Bifurcation Model Research Articles

Research on the bifurcation approach for turbulent flows with rotation and curvature: effect of the base models

PurposeThis study aims to research the prediction performance of the bifurcation approach with different base models in different kinds of turbulent flows with rotation and curvature.Design/methodology/approachThe k−ω and Shear-Stress Transport (SST) k−ω models are modified by using the complete eddy viscosity coefficient expression, and the latter is modified by using two sets of model coefficients. The two bifurcation models were tested in three cases: rotating channel flow with system rotation, Taylor–Couette flow with wall rotation and curvature effect and swirling flow through an abrupt axisymmetric expansion with inlet swirling flow.FindingsIn these flows, the bifurcation approach can significantly improve the prediction performance of the base model in the fluctuation velocity. The deviation of the BSkO model is slightly superior to the BkO model by about 2% in the Taylor–Couette flow. The prediction effect of the root-mean-square (RMS) velocity of the BSkO model increases by about 4–5% as the number of grids increases about 2.37 times, and the best is the Large Eddy Simulation (LES) grid used. Finally, compared with the SST k−ω model, the average iteration time of the SST with curvature correction (SST-CC), bifurcation k−ω (BkO) and bifurcation SST k−ω (BSkO) models increased by 27.7%, 86.9% and 62.3%, respectively.Originality/valueThis study is helpful to understand further the application of the bifurcation method in the turbulence model.

Quantification of shunt fraction using contrast ultrasound and indicator dilution in an in vitro model

Transthoracic saline contrast echocardiography is commonly used to assess intrathoracic shunt flow in vivo. Though the technique has many advantages (safe, simple, repeatable), the measurement technique lacks specificity, and the contrast agent has limited stability. This study sought to determine if the indicator dilution modeling technique could be applied to ultrasound contrast data to quantify shunt fraction and to determine if buoyant force has a significant effect on microbubble pathway determination at a “vascular” bifurcation. A model of the pulmonary circuit was perfused with blood at three distinct flow rates (low, medium and high) over shunt fractions ranging from ∼2–10 %. The buoyancy effect on contrast was quantified using a simplified in vitro model of a vascular bifurcation that had an upper and lower outflow tract where saline contrast formed from carbon monoxide (CO) gas passed through the bifurcation, was collected and quantified. The indicator dilution model was found to have a mean bias of − 3.2 % for the low flow stage, − 2.6 % for the medium flow stage and − 1.4 % for the high flow stage compared to volumetric measurements, suggesting agreement increases with increasing flow rate. Investigations of the buoyant effects revealed that at lower flow rates, contrast bubbles that encounter a bifurcation will favor the upper outflow tract over the lower. However, this effect is reduced by increasing the flow rate two-fold. These data identify that application of indicator dilution theory to contrast ultrasound data and the pathway ultrasound contrast travels in a network of tubules is flow dependent.

Voltage Stability of Spacecraft Electric Power Systems for Deep Space Exploration

The future of deep space exploration requires high levels of reliability in critical subsystems such as the electrical power system. This paper provides an analysis of voltage stability of direct current (DC) microgrids for spacecraft applications. Bifurcation theory is used to determine the behavior of the system and identify the major causes of voltage instability. The analytical results of the bifurcation model are experimentally verified through a series of tests emulating probable operating conditions of the spacecraft. The findings of this paper are applicable to similar classes of islanded (grid forming) DC electric power systems including aerospace vehicles, shipboard systems, and terrestrial microgrids.

