Asymmetric Bifurcation Research Articles

Partitioning of dense RBC suspensions in single microfluidic bifurcations: role of cell deformability and bifurcation angle

Red blood cells (RBCs) are a key determinant of human physiology and their behaviour becomes extremely heterogeneous as they navigate in narrow, bifurcating vessels in the microvasculature, affecting local haemodynamics. This is due to partitioning in bifurcations which is dependent on the biomechanical properties of RBCs, especially deformability. We examine the effect of deformability on the haematocrit distributions of dense RBC suspensions flowing in a single, asymmetric Y-shaped bifurcation, experimentally. Human RBC suspensions (healthy and artificially hardened) at 20% haematocrit (Ht) were perfused through the microchannels at different flow ratios between the outlet branches, and negligible inertia, and imaged to infer cell distributions. Notable differences in the shape of the haematocrit distributions were observed between healthy and hardened RBCs near the bifurcation apex. These lead to more asymmetric distributions for healthy RBCs in the daughter and outlet branches with cells accumulating near the inner channel walls, exhibiting distinct hematocrit peaks which are sharper for healthy RBCs. Although the hematocrit distributions differed locally, similar partitioning characteristics were observed for both suspensions. Comparisons with RBC distributions measured in a T-shaped bifurcation showed that the bifurcation angle affects the haematocrit characteristics of the healthy RBCs and not the hardened ones. The extent of RBC partitioning was found similar in both geometries and suspensions. The study highlights the differences between local and global characteristics which impact RBC distribution in more complex, multi-bifurcation networks.

Investigations on fluid flow and mixing in fractal tree like biomimetic microchannel based on Murray's law

In this novel study, nature inspired biomimetic based micromixers with asymmetric bifurcation are designed and analysed, incorporating daughter vessel ratios (rdv) of 0.6, 0.7, 0.8, and 0.9 based on Murray's law. By leveraging the concept of Murray's law, four micromixers were developed to address the challenges of mixing at the microscale. Achieving efficient mixing is crucial for microfluidic devices in bioengineering and chemical applications. In this work, we examined asymmetric and symmetric bifurcated micromixers across a wide range of Reynolds numbers, from 0.01 to 300. The results demonstrate that almost all the Reynolds number are better handled by the asymmetric bifurcated micromixer having rdv=0.8. The unbalanced collision of the two fluid streams in this configuration promotes enhanced mixing performance. In contrast, the symmetric micromixer, which lacks such imbalances, shows comparable mixing performance across different Reynolds numbers, except for a Reynolds number of 10. In some cases of asymmetric bifurcated micromixers, inadequate mixing occurred due to the dominance of the larger daughter vessel, impeding the participation of the smaller one in the mixing process. The research reveals that asymmetric bifurcated micromixers with rdv=0.8 are exhibit slightly higher mixing efficiency than symmetric bifurcated micromixers with rdv=1.0.

Prototypical autism: New diagnostic criteria and asymmetrical bifurcation model

The current “autism spectrum” DSM 5 diagnostic criteria and autism standardized diagnostic instruments promote considerable heterogeneity or clinical indecision and may be detrimental to the advancement of fundamental research on autism mechanisms. To increase clinical specificity and reorient research towards core autistic presentations, we propose new diagnostic criteria for prototypical autism during the age of 2- to 5-years. We include autism within other non-dominant, familiarly aggregated phenomena sharing asymmetrical developmental bifurcations, such as twin pregnancy, left handedness, and breech presentation/delivery. Following this model, nature, trajectory, and positive/negative signs structure of autism would result from the polarized problem of whether or not language and information is processed in a socially biased manner. Prototypical autism would follow a canonical developmental trajectory by which a gradual decline in social bias in the processing of incoming information, overtly beginning at the end of the first year, bifurcates into a prototypical autistic presentation in the second half of the second year of life. This bifurcation event is followed by a plateau, in which these atypicalities show maximal stringency and distinctiveness, and then ultimately, in most cases, by partial normalization. During the plateau period, the orientation towards, and processing of, information is considerably modified, with an absence of bias for social information, contrasting with a high level of interest in complex, unbiased information, independently of its social or non-social nature. Integrating autism into asymmetrical developmental bifurcations would explain the absence of deleterious neurological and genetic markers and the presence of familial transmission in canonical autistic presentations.

Numerical assessment of recellularization conditions to vessel occlusion.

