Composite spiral waves in discrete-time systems

Spiral waves are a type of typical pattern in open reaction-diffusion systems far from thermodynamic equilibrium. The study of spiral waves has attracted great interest because of its nonlinear characteristics and extensive applications. However, the study of spiral waves has been confined to continuous-time systems, while spiral waves in discrete …

Segmented spiral waves in a reaction-diffusion system | PNAS

The visually striking spiral concentration waves found in a number of reaction-diffusion systems have fascinated scientists since their discovery in the Belousov–Zhabotinsky (BZ) system more than three decades ago.Subsequent observations of spiral patterns in such diverse systems as aggregating slime molds (), developing …

Emergence of large-scale mechanical spiral waves in …

Fig. 1: Self-organization of propagating spiral waves with stationary cores in quasi-two-dimensional bacterial living matter. Fig. 2: Analysis of cell density variation and single-cell ...

Asymptotic theory for spiral wave reflections

The spiral waves at the final point in the plotted trajectory are visualized by the u-field of the model. Both cases shown use the same dimensions: 25×40 space units. ... Jacob Langham ...

Asymptotic dynamics of reflecting spiral waves

Jacob Langham, Irina Biktasheva, and Dwight Barkley. Phys. Rev. E 90, 062902 – Published 1 December 2014. More. PDF HTML Export Citation. Abstract. …

Asymptotic dynamics of reflecting spiral waves

spiral-wave reflections in these two studies is that the angle of reflection is essentially independent of the angle of incidence for a large range of incident angles. Indeed, the reflection ... JACOB LANGHAM, IRINA BIKTASHEVA, AND DWIGHT BARKLEY PHYSICAL REVIEW E 90, 062902 (2014) (a) (b) FIG. 1. (Color online) Two examples of …

Dynamics of spiral waves driven by a dichotomous periodic …

In the absence of the external forcing, we have created a spiral wave by truncating a traveling pulse, and examined its motion as a function of ε.When ε>0.00456, the system supports the formation and propagation of rigidly rotating spiral waves.As ε is decreased across a critical value (ε=0.00456), the system will undergo a transition from …

Asymptotic dynamics of reflecting spiral waves

spiral-wave reflections in these two studies is that the angle of reflection is essentially independent of the angle of incidence for a large range of incident angles. Indeed, the …

Interacting spiral wave patterns underlie complex brain

To further validate our approach, we simulate a spiral wave by rotating (clockwise or anticlockwise) a one-dimensional sine wave around a fixed centre with uniform rotating speed of 0.12 rad/s and ...

Spiral Waves in Integrate-and-Fire Neural Networks

The formation of propagating spiral waves is studied in a randomly connected neural network composed of integrate-and-fire neurons with recovery period and excitatory connections using computer simulations. Network activity is initiated by periodic stimulation at a single point. The results suggest that spiral waves can arise in such a network ...

Control of spiral waves in excitable media

The propagation of spiral-shaped excitation waves is a prominent example of self-organization in nonequilibrium systems. The properties of these waves are studied in a chemical model system––the Belousov–Zhabotinsky (BZ) reaction––and in various biological excitable media such as heart or neuronal tissue. An important aspect lies in ...

Phys. Rev. E 102, 032411 (2020)

Spiral waves of excitation are common in many physical, chemical, and biological systems. In physiological systems like the heart, such waves can lead to cardiac arrhythmias and need to be eliminated. Spiral waves anchor to heterogeneities in the excitable medium, and to eliminate them they need to be unpinned first. Several groups …

Spiral | Definition, Examples, & Facts | Britannica

spiral, plane curve that, in general, winds around a point while moving ever farther from the point. Many kinds of spirals are known, the first dating from the days of ancient Greece. The curves are observed in nature, and human beings have used them in machines and in ornament, notably architectural—for example, the whorl in an Ionic capital.

New Mechanism of Spiral Wave Initiation in a Reaction …

Abstract. Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone.". Previous studies of vulnerability ...

Feedback-mediated control of spiral waves

1.. IntroductionSpiral waves are among the most prominent examples of spatio-temporal pattern in excitable and oscillatory media [1], [2], [3], [4].They have been observed in systems of quite different nature like the social amoeba colonies [5], the chemical Belousov–Zhabotinsky (BZ) reaction [6], [7], in heart muscle [8], [9], in the …

Spiral-Waves-Boundary-Sinks-and-Spectra

The continuation code uses a mixture of secant and simple continuation methods. Asymptotic Wave Trains: continue_wave_train Secant continuation. Spiral Waves on Disks: continue_spiral Secant …

Spiral Wave Propagation in Communities with Spatially …

Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still unclear. Here, we use a minimal FitzHugh-Nagumo-type model to investigate excitable wave propagation in a two …

Genshin Impact Spiral Abyss Guide (Version 4.3)

