Spiral Turbulence Research Articles

Unpinning and elimination of spiral waves and turbulence through local optogenetical illumination.

Spiral waves in cardiac tissue have been identified as a significant factor leading to life-threatening arrhythmias and ventricular fibrillation. Consequently, understanding the mechanisms underlying the dynamics of such waves and exploring strategies for their elimination have garnered substantial interest and emerged as crucial research objectives. Spiral waves often become pinned (trapped) at anatomical obstacles in cardiac tissue, resulting in increased stability and posing challenges for their elimination. The unpinning of spiral waves can be achieved through the application of an external electric field and has been the subject of previous research. Recently, optogenetics has emerged as an alternative method to modulate electrical activity by illumination of cardiac tissue. In this paper, we employ mathematical modeling to investigate the potential of utilizing local illumination to unpin and eliminate spiral waves in cardiac tissue. We also extend this methodology to explore the effects of more complex turbulent excitation patterns. We conduct simulations using low-dimensional (Barkley) and ionic (Fenton-Karma) models of cardiac tissue, incorporating optogenetical channels. Our findings demonstrate that local suprathreshold illumination can successfully unpin spiral waves in 100% of cases. Notably, unlike unpinning by electrical field stimulation, this approach does not necessitate precise timing of stimulus application during a specific phase of rotation. Additionally, we demonstrate that periodic optogenetical stimulation can effectively eliminate both unpinned spiral waves and turbulence by moving them toward the boundary via an antitachycardia pacing mechanism.

Effects of the geometrical parameters on rectification characteristics of convergence angle throttle orifice plates

Under severe operating conditions, the conventional porous plates are rendered ineffective in rectifying the spiral turbulence generated during the steam flow and pressure adjustment process by the primary pressure-reducing valve (PPRV). To address this limitation, an innovative throttle plate with a convergent angle structure is proposed based on the conventional uniformly distributed porous plate in this study. The design aims to rectify the spiral turbulence generated after PPRV and elucidate its formation mechanism. However, there is currently no clear understanding or reliable prediction method for the pressure loss coefficient due to various structural factors influencing the rectification characteristics and pressure drop properties of the converging angle structure throttle orifice plate. This lack of knowledge severely hampers practical applications of this new plate in pressure-reducing desuperheating devices. To address this issue, the present study investigates the underlying mechanisms governing the rectification characteristics and flow resistance properties of a throttle orifice plate with a converging angle structure through experimental investigations and numerical simulations. The focus is on geometric parameters including the converging angle (θ), orifice diameter (d), throttle diameter ratio (β), and plate thickness (h). The findings suggest that the incorporation of a converging angle structure throttle orifice plate is advantageous in achieving effective rectification of spiral turbulence in the secondary pressure pipeline of the pressure-reducing desuperheating device. This modification reduces the required channel distance for enhancing unstable flow, diminishes velocity non-uniformity, and augments the rectification and control capabilities of the medium.

Post-dynamical inspiral phase of common envelope evolution

During common envelope evolution, an initially weak magnetic field may undergo amplification by interacting with spiral density waves and turbulence generated in the stellar envelope by the inspiralling companion. Using 3D magnetohydrodynamical simulations on adaptively refined spherical grids with excised central regions, we studied the amplification of magnetic fields and their effect on the envelope structure, dynamics, and the orbital evolution of the binary during the post-dynamical inspiral phase. About 95% of magnetic energy amplification arises from magnetic field stretching, folding, and winding due to differential rotation and turbulence while compression against magnetic pressure accounts for the remaining ∼5%. Magnetic energy production peaks at a scale of 3ab, where ab is the semimajor axis of the central binary’s orbit. Because the magnetic energy production declines at large radial scales, the conditions are not favorable for the formation of magnetically collimated bipolar jet-like outflows unless they are generated on small scales near the individual cores, which we did not resolve. Magnetic fields have a negligible impact on binary orbit evolution, mean kinetic energy, and the disk-like morphology of angular momentum transport, but turbulent Maxwell stress can dominate Reynolds stress when accretion onto the central binary is allowed, leading to an α-disk parameter of ≃0.034. Finally, we discovered accretion streams arising from the stabilizing effect of the magnetic tension from the toroidal field about the orbital plane, which prevents overdensities from being destroyed by turbulence and enables them to accumulate mass and eventually migrate toward the binary.

