Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Stabilization of parametric roll resonance with active u-tanks via Lyapunov control design

Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via simulation on a high-fidelity model of a vessel under parametric roll resonance.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Stability analysis of STATCOM in distribution networks

This chapter presents the stability analysis based on bifurcation theory of the distribution static compensator (DSTATCOM) operating both in current control mode as in voltage control mode. The bifurcation analysis allows delimiting the operating zones of nonlinear power systems and hence the computation of these boundaries is of interest for practical design and planning purposes. Suitable mathematical representations of the DSTATCOM are proposed to carry out the bifurcation analyses efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the Point of Common Coupling (PCC). In addition, the stability regions in the control gain space are computed, and the DC capacitor and AC capacitor impact on the stability are analyzed in detail. It is shown through bifurcation analysis that the loss of stability in the DSTATCOM is in general due to the emergence of oscillatory dynamics. The observations are verified through detailed simulation studies.

Analysis of impedance matched circuit for wireless power transfer

Typical wireless power transfer systems utilize series compensation circuit which is based on magnetic coupling and resonance principles that was first developed by Tesla. However, changes in coupling caused by gap distance, alignment and orientation variations can lead to reduce power transfer efficiencies and the transferred power levels. This paper proposes impedance matched circuit to reduce frequency bifurcation effect and improve on the transferred power level, efficiency and total harmonic distortion (THD) performance of the series compensation circuit. A comprehensive mathematical analysis is performed for both series and impedance matched circuits to show the frequency bifurcation effects in terms of input impedance, variations in transferred power levels and efficiencies. Matlab/Simulink results validate the theoretical analysis and shows the circuits’ THD performance when circuits are fed with power electronic converters.

Cooperative choice and its framing effect under threshold uncertainty in a provision point mechanism

This paper explores how threshold uncertainty affects cooperative behaviors in the provision of public goods and the prevention of public bads. The following facts motivate our study. First, environmental (resource) problems are either framed as public bads prevention or public goods provision. Second, the occurrence of these problems is characterized by thresholds that are interchangeably represented as "nonconvexity," "bifurcation," "bi-stability," or "catastrophes." Third, the threshold location is mostly unknown. We employ a provision point mechanism with threshold uncertainty and analyze the responses of cooperative behaviors to uncertainty and to the framing for each type of social preferences categorized by a value orientation test. We find that aggregate framing effects are negligible, although the response to the frame is the opposite depending on the type of social preferences. "Cooperative" subjects become more cooperative in negative frames than in positive frames, whereas "individualistic" subjects are less cooperative in negative frames than in positive ones. This finding implies that the insignificance of aggregate framing effects arises from behavioral asymmetry. We also find that the percentage of cooperative choices non-monotonically varies with the degree of threshold uncertainty, irrespective of framing and value orientation. Specifically, the degree of cooperation is highest at intermediate levels of threshold uncertainty and decreases as the uncertainty becomes sufficiently large.

Natural convection in a triangular enclosure heated from below and non-uniformly cooled from top

This study is concerned with transient natural convection in an isosceles triangular enclosure subject to non-uniformly cooling at the inclined surfaces and uniformly heating at the base. The numerical simulations of the unsteady flows over a range of Rayleigh numbers and aspect ratios are carried out using Finite Volume Method. Since the upper inclined surfaces are linearly cooled and the bottom surface is heated, the flow is potentially unstable. It is revealed from the numerical simulations that the transient flow development in the enclosure can be classified into three distinct stages; an early stage, a transitional stage, and a steady stage. The flow inside the enclosure depends significantly on the governing parameters, Rayleigh number and aspect ratio. The effect of Rayleigh number and aspect ratio on the flow development and heat transfer rate are discussed. The key finding for this study is to analyze the pitchfork bifurcation of the flow about the geometric center line. The heat transfer through the roof and the ceiling as a form of Nusselt number is reported in this study.

Effect of inflow and outflow angles on the computational hemodynamics in abdominal aortic aneurysm

To help with the clinical screening and diagnosis of abdominal aortic aneurysm (AAA), we evaluated the effect of inflow angle (IA) and outflow bifurcation angle (BA) on the distribution of blood flow and wall shear stress (WSS) in an idealized AAA model. A 2D incompressible Newtonian flow is assumed and the computational simulation is performed using finite volume method. The results showed that the largest WSS often located at the proximal and the distal end of the AAA. An increase in IA resulted in an increase in maximum WSS. We also found that WSS was maximal when BA was 90°. IA and BA are two important geometrical factors, they may help with AAA risk assessment along with the commonly used AAA diameter.

