Experimental Bifurcation Research Articles

Endovascular Coil Embolization of Microsurgically Produced Experimental Bifurcation Aneurysms in Rabbits

Background Endovascular treatment of cerebral aneurysms is a relatively new method, since only a few animal models and data are available. The present experimental study was performed in order to establish an appropriate aneurysm animal model, to determine the rate of permanent occlusion, and to correlate radiologic and morphologic findings. Methods End-to-side anastomoses of both common carotid arteries were performed microsurgically in 53 chinchilla rabbits. Venous pouches were adapted into the newly created bifurcation, resulting in berry-shaped aneurysms comparable to those in humans with regard to size and hemodynamics. Platinum and tungsten coils were used for endovascular embolization. The embolized aneurysms were investigated radiologically and morphologically. Results Twenty-three carotid bifurcation aneurysms remained for testing endovascular therapeutic approaches. The morphologic examinations of 13 embolized aneurysms revealed in no instance a complete obliteration, even in the three cases that were considered completely embolized according to angiographic criteria. Conclusions The present animal model is an optimal tool for endovascular research. Analysis of the results of coil obliteration revealed a considerable discrepancy between radiologic and pathologic findings. The radiologic degree of aneurysm occlusion was overestimated.

NO Reduction by CO over a Pt/Al2O3 Catalyst: Reaction Kinetics and Experimental Bifurcation Behavior

The kinetic behavior of NO reduction by CO over a Pt/Al2O3 catalyst has been investigated in the temperature range of 465−520 K. The NO + CO reaction exhibits isothermal steady-state multiplicity. A high-conversion steady state was obtained starting with a net oxidizing feed composition ([NO]0 > [CO]0), and a low-conversion steady state was obtained for a net reducing initial feed composition ([NO]0 < [CO]0). A significant amount of N2O was observed as a reaction product, particularly for the high-conversion steady states. The selectivity toward N2O decreased with increasing NO conversion. For the high-conversion steady states, the N2O selectivity decreased rapidly with a decrease in the feed [NO]0/[CO]0 ratio below a critical value of 1.5. The N2O + CO reaction was found to occur to a significant extent. The steady-state bifurcation behavior has been used to discriminate among three kinetic models.

Reduction of detailed kinetic mechanisms for ignition and extinction of premixed hydrogen/air flames

A new method is proposed to reduce complex kinetic mechanisms to a few elementary reaction steps which predict accurately ignitions and extinctions of spatially distributed systems. This method combines principal component analysis with sensitivity analysis and is applied to the stability of premixed hydrogen/air flames near surfaces using numerical bifurcation theory. The full mechanism of 40 reactions of hydrogen/air flames is reduced to various elementary mechanisms which can predict ignition and extinction temperatures at atmospheric pressure with a maximum error of ∼ 0.3 and 3%, respectively. The quasisteady-state approximation of all species near critical points is examined, and the mechanisms leading to instabilities are discussed as a function of reactor pressure. This analysis leads to only three reactions whose rates are linear combinations of five elementary reactions. It is shown that some fast reactions do not affect critical points. In addition, elimination of slow initiation reactions results in change of an ignition from a turning point to a transcritical bifurcation point. Analytical criteria for ignition and extinction are also proposed. Using these criteria, the accuracy in estimating kinetic parameters from experimental bifurcation data is assessed.

An experimental study of bifurcation, chaos, and dimensionality in a system forced through a bifurcation parameter

An experimental study of a system that is parametrically excited through a bifurcation parameter is presented. The system consits of a lightly-damped, flexible beam which is buckled and unbuckled magnetically: it is parametrically excited by driving an electromagnet with a low-frequency sine wave. For voltage amplitudes in excess of the static bifurcation value, the beam slowly switches between the one-and two-well configurations. Experimental static and dynamic bifurcation results are presented. Static bifurcatons for the system are shown to involve a butterfly catastrophe. The dynamic bifurcation diagram, obtained with an automated data acquisition system, shows several period-doubling sequences, jump phenomena, and a chaotic region. Poincare sections of a chaotic steady-state are obtained for various values of the driving phase, and the correlation dimension of the chaotic attractor is estimated over a large scaling region. Singular system analysis is used to demonstrate the effect of delay time on the noise level in delay-reconstructions, and to provide an independent check on the dimension estimate by directly estimating the number of independent coordinates from time series data. The correlation dimension is also estimated using the delay-reconstructed data and shown to be in good agrement with the value obtained from the Poincare sections. The bifurcation and dimension results are used together with physical sonsiderations to derive the general form of a single-degree-of-freedom model for the experimental system.

Experimental bifurcation analysis of the cobalt/phosphoric acid electrochemical oscillator

The dynamical behaviour of the I-E polarization curves of the Co 1 M H 3PO 4 electrochemical oscillator is studied as the potential varies across the active/passive transition of the Co electrode. An oscillatory potential region exists between the two stable steady-states where a hysteresis loop is formed by the sudden decrease (Co passivation) and increase (Co activation) of the current as the potential is scanned forward and backward. In the present study an attempt is made towards an experimental determination of the bifurcation structure of the Co 1 M H 3PO 4 system. Transition from the active steadystate (SS1) to the oscillatory state (OSC), and vice versa, is accompanied by a hysteresis and occurs at critical potential values via a generalised Hopf bifurcation. The identification of the generalised Hopf bifurcation is based on the presence of hysteresis, the sudden appearance of full amplitude oscillations during the transition SS1 → OSC and on the fact that the transition OSC → SS1 occurs with oscillations of a finite amplitude. On the other side of the loop, transition from the oscillatory region to the passive steady-state (SS2) goes via a saddle-type bifurcation. The period lengthening during the transition OSC → SS2, the existence of small hysteresis and the fact that oscillations appear and disappear with almost their full amplitude ensure a saddle-type bifurcation. Some of the bifurcation features are discussed on the basis of the surface processes taking place at the Co electrode and compared with the Fe 2 M H 2SO 4 electrochemical oscillator that was previously investigated. Potential and current perturbation experiments applied close to bifurcation points indicate that the Co 1 M H 3PO 4 system does not exhibit excitability in the corresponding regions where Fe 2 M H 2SO 4 does. Micrographs taken by the scanning electron microscope and examination of the chloride effect on the dynamical behaviour of the Co 1 M H 3PO 4 system support further the relation between the experimental findings and the mechanism leading to the non-linear behaviour across the active-passive transition.