К теории спиральной турбулентности немагнитного астрофизического диска. Образование крупномасштабных вихревых структур

A closed system of three-dimensional hydrodynamic equations of the mean motion scale is presented for modeling spiral turbulence in a rotating astrophysical disk. The diffusion equations for the averaged vortex and the integral vortex spirality transport equation are derived. A general concept of the emergence of energy-consuming mezoscale coherent vortex structures in a thermodynamically open subsystem of turbulent chaos, associated with the realization of the inverse cascade of kine-tic energy in mirror-nonsymmetric disk turbulence, is formulated. It is shown that negative viscosity in the rotating disk three-dimensional system is apparently a manifestation of cascade processes in spiral turbulence, when an inverse energy transfer from small vortices to larger ones is realized. It is also shown that a relatively long decay of turbulence in the disk is associated with the absence of reflective symmetry of the anisotropic field of turbulent velocities relative to its equatorial plane. The work is of a review character, made with the aim of improving new models of astrophysical nonmagnetic disks for which the effects of spiral turbulence play a determining role.

Spiral dynamics in oscillatory bilayer systems with an inhomogeneous inter-layer coupling

Spiral dynamics in the oscillatory bilayer system with an inhomogeneous inter-layer coupling and a spiral-resting initial state are studied, where the square coupled patches are arranged into a square lattice array. Depending on the patch side length, the lattice space and the coupling strength, different dynamical behaviors can be observed. The complete synchronization of two spiral waves easily occurs when the coupled areas occupy a larger proportion in the whole region. The bilayer system can also show several typical asynchronous patterns, where the spiral with the closed tip path, the spiral with the complex phase shifting, the state with multiple spirals, the spiral turbulence, and the non-smooth traveling pulses can be formed in the single layers of the bilayer. The variable difference functions are computed, and three types of asymptotic behaviors are identified, which include the behaviors of approaching the constant, periodic variation, and aperiodic variation around the constant. These asymptotic behaviors can describe some properties of the bilayer patterns after a transient interval. For example, the variable difference function has a periodical asymptotic behavior when the spiral with the closed tip path is formed in the single layer. The heterogeneity of inter-layer coupling can also induce some complex tip trajectories.

Generalized quasi-linear approximation and non-normality in Taylor-Couette spiral turbulence.

Taylor-Couette flow is well known to admit a spiral turbulence state in which laminar and turbulent patches coexist around the cylinder. This flow state is quite complex, with delicate internal structure, and it can be traced into certain regimes of linear stability. This behaviour is believed to be connected to the non-normality of the linear operator, which is itself a function of the control parameters. Using spiral turbulence in both linearly stable and unstable regimes, we investigate the effectiveness of the generalized quasi-linear approximation (GQL), an extension of quasi-linear theory designed to capture the essential aspects of turbulent flows. We find that GQL performs much better in the supercritical regime than the subcritical. By including only a small number of modes in the nonlinear interactions, GQL simulations maintain a turbulent-like state when in the supercritical regime. However, a much larger number is required to avoid returning to the laminar state when in the subcritical regime. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow

We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor–Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting–rotating waves (DRW) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circular Couette flow, is determined by the upper and lower branches of DRW solutions originated at saddle-node bifurcations. The mechanism whereby these solutions self-sustain, and the chaotic dynamics they induce, are conspicuously reminiscent of other subcritical shear flows. Remarkably, the flow properties of DRW persist even as the Reynolds number is increased beyond the linear stability threshold of the base flow. Simulations in a narrow parallelogram domain stretched in the azimuthal direction to revolve around the apparatus a full turn confirm that self-sustained vortices eventually concentrate into a localised pattern. The resulting statistical steady state satisfactorily reproduces qualitatively, and to a certain degree also quantitatively, the topology and properties of spiral turbulence as calculated in a large periodic domain of sufficient aspect ratio that is representative of the real system.

Removal of spiral turbulence by virtual electrodes through the use of a circularly polarized electric field.

Heart disease is the leading cause of death and is often accompanied by cardiac fibrillation. Defibrillation using the virtual electrode effects is a promising alternative compared to using the high-voltage electric shock in the clinic. Our earlier works [S. L. Murphy, K. D. Kochanek, J. Xu, and E. Arias, NCHS Data Brief 427 (2021); R. A. Gray, A. M. Pertsov, and J. Jalife, Nature 392, 75-78 (1998); F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, Nature 392, 78-82 (1998); M. Santini, C. Pandozi, G. Altamura, G. Gentilucci, M. Villani, M. C. Scianaro, A. Castro, F. Ammirati, and B. Magris, J. Interv. Card. Electrophysiol. 3, 45-51 (1999).] prove that, compared with other external electric fields, a low voltage circularly polarized electric field is more efficient in turning non-excitable defects in cardiac tissue into virtual electrodes. It, therefore, needs lower voltage to stimulate the excitation waves and causes less harm to reset the spiral turbulence of cardiac excitation for defibrillation. In this paper, we investigate the virtual electrode effect of multiple defects by the circularly polarized electric field for the removal of spiral turbulence. Considering different shapes, sizes, and distributions of multiple defects, we reveal the phase locking of stimulated excitations around multiple virtual electrodes. Furthermore, the circularly polarized electric field parameters are optimized to remove the spiral turbulence.

