Pyrolysis behaviors dominated by the reaction–diffusion mechanism in the fluorine-free metal–organic decomposition process

2020 ◽  
Vol 8 (48) ◽  
pp. 17417-17428
Author(s):  
Jiangtao Shi ◽  
Yue Zhao ◽  
Yue Wu ◽  
Jingyuan Chu ◽  
Xiao Tang ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Decomposition Process ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Metal Organic ◽  
Free Metal ◽  
Organic Decomposition

In this work, pyrolysis behaviors dominated by the reaction–diffusion mechanism were investigated. And one-dimensional reaction–diffusion model is proposed.

Stability and Hopf Bifurcation in a Reaction–Diffusion Model with Chemotaxis and Nonlocal Delay Effect

2018 ◽  
Vol 28 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Dong Li ◽  
Shangjiang Guo
Keyword(s):  
Hopf Bifurcation ◽  
Diffusion Model ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
High Concentration ◽  
Delay Effect ◽  
One Dimensional ◽  
Nonlocal Delay ◽  
Reaction Diffusion Model ◽  
Steady State Solutions

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction–diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov–Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

scholarly journals Formation of periodic pigment spots by the reaction-diffusion mechanism

2018 ◽  
Author(s):  
Baoqing Ding ◽  
Erin L. Patterson ◽  
Srinidhi V. Holalu ◽  
Jingjian Li ◽  
Grace A. Johnson ◽  
...  
Keyword(s):  
Long Range ◽  
Diffusion Model ◽  
Feedback Loop ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Pollinator Visitation ◽  
Reaction Diffusion Model ◽  
Inhibitory Feedback ◽  
R2r3 Myb ◽  
Diffusion Networks

AbstractMany organisms exhibit visually striking spotted or striped pigmentation patterns. Turing’s reaction-diffusion model postulates that such periodic pigmentation patterns form when a local autocatalytic feedback loop and a long-range inhibitory feedback loop interact. At its simplest, this network only requires one self-activating activator that also activates a repressor, which inhibits the activator and diffuses to neighboring cells. However, the molecular activators and repressors fully fitting this versatile model remain elusive. Here, we characterize an R2R3-MYB activator and an R3-MYB repressor in monkeyflowers that correspond to Turing’s model and explain how periodic anthocyanin spots form. Notably, disrupting this pattern impacts pollinator visitation. Thus, subtle changes in simple reaction-diffusion networks are likely essential contributors to the evolution of the remarkable diversity of periodic pigmentation patterns in flowers.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations
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