Experimental Bifurcation Research Articles

Effect of wall friction on subharmonic bifurcations of impact in vertically vibrated granular beds

Granular materials consist of a large number of discrete solid particles. When subjected to external vibrations, they exhibit various intricate dynamical behaviors, Which usually depend in a complicated way on many physical factors, such as air dragging, friction from the container wall and so forth. In this work, vertical vibrations are applied to a bed of stainless-steel spheres contained in a glass tube, and the subharmonic bifurcations of impact of particles on the container bottom are investigated. To eliminate the effects of air dragging, we evacuate the container or perforate the container bottom to make it quite permeable to the air. Experiments performed in such containers reveal that the impact bifurcations are controlled solely by the normalized vibration acceleration, but independent of the particle size, the filling height of particles, and the frequency of forced vibration. The sliding friction from the container wall is treated as a constant one with the direction opposite to the velocity relative to the container wall. By involving this damping term into the completely inelastic bouncing ball model, an explanation for the experimental results is made. Simulations on the averaged experimental bifurcation points indicate that the magnitude of wall friction is about 10% of the total weight of the particles.

Stability and Feigenbaum’s Universality in Two Dimensional Chaotic Map

In this paper a two dimensional non linear map is taken whose period doubling dynamical behavior has been analyzed. The bifurcation points have been calculated numerically and have been observed that the map follows a universal behavior that has been proposed by Feigenbaum. With the help of experimental bifurcation points the accumulation point where chaos starts has been calculated. where a, b, r > 0. Murray(10,11) gave a special case of the above model taking a=b and it is noticed that the model is unrealistic in the sense that the solutions can grow unboundedly with t. Hone, Irle and Thurura(7) discussed some of the beautiful aspects of dynamical behavior of the above said model and they have suggested a more realistic model

Study on Nonlinear Friction-Induced Vibration in Water-Lubricated Rubber Stern Tube Bearings

Nonlinear friction-induced vibration deteriorated the performance of marine rubber stern tube bearings (RSTB) in a wide variety of propulsion system. In the paper, this study was performed on the level of both practical and experimental bifurcation analysis. Hereto, an experimental set-up of SSB-100 marine stern tube bearing test machine was applied to carry on this project. The synthesis of these practical and experimental results confirmed that nonlinear friction- induced vibration was due to a subtle balance of negative damping at lower speeds or viscous friction at higher speeds. Furthermore, it was shown how these essential friction characteristics depended on physical conditions such as temperature, normal forces and the material properties in the frictional contact.

E-019 Novel aneurysm neck reconstruction device: initial experience in an experimental pre-clinical bifurcation aneurysm model

IntroductionTreatment of wide necked bifurcation aneurysms often poses procedural and long-term outcome challenges. We describe the initial preclinical experience with the Pulsar Vascular Aneurysm Neck Reconstruction Device (PVANRD) in a...

Novel aneurysm neck reconstruction device: initial experience in an experimental preclinical bifurcation aneurysm model

IntroductionTreatment of wide-necked bifurcation aneurysms often poses procedural and long-term outcome challenges. The initial preclinical experience with the Pulsar Vascular Aneurysm Neck Reconstruction Device (PVANRD) in a canine bifurcation model...

Flow diverters failing to occlude experimental bifurcation or curved sidewall aneurysms: an in vivo study in canines