Hemodynamic Impact of Snoring on Carotid Artery after Stent Implantation: The Role of Oscillation

Purpose Snoring is common in overweight and old patients treated by endovascular stenting. Studies have proved a correlation between snoring and carotid stenosis, thus, snoring after carotid artery stenting (CAS) might promote or worsen clinical performance. Methods This study tested this hypothesis by constructing a patient-specific carotid bifurcation model and numerically analyzing hemodynamic changes of the carotid artery under different snoring conditions. These conditions included small and large amplitude, low and high frequency, and different age groups. Results The results found that high amplitude snoring suppressed the disturbed flow at the stented segment, while the downstream region of ICA became more chaotic, accounting for in-stent intimal restenosis and thrombosis. Furthermore, local blood flow patterns of elder groups with snoring symptoms were more likely to be changed due to low-speed flow, increasing the possibility of vascular remodeling and thrombosis. Besides, increased snoring frequency hardly influenced the local disturbed flow. Conclusions Therefore, older adults should receive medical treatment actively after stenting for high amplitude snoring as soon as possible to avoid potential adverse events.

Güçlü Allee Etkili Av-Avcı Modelinin Kararlılığı, Neimark-Sacker Çatallanma Analizi ve Kaos Kontrol

In this study, the dynamical behaviors of a prey–predator model with multiple strong Allee effect are investigated. The fixed points of the model are examined for existence and topological classification. By selecting as the bifurcation parameter $\beta$, it is demonstrated that the model can experience a Neimark-Sacker bifurcation at the unique positive fixed point. Bifurcation theory is used to present the Neimark-Sacker bifurcation conditions of existence and the direction of the bifurcation. Additionally, some numerical simulations are provided to back up the analytical result. Following that, the model's bifurcation diagram and the triangle-shaped stability zone are provided.

Simulation of LDL permeation into multilayer wall of a coronary bifurcation using WSS-dependent model: effects of hemorheology.

Atherosclerosis, due to the permeation of low-density lipoprotein (LDL) particles into the arterial wall, is one of the most common and deadly diseases in today's world. Due to its importance, numerous studies have been conducted on the factors affecting this disease. In this study, using numerical simulation, the effects of Wall Shear Stress (WSS), non-Newtonian behavior of blood, different values of hematocrit and blood pressure on LDL permeation into the arterial wall layers are investigated in a 4-layer wall model of a coronary bifurcation. To obtain the velocity and concentration fields in the fluid domain, the Navier-Stokes, Brinkman, and mass transfer equations are numerically solved in the lumen and wall layers. Results show that it is important to consider the effects of WSS on transport properties of endothelium layer in bifurcations and this leads to completely different concentration profiles compared to the constant properties model. Our computations show that a giant accumulation of LDL in the intima layer of the outer wall of the left anterior descending artery, especially in low WSS regions, may lead to atherosclerosis. It is also, necessary to consider the non-Newtonian behavior of blood in bifurcations due to its direct effect on WSS. A pressure-induced increase in the half-width of leaky junctions may be responsible for the higher risk of atherosclerosis in hypertension. In addition, it is shown that the dominant mechanism in LDL permeation into the wall is convection, and also, hypertension increases the effect of mass transfer by convection mechanism more than the diffusion mechanism. Furthermore, our results are consistent with various clinical studies.

Comparison of blood flow analysis in stenosed and stented carotid artery bifurcation models

Comparison of blood flow analysis in stenosed and stented carotid artery bifurcation models

Flow-based method demonstrates improved accuracy for calculating wall shear stress in arterial flows from 4D flow MRI data

Four-dimensional flow magnetic resonance imaging (i.e., 4D flow MRI) has become a valuable tool for the in vivo assessment of blood flow within large vessels and cardiac chambers. As wall shear stress (WSS) has been correlated with the development and progression of cardiovascular disease, focus has been directed at developing techniques to quantify WSS directly from 4D flow MRI data. The goal of this study was to compare the accuracy of two such techniques – termed the velocity and flow-based methods – in the setting of simplified and complex flow scenarios. Synthetic MR data were created from exact solutions to the Navier-Stokes equations for the steady and pulsatile flow of an incompressible, Newtonian fluid through a rigid cylinder. In addition, synthetic MR data were created from the predicted velocity fields derived from a fluid–structure interaction (FSI) model of pulsatile flow through a thick-walled, multi-layered model of the carotid bifurcation. Compared to the analytical solutions for steady and pulsatile flow, the flow-based method demonstrated greater accuracy than the velocity-based method in calculating WSS across all changes in fluid velocity/flow rate, tube radius, and image signal-to-noise (p < 0.001). Furthermore, the velocity-based method was more sensitive to boundary segmentation than the flow-based method. When compared to results from the FSI model, the flow-based method demonstrated greater accuracy than the velocity-based method with average differences in time-averaged WSS of 0.31 ± 1.03 Pa and 0.45 ± 1.03 Pa, respectively (p <0.005). These results have implications on the utility, accuracy, and clinical translational of methods to determine WSS from 4D flow MRI.

