. (2008) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2008.02.004 · Cited by 5
Understanding oscillatory behaviour of gibbsite precipitation circuits
Bekker, A. V., Li, T. S., & Livk, I. (2015) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2015.07.006 · Cited by 5
“This temperature wave propagation study was further extended to CSTR in series and pipe reactors (Jensen and Ray, 1982; Razón and Schmitz, 1987).”
Background
Multiscale Analysis to Determine the Sensitive Zones for Temperature Sensor Location in Tubular Reactors
Moguel‐Castañeda, J. G., Hernandez‐Ayala, J. L., Gomez‐Rodriguez, R., Bastidas‐Oyanedel, J., & Hernández‐Martínez, E. (2021) · Chemical Engineering & Technology · doi:10.1002/ceat.202000053 · Cited by 5
ELEMENT METHOD TO NONLINEAR TRANSIENT DIFFUSION-CONVECTION-REACTION SYSTEM
Park, S.-K. (1995) · Chemical Engineering Communications · doi:10.1080/00986449508936403 · Cited by 5
Model Reactors and Their Design Equations
Hlaváček, V., Puszynski, J. A., Viljoen, H. J., & Gatica, J. E. (2000) · Ullmann's Encyclopedia of Industrial Chemistry · doi:10.1002/14356007.b04_121 · Cited by 5
Constructive nonlinear dynamics in process systems engineering
Marquardt, W., & Mönnigmann, M. (2004) · Computer-aided chemical engineering/Computer aided chemical engineering · doi:10.1016/s1570-7946(04)80086-5 · Cited by 5
Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs
Moadeli, B., Cassol, G. O., & Dubljevic, S. (2025) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.25629 · Cited by 4
Feedforward control design under input constraints for a tubular reactor model
Wieland, P., Meurer, T., Graichen, K., & Zeitz, Μ. (2006) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2006.377031 · Cited by 4
“Well-known examples concern tubular and fixed-bed reactors with multiple steady states and complex dynamical behavior [1].”
Background
Micromixing effects on the dynamic behavior of continuous free-radical solution polymerization tank reactors
Oechsler, B. F., Melo, P. A., & Pinto, J. C. (2016) · Applied Mathematical Modelling · doi:10.1016/j.apm.2016.10.019 · Cited by 4
p-version least-squares finite element formulation of a system of convection-reaction nonlinear equations—Fixed bed o-xylene oxidation
Vijayaraghavan, K., & Surana, K. S. (1997) · Computers & Structures · doi:10.1016/s0045-7949(96)00216-7 · Cited by 4
MULTIPLE STEADY STATES OF ADIABATIC FIXED-BED REACTORS
Dougherty, R. C., Thygeson, J. R., & Hu, R. (1993) · Chemical Engineering Communications · doi:10.1080/00986449308936216 · Cited by 4
Feedforward ouput-feedback control for a class of exothermic tubular reactors
Nájera, I., Álvarez, J., & Baratti, R. (2015) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2015.09.111 · Cited by 4
On the nonlinear dynamics of biomass throated tubular gasification reactors
Santamaría-Padilla, L., Badillo-Hernández, U., Álvarez, J., & Álvarez-Icaza, L. A. (2022) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2022.107828 · Cited by 4
Complex nonlinear behaviour of a fixed bed reactor with reactant recycle
Recke, B., & Jørgensen, S. B. (1999) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(99)80044-1 · Cited by 4
A Detection Algorithm for Bifurcations in Dynamical Systems using Reduced Order Models
Wattamwar, S. K., Weiland, S., & Backx, T. (2008) · IFAC Proceedings Volumes · doi:10.3182/20080706-5-kr-1001.01856 · Cited by 4
“In Jensen and Ray [1982], three steady states are reported for these parameter ranges.”
