scholarly journals Relations between Geometric Parameters and Numerical Simulation Accuracy in Modeling Signal Transmission in the Presynaptic Bouton

2021 ◽  
Vol 11 (6) ◽  
pp. 2811
Author(s):  
Maciej Gierdziewicz
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Complex Shape ◽  
Nonlinear Term ◽  
Signal Transmission ◽  
Tetrahedral Mesh ◽  
Mesh Quality ◽  
Simulation Accuracy ◽  
Simulation Methodology

In order to examine nerve impulses by means of simulation methodology, the models of all parts of nervous system, well suited for numerical modeling, are needed. In this paper the problem of setting up such a model, namely, that of a presynaptic bouton, is addressed. Simulation of the neurotransmitter flow inside the presynaptic bouton is performed. The transport is modeled with a partial differential equation with an additional nonlinear term. Two ways of modeling the bouton are applied. One of them let reflect a complex shape of the bouton and of some inner organelles. The influence of the generated mesh quality on the accuracy of numerical simulations is studied by comparing the released amount of neurotransmitter. The only mesh that produced diminished output was the worst one. The conclusion is that even slightly optimized tetrahedral mesh is suitable for calculations.

Numerical Simulation of Orientation Distribution on Fibers Suspensions in Planar Extensional Field

2013 ◽  
Vol 395-396 ◽  
pp. 1174-1178
Author(s):  
Pei Fang Luo ◽  
Zan Huang
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Orientation Distribution ◽  
Specific Form ◽  
Fiber Orientation Distribution ◽  
Planar Extensional Flow

A mathematical model of evolution process is adopted to simulate orientation distribution of fibers suspensions in planar extensional flow, i.e., specific form of Fokker-Plank partial differential equation and Jeffery equation. The analytical solution of differential equation on forecast fiber orientation distribution is deduced.

NUMERICAL SIMULATION OF THE KdV-MKdV EQUATION

1994 ◽  
Vol 05 (02) ◽  
pp. 407-410 ◽  
Author(s):  
THIAB R. TAHA
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Numerical Experiments ◽  
Nonlinear Partial Differential Equation ◽  
Method Of Lines ◽  
Inverse Scattering Transform ◽  
Mkdv Equation ◽  
Scattering Transform ◽  
The Method Of Lines

In this paper two numerical schemes for the numerical simulation of the nonlinear partial differential equation ut+6αuux+6βu2ux+uxxx=0 are implemented by the method of lines (MOL). The first scheme is based on the inverse scattering transform (IST), and the second scheme is a combination of the IST schemes for the Korteweg-de Vries (KdV) and modified KdV (MKdV) equations. The only difference between the two schemes is in the discretization of the nonlinear terms. Numerical experiments have shown that the first scheme is significantly more accurate than the second one. This demonstrates the importance of a proper discretization of nonlinear terms when a numerical method is designed for solving a nonlinear differential equation.

PID Control System for a Distributed Parameter Process

2014 ◽  
Vol 555 ◽  
pp. 222-231 ◽  
Author(s):  
Mihaela Ligia Ungureşan ◽  
Vlad Mureşan
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Control System ◽  
Control Systems ◽  
Pid Control ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Pid Algorithm

This paper presents the numerical simulation of a control system, with PID algorithm, for a process modeled through a partial differential equation of second order (PDE II.2), with respect to time (t) and to a spatial variable (p). Because these types of control systems are less usual, this paper develops a case study, with a program run on the computer. The details of using the PID control are pointed out, for an example of a system which contains a process with PDE II.2 structure.

Isogeometric Analysis of Heat Transfer in Fluids

2011 ◽  
Vol 105-107 ◽  
pp. 2174-2178
Author(s):  
Wen Lei Zhang ◽  
Rong Mo ◽  
Neng Wan ◽  
Qin Zhang
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Isogeometric Analysis ◽  
Two Dimensions ◽  
Programming Algorithm ◽  
Nurbs Basis Function ◽  
Numerical Formulation

This paper is devoted to the numerical simulation of heat transfer in fluids. We develop a numerical formulation based on isogeometric analysis that permits straightforward construction of higher order smooth NURBS approximation. Firstly, we introduce the partial differential equation (PDE) which servers as basis for the whole paper. Then, we introduce Lagrange multiplier method to deal with essentional boundary contions accroding to the nature of NURBS basis function. After getting the Equivalent integral equation, the isogeometric solving format is established based on the idea of isoparametric which is the necessary fundamentals of Isogeometric Analysis. We also discuss the programming algorithm of isogeometric analysis based on Matlab. Finally, a numerical example in two dimensions is presented that illustrate the effectiveness and robustness of our approach.

DISCRETIZATION OF STATIONARY SOLUTIONS OF SPDE'S BY EXTERNAL APPROXIMATION IN SPACE AND TIME

2010 ◽  
Vol 20 (09) ◽  
pp. 2835-2850 ◽  
Author(s):  
A. OGROWSKY ◽  
B. SCHMALFUSS
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Additive Noise ◽  
Nonlinear Term ◽  
Stationary Solutions ◽  
Space Time ◽  
Partial Differential ◽  
Random Fixed Point ◽  
Random Fixed Points

We consider a stochastic partial differential equation with additive noise satisfying a strong dissipativity condition for the nonlinear term such that this equation has a random fixed point. The goal of this article is to approximate this fixed point by space and space-time discretizations of a stochastic differential equation or more precisely, a conjugate random partial differential equation. For these discretizations external schemes are used. We show the convergence of the random fixed points of the space and space-time discretizations to the random fixed point of the original partial differential equation.

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