MRI-based fatigue analysis predicts plaque vulnerability: A study comparing symptomatic and asymptomatic individuals

BACKGROUND: Rupture of atheromatous plaque in the carotid artery often leads to thrombosis and subsequent stroke. The mechanism of plaque rupture is not entirely clear but is thought to be a multi-factorial process involving thinning and weakening of the fibrous cap and biomechanical stress as the trigger leading to plaque rupture. As the cardiovascular system is a classic fatigue environment, the weakening of plaque leading to rupture may be a fatigue process, which is a symptomatically quiescent but potentially progressive failure process. In this study, we used a fatigue analysis based on in vivo magnetic resonance imaging (MRI) to investigate the rupture initiation location, crack propagation path and fatigue life within plaques of asymptomatic and symptomatic individuals. METHODS: Forty non-consecutive subjects (20 symptomatic and 20 asymptomatic) underwent high-resolution multi-sequence in vivo MRI of the carotid bifurcation. Fatigue analysis was performed based on the plaque geometry derived from in vivo MRI of the carotid artery at the point of maximum stenosis. Paris’ Law in fracture mechanics is adopted to determine the fatigue crack growth rate. Incremental crack propagation was dynamically simulated based on stress distributions. Plaque initiation location, crack propagation path and fatigue cycle of symptomatic and asymptomatic individuals were compared. RESULTS: Cracks were often found to begin at the lumen wall at areas of stress concentration. The preferred rupture direction was radial from the lumen center. The crack initially advanced slowly but accelerated as it developed, depending on plaque morphology. The fatigue cycles of symptomatic plaques were significantly less than those in the asymptomatic group (2.3 ± 0.9 vs 3.1 ± 0.7 (x106); p = 0.003). CONCLUSIONS: The number of cycles to rupture in symptomatic patients was higher than those predicted in asymptomatic patients by fatigue analysis, suggesting the possibility that plaques with a less fatigue life may be more prone to be symptomatic and rupture. If further validated by large-scale longitudinal studies, fatigue analysis based on high resolution in vivo MRI could potentially act as a useful tool for risk assessment of carotid atheroma.

The mechanical triggers of plaque rupture: Shear stress vs pressure gradient

The aim of this study was to evaluate the mechanical triggers that may cause plaque rupture. Wall shear stress (WSS) and pressure gradient are the direct mechanical forces acting on the plaque in a stenotic artery. Their influence on plaque stability is thought to be controversial. This study used a physiologically realistic, pulsatile flow, two-dimensional, cine phase-contrast MRI sequence in a patient with a 70% carotid stenosis. Instead of considering the full patient-specific carotid bifurcation derived from MRI, only the plaque region has been modelled by means of the idealised flow model. WSS reached a local maximum just distal to the stenosis followed by a negative local minimum. A pressure drop across the stenosis was found which varied significantly during systole and diastole. The ratio of the relative importance of WSS and pressure was assessed and was found to be less than 0.07% for all time phases, even at the throat of the stenosis. In conclusion, although the local high WSS at the stenosis may damage the endothelium and fissure plaque, the magnitude of WSS is small compared with the overall loading on plaque. Therefore, pressure may be the main mechanical trigger for plaque rupture and risk stratification using stress analysis of plaque stability may only need to consider the pressure effect.

Study of reproducibility of human arterial plaque reconstruction and its effects on stress analysis based on multispectral in vivo magnetic resonance imaging

Purpose: To quantify the uncertainties of carotid plaque morphology reconstruction based on patient-specific multispectral in vivo magnetic resonance imaging (MRI) and their impacts on the plaque stress analysis. Materials and Methods: In this study, three independent investigators were invited to reconstruct the carotid bifurcation with plaque based on MR images from two subjects to study the geometry reconstruction reproducibility. Finite element stress analyses were performed on the carotid bifurcations, as well as the models with artificially modified plaque geometries to mimic the image segmentation uncertainties, to study the impacts of the uncertainties to the stress prediction. Results: Plaque reconstruction reproducibility was generally high in the study. The uncertainties among interobservers are around one or the subpixel level. It also shows that the predicted stress is relatively less sensitive to the arterial wall segmentation uncertainties, and more affected by the accuracy of lipid region definition. For a model with lipid core region artificially increased by adding one pixel on the lipid region boundary, it will significantly increase the maximum Von Mises Stress in fibrous cap (>100%) compared with the baseline model for all subjects. Conclusion: The current in vivo MRI in the carotid plaque could provide useful and reliable information for plaque morphology. The accuracy of stress analysis based on plaque geometry is subject to MRI quality. The improved resolution/quality in plaque imaging with newly developed MRI protocols would generate more realistic stress predictions.

Carotid arterial plaque stress analysis using fluid-structure interactive simulation based on in-vivo magnetic resonance images of four patients

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress (WTS) is usually recognized as a primary trigger for the rupture of vulnerable plaque. The present study used the in-vivo high-resolution multi-spectral magnetic resonance imaging (MRI) for carotid arterial plaque morphology reconstruction. Image segmentation of different plaque components was based on the multi-spectral MRI and co-registered with different sequences for the patient. Stress analysis was performed on totally four subjects with different plaque burden by fluid-structure interaction (FSI) simulations. Wall shear stress distributions are highly related to the degree of stenosis, while the level of its magnitude is much lower than the WTS in the fibrous cap. WTS is higher in the luminal wall and lower at the outer wall, with the lowest stress at the lipid region. Local stress concentrations are well confined in the thinner fibrous cap region, and usually locating in the plaque shoulder; the introduction of relative stress variation during a cycle in the fibrous cap can be a potential indicator for plaque fatigue process in the thin fibrous cap. According to stress analysis of the four subjects, a risk assessment in terms of mechanical factors could be made, which may be helpful in clinical practice. However, more subjects with patient specific analysis are desirable for plaque-stability study.

Structural analysis and magnetic resonance imaging predict plaque vulnerability: A study comparing symptomatic and asymptomatic individuals

Background: More than half of all cerebral ischemic events are the result of rupture of extracranial plaques. The clinical determination of carotid plaque vulnerability is currently based solely on luminal stenosis; however, it has been increasingly suggested that plaque morphology and biomechanical stress should also be considered. We used finite element analysis based on in vivo magnetic resonance imaging (MRI) to simulate the stress distributions within plaques of asymptomatic and symptomatic individuals. Methods: Thirty nonconsecutive subjects (15 symptomatic and 15 asymptomatic) underwent high-resolution multisequence in vivo MRI of the carotid bifurcation. Stress analysis was performed based on the geometry derived from in vivo MRI of the carotid artery at the point of maximal stenosis. The finite element analysis model considered plaque components to be hyperelastic. The peak stresses within the plaques of symptomatic and asymptomatic individuals were compared. Results: High stress concentrations were found at the shoulder regions of symptomatic plaques, and the maximal stresses predicted in this group were significantly higher than those in the asymptomatic group (508.2 ± 193.1 vs 269.6 ± 107.9 kPa; P = .004). Conclusions: Maximal predicted plaque stresses in symptomatic patients were higher than those predicted in asymptomatic patients by finite element analysis, suggesting the possibility that plaques with higher stresses may be more prone to be symptomatic and rupture. If further validated by large-scale longitudinal studies, biomechanical stress analysis based on high resolution in vivo MRI could potentially act as a useful tool for risk assessment of carotid atheroma. It may help in the identification of patients with asymptomatic carotid atheroma at greatest risk of developing symptoms or mild-to-moderate symptomatic stenoses, which currently fall outside current clinical guidelines for intervention.

Real-time wide-area loading margin sensitivity (WALMS) in power systems

Loading margin sensitivity (LMS) has been widely used in applications in the realm of voltage stability assessment and control. Typically, LMS is derived based on system equilibrium equations near bifurcation and therefore requires full detailed system model and significant computation effort. Availability of phasor measurement units (PMUs) due to the recent development of wide-area monitoring system (WAMS) provides an alternative computation-friendly approach for calculating LMS. With such motivation, this work proposes measurement-based wide-area loading margin sensitivity (WALMS) in bulk power systems. The proposed sensitivity, with its simplicity, has great potential to be embedded in real-time applications. Moreover, the calculation of the WALMS is not limited to low voltage near bifurcation point. A case study on IEEE 39-bus system verifies the proposed sensitivity. Finally, a voltage control scenario demonstrates the potential application of the WALMS.

Involvement of Ca2+-dependent hyperpolarization in sleep duration in mammals

The detailed molecular mechanisms underlying the regulation of sleep duration in mammals are still elusive. To address this challenge, we constructed a simple computational model, which recapitulates the electrophysiological characteristics of the slow-wave sleep and awake states. Comprehensive bifurcation analysis predicted that a Ca2+-dependent hyperpolarization pathway may play a role in slow-wave sleep and hence in the regulation of sleep duration. To experimentally validate the prediction, we generate and analyze 21 KO mice. Here we found that impaired Ca2+-dependent K+ channels (Kcnn2 and Kcnn3), voltage-gated Ca2+ channels (Cacna1g and Cacna1h), or Ca2+/calmodulin-dependent kinases (Camk2a and Camk2b) decrease sleep duration, while impaired plasma membrane Ca2+ ATPase (Atp2b3) increases sleep duration. Pharmacological intervention and whole-brain imaging validated that impaired NMDA receptors reduce sleep duration and directly increase the excitability of cells. Based on these results, we propose a hypothesis that a Ca2+-dependent hyperpolarization pathway underlies the regulation of sleep duration in mammals.