Time-Resolved Wall Shear Rate Mapping Using High-Frame-Rate Ultrasound Imaging.

In atherosclerosis, low wall shear stress (WSS) is known to favor plaque development, while high WSS increases plaque rupture risk. To improve plaque diagnostics, WSS monitoring is crucial. Here, we propose wall shear imaging (WASHI), a noninvasive contrast-free framework that leverages high-frame-rate ultrasound (HiFRUS) to map the wall shear rate (WSR) that relates to WSS by the blood viscosity coefficient. Our method measures WSR as the tangential flow velocity gradient along the arterial wall from the flow vector field derived using a multi-angle vector Doppler technique. To improve the WSR estimation performance, WASHI semiautomatically tracks the wall position throughout the cardiac cycle. WASHI was first evaluated with an in vitro linear WSR gradient model; the estimated WSR was consistent with theoretical values (an average error of 4.6% ± 12.4 %). The framework was then tested on healthy and diseased carotid bifurcation models. In both scenarios, key spatiotemporal dynamics of WSR were noted: 1) oscillating shear patterns were present in the carotid bulb and downstream to the internal carotid artery (ICA) where retrograde flow occurs; and 2) high WSR was observed particularly in the diseased model where the measured WSR peaked at 810 [Formula: see text] due to flow jetting. We also showed that WASHI could consistently track arterial wall motion to map its WSR. Overall, WASHI enables high temporal resolution mapping of WSR that could facilitate investigations on causal effects between WSS and atherosclerosis.

Air-entrained vortex in open intake: Time–frequency analysis and the interaction with subsurface vortices

In this paper, the simple coupled level-set and volume of fluid and bifurcation models are used for the accurate prediction of the flow in an open pump intake with a vertical pipe. The continuous wavelet transform, which is suitable for the vortex detection, is applied to the pressure signals near both air-entrained and subsurface vortices. Low-frequency with long duration for air-entrained vortex due to the vortex wandering and broadband with short duration for floor vortices (dominant in subsurface vortices) due to the generation of extreme strong vortex are observed. The vortex motion mechanism is revealed by the analysis of the transport equation of the vertical vorticity's enstrophy. Different from the previous results in which the tilting effect controls the vortex motion, the stretching effect is found to be dominating when it is large enough. When going through the bell mouth, the air-entrained vortex's vorticity changes the sign and strengthens the vortex with the same sign. On the plane near the bell mouth, three vortex patterns, including co-rotating pair, merging, and counter-rotating pair, are observed. The onset criterion of the vortex merging at a/b = 0.29–0.32 is found to be applicable to the present case. The counter-rotating pair is found to be more stable. Air-entrained vortex serves as an amplification of the strong vortices generated from the subsurface.

Numerical analysis of streaming potential induced by loads in micro-pores of articular cartilage

In order to understand the distribution of streaming potentials in cartilage pores, this paper established finite element model to analyze. The results showed that the streaming potential in cartilage micro-pores increased along the axis. The electric potential in 5 μm straight micro-pore was about 50 μV, and the electric potential of curved bifurcation model was about 30 μV. The pressure and Zeta potential had a linear growth relationship with the streaming potential. The streaming potential decreased with the increase of ion concentration until ion concentration was saturated. These results could provide a theoretical basis for cartilage research.