To ensure the functional properties of an organ generated by the process of decellularization and recellularization, the initial density and distribution of seeding cells in the parenchymal space should be maximized. However, achieving a uniform distribution of cells across the entire organ is not straightforward because of vessel occlusion. This study assessed vessel occlusion during recellularization under different conditions. A combination of the electrical analog permeability (EPA) model, computational fluid dynamics (CFD), and discrete element method (DEM) was employed to describe the vessel occlusion phenomenon. In particular, realistic flow distributions in vascular trees of the decellularized organ were indicated by the EPA model. The cell suspension flow was modeled by a coupled CFD-DEM model, whereby living cells were presented as a discrete phase (solved by the DEM solver), and the culture medium was modeled as the fluid phase (solved by CFD solver). The cell suspension velocity was reduced up to 47% after decellularization, which directly affected cell movement. Simulation results also indicate that the occurrence of vessel occlusion was promoted by gravity direction in the asymmetric bifurcation and increased as the cell concentration increased. The assessment of vessel occlusion under different conditions was quantitatively investigated. The model provides insights into the dynamics of cells in the vessel compartment, allowing for the selection of optimum seeding parameters for the recellularization process.

FRACTAL ANALYSIS FOR THERMAL CONDUCTIVITY OF DUAL POROUS MEDIA EMBEDDED WITH ASYMMETRIC TREE-LIKE BIFURCATION NETWORKS

Heat transport in tree-like bifurcation networks has been widely studied in various fields. In this work, we investigate heat conduction in the dual porous media embedded with asymmetric tree-like bifurcation networks. In addition, considering the effects of nonuniform tube shape, we assume that the bifurcated tube shows sinusoidal fluctuations. Based on the fractal distribution of pore size and bifurcation structure, we established a dimensionless effective thermal conductivity (ETC) model of the dual porous media. The dimensionless ETC ([Formula: see text] obtained is related to the porosity ([Formula: see text], the fluid–solid thermal conductivity ratio ([Formula: see text], the pore area fractal dimension [Formula: see text] and the structural parameters of the bifurcation network (bifurcation level [Formula: see text], length ratio [Formula: see text], radius ratio [Formula: see text], fluctuation amplitude factor [Formula: see text], bifurcation angle [Formula: see text]. To verify the validity of this model, a comparison of the present dimensionless ETC model with available experimental data was carried out and the results were in good agreement. We have discussed the effects of each parameter on the dimensionless thermal conductivity in detail and constructed parametric planes to evaluate the structural parameters more directly. The model has positive implications for revealing the heat transport mechanism in asymmetric tree-like bifurcation dual porous media.

Complex dynamics in a novel jerk system with septic nonlinearity: analysis, control, and circuit realization

This work proposes a new chaotic jerk system with septic nonlinearity. The new system presents odd symmetry and undergoes typical behaviors including period doubling, merging crisis, spontaneous symmetry breaking, coexisting attractors and coexisting bubbles of bifurcations as well. The most gratifying feature discovered in this article, is the occurrence of up to eight coexisting attractors for appropriate sets of parameters. This latter feature is uncommon for a chaotic system as simple as the model proposed in this work (e.g. not reported in cubic, quintic or hyperbolic sine models). Multistability control is achieved by following the linear augmentation approach. We numerically prove that the multistable septic chaotic system can be adjusted to develop a monostable behavior when smoothly monitoring the coupling strength. More interestingly, it is found that the coupling breaks the symmetry of the chaotic jerk system and thus induces new patterns including asymmetric Hopf bifurcations; coexisting non-symmetric bubbles, critical phenomena, coexisting multiple asymmetric attractors, just to name a few. On this line, the linear augmentation scheme can be regarded as a simple means for inducing new features in odd symmetric chaotic systems. PSPICE simulation results captured from an electronic analog of the proposed septic jerk system are consistent with the theoretical investigations.

Versatile benchmark model reproducing snap-through, asymmetric, symmetric unstable/stable, and multiple bifurcation including hill-top branching in structural instability

This paper proposes a simple yet innovative two degrees of freedom (2-DoFs) benchmark model for structural instability. The proposed rigid-body-spring model is versatile in that it reproduces various kinds of instability phenomena. Its parameter combinations comprehensively realize snap-through, asymmetric, symmetric unstable/stable, and multiple bifurcation including hill-top branching in structural stability problems. Governing equations including the total potential energy, nonlinear equilibrium equations, stiffness matrix (Jacobian), and stability information are all explicitly formulated. For post-buckling analysis, path branching is visualized for intuitive diagnosis. The versatile benchmark model is expected to yield a qualitative understanding of the instability mechanism depending on the model parameters. The benchmark model also contributes to the phenomenological understanding of stability design.

