Correction to: General conditions for Turing and wave instabilities in reaction–diffusion systems

Villar-Sepúlveda, Edgardo; Champneys, Alan R

doi:10.1007/s00285-023-01884-x

Cited by 2 publications

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“…In Figure 5 , we display these three oscillatory patterns (HO, TW, SW) in a spatially extended system. In contrast to the zero wavenumber Hopf bifurcation, the finite wavenumber Hopf bifurcation requires a three-variable system ( Yochelis et al, 2008 ; Stich et al, 2009 ; Anma et al, 2012 ; Hata et al, 2014 ; Villar-Sepúlveda and Champneys, 2023 ). In Box 4 , we provide additional heuristic details about the richness of the primary finite wavenumber Hopf bifurcation.…”

Section: What Type Of Theory Do We Need?mentioning

confidence: 99%

“…So far, we can use mathematics to exclude some mechanisms. For example, we know that a finite wavenumber Hopf bifurcation to TW and SW cannot arise in two variable RD models ( Villar-Sepúlveda and Champneys, 2023 ). A third component is required to account for trains of pulses emanating from a single localized stimulus (e.g., see Yochelis et al, 2008 ; Yochelis et al, 2015 ).…”

Section: What Type Of Theory Do We Need?mentioning

confidence: 99%

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From actin waves to mechanism and back: How theory aids biological understanding

Beta

Edelstein‐Keshet

Gov

et al. 2023

eLife

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Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

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Section: What Type Of Theory Do We Need?mentioning

confidence: 99%

Section: What Type Of Theory Do We Need?mentioning

confidence: 99%

From actin waves to mechanism and back: How theory aids biological understanding

Beta

Edelstein‐Keshet

Gov

et al. 2023

eLife

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The appearance of standing wave structures in the reaction medium during the diffusion development of the chain reaction process

Sargsyan,

Silveistr,

Lysyi

et al. 2023

Scientific Herald of Uzhhorod University Series Physics

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Relevance. Understanding the dynamic behavior of radicals in reactors undergoing gas-phase oxidation of organic substances is crucial for optimizing reactor design and safety across industries. Purpose. This study aims to elucidate the emergence of standing wave structures influenced by feedback mechanisms in reactors with cylindrical and spherical symmetry, using mathematical principles governing the propagation of oscillations and shock waves in diffusion-driven chain reactions. Methodology. Materials and methods for the research included a computer simulation using MATHCAD 2001i, and comparative analysis of experimental data obtained from reactor experiments. The computational modeling revealed vivid formations of standing wave structures in reactors influenced by feedback mechanisms. Results. The impact of reverse connections in reactors with cylindrical and spherical symmetry significantly contributed to the formation of various standing wave structures of radical concentrations within the reaction zone. It was found that these structures were largely imperceptible visually and could only be observed when the reaction was accompanied by intense light emission. These visual representations served as compelling evidence of the intricate interplay between reaction kinetics and feedback effects. The study emphasized the importance of understanding and predicting the root causes of instabilities, ultimately enhancing the reliability and safety of reactors across various industries. The results demonstrated a correlation between specific feedback mechanisms and the spatial distribution of standing wave structures. Conclusions. The derived computational patterns, as presented in this paper, provide compelling evidence supporting the feasibility of standing wave structure formation within reactors when influenced by feedback mechanisms. The study unveiled the potential for fine-tuning reactor parameters to influence the formation and stability of these structures. The findings represented a significant stride towards a more comprehensive understanding of dynamic regimes in reactors, with implications for reactor design, operation, and safety protocols. The insights garnered from uncovering standing wave structures influenced by feedback mechanisms offered valuable opportunities to optimize reactor design and operational safety, leading to more efficient and sustainable processes

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Correction to: General conditions for Turing and wave instabilities in reaction–diffusion systems

Cited by 2 publications

References 0 publications

From actin waves to mechanism and back: How theory aids biological understanding

From actin waves to mechanism and back: How theory aids biological understanding

The appearance of standing wave structures in the reaction medium during the diffusion development of the chain reaction process

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