Development and transition of target waves in the network of Hindmarsh–Rose neurons under electromagnetic radiation

The pattern transition of target waves in Hindmarsh–Rose neuron network exposed to fixed and periodic electromagnetic radiation is reported in this paper. Our numerical results confirm that local periodical excitation can induce stable propagating target waves from the network. It is found that fixed electromagnetic radiation has great effect on the propagating target waves, and that these target waves can be obviously blocked by increasing the intensity of fixed electromagnetic radiation. We find that the periodic electromagnetic radiation with appropriate amplitude and frequency can break the target waves and induce spatiotemporal turbulence and spiral waves from the broken target waves. Our numerical simulations show that the influence of periodic electromagnetic radiation on the dynamics of target waves is complex, and that although both increasing the amplitude and decreasing the frequency can break the target waves and induce spiral waves and chaos from the network, extensive numerical results find that lower frequency is more easy to terminate the target waves and generate spiral waves and spatiotemporal chaos. The numerical simulations also show that fixed and periodic electromagnetic radiation have influence on the pattern transition of the target waves in the network, but periodic electromagnetic radiation is more helpful to develop spiral waves and turbulence from the network.

Control of spiral waves in excitable media under polarized electric fields

Spiral waves are ubiquitous in diverse physical, chemical, and biological systems. Periodic external fields, such as polarized electric fields, especially circularly polarized electric fields which possess rotation symmetry may have significant effects on spiral wave dynamics. In this paper, control of spiral waves in excitable media under polarized electric fields is reviewed, including resonant drift, synchronization, chiral symmetry breaking, stabilization of multiarmed spiral waves, spiral waves in subexcitable media, control of scroll wave turbulence, unpinning of spiral waves in cardiac tissues, control of spiral wave turbulence in cardiac tissues, etc.

Turbulent pattern in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction.

Chemical turbulence was observed experimentally in the 1,4-cyclohexanedione Belousov-Zhabotinsky (CHD-BZ) reaction in a double layer consisting of a catalyst-loaded gel and uncatalyzed liquid on a Petri dish. The chemical patterns in the CHD-BZ reaction occur spontaneously in various forms as follows: the initial, regular, transient, and turbulent patterns, subsequently. These four patterns are characterized by using the two-dimensional Fourier transform (2D-FT). Mechanism of the onset of the turbulence in the CHD-BZ reaction is proposed. Turbulence in the CHD-BZ reaction is reproducible under a well defined protocol and it exists for a period of time of about 50 minutes, which is sufficiently long to offer a good opportunity to study and control the turbulence in the future. Two models of the BZ reaction were used to simulate the spiral breakup. Both are capable of producing spiral turbulence from initially regular patterns in each layer and reflect certain features of dynamics observed in experiments.

Spiral wave in a two-layer neuronal network

Multi-layer networks are quite fundamental to study structural and functional properties of various biological systems. In this study, a two-layer neuronal network is considered and the interactions between the spiral pattern in one layer and a homogeneous state in the other layer, under the effect of inter-layer bidirectional connection are investigated. Spiral wave has been confirmed to play a significant role in many complex systems. In this regard, in laminar structured systems in particular, it is crucial to study the dynamics of the spiral wave affected by the inter-layer interactions. Here, for each layer (sub-network), a regular network with eight-neighbor connection is designed. For the local dynamics of each neuron, the magnetic Fitzhugh–Nagumo (FN) neuronal model is introduced. The results show that depending on the level of interactions between the two layers, four different types of collective electrical activity can occur. When the inter-layer connection is weak, the layer with spiral pattern does not change while the homogeneous state of the other layer is broken by a blurred spiral pattern. As the inter-layer connection is strengthened, the dynamics of the spiral wave changes significantly, leading to unstable spiral wave and spiral turbulence. However, by a further increase in the inter-layer coupling strength, the spiral wave does not exist at all.

Suppression of spiral wave turbulence by means of periodic plane waves in two-layer excitable media

Abstract Spiral waves are relatively common, yet fascinating, visually appealing, and important phenomena in many nonlinear dynamical systems. The emergence of spiral waves in the heart’s atrium, for example, signals abnormality that can lead to arrhythmias such as atrial flutter and atrial fibrillation. Spiral waves have also been associated with the disruption of resting states in the human brain, which are crucial for unimpaired cognitive ability and information processing. Here we consider two-layer excitable media, where spiral wave turbulence is triggered as the initial state. We study the effects of periodic plane waves on the dynamics of spiral wave turbulence, in particular by varying their spatial frequency. Our research shows that planes waves with low spatial frequency are in general too weak to overcome spiral wave turbulence. But when the spatial frequency is sufficiently increased, the plane waves can overcome spiral wave turbulence and impose a stripped spatial pattern over the excitable media. By increasing the spatial frequency of the plane waves even further, we show that it is possible to minimize the time needed to destroy spiral wave turbulence, although we also observe an upper limit beyond which the recurrence of turbulence is likely. This is linked to residual spirals that remain following a too rash elimination attempt, which then gradually regain footing across the whole medium.

Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation

The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures.

Synchronization transmission of spiral wave and turbulence in uncertain time-delay neuronal networks

In this paper, a new technology is proposed to research the problem of the synchronization transmission of spiral wave and turbulence between uncertain time-delay neuronal networks with different node numbers and topologies. In order to construct the Lyapunov–Krasovskii functional of the network, a special function is designed. According to our scheme, the uncertain time-delay neuronal network can transfer synchronously the spiral wave and turbulence, especially the chattering near the synchronization target can also be eliminated, which indicates that the synchronization performance of the network is more stable. At the same time, the recognition law of the network coupled matrix element is also designed to replace effectively the uncertain coupled matrix element in the network.

Control of transversal instabilities in reaction-diffusion systems

In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

A basic lattice model of an excitable medium: Kinetic Monte Carlo simulations

The simplest stochastic lattice model of an excitable medium is considered. Each lattice cell can be in one of three states: excited, refractory, or quiescent. Transitions between different cell states occur with the prescribed probabilities. The model is designed for studying the transfer of excitation in the cardiac muscle and nerve fiber at the cellular and subcellular levels, and also for modeling the spreading of epidemics. Elementary events on the lattice are simulated by the kinetic Monte Carlo method, which consists in constructing a Markov chain of the lattice states corresponding to the solution of the master equation. An effective algorithm for implementing the Kinetic Monte Carlo simulations is suggested. The number of the arithmetic operations at each time step of the proposed algorithm is practically independent of the lattice size, which enables making calculations on two- and three-dimensional lattices of a very large size (more than 109 cells). It is shown that the model reproduces the basic spatiotemporal structures (solitary traveling pulses, pulse trains, concentric and spiral waves, and spiral turbulence) characteristic of an excitable medium. The basic properties of traveling pulses and spiral waves for the considered stochastic lattice model are studied and compared with the known properties of deterministic equations of the reaction-diffusion type, which are usually employed for modeling excitable media.

Characterization of hydrodynamics and electrochemical treatment of dye wastewater in two types of tubular electrochemical reactors

Electrochemical treatment is an environmentally friendly method of removing pollutants from industrial wastewater, and tubular electrochemical reactor is one kind of electrochemical reactor. However, the flow field on the electrode surface in a traditional concentric tubular reactor is not homogeneous, leading to low treatment efficiency of the reactors. Therefore, a new tubular electrochemical reactor based on spiral flow caused by a turbulence promoter is presented. In this work, fluid flow and hydrodynamics of the new tubular electrochemical reactor using computational fluid dynamics (CFD) method are studied by comparing them to the traditional one. The electro-oxidation of methylene blue simulation wastewater treatment was developed to analyze the processing efficiency of the two types of electrochemical reactors. In the new tubular electrochemical reactor, due to the presence of spiral turbulence promoter, the mean flow rate and turbulent intensity were clearly increased by 500-700% and nearly 200% compared to that of the traditional one, respectively. Under the same inlet-velocity, the removal rates of wastewater in the new tubular electrochemical reactor were also improved.

Additive noise driven phase transitions in a predator-prey system

We explore the impact of additive noise on phase transitions in a predator-prey system, which is formulated by stochastic partial differential equations (SPDEs). The system is observed to experience twice phase transitions under certain level of additive noise. We extend the multiple scaling approach from single SPDE to multiple SPDEs and find a necessary and sufficient condition to excite the occurrence of the first transition from a spatially homogeneous state to a spatially regular spiral wave. Numerical experiments show the second phase transition from the regular spatial pattern to spiral turbulence. We conclude that additive noise has a destabilising effect on population dynamics by triggering the onset of Hopf bifurcation.

Synchronization transmission of spiral wave and turbulence within the uncertain switching network

We consider the synchronization transmission problem of spiral wave and turbulence within the uncertain switching network. Through constructing reasonably the Lyapunov function of the network, the uncertain switching network not only can transfer synchronously the spiral wave and turbulence originated from the synchronization target, but also the chattering near the synchronization target can be eliminated, which indicates that the synchronization performance of the network is more stable. At the same time, the adaptive laws of the uncertain parameters are designed and the uncertain parameters in the switching network nodes are replaced effectively.