BackgroundMethodInfluential
A model reduction-based optimisation framework for large-scale simulators using iterative solvers
Bonis, I., & Theodoropoulos, C. (2008) · Computer-aided chemical engineering/Computer aided chemical engineering · doi:10.1016/s1570-7946(08)80096-x · Cited by 4
The Bifurcation Behavior of an Autothermal Packed Bed Tubular Reactor
Adomaitis, R. A., & Çınar, A. (1987) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)55439-7 · Cited by 4
Backstepping Control of a Class of Space-Time-Varying Linear Parabolic PDEs via Time Invariant Kernel Functions
Chen, Q., Zheng, J. P., & Zhu, G. (2024) · SIAM Journal on Control and Optimization · doi:10.1137/23m1556836 · Cited by 3
The parameter domain of convective instability of the adiabatic packed‐bed reactor
Yakhnin, V. Z., Rattanayotsakun, S., Jaree, A., & Menzinger, M. (2015) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.22296 · Cited by 3
Multiplicity pattern in the nonisothermal nonadiabatic packed bed chemical reactor
Juncu, G., & Floarea, O. (1995) · Computers & Chemical Engineering · doi:10.1016/0098-1354(94)00101-s · Cited by 3
Imaging Gas Flow in Gas–Solid Catalytic Systems by Near-Infrared Tomography
Aiouache, F. (2017) · Advances in chemical engineering · doi:10.1016/bs.ache.2017.07.002 · Cited by 3
Reduced Order Optimization of Large-Scale Nonlinear Systems with Nonlinear Inequality Constraints Using Steady State Simulators
Petsagkourakis, P., Bonis, I., & Theodoropoulos, C. (2018) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.8b00033 · Cited by 3
Spontaneous, random oscillations in the rate of CO oxidation over Pt/Alumina
Chakrabarty, T., Hudgins, R. R., & Silveston, P. L. (1987) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.5450650428 · Cited by 3
The occurrence of chaos in a tubular reactor with axial diffusion
Pellegrini, L. A., Albertoni, S., & Biardi, G. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)87077-4 · Cited by 3
STEADY STATE MULTIPLICITY BEHAVIOR OF AN ADIABATIC PLUG-FLOW REACTOR WITH NONUNIFORMLY ACTIVE CATALYST
Lee, C. K., & Varma, A. (1987) · Chemical Engineering Communications · doi:10.1080/00986448708911973 · Cited by 3
Generative learning for slow manifolds and bifurcation diagrams
Crabtree, E., Giovanis, D. G., Evangelou, N., Bello‐Rivas, J. M., & Kevrekidis, I. G. (2025) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2025.109544 · Cited by 2
Fixed-bed reactors for exothermic reactions: A qualitative relation between start-up time and traveling waves velocity
Fache, A., Marías, F., Castaldi, M. J., Lugo-Pimentel, M., NIKITIN, Y. K. E. E., & Moutushi, T. (2021) · Chemical Engineering Science · doi:10.1016/j.ces.2021.116504 · Cited by 2
Chemical Reactor Dynamics: Stability of Steady States
Chicone, C. C., Latushkin, Y., & Retzloff, D. G. (1996) · Mathematical Methods in the Applied Sciences · doi:10.1002/(sici)1099-1476(19960325)19:5 · Cited by 2
Moving Horizon Estimator Design for a Nonlinear Diffusion-Reaction System with Sensor Dynamics
Dongmo, M. K. J., & Meurer, T. (2022) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2022.09.076 · Cited by 2
Physical Implications of Periodic Solutions in a Fixed Bed Reactor with Recycle
Recke, B., & Jørgensen, S. B. (1995) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)47039-x · Cited by 2
Identification of low order models for large scale processes
Wattamwar, S. (2006) · TU/e Research Portal · doi:10.6100/ir657524 · Cited by 2
“In Jensen and Ray (1982), three steady states are reported for these parameter values. However, it is difficult to observe the middle steady state by the dynamic simulations. Similar to a CSTR, the middle steady state is usually said to be unstable. Numerical techniques suggested by Doedel et al. (1997), shows that th…”
Background
Flatness-Based Tracking Control for Parabolic Distributed-Parameter Systems with Boundary Input (Flachheitsbasierte Folgeregelung für parabolische verteilt-parametrische Systeme mit Randeingriff)
Meurer, T., & Zeitz, Μ. (2006) · at - Automatisierungstechnik · doi:10.1524/auto.2006.54.8.372 · Cited by 2
Dynamics of a Packed Bed Reactor with Reactant Recycle
Brabrand, H., & Jørgensen, S. B. (1992) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)50976-3 · Cited by 2