This Genshin Impact's Spiral Abyss guide for Version 4.3 will discuss about how to tackle the game's hardest content, including how to compose team compositions for each Floor, organizing your strategies against multiple enemy waves, which marks the return of Sumeru-based enemies, and adapt to the Ley Lines' effects to win your full-star …

When do chemical synapses modulate the formation of spiral waves …

3.1 Birth of spiral waves: the effect of sigmoidal slope (lambda ) and firing threshold (theta ). The beginning of the result section examines the potential effect of sigmoidal steepness around its defined threshold. In the mathematical description of chemical synapses, the response saturation speed is modeled by sigmoid S-curve slope …

Impact of noise on the instability of spiral waves in

This study presents a stochastic two-dimensional mathematical model of human AF and explores how Gaussian white noise affects the instability of spiral …

Reaction-Diffusion Patterns and Waves: From Chemical

3.2 Breakup of 3D Scroll Waves. The natural extension of spiral waves in two dimensions are scroll waves in three dimensions. Straight scroll waves rotate with constant frequency. However, under certain conditions the filament of the scroll is not straight but takes a helical shape under meandering or when an external twist is imposed.

Segmented spiral waves in a reaction-diffusion system | PNAS

The visually striking spiral concentration waves found in a number of reaction-diffusion systems have fascinated scientists since their discovery in the Belousov–Zhabotinsky (BZ) system more than three decades ago.Subsequent observations of spiral patterns in such diverse systems as aggregating slime molds (), developing oocytes (), cardiac muscle (4, …

Formation of spiral waves in cylindrical containers under …

Most spiral waves known, e.g. from reaction–diffusion systems, propagate either outwards from or inwards into the spiral centre (Vanag & Epstein Reference Vanag and Epstein 2001). Such a radial propagation, also in contrast to vertically excited spiral Faraday waves (Kiyashko et al. Reference Kiyashko, Korzinov, Rabinovich and Tsimring 1996 ...

[2002.10352] Spiral waves: linear and nonlinear theory

Spiral waves: linear and nonlinear theory. Björn Sandstede, Arnd Scheel. Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather than studying existence in a ...

[1401.7626] Asymptotic dynamics of reflecting spiral waves

Jacob Langham, Irina Biktasheva, Dwight Barkley. Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as …

Researchers Map Rotating Spiral Waves in Live Human Hearts

Mapping the Heart. To generate the conditions for spiral waves, the researchers applied timed electric shocks to the heart. Then, to visualize and record the spiral waves, they injected florescent dyes for voltage and calcium into the blood substitute that keeps the heart alive. The changes in light intensity enable them to record signals ...

Spots, stripes, and spiral waves in models for static and …

Waves of F-actin or of u (here associated with the GTPase Rac) that impinge on the cell edge (1) lead to local protrusion. A new burst produces additional waves that split and move towards the cell edge (2a,b,c). Colliding waves sometimes create local spiral waves (3a,b,c) in the cell interior, and lead to continued cell shape deformations.

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(PDF) Spiral waves and the heart

Spiral waves are nonlinear waves that rotate around an organizing center (i.e. core) [Gray & Jalife, 1996]. They are one of the most typical two-dimensional spatiotemporal patterns in excitable or ...

(PDF) Drift and Meander of Spiral Waves

Jacob Langham; Dwight Barkley; Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with ...

Resonant drift of synchronized spiral waves in excitable …

First row: Trajectories of spiral tip without control at (a) f = 3.2, (b) f = 3.42, and (c) f = 3.45. Second row: Spiral waves are synchronized by the CPEF accompanied by a constant phase ...

Non-specular reflections in a macroscopic system with …

Non-specular reflections in a macroscopic system with wave-particle duality: Spiral waves in bounded media. Jacob Langham and Dwight Barkley. Citation: Chaos 23, 013134 …

Spiral Wave Dynamics in Neocortex: Neuron

Although spiral waves are ubiquitous features of nature and have been observed in many biological systems, their existence and potential function in mammalian cerebral cortex remain uncertain. Using voltage-sensitive dye imaging, we found that spiral waves occur frequently in the neocortex in vivo, both during pharmacologically induced oscillations …

Spiral Wave

The term spiral waves is generally used to describe reentrant activity in two dimensions. The center of the spiral wave is called the core and the distribution of the core in three dimensions is referred to as the filament (Fig. 5).The three-dimensional form of the spiral wave is called a scroll wave (Pertsov and Jalife, 1995).In its simplest form, the scroll …

Spiral bandwidth of four-wave mixing in Rb vapour

Energy levels and wavelengths. Two near-infrared pump fields (780 and 776 nm) generate an infrared field (5.2 μm) and a blue field (420 nm). With Gaussian pump beams, this resonantly enhanced ...