Generalized model for steady-state bifurcations without parameters in memristor-based oscillators with lines of equilibria

We demonstrate how the pitchfork, transcritical and saddle-node bifurcations of steady states observed in dynamical systems with a finite number of isolated equilibrium points occur in systems with lines of equilibria. The exploration is carried out by using the numerical simulation and linear stability analysis applied to a model of a memristor-based circuit. All the discussed bifurcation scenarios are considered in the context of models with the piecewise-smooth memristor current-voltage characteristic (Chua’s memristor), as well as on examples of oscillators with the memristor nonlinearity that is smooth everywhere. Finally, we compare the dynamics of ideal-memristor-based oscillators with the behavior of models taking into account the memristor forgetting effect. The presented results are obtained for electronic circuit models, but the studied bifurcation phenomena can be exhibited by systems with lines of equilibria of any nature.

EFFECTS OF SAND THERAPY ON FLUID DYNAMICS OF BLOOD IN THE POPLITEAL ARTERY BASED ON THE EULER MULTIPHASE MODEL

The effect of sand therapy on the hemodynamics of the popliteal artery (POA) was investigated to elucidate its mechanism in atherosclerosis physiotherapy. The hemodynamic parameters of the POA before and after sand therapy were obtained from 58 subjects and statistically analyzed. A three-dimensional finite element model of POA bifurcation was established. Blood was regarded as a triple-phase flow composed of plasma, red blood cells (RBCs), and white blood cells (WBCs). Using computational fluid dynamics (CFD), blood flow velocity, wall shear stress (WSS), and blood cell volume distribution before and after sand therapy were calculated. Sand therapy could reduce the vortex and reflux in blood vessels. The maximum increase in blood axial velocity was 34.38%. The maximum WSS increased by 22.82 Pa and the blood cells gradually moved away from the vessel wall and toward the axis of the blood vessel. The reduction in vortex and reflux, and the increase in blood axial velocity after sand therapy are beneficial in reducing the accumulation of cholesterol and other substances, thereby alleviating the formation of atherosclerotic plaques and lipid streaks. The rise in WSS slows the tendency of arterial vascular thickening in regions of low WSS. The movement of blood cells to the axis of blood vessels can reduce the possibility of thrombosis caused by blood cells squeezing on the blood vessel walls. These findings suggest that sand therapy may slow atherosclerosis progression.

Analysis of a Cournot-Bertrand Duoploy Game with Differentiated Products: Stability, Bifurcation and Control

this work, we investigate a Cournot-Bertrand duopoly model with product differentiation between two different firms, where one company uses price as a decision variable and the other uses quantity. The stability of the Nash equilibrium point is investigated, and the role of the parameters on the model stability is studied. It is shown that the system experiences three different types of bifurcations when the parameters go through the different boundary curves of the stability region. Furthermore, the model's bifurcation is controlled using a hybrid control strategy.

Influence of Altered Pressures on Flow Dynamics in Carotid Bifurcation System Using Numerical Methods

The application of numerical methods like CFD to understand hemodynamics in arteries has excellent potential to solve complex flow problems. In recent years, CFD has been primarily used in the hemodynamics of the carotid artery due to advances in computational resources. This technique is widely used to obtain knowledge on hemodynamics, predict the risk factors for the development and progression of the atherosclerotic lesion, and analyze local flow profiles due to changes in the carotid artery geometry. This fundamental study will be supportive in observing the blood flow behavior through arteries and studying arterial diseases. The present study investigates three different subject-specific carotid bifurcation models under altered blood pressure conditions. Subject-specific 3D carotid bifurcation modeling is carried out using Materialize software. Unsteady flow simulation is conducted in ANSYS Fluent under the rigid wall and Newtonian conditions. The haemodynamic parameters such as vorticity, helicity, and time-averaged wall shear stress (TAWSS) were evaluated to understand better the beginning and progression of atherosclerotic plaques in the bifurcation. Also, the influence of geometric variation in the bifurcation region was investigated, and it was observed that this region causes significant vortex formation zones. A noticeable reduction in velocity and backflow formation was observed, which reduced the shear stress. It is established that the regions of low TAWSS along the bifurcation region are likely to develop atherosclerosis.

Retrieval practice plus feedback benefits a third language vocabulary learning

ABSTRACT Three experiments explored how retrieval practice and corrective feedback affect a third language (L3) vocabulary learning. In the first two experiments, Chinese–English bilinguals without prior French language experience studied English (Second Language, L2)–French (L3) word pairs in repeated studying or retrieval practice without (Experiment 1)/with (Experiment 2) corrective feedback. A final recognition test was administered after a 30-min retention interval. Experiment 3 was identical to Experiment 2 in all respects, except that Chinese (First Language, L1)–French (L3) word pairs were used as study materials. Experiment 1 found that repeated studying led to greater accuracy and faster response time on the final test than retrieval practice without feedback. However, the opposite results were found in Experiment 2: retrieval practice with feedback yielded superior performance compared with repeated studying. The benefit of retrieval practice plus feedback was also found in Experiment 3, while it produced larger gains than Experiment 2. These results demonstrate that retrieval practice plus feedback is a powerful learning strategy, and L1–L3 learning is more effective than L2–L3 learning for L3 vocabulary learning. Our findings support the bifurcation model of the retrieval practice effect.

Transient wall shear stress estimation in coronary bifurcations using convolutional neural networks

Background and ObjectiveHaemodynamic metrics, such as blood flow induced shear stresses at the inner vessel lumen, are associated with the development and progression of coronary artery disease. Understanding these metrics may therefore improve the assessment of an individual’s coronary disease risk. However, the calculation of such luminal Wall Shear Stress (WSS) using traditional Computational Fluid Dynamics (CFD) methods is relatively slow and computationally expensive. As a result, CFD based haemodynamic computation is not suitable for integrated and large-scale use in clinical settings. MethodsIn this work, deep learning techniques are proposed as an alternative method to CFD, whereby luminal WSS magnitude can be predicted in coronary bifurcations throughout the cardiac cycle based on the steady state solution (which takes <120 seconds to calculate including preprocessing), vessel geometry and additional global features. The deep learning model is trained on a dataset of 101 patient-specific and 2626 synthetic left main bifurcation models with 26 separate patient-specific cases used as the test set. ResultsThe model showed high fidelity predictions with <5% (normalised against mean WSS magnitude) deviation to CFD derived values as the gold-standard method, while being orders of magnitude faster with on average <2 minutes versus 3 hours computation for transient CFD. ConclusionsThis method therefore offers a new approach to substantially reduce the computational cost involved in, for example, large-scale population studies of coronary haemodynamic metrics, and may therefore open the pathway for future clinical integration.

A comparison of Newtonian and non-Newtonian pulsatile blood rheology in carotid bifurcation through fluid–solid interaction hemodynamic assessment based on experimental data

Endothelial cells play a crucial role in the arterial homeostasis. In addition to physiological risk factors, abnormal levels of hemodynamic parameters induced by the pulsatile flow contribute to atherosclerotic plaque formation and development. In this study, we used an experimental setup to study the hemodynamics of Newtonian and non-Newtonian blood flow on a deformable model of human carotid bifurcation. The flow/pressure pulses of the experimental model were fed into a fluid–structure interaction numerical model, and respective hemodynamic parameters were obtained and compared between the two flow regimes. Results revealed noticeable differences among the two flow regimes when the pulsatile nature of blood flow and pressure were considered, with more distinct differences near junction sites. Velocity profiles of the non-Newtonian model were more flattened with higher back flow during the diastole. The shear stress waves as well as shear-dependent parameters, such as oscillatory shear index, relative residence time, and vorticity, as well as wall stress and strain, also indicated significant differences among the two models. Regardless of flow regime, results showed a good agreement with clinical outcomes in human carotid bifurcation, especially the carotid sinus. Near the bifurcation, marked fluctuations of shear stress are evident. Around the junction site, wall pulsation experienced variations up to five times of the normal pulse span. The quantified hemodynamic parameters obtained from proposed accurate model of carotid bifurcation may help to achieve technological solutions to adjust the out of biological ranges of these parameters, and avoid atheroma formation or treat the diseased artery.