Flow diverters (FDs) are increasingly used to treat complex intracranial aneurysms, but preclinical studies that could guide clinical applications are lacking. The authors designed a modular aneurysm model in canines to address this problem. Three variants of one modular aneurysm model were constructed in 21 animals. Sidewall (n=5), curved sidewall (n=5), and end-wall bifurcation (n=7) aneurysms were treated with prototype 36-wire FDs. Four more end-wall bifurcation aneurysms were treated with prototype 48-wire lower-porosity FDs. Angiographic results postimplantation and at 3 months were scored with an ordinal scale. Animals were euthanized at 3 (n=17) or 6 (n=3) months, and the FD covering the aneurysm ostium was photographed to analyze metallic porosity and amount of neointima formation. Straight sidewall aneurysms were better occluded than curved sidewall and end-wall bifurcation aneurysms at the 3-month angiography follow-up (p=0.010). Flow diverters failed to occlude curved sidewall aneurysms (n=0/5) and all but one (n=1/7) end-wall bifurcation aneurysm. Angiographic results were no better (n=0/4) using a 48-wire FD (p=0.788). Branches jailed by the FD (n=16) remained patent in all cases. Metallic porosity was decreased (p=0.014) and neointimal closure of the aneurysm ostium was more complete (p=0.040) in sidewall aneurysms than in curved or bifurcation variants of the model. Flow diverters may succeed in treating straight sidewall aneurysms, but the same device repeatedly fails to occlude curved sidewall and end-wall bifurcation aneurysms. In vivo studies can be designed to test basic principles that, once validated, may serve to guide clinical use of new devices.

An experimental study of discharge partitioning and flow structure at symmetrical bifurcations

ABSTRACTRecent research has examined the factors controlling the geometrical configuration of bifurcations, determined the range of stability conditions for a number of bifurcation types and assessed the impact of perturbations on bifurcation evolution. However, the flow division process and the parameters that influence flow and sediment partitioning are still poorly characterized. To identify and isolate these parameters, three‐dimensional velocities were measured at 11 cross‐sections in a fixed‐walled experimental bifurcation. Water surface gradients were controlled, and systematically varied, using a weir in each distributary.As may be expected, the steepest distributary conveyed the most discharge (was dominant) while the mildest distributary conveyed the least discharge (was subordinate). A zone of water surface super‐elevation was co‐located with the bifurcation in symmetric cases or displaced into the subordinate branch in asymmetric cases. Downstream of a relatively acute‐angled bifurcation, primary velocity cores were near to the water surface and against the inner banks, with near‐bed zones of lower primary velocity at the outer banks. Downstream of an obtuse‐angled bifurcation, velocity cores were initially at the outer banks, with near‐bed zones of lower velocities at the inner banks, but patterns soon reverted to match the acute‐angled case. A single secondary flow cell was generated in each distributary, with water flowing inwards at the water surface and outwards at the bed. Circulation was relatively enhanced within the subordinate branch, which may help explain why subordinate distributaries remain open, may play a role in determining the size of commonly‐observed topographic features, and may thus exert some control on the stability of asymmetric bifurcations. Further, because larger values of circulation result from larger gradient disadvantages, the length of confluence–diffluence units in braided rivers or between diffluences within delta distributary networks may vary depending upon flow structures inherited from upstream and whether, and how, they are fed by dominant or subordinate distributaries. Copyright © 2011 John Wiley & Sons, Ltd.

Topological similarities in electrical and hydrological drainage networks

Under an electric field, spherical conducting particles in a dielectric liquid assemble into a dendritic tree in order to dissipate charge. Several topological measures characterize such networks, including degree distributions, Strahler numbers, and total external pathlengths. Here, scaling laws relating these measures to the number of nodes in the system are presented and shown to match diffusion limited aggregation (DLA) structures. Experimental bifurcation and stream-length ratios in this easily reproducible laboratory experiment are found to agree with DLA simulations and Horton’s laws for river networks. Certain scaling relations in transportation networks are known to originate from general features of networks. Here we find the experimental structures share properties with hydrological drainage networks.

Experimental bifurcation diagram of a circuit-implemented neuron model

An experimental bifurcation diagram of a circuit implementing an approximation of the Hindmarsh–Rose (HR) neuron model is presented. Measured asymptotic time series of circuit voltages are automatically classified through an ad hoc algorithm. The resulting two-dimensional experimental bifurcation diagram evidences a good match with respect to the numerical results available for both the approximated and original HR model. Moreover, the experimentally obtained current–frequency curve is very similar to that of the original model. The obtained results are both a proof of concept of a quite general method developed in the last few years for the approximation and implementation of nonlinear dynamical systems and a first step towards the realisation in silico of HR neuron networks with tunable parameters.

