On Unstable Solutions with a Nonmonotone Boundary Layer in a Two-Dimensional Reaction-Diffusion Problem

2021 ◽  
Vol 110 (5-6) ◽  
pp. 922-931
Author(s):  
N. N. Nefedov ◽  
E. I. Nikulin
Keyword(s):  
Boundary Layer ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Unstable Solutions

Two-dimensional finite element model to study unsteady state Ca2+ diffusion in neuron involving ER LEAK and SERCA

2015 ◽  
Vol 08 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Amrita Jha ◽  
Neeru Adlakha
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Element Model ◽  
Diffusion Problem ◽  
Physiological Parameters ◽  
Communication Process ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Unsteady State

In this paper, finite element approach using two-dimensional unsteady state problem has been developed to study radial and angular calcium diffusion problem in neurons. Calcium is responsible messenger for transmitting information in communication process between neurons. The most important Ca 2+ binding proteins for the dynamics of Ca 2+ is itself buffer and other physiological parameters are located in Ca 2+ stores. In this study, the model incorporates the physiological parameters like diffusion coefficient, receptors, exogenous buffers etc. Appropriate boundary conditions have been framed in view of the physiological conditions. Computer simulations in MATLAB 7.11 are employed to investigate mathematical models of reaction–diffusion equation, the details of the implementation can heavily affect the numerical solutions and, thus, the outcome simulated on Core(TM) i3 CPU M 330 @ 2.13 GHz processing speed and 3 GB memory.

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