Vortex formation and associated aneurysmogenic transverse rotational shear stress near the apex of wide-angle cerebral bifurcations.

Aneurysm formation preferentially occurs at the site of wide-angle cerebral arterial bifurcations, which were recently shown to have a high longitudinal positive wall shear stress (WSS) gradient that promotes aneurysm formation. The authors sought to explore the other components of the hemodynamic environment that are altered with increasing bifurcation angle in the apical region and the effects of these components on WSS patterns on the vessel wall that may modulate aneurysm genesis and progression. Parametric models of symmetrical and asymmetrical bifurcations were created with increasing bifurcation angles (45°-240°), and 3D rotational angiography models of 13 middle cerebral artery (MCA) bifurcations (7 aneurysmal, 6 controls) were analyzed using computational fluid dynamics. For aneurysmal bifurcations, the aneurysm was digitally removed to uncover hemodynamics at the apex. WSS vectors along cross-sectional planes distal to the bifurcation apex were decomposed as orthogonal projections to the cut plane into longitudinal and transverse (tangential to the cross-sectional plane) components. Transverse rotational WSS (TRWSS) and TRWSS gradients (TRWSSGs) were sampled and evaluated at the apex and immediately distal from the apex. In parametric models, increased bifurcation angle was associated with transverse flow vortex formation with emergence of an associated apical high TRWSS with highly aneurysmogenic positive TRWSSGs. While TRWSS decayed rapidly away from the apex in narrow-angle bifurcations, it remained greatly elevated for many radii downstream in aneurysm-prone wider bifurcations. In asymmetrical bifurcations, TRWSS was higher on the aneurysm-prone daughter vessel associated with the wider angle. Patient-derived models with aneurysmal bifurcations had wider angles (149.33° ± 12.56° vs 98.17° ± 8.67°, p < 0.001), with significantly higher maximum TRWSS (1.37 ± 0.67 vs 0.48 ± 0.23 Pa, p = 0.01) and TRWSSG (1.78 ± 0.92 vs 0.76 ± 0.50 Pa/mm, p = 0.03) compared to control nonaneurysmal bifurcations. Wider vascular bifurcations are associated with a novel and to the authors' knowledge previously undescribed transverse component rotational wall shear stress associated with a positive (aneurysmogenic) spatial gradient. The resulting hemodynamic insult, demonstrated in both parametric models and patient-based anatomy, is noted to decay rapidly away from the protection of the medial pad in healthy narrow-angle bifurcations but remain elevated distally downstream of wide-angle aneurysm-prone bifurcations. This TRWSS serves as a new contribution to the hemodynamic environment favoring aneurysm formation and progression at wide cerebral bifurcations and may have clinical implications favoring interventions that reduce bifurcation angle.

ЭМЕРДЖЕНТНЫЕ СВОЙСТВА ЭТНИЧЕСКОЙ СИСТЕМЫ

Objective of the study is to analyze the interrelationships of structural changes in the ethnosystem with the appearance of new emergent properties in the process of ethnogenesis. The methodological basis of the research is based on the conceptual provisions of the synergetic scientific direction, including modeling methods, principles of the theory of self-organization, nonlinear thinking using bifurcation, dissipative and other development models. Research results. It is shown that with a quasi-equilibrium state of the ethnic system, it is possible to track changes in the ethnic structure, predict its new emergent properties and development prospects. A theoretical description of the process of new qualities of the ethnosystem’s formation after the bifurcation point is impossible. Prospects of the study. The application of synergetic methods to the analysis of ethnogenesis processes will allow modeling the spectrum of possible trajectories of the ethnosystem development in order to design social management strategies aimed at minimizing the losses of the ethnosystem in a state of catastrophe.