Bifurcation diagrams of the heterogeneous catalytic oxidation of methanol

The experimental bifurcation diagrams of the heterogeneous catalytic oxidation of methanol on Pd have been determined by changing the concentration of methanol or oxygen in the feed. Hopf bifurcations have been obtained.

Modeling periodic and chaotic dynamics in anodic nickel dissolution

A systematic approach for modeling and parameters estimation of the motions andsingularities observed in anodic nickel dissolution in sulfuric acid is presented. The observed and modeled behaviors include bistability, periodic oscillations bounded by Hopf and saddle loop bifurcations, the disappearance of these transitions ina double-zero singularity, and the existence of chaotic solutions which are bounded by a period-doubling transition. The modeling and parameter estimation are based on comparison of the experimental and simulated bifurcation maps, showing domains of different characteristic behaviors in the plane of applied constant current vs acid concentration

Dynamics of the heterogeneous catalytic oxidation of ethanol—I. Analysis of experimental bifurcation diagrams

Experimental bifurcation diagrams for the heterogeneous catalytic oxidation of ethanol on a supported palladium catalyst are presented, depending on the oxygen or the ethanol content in the feed as control parameters. The identification of the bifurcations leads to a proposal for the formal construction of a mathematical model following Sheintuch and Luss (1985, Chem. Engng Sci. 40, 1653–1664; 1987a, Chem. Engng Sci. 42, 41–52; 1987b, Chem. Engng Sci. 42, 233–243). The identification of a global Hopf bifurcation in the experimental system requires an extension of their model.

Application of the feedback-induced bifurcation method to a catalytic reaction system

The feedback-induced bifurcation method has been examined as applied to CO oxidation on RhAl 2O 3. Experimental Hopf bifurcation data obtained from operation of the reaction system under feedback control based on measurement of the gas-phase concentration of CO was reproduced by two reaction models. However, a clear distinction between the Hopf bifurcation behavior of the two models was identified when the feedback control was based on the fractional coverage of a surface carbonyl species. Higher-order dynamics resulting from closed-loop operation of the reaction system were also observed. The usefulness of various types of experimental feedback-induced bifurcations as applied to model development is discussed.

Intentional manipulation of closed-loop time delay for model validation using feedback-induced bifurcation

Hopf bifurcation of a simple isothermal stirred tank without reaction is possible through the introduction of time-delayed feedback. By manipulating the time delay and a single feedback gain as bifurcation parameters, sensitive experiments were performed to test the validity of a model that describes the dynamic behavior of the combined components in an experimental gas-phase reactor flow system. Experimental bifurcations to sustained oscillations show that the stability of the reactor system is strongly influenced by delay. The relationships of time delay to Hopf bifurcation gains and frequencies provide a very sensitive basis for model comparisons. These type of comparisons are used to demonstrate the accuracy of the proposed model for the experimental system. The effect of noise and data sampling rate are then investigated by numerical simulation with the model. The complete model is necessary for analyzing bifurcation experiments including the effects of catalytic reaction.

EXPERIMENTAL INVESTIGATIONS USING FEEDBACK-INDUCED BIFURCATION: CARBONMONOXIDE OXIDATION OVER SUPPORTED SILVER

The use of feedback-induced bifurcation experiments for discriminating between rival models for the CO-02 reaction over supported silver is investigated. Model parameters are estimated or bounded by fitting the postulated kinetic mechanisms to steady-state and transient step-response data. Experimental steady-state bifurcation data is accurately reproduced by the models but each model fails to simulate adequately the Hopf bifurcation results. The dynamic bifurcation results are found to be sensitive to small time-scale dynamics that could not be resolved from the step-response experiments. Long transients in the catalyst activity are observed that cannot be reproduced by the kinetic models.

Experimental investigation of controller-induced bifurcation in a fixed-bed autothermal reactor

“Snap-through” Hopf bifurcations are induced in a laboratory autothermal reactor by the destabilizing effects of a single proportional controller. These unexpected and dramatic phenomena are predicted a priori by a bifurcation analysis of the model equations with the controller gain as the bifurcation parameter. The experimental bifurcation data are used in a parameter estimation study which yields an extremely accurate dynamic model for the nonlinear system.

Experimental bifurcation defects in dogs

This study utilizes andf experimental model in beagle dogs in which chronic bifurcation defects are induced by passing a round bur through the denuded bifurcations of the premolars in the lower jaw (Ellegaard et al. 1973). Immediate spontaneous healing was avoided by inserting a steel wire through the created bifurcation defects. The wire was ligated over the crown and left in place for six weeks. A split mouth technique was used in order to compare the furcation lesions at two and nine months after creation. Histological observations and meansurements indicate that chronic lesions with characteristics similar to those in man were obtained.