Application of a simple rule for the design of micro- or meso-scale cooled reactors in a heat transfer limited regime
Deshpande, K., Zeng, J., Dixit, R. S., West, D. H., & Jean, D. (2024) · Reaction Chemistry & Engineering · doi:10.1039/d4re00128a · Cited by 1
A novel transformation for exponential stabilization of a cascade heat PDE-ODE system with unknown disturbance
Guo, Y.-M., Liu, J.-J., & Guo, B. (2026) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2026.108641 · Cited by 1
Multiplicity in the partial oxidation of propylene over a copper‐molybdena catalyst
Labastida‐Bardales, J. R., Hudgins, R. R., & Silveston, P. L. (1989) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.5450670311 · Cited by 1
Influence of internal heat removal upon effectiveness, stability of an exothermic catalytic film: Implications for process intensification
Honda, G. S., & Wilhite, B. A. (2011) · Chemical Engineering Science · doi:10.1016/j.ces.2011.10.013 · Cited by 1
Robust stability analysis of Koopman based MPC system
Verma, G., Heath, W. P., & Theodoropoulos, C. (2024) · Computer-aided chemical engineering/Computer aided chemical engineering · doi:10.1016/b978-0-443-28824-1.50322-7 · Cited by 1
Sampled-Data Boundary Feedback Control for Distributed PDE-ODE Cascade Systems
Qiu, R., Xu, X., Liu, L., & Feng, G. (2025) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc63710.2025.11107935 · Cited by 1
“Among these, parabolic PDE-ODE cascade systems find use across various fields [4]–[7], and boundary control for these systems attract much attention [3], [8]–[10].”
Application of higher-order discretization to parametric dependence of partial differential equations describing tubular flow reactors
Kim, S. H., & Kwon, Y.-J. (2000) · Korean Journal of Chemical Engineering · doi:10.1007/bf02789255 · Cited by 1
“In the meanwhile, the analysis of parametric dependence in partial differential equations is still at the very beginning although some algorithms for locating Hopf-bifurcation points have been published [Hassard and El-Henawy, 1981; Jensen and Ray, 1982; Nandapurkar and Hlavacek, 1984].”
Method
Backstepping für gekoppelte parabolische Systeme mit ortsabhängigen Koeffizienten
Deutscher, J., & Kerschbaum, S. (2018) · at - Automatisierungstechnik · doi:10.1515/auto-2018-0012 · Cited by 1
FIXED BED REACTOR DYNAMICS AND CONTROL – A REVIEW
Jørgensen, S. B. (1988) · Elsevier eBooks · doi:10.1016/b978-0-08-034917-6.50006-4 · Cited by 1
The Bifurcation Behavior of an Autothermal Packed Bed Tubular Reactor
Adomaitis, R. A., & Çınar, A. (1987) · doi:10.1109/acc.1987.4172566 · Cited by 1
Generation of oscillatory solutions in a porous catalyst pellet
Burghardt, A., & Berezowski, M. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(97)00021-3 · Cited by 1
Modelling of Pyrolytic Laser Direct-Writing from Thin Metalorganic Films
Price, P. E., & Jensen, K. F. (1988) · MRS Proceedings · doi:10.1557/proc-129-107 · Cited by 1
Self-citation
Multiplicity and Stability in Distributed-Parameter Systems (DPS)
Kubı́ček, M., & Marek, M. (1983) · Springer eBooks · doi:10.1007/978-3-642-85957-1_3 · Cited by 1
Modeling, Analysis and Control of Nonlinear Switching Systems
Kaisare, N. S. (2004) · SMARTech Repository (Georgia Institute of Technology) · Cited by 1
DYNAMICS OF A PACKED BED REACTOR WITH REACTANT RECYCLE
Brabrand, H., & Jørgensen, S. B. (1993) · Elsevier eBooks · doi:10.1016/b978-0-08-041711-0.50017-9 · Cited by 1
Multiplicity-Induced Oscillations in Porous Catalysts
Fiedler, B. (1985) · Springer series in synergetics · doi:10.1007/978-3-642-70332-4_6 · Cited by 1
PHYSICAL IMPLICATIONS OF PERIODIC SOLUTIONS IN A FIXED BED REACTOR WITH RECYCLE
Recke, B., & Jørgensen, S. B. (1995) · Elsevier eBooks · doi:10.1016/b978-0-08-042368-5.50037-x · Cited by 1
Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems
Utz, T., Graichen, K., & Kugi, A. (2013) · IFIP International Federation for Information Processing/IFIP · doi:10.1007/978-3-642-36062-6_30
“A large class of chemical reactors with an interaction of diffusive, convective, and reactive effects leads to infinite-dimensional mathematical models in the form of nonlinear boundary-controlled parabolic partial differential equations (PDEs) [6].”
