scholarly journals Solutions of the 4-species quadratic reaction-diffusion system are bounded and C∞-smooth, in any space dimension

2019 ◽  
Vol 12 (7) ◽  
pp. 1773-1804 ◽  
Author(s):  
M. Cristina Caputo ◽  
Thierry Goudon ◽  
Alexis F. Vasseur
2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Jan Eisner ◽  
Martin Väth

AbstractWe consider a reaction-diffusion system of activator-inhibitor or substrate-depletion type in one space dimension which is subject to diffusion-driven instability. We determine the change of bifurcation when a pure Neumann condition is supplemented with a Signorini condition. We show that this change differs essentially from the known case when also Dirichlet conditions are assumed.


1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Keiichi Kataoka ◽  
Hironori Fujita ◽  
Mutsumi Isa ◽  
Shimpei Gotoh ◽  
Akira Arasaki ◽  
...  

AbstractMorphological variations in human teeth have long been recognized and, in particular, the spatial and temporal distribution of two patterns of dental features in Asia, i.e., Sinodonty and Sundadonty, have contributed to our understanding of the human migration history. However, the molecular mechanisms underlying such dental variations have not yet been completely elucidated. Recent studies have clarified that a nonsynonymous variant in the ectodysplasin A receptor gene (EDAR370V/A; rs3827760) contributes to crown traits related to Sinodonty. In this study, we examined the association between theEDARpolymorphism and tooth root traits by using computed tomography images and identified that the effects of theEDARvariant on the number and shape of roots differed depending on the tooth type. In addition, to better understand tooth root morphogenesis, a computational analysis for patterns of tooth roots was performed, assuming a reaction–diffusion system. The computational study suggested that the complicated effects of theEDARpolymorphism could be explained when it is considered that EDAR modifies the syntheses of multiple related molecules working in the reaction–diffusion dynamics. In this study, we shed light on the molecular mechanisms of tooth root morphogenesis, which are less understood in comparison to those of tooth crown morphogenesis.


2021 ◽  
Vol 31 (3) ◽  
pp. 033118
Author(s):  
Margaret K. McGuire ◽  
Chase A. Fuller ◽  
John F. Lindner ◽  
Niklas Manz

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll

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