Experimental bifurcations and chaos in a modified self-sustained macro electromechanical system

A class of self-sustained Macro ElectroMechanical (MaEMS) Systems is made up of a Rayleigh–Duffing oscillator actuating a mechanical arm through a magnetic coupling. In this paper, to avoid experimental constraints, an audio amplifier is added to the device. Quenching phenomenon, bifurcation and chaos are predicted and shown to occur in a device of this class of MaEMS. Especially by using linear stability analysis, the condition for the quenching phenomenon is derived. Chaos and bifurcation are predicted using Lyapunov exponent and bifurcation diagram. A prototype of device is designed and fabricated. Experimental results for this device that are consistent with results from theoretical investigations are presented and convincingly show quenching phenomenon, bifurcation and chaos.

Dynamically stable, self-similarly evolving, and self-organized states of high beta tokamak and reversed pinch plasmas and advanced active control

Generalized simultaneous eigenvalue equations derived from a generalized theory of self-organization are applied to a set of simultaneous equations for two-fluid model plasmas. An advanced active control by using theoretical time constants is proposed by predicting quantities to be controlled. Typical high beta numerical configurations are presented for the ultra low q tokamak plasmas and the reversed-field pinch (RFP) ones in cylindrical geometry by solving the set of simultaneous eigenvalue equations. Improved confinement with no detectable saw-teeth oscillations in tokamak experiments is reasonably explained by the shortest time constant of ion flow. The shortest time constant of poloidal ion flow is shown to be a reasonable mechanism for suppression of magnetic fluctuations by pulsed poloidal current drives in RFP experiments. The bifurcation from basic eigenmodes to mixed ones deduced from stability conditions for eigenvalues is shown to be a good candidate for the experimental bifurcation from standard RFP plasmas to their improved confinement regimes.Generalized simultaneous eigenvalue equations derived from a generalized theory of self-organization are applied to a set of simultaneous equations for two-fluid model plasmas. An advanced active control by using theoretical time constants is proposed by predicting quantities to be controlled. Typical high beta numerical configurations are presented for the ultra low q tokamak plasmas and the reversed-field pinch (RFP) ones in cylindrical geometry by solving the set of simultaneous eigenvalue equations. Improved confinement with no detectable saw-teeth oscillations in tokamak experiments is reasonably explained by the shortest time constant of ion flow. The shortest time constant of poloidal ion flow is shown to be a reasonable mechanism for suppression of magnetic fluctuations by pulsed poloidal current drives in RFP experiments. The bifurcation from basic eigenmodes to mixed ones deduced from stability conditions for eigenvalues is shown to be a good candidate for the experimental bifurcation from stand...

Angiographic and artefact-free computed tomography imaging of experimental aneurysms embolised with hydrogel filaments

We compared experimental rabbit carotid bifurcation aneurysms embolised with platinum coils or hydrogel filaments by using digital subtraction angiography (DSA) and computed tomography angiography (CTA). Embolisation was performed using platinum coils (n = 2), hydrogel filaments loaded with iodine (n = 3) and hydrogel filaments loaded with barium sulphate (n = 3). In one case, a stent was deployed in the parent vessel to determine the effect of hydrogel filaments on stent visualisation. DSA evaluations occurred immediately post-treatment. CTA evaluations occurred at 0-13 weeks post-treatment. The DSA and CTA images were evaluated for the lack of artefacts and the visibilities of the embolic mass, individual coils and residual flow in the aneurysm sac and neck. The DSA results were largely concordant among the three groups. The embolic masses were readily evident with some individual coils being distinguished. In the aneurysms embolised with hydrogel filaments, visualisation of the individual coils, residual flow and stent with minor or no artefacts was possible using CTA. On the other hand, the beam hardening artefacts precluded analysis of aneurysms embolised with platinum coils. CTA-compatible embolic devices could have wide applications in diverse locations throughout the vasculature, particularly in combination with stents or stent grafts.

TREATMENT OF EXPERIMENTAL ANEURYSMS WITH AN EMBOLIC-CONTAINING DEVICE AND LIQUID EMBOLIC AGENT

To assess the feasibility and analyze angiographic and histological results of experimental aneurysms treated with an embolic-containing device (ECD) and to test a liquid embolic agent (LEA), N-butyl cyanoacrylate. Four experimental large bifurcation aneurysms and 1 large sidewall aneurysm were created in 5 dogs. These venous pouch aneurysms were occluded endosaccularly with an ECD and N-butyl cyanoacrylate. Angiographic and/or histopathological data were analyzed at 1 day (bifurcation), 1 week (bifurcation), 4 months (sidewall), 6 months (bifurcation), and 12 months (bifurcation). Aneurysm dimensions were 16 to 18 mm in length, 6 to 8 mm in width, and a neck measuring 6 to 8 mm. Immediately after the procedure, 2 of 4 bifurcation aneurysms were 100% occluded. In one case, glue had spilled into the parent artery. One occluded aneurysm recanalized at 6 months. One occluded aneurysm remained closed at 12 months. Histopathological analysis of the 6- and 12-month specimens showed adherence of glue to the aneurysm wall, no appreciable inflammatory response to the ECD, and aneurysm wall fibrosis with adventitial chronic inflammation. The aneurysm necks were covered by neointima with the presence of endothelialization. Within the limitations of this experimental study, treatment of large, wide-necked aneurysms with the ECD and LEA may be feasible. Suboptimal technique and ECD geometry can cause leakage of LEA into the parent vessel or incomplete apposition of the ECD/glue to the aneurysm wall. However, the ECD and glue injection technique did achieve complete occlusion in 1 aneurysm that persisted 1 year later. The histopathological findings in this instance are moderately encouraging. Further investigations of an ECD with N-butyl cyanoacrylate or another LEA are warranted.

Experimental bifurcations and homoclinic chaos in a laser with a saturable absorber

The shape and the peak values of the pulses from a passive Q-switching CO2 laser with SF6 as saturable absorber were detected while the laser was tuned in frequency across a longitudinal mode. A succession of stability windows, typical for bifurcation diagrams in the homoclinic scenario, was observed and the widths of those windows were measured. The expansion rate of the undulations in individual pulses was also obtained and compared to Floquet's multipliers given by the ratio of widths in consecutive windows. The dynamics is consistent with a homoclinic tangency to a periodic orbit.

Interval Change in Size of Venous Pouch Canine Bifurcation Aneurysms over a 10-Month Period

The natural history study of experimental aneurysms is important for the evaluation of new endovascular occlusion devices. Our purpose was to evaluate the natural history of experimental venous pouch bifurcation aneurysms in mongrel dogs up to a 10-month period. Serial digital subtraction angiography was performed in 5 bifurcation aneurysms 1, 4, 7, and 10 months after surgical creation. Aneurysm dimensions, including height, width, and neck diameter, and animal body weights were measured. Comparisons of each parameter were performed using the Friedman test and the paired Wilcoxon signed-rank test. Four of 5 aneurysms were patent during a 10-month follow-up period. One aneurysm was regarded as a partially thrombosed aneurysm at 1 month, though the extent of partial thrombosis lessened at 10 months. Bifurcation aneurysms progressively increased in size (aneurysm height, width, and neck diameter) during the first several months. If this experimental model is used to evaluate new endovascular devices for cerebral aneurysm treatment, investigators should be aware of early progressive aneurysm enlargement.

THE BIFURCATION STRUCTURE OF FIRING PATTERN TRANSITIONS IN THE CHAY NEURONAL PACEMAKER MODEL

Different transitions of neuronal firing patterns are explored by the combination of experimental results, numerical simulation and bifurcation analysis. Three types of firing sequences with respect to extracellular calcium concentration ([ Ca 2+] o ) were observed in experiments on neural pacemakers. In accordance with them, the corresponding transitions of neuronal firing patterns are surveyed by standard bifurcation analysis of the Chay model, where λn corresponds to different nerve fibers and VC is the dynamical parameter. The results are listed in this paper. Firstly, it is obtained that the transitions of periodic firing patterns from period-1 bursting to period-1 spiking without any bifurcation, from period-1 to -2 to -1 through a pair of period-doubling bifurcations and from period-1 to -2 to -1 through two pairs of period-doubling bifurcations. Secondly, one supercritical and two subcritical period-doubling bursting sequences with different appearances lead to chaos, respectively. Then the former transits directly to an inverse supercritical period-doubling spiking sequence via chaos, and the latter transit to it through the period-adding bursting sequences from period-1 to -3 and from -1 to -5 with chaotic bursting, respectively. Thirdly, we reveal the true nature of period-adding bursting sequence without chaotic bursting. Every periodic bursting is closely related to two period-doubling bifurcations of the corresponding periodic spiking, except for period-1 bursting appearing via Hopf bifurcation and disappearing via period-doubling bifurcation. As a consequence, the period-adding bursting sequence without chaotic bursting has a compound structure of elementary bifurcations with transitions from spiking to bursting. Thus period-adding bifurcation without chaos cannot be regarded as a new elementary bifurcation.

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.

Experimental bifurcation diagram of a solid state laser with optical injection

A method is presented for the automatic construction of an experimental bifurcation diagram of an optically injected solid state laser. From measured time series of laser output intensity, different identifiers of aspects of the dynamics are derived. Combinations of these identifiers are then used to characterize different possible bifurcations. The resulting experimental bifurcation diagram in the plane of injection strength versus detuning includes saddle-node, Hopf, period-doubling and torus bifurcations. It is shown to agree well with a theoretical bifurcation analysis of a corresponding rate equation model.

Assessment of Matrix coils in a canine model of a large bifurcation aneurysm

Controversy exists as to whether Matrix coils are an improvement over bare platinum coils in preventing aneurysm recanalization in endosaccularly coiled large aneurysms. We investigated Matrix coils in a dog model of a wide-necked large bifurcation aneurysm. Six experimental aneurysms were created in dogs and these aneurysms were endosaccularly coiled with 100% Matrix coils. Angiographic and histopathological data were analyzed at 2 weeks and at 3 months. Average aneurysm dimensions were length 17.8 mm, width 8.3 mm, and neck 6.2 mm. Aneurysm coil filling ranged 24.1-41.8% by volume. At 14 days, three of six Matrix-treated aneurysms showed coil compaction and aneurysm recanalization. At 3 months, one additional Matrix-treated aneurysm showed delayed coil compaction and aneurysm recanalization. At 3 months, in three harvested aneurysms, the average measured neck neointima was 0.150 +/- 0.14 mm. However, in two of the three aneurysms harvested at 3 months, aneurysm recanalization had occurred with neointimal tissue not completely covering the aneurysm orifice. Thick connective fibrous intercoil tissue was observed. No immediate or delayed thrombus formation had occurred. Based on limited data in an experimental bifurcation aneurysm in dogs, Matrix coils appear to induce a thicker aneurysm neck neointima tissue and intercoil granulation response but appear prone to coil compaction and aneurysm recanalization. Modifications to the Matrix coil are likely needed to improve angiographic results in large aneurysms.

Friction-induced limit cycling in flexible rotor systems: An experimental drill-string set-up

Friction-induced limit cycling deteriorates system performance in a wide variety of mechanical systems. In this paper, we study the way in which essential friction characteristics affect the occurrence and nature of friction-induced limit cycling in an experimental drill-string set-up. This study is performed on the level of a Lyapunov-based stability analysis and on the level of both numerical and experimental bifurcation analyses. The synthesis of these results confirms that friction-induced limit cycling is due to a subtle balance between negative damping at lower velocities and viscous friction at higher velocities. Moreover, it is shown how these essential friction characteristics depend on physical conditions such as temperature and normal forces in the frictional contact in the experimental set-up.