Effects of spatial discretization errors on the steady-state multiplicity of a one-dimensional tubular reactor model with intraparticle transport
Hsuen, H.-K. (1996) · Chemical Engineering Science · doi:10.1016/0009-2509(96)00256-4
Zustandsschätzung für Rohrreaktoren mit Messungen am Reaktoraustritt (State Estimation for Tubular Reactors with Measurements at the Outlet only)
Gesthuisen, R., & Engell, S. (2000) · at - Automatisierungstechnik · doi:10.1524/auto.2000.48.10.505
New stability analysis based on iterative sampling and optimization
Ierapetritou, M., & Khinast, J. (2002) · AIChE Journal · doi:10.1002/aic.690480119
Steady-state constrained optimisation for input/output large-scale systems
Bonis, I., & Theodoropoulos, C. (2009) · Computer-aided chemical engineering/Computer aided chemical engineering · doi:10.1016/s1570-7946(09)70109-9
The Impact of Thermal Coupling on Catalyst Behavior in Wall-Coated Heat-Exchanger Microreactors
Honda, G. S. (2010) · OpenCommons - UConn (University of Connecticut)
Understanding oscillatory behaviour of gibbsite precipitation circuits
Bekker, A. V., Li, T. S., & Livk, I. (2014) · Chemeca 2014: Processing excellence; Powering our future
Análisis de la operación periódica en reactores químicos
Herver, T., & Elivira, D. (2015)
Adaptive Control Based on Passive Identifier for Uncertain Coupled Parabolic Equations
Li, J., & Xu, Z. (2019) · IEEE Access · doi:10.1109/access.2019.2960413
“The above equations can be viewed as a linearized Chemical Tubular Reactor model with constant parameters (see [1]–[3], [10]) whose control problems (such as stabilization) are of great practical importance in chemical reaction.”
Background
Estudios sobre cinética matemática y coeficientes de momentum y calor
Guevara, F. G. M. (2017) · doi:10.24275/uami.0v838058r
Model Predictive Control of Non-Isothermal Dispersive Chemical Tubular Reactors with Recycle Flow
Khatibi, S. (2020) · ERA: Education and Research Archive (University of Alberta) · doi:10.7939/r3-09n5-xc59
Split Iteration Technique to Determine Hopf Bifurcation Points
Liu, C., & Han, Y. (2024) · International Conference on Mathematics and Artificial Intelligence (ICMAI) · doi:10.1145/3670085.3670093
Efficient approximation of the Koopman operator for large-scale nonlinear systems
Verma, G., Heath, W. P., & Theodoropoulos, C. (2025) · Systems and Control Transactions · doi:10.69997/sct.169758
Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay
Moadeli, B., & Dubljevic, S. S. (2025) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.70189
Steam‐methane reforming on a Joule‐heated Ni/ ZrO 2 coated FeCrAl wire: Rate enhancement, support effects and multiplicity
Ledesma, E. B., Patel, D., & Harold, M. P. (2026) · AIChE Journal · doi:10.1002/aic.70618

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)
DOI: 10.1016/0009-2509(82)80155-3
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
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
www.elsevier.com/legal/tdmrep-license (tdm)
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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

The bifurcation behavior of tubular reactors

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks