Continuously stirred decanting reactor: Operability and stability considerations

Khinast, Johannes; Luss, Dan; Harold, Michael P.; Ostermaier, J.J.; McGill, Rebecca

doi:10.1002/aic.690440214

Cited by 12 publications

(9 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other reactors, such as two-phase decanting reactors, show a large Ž number of not-connected solution branches Harold et al, . 1996;Khinast et al, 1998 and it is not guaranteed that all the solution branches are found. Therefore, it would be advantageous to develop simple, not system-specific, methods based on random searches that are able to detect the various attractors in the parameter space.…”

Section: žmentioning

confidence: 97%

See 1 more Smart Citation

New stability analysis based on iterative sampling and optimization

Ierapetritou

Khinast

2002

AIChE Journal

View full text Add to dashboard Cite

Section: žmentioning

confidence: 97%

“…ferential equations Kubıcek and Holodniok, 1987 , numerical difficulties usually arise in its application to periodic systems described by a set of partial differential equations. Dynamics of periodically operated reactors were extensively an-Ž alyzed using methods developed by Khinast et al 1998Khinast et al , 1999Khinast et al , . 2000 .…”

Section: žmentioning

confidence: 99%

New stability analysis based on iterative sampling and optimization

Ierapetritou

Khinast

2002

AIChE Journal

View full text Add to dashboard Cite

“…Column 3 of Table 2 illustrates the types of bifurcation diagrams that exist at critical singular points on the various boundaries (HS, isola surface, or BLS) between the regions of the restricted parameter space. Columns 2 and 4 of Table 2 display the bifurcation diagrams obtained by universal unfolding of these hypersurfaces, with universal unfolding defined as perturbation away from the surface by a small change of a parameter other than l (8,31). Unfolding HS leads to two possible scenarios, either a monotonically dependent bifurcation diagram with no limit point, or a hysteretic loop type bifurcation diagram (bistability) with two limit points that coalesce on the critical hysteresis surface (HS).…”

Section: Bifurcation Diagrams Singularity Theory and Classification Diagramsmentioning

confidence: 99%

“…Further details of the equations and methods for calculation of steady-state singular points (8,31,69) are given here. The codimension-1 singularity termed a limit point is defined by the set of conditions fðx; lð¼ ½5-HTÞ; PÞ ¼ 0 Jðx; l; PÞ Á u ¼ 0 AEu; uae ¼ 1…”

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Bifurcation and Singularity Analysis of a Molecular Network for the Induction of Long-Term Memory

Song

Smolen

Av-Ron

et al. 2006

Biophysical Journal

View full text Add to dashboard Cite

Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis.

show abstract