Differential-flow-induced transition of traveling wave patterns and wave splitting

Ghosh, Sucharita; Paul, Shibashis; Ray, Deb Shankar

doi:10.1103/physreve.94.042223

Cited by 10 publications

(5 citation statements)

References 45 publications

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“…We expect that this will manifest patterns which move in time, or even less regular wave patterns. Temporal eigenvalues with non-zero imaginary part and resulting wave instabilities have previously been observed in reaction-diffusion-advection systems (Rovinsky & Menzinger 1992;Flach et al 2007;Berenstein 2012a,b;Ghosh et al 2016). This will typically correspond to translation of spatial patterns with the fluid flow.…”

Section: Instability In a 2-d Rectangular Channel Flowmentioning

confidence: 71%

“…2007; Berenstein 2012 a , b ; Ghosh et al. 2016). This will typically correspond to translation of spatial patterns with the fluid flow.…”

Section: Pattern Formation In Channels Pipes and Ductsmentioning

confidence: 99%

“…This corresponds to an oscillatory or wave Turing instability, meaning that patterns which are formed under diffusion may move or propagate in time, in contrast to classical Turing patterns which remain stationary in time. Oscillatory or wave type instabilities have attracted attention in the literature, and can emerge even in the absence of advection in higher-dimensional systems (Yang et al 2002;Yang & Epstein 2003), although such instabilities are commonly observed in various reaction-diffusion-advection systems studied in the literature (Rovinsky & Menzinger 1992;Flach et al 2007;Berenstein 2012a,b;Ghosh et al 2016).…”

Section: The General Scalar Sturm-liouville Problemmentioning

confidence: 99%

“…In addition to the Turing instability, such reaction–diffusion–advection systems are known to admit wave instabilities (Rovinsky & Menzinger 1992; Flach et al. 2007; Berenstein 2012 a , b ; Ghosh, Paul & Ray 2016), including the case where the inhibitor is immobile (Dawson, Lawniczak & Kapral 1994). Both stationary and travelling patterns may coexist in such reaction–diffusion–advection systems (Satnoianu 2003), and wave instabilities manifest in chemical (Riaz, Kar & Ray 2004) and ecological (Malchow 1995, 2000) models.…”

Section: Introductionmentioning

confidence: 99%

“…Satnoianu & Menzinger (2002) investigated reactive flows as a way of introducing inexact phase differences within Turing patterns, while Andresén et al (1999) used advection to find Turing patterns with equal diffusion coefficients that would not be possible in the absence of advection. In addition to the Turing instability, such reaction-diffusion-advection systems are known to admit wave instabilities (Rovinsky & Menzinger 1992;Flach et al 2007;Berenstein 2012a,b;Ghosh, Paul & Ray 2016), including the case where the inhibitor is immobile (Dawson, Lawniczak & Kapral 1994). Both stationary and travelling patterns may coexist in such reaction-diffusion-advection systems (Satnoianu 2003), and wave instabilities manifest in chemical (Riaz, Kar & Ray 2004) and ecological (Malchow 1995(Malchow , 2000 models.…”

Section: Introductionmentioning

confidence: 99%

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Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains

2019

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We study spatial and spatio-temporal pattern formation emergent from reaction–diffusion–advection systems formed by considering reaction–diffusion systems coupled to prescribed fluid flows. While there have been a number of studies on the planar dynamics of such systems and the resulting instabilities and spatio-temporal patterning in the plane, less has been done on complicated flows in complex domains. We consider a general approach for the study of bounded domains in order to model two- and three-dimensional geometries which are more likely to be of relevance for modelling dynamics within fluid vessels used in experiments. Considering a variety of problem geometries with finite cross-sections, such as two-dimensional channels, three-dimensional ducts and three-dimensional pipes, we demonstrate the role cross-section geometry plays in pattern formation under such systems. We find that the generic instability is that of an oscillatory or wave Turing instability, resulting in patterns which change in time, often being advected with the fluid flow. As in previous works, we observe a change in patterns formed when progressing from zero to weak to strong advection for uniform advection across the domain, with particularly strong advection destroying patterns. One novel finding is that heterogeneous fluid flow can induce qualitatively different patterns across the domain. For instance, Poiseuille flow with maximal advection in the centre of a vessel and zero advection at the boundary of a vessel is shown to exhibit patterns in the centre of the vessel which are different from patterns near the boundary, with differences attributed to the differential local advection within each region of the vessel. Additionally, we observe sheared patterns, which appear due to gradients in the fluid velocity, and cannot be obtained via any kind of uniform flow. Finally we also explore flow in more complex domains, including wavy-walled channels, continuous stirred-tank reactors, U-shaped pipes and a toroidal domain, in order to demonstrate behaviours when the flow is both heterogeneous and bidirectional, as well as to demonstrate that our results still apply for complex finite domains. Our analysis suggests that such non-trivial advection results in moving patterns which are more complex than observed in simpler reaction–diffusion–advection, and may be more characteristic of realistic flow regimes in biological media.

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Section: Instability In a 2-d Rectangular Channel Flowmentioning

confidence: 71%

“…2007; Berenstein 2012 a , b ; Ghosh et al. 2016). This will typically correspond to translation of spatial patterns with the fluid flow.…”

Section: Pattern Formation In Channels Pipes and Ductsmentioning

confidence: 99%

Section: The General Scalar Sturm-liouville Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains

2019

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Catalytic Membrane Reactor Model as a Laboratory for Pattern Emergence in Reaction‐diffusion‐advection Media

Yochelis

2018

Israel Journal of Chemistry

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Reaction‐diffusion‐advection media on semi‐infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. To demonstrate the rich emergence of nonlinear traveling waves and stationary periodic states, we review results obtained using a membrane reactor as a case model. Such solutions coexist in overlapping parameter regimes and their temporal stability is determined by the boundary conditions which either preserve or destroy the translational symmetry, i. e., selection mechanisms under realistic Danckwerts boundary conditions. A brief outlook is given at the end.

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Spatiotemporal patterns of reaction–diffusion systems with advection mechanisms on large-scale regular networks

He,

2024

Chaos, Solitons & Fractals

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Differential-flow-induced transition of traveling wave patterns and wave splitting

Cited by 10 publications

References 45 publications

Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains

Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains

Catalytic Membrane Reactor Model as a Laboratory for Pattern Emergence in Reaction‐diffusion‐advection Media

Spatiotemporal patterns of reaction–diffusion systems with advection mechanisms on large-scale regular networks

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