Wrinkling as a mechanical instability in growing annular hyperelastic plates

Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in an incompressible annular hyperelastic plate. The governing differential equations for a two-dimensional plate system are derived using a variational principle with no apriori kinematic assumptions in the thickness direction. A linear bifurcation analysis is performed to investigate the stability behaviour of the growing hyperelastic annular plate by considering both axisymmetric and asymmetric perturbations. The resulting differential equations are then solved numerically using the compound matrix method to evaluate the critical growth factor that leads to wrinkling. The effect of boundary constraints, thickness, and radius ratio of the annular plate on the critical growth factor is studied. For most of the considered cases, an asymmetric bifurcation is the preferred mode of instability for an annular plate. Our results are useful to model the physics of wrinkling phenomena in growing planar soft tissues, swelling hydrogels, and pattern transition in two-dimensional films growing on an elastic substrate.

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.

Multistable dynamics and control of a new 4D memristive chaotic Sprott B system

This work proposes and investigates the dynamic behavior of a new memristive chaotic Sprott B system. One of the interesting features of this system is that it has a bias term that can adjust the symmetry of the proposed model, inducing both homogeneous and heterogeneous behaviors. Indeed, the introduced memristive system can turn from rotational symmetry (RS) to rotational symmetry broken (RSB) system in the presence or the absence of this bias term. In the RS system (i.e., absence of the bias term), pairs of symmetric attractors are formed, and the scenario of attractor merging is observed. Coexisting symmetric attractors and bifurcations with up to four solutions are perfectly investigated. In the RSB system (i.e., the bias term is non-zero), many interesting phenomena are demonstrated, including asymmetric attractors, coexisting asymmetric bifurcations, various types of coexisting asymmetric solutions, and period-doubling transition to chaos. We perfectly demonstrate that the new asymmetric/symmetric memristive system exhibits the exciting phenomenon of partial amplitude control (PAC) and offset boosting. Also, we show how it is possible to control the amplitude and the offset of the chaotic signals generated for some technological exploitation. Finally, coexisting solutions (i.e., multistability) found in the novel memristive system are further controlled based on a linear augmentation (LA) scheme. Our numerical findings demonstrated the effectiveness of the control technic through interior crisis, reverse period-doubling scenario, and symmetry restoring crisis. The coupled memristive system remains stable with its unique survived periodic attractor for higher values of the coupling strength.

On the behavior of inhaled fibers in a replica of the first airway bifurcation under steady flow conditions

Inhaled fibers can potentially cause inflammation of the lung tissue and interstitium, which after long-term exposure may lead to lung cancer, malignant mesothelioma, or pulmonary and pleural fibrosis. To reduce the risk and set the appropriate occupational hygiene regulations, it is important to be able to precisely calculate the fate of inhaled fibers depending on their physical characteristics and inhalation conditions. In the absence of experimental data on the real behavior - trajectories, orientation and flipping - of inhaled fibers, a new test rig was assembled for visualization and recording of flowing fibers in a replica of the human trachea and the first bronchial bifurcation. Fibers prepared from commercially produced glass fibers have been processed, dispersed, and introduced into the airway replica. Visualization was performed using a powerful LED light and a high-speed camera. The flow of fibers was evaluated upstream and downstream of the realistic asymmetrical bifurcation and dependence on flow conditions was sought. The fractions of parallelly and perpendicularly flowing fibers were statistically evaluated in three locations. The frequency of flipping was also analyzed. The results show that the parallel orientation of the fibers is less dominant than expected. The fiber orientation tables for various conditions can be used to adjust and improve computational simulations of inhaled fibers in the human airways.

Dynamical Effects of Offset Terms on a Modified Chua’s Oscillator and Its Circuit Implementation

This paper addresses the effects of offset terms on the dynamics of a modified Chua’s oscillator. The mathematical model is derived using Kirchhoff’s laws. The model is analyzed with the help of the maximal Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction. The investigations show that the offset terms break the symmetry of the system, generating more complex nonlinear phenomena like coexisting asymmetric bifurcations, coexisting asymmetric attractors, asymmetric double-scroll chaotic attractors and asymmetric attraction basins. Also, a hidden attractor (period-1 limit cycle) is found when varying the initial conditions. More interestingly, this latter attractor coexists with all other self-excited ones. A microcontroller-based implementation of the circuit is carried out to verify the numerical investigations.

A Solution of the Junction Riemann Problem for 1D Hyperbolic Balance Laws in Networks including Supersonic Flow Conditions on Elastic Collapsible Tubes

The numerical modeling of one-dimensional (1D) domains joined by symmetric or asymmetric bifurcations or arbitrary junctions is still a challenge in the context of hyperbolic balance laws with application to flow in pipes, open channels or blood vessels, among others. The formulation of the Junction Riemann Problem (JRP) under subsonic conditions in 1D flow is clearly defined and solved by current methods, but they fail when sonic or supersonic conditions appear. Formulations coupling the 1D model for the vessels or pipes with other container-like formulations for junctions have been presented, requiring extra information such as assumed bulk mechanical properties and geometrical properties or the extension to more dimensions. To the best of our knowledge, in this work, the JRP is solved for the first time allowing solutions for all types of transitions and for any number of vessels, without requiring the definition of any extra information. The resulting JRP solver is theoretically well-founded, robust and simple, and returns the evolving state for the conserved variables in all vessels, allowing the use of any numerical method in the resolution of the inner cells used for the space-discretization of the vessels. The methodology of the proposed solver is presented in detail. The JRP solver is directly applicable if energy losses at the junctions are defined. Straightforward extension to other 1D hyperbolic flows can be performed.

Extreme Multistability and Antimonotonicity in a Shinriki Oscillator with Two Flux-Controlled Memristors

This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor’s flux and charge. The uncertain plane equilibrium is transfered into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux–charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use.

Pulsatile flow dynamics in symmetric and asymmetric bifurcating vessels

Bifurcating vessel is a characteristic feature of biological systems such as arteries in the cardiovascular system and pulmonary airways. In cardiovascular system, the bifurcations are often asymmetric, flow is pulsatile, and the fluid, blood, shows a complex rheology. In this work, we study computationally pulsatile flow in planar symmetric and asymmetric, three-dimensional bifurcating vessels. The fluid is considered to be Newtonian as well as non-Newtonian following Carreau's model, and the results are compared. While the flow divides in the two daughter tubes equally in symmetric bifurcations, the flow distribution is time-dependent during a cardiac cycle in asymmetric bifurcations. The flow pattern changes significantly during a cardiac cycle. The secondary flow caused by a turning streamline is analyzed in terms of secondary velocity, vorticity, and helicity. Significant variation is observed in the secondary flow in a cardiac cycle. The secondary flow is observed to be stronger at the start of the diastole despite reduced flow rate. The separated flow on the outer wall causes a significant reduction in time-averaged wall shear stress, a biomarker to assess the possibility of atherosclerotic plaque development. While no significant difference is observed in the results obtained for Newtonian and non-Newtonian fluids at high shear rates, for example, during systole, significant differences are observed when the shear rate is low, during diastole or in the separation region. The velocity profile for the non-Newtonian fluid is observed to be flatter than that for Newtonian fluid. Further oscillatory shearing index, relative residence time, the parameters used as biomarkers are presented.

Symmetric and asymmetric bifurcations of natural convection inside circular cavity in the route to chaos

Natural convection occurs when pipe floating at the water surface during night, which can be regarded as a circular cross-section enclosure heated from below and cooled from the top. Numerical investigation is carried out with focuses on the flow configurations in the route to chaos. When Ra is lower than 103, convection is neglectable and conduction dominate the heat transfer. The flow becomes chaos and unsteady when Ra increases to 108. In the route to chaos, the number of cell increase with the decrease of the cell size. It is found that a symmetric to asymmetric bifurcation of flow configuration followed by a asymmetric to symmetric exist for Ra between 103 to 106.

Effects of sediment grain size and channel slope on the stability of river bifurcations

AbstractChannel bifurcations can be found in river network systems from high gradient gravel‐bed rivers to fine‐grained low gradient deltas. In these systems, bifurcations often evolve asymmetrically such that one downstream channel silts up and the other deepens and, in most cases, they eventually avulse. Past analytical and numerical studies showed that symmetric bifurcations are unstable in high and low Shields stress conditions resulting in asymmetric bifurcations and avulsion, while they can be stable in the mid‐Shields range, but this range is smaller for larger width‐to‐depth ratio. Here, using a one‐dimensional (1D) numerical model, we show that effects of sediment grain size and of channel slope are much larger than expected for low‐gradient systems when a sediment transport relation is used that separates between bedload and suspended load transport. We found that the range of Shields stress conditions with unstable symmetric bifurcations expanded for lower channel slopes and for finer sediment. In high sediment mobility, suspended load increasingly dominates the sediment transport, which increases the sediment transport nonlinearity and lowers the relative influence of the stabilizing transverse bedslope‐driven flux. Contrary to previous works, we found another stable symmetric solution in high Shields stress, but this only occurs in the systems with small width‐to‐depth ratio. This indicates that suspended load‐dominated bifurcations of lowland rivers are more likely to develop into highly asymmetric channels than previously thought. This explains the tendency of channel avulsion observed in many systems.

Bifurcation analysis of elastic residually-stressed circular cylindrical tubes

The theory of superimposed incremental elastic deformations is applied to a deformed configuration of a residually-stressed circular cylindrical tube. The tube is subject to internal or external pressure and an axial load that maintain its circular cylindrical shape, and then bifurcations from this shape are analysed. Detailed governing equations and boundary conditions are provided for axisymmetric, prismatic and asymmetric bifurcations for a general form of strain–energy function that incorporates radial and circumferential residual stress components. The theory is applied to a simple model strain–energy function with two material parameters and a parameter that reflects the magnitude of the residual stress. Numerical computations are used to illustrate the dependence of the results of the bifurcation analysis on these parameters and the axial and radial underlying deformation. It is shown that in general the presence of residual stress has a significant effect compared with the corresponding results without residual stress.

‘Sons of Bengal’ and the Absent Daughters: Gender, Performativity and Nationalism in Bengali Juvenile Literature

This article looks at the asymmetrical bifurcation of gender roles and performativity that is reflected palpably within Bengali juvenile literature of the twentieth century. These writings strove to venerate a cult of hypermasculinity through the portrayal of brave, assertive Bengali heroes who engaged in various escapades in distant lands or in the solving of mysteries and crimes, either alone or accompanied by male confidantes who remain completely devoted to them. This dominant cultural trope was consciously employed as a challenge to the imperial, racist stereotypes of the effeminate Bengali man who was imagined to be inferior to the virile, robust and intellectually superior Englishman. However, the role of women within such diegetic portrayals is liminal or conspicuously absent; female readers are conditioned to “wallow in the reflected glory of their heroes” (Mukherjee para. 13). This paper also looks into the politics of sexuality and nationalism involved within the celebration of male homosocial bonding over heteronormative relationships, thereby leading to the almost complete effacement of female agency.

Multiple bifurcation paths visualized by a computational asymptotic stability theory

Multiple bifurcation (MB) is a compound stability problem of nonlinear structures, in which the singular system stiffness matrix at the stability point coincidentally undergoes two or more zero eigenvalues. The corresponding critical eigenvectors are generally coupled in the actual buckling modes, as frequently observed in symmetric structures.This paper presents a practical diagnosis to visualize all secondary paths branching from the compound stability point when the stiffness matrix is deficient in rank by two. To find post-critical equilibria around an MB point (MBP), asymptotic expansions are assumed to consist of two homogeneous and one particular solution of the singular stiffness equations. Furthermore, hyper-dual numbers are introduced to numerically evaluate the derivatives of the system stiffness with respect to the nodal degrees-of-freedom. The resulting bifurcation equations are a set of three simultaneous cubic polynomial equations with unknown perturbation parameters that can be solved by a popular graphical software. The number and location of existing equilibria above and beneath the MBP at the load level can exactly indicate each type of branching path, such as asymmetric, unstable, or stable symmetric bifurcation paths.Two numerical examples demonstrate that the proposed asymptotic theory can reliably diagnose MB. The first one is the Augusti model, i.e., a simple rigid column supported by elastic springs that shows that the numerical prediction by the proposed method is consistent with Augusti’s analytical results. The second example was computed using the plate and shell finite element (FE) program to verify that the asymptotically expanded and visually solved bifurcation equations work well and can be implemented in existing FE codes for stability analysis, including imperfection-sensitivity and optimization.