The Influence of the Diffusion Space Geometry on Behavior of some Processes in Biochemistry and Electrochemistry

2000 ◽  
Vol 5 ◽  
pp. 3-38 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys ◽  
M. Sapagovas ◽  
A. Survila
Keyword(s):  
Mathematical Model ◽  
Reaction Diffusion ◽  
Electrode Reaction ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Carbon Paste ◽  
Diffusion Type ◽  
Function Modelling ◽  
Partially Blocked Electrodes ◽  
The Mathematical Model

The reaction-diffusion and diffusion equations were applied for modelling of some processes in biochemistry and electrochemistry. Modelling of the amperometric biosensors based on carbon paste electrodes encrusted with a single nonhomogeneous microreactor is analyzed. The mathematical model of the biosensor operation is based on nonstationary reaction-diffusion equations containing a non-linear term given by Michaelis-Menten function. Modelling of a simple redox-electrode reaction, involving two soluble species, is also considered. The model of the electrode behavior, taking into account the resist layer of the partially blocked electrodes, was expressed as a system of differential equations of the diffusion type with initial and boundary conditions. The mathematical model generalizing both processes: biochemical and electrochemical is presented in this paper. The generalized problem was solved numerically. The finite-difference technique was used for discretisation of the model. Using the numerical solution of the generalized problem, the influence of the size, shape and position of a microreactor as well as the thickness of the resist layer on the current dynamics was investigated.

scholarly journals Kompiuterinis optinio biojutiklio savybių tyrimas taikant bedimensį modelį

2009 ◽  
Vol 50 ◽  
pp. 306-310
Author(s):  
Evelina Gaidamauskaitė ◽  
Romas Baronas
Keyword(s):  
Mathematical Model ◽  
Digital Simulation ◽  
Reaction Diffusion ◽  
Optical Biosensor ◽  
Reaction Diffusion Equations ◽  
Computational Investigation ◽  
Linear Reaction ◽  
The Mathematical Model ◽  
Enzyme Layer ◽  
Biosensor Response

Šiame darbe, siekiant nustatyti pagrindinius kinetinius peroksidazinio optinio biojutiklio matematinio modelio parametrus, buvo sudarytas bedimensis modelis. Biojutikliui taikomos reakcijos-difuzijos lygtys su netiesiniu nariu, aprašančiu fermentinę reakciją. Biojutiklio veikimas modeliuojamas fermento ir difuzijos sluoksniuose. Ištirta biojutiklio atsako ir jautrio priklausomybė nuo bedimensio biojutiklio modulio. Suformuluotas uždavinys sprendžiamas baigtinių skirtumų metodu. Gauti rezultatai pagrindžia šio modelio pritaikomumą. Atliekami peroksidazinio optinio biojutiklio eksperimentiniai tyrimai leis nustatyti modelio taikymo ribas.A Computational Investigation of the Optical Biosensor by a Dimensionless ModelEvelina Gaidamauskaitė, Romas Baronas SummaryIn order to determine the main governing parameters, a dimensionless mathematical model of a peroxidase-based optical biosensor is derived. The mathematical model of the biosensor is based on a system of non-linear reaction-diffusion equations. The modelled biosensor comprises two compartments, an enzyme layer and an outer diffusion layer. The influence of the dimensionless diffusion modulus on the biosensor response and the sensitivity is investigated. The digital simulation was carried out using a finite difference method.

scholarly journals An ADI Method for the Numerical Solution of 3D Fractional Reaction-Diffusion Equations

2020 ◽  
Vol 4 (4) ◽  
pp. 57
Author(s):  
Moreno Concezzi ◽  
Renato Spigler
Keyword(s):  
Fluid Flows ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Three Dimensions ◽  
Diffusion Equations ◽  
Diffusion Type ◽  
Pagerank Algorithm ◽  
Adi Method ◽  
Alternating Direction ◽  
Flows Through Porous Media

A numerical method for solving fractional partial differential equations (fPDEs) of the diffusion and reaction–diffusion type, subject to Dirichlet boundary data, in three dimensions is developed. Such fPDEs may describe fluid flows through porous media better than classical diffusion equations. This is a new, fractional version of the Alternating Direction Implicit (ADI) method, where the source term is balanced, in that its effect is split in the three space directions, and it may be relevant, especially in the case of anisotropy. The method is unconditionally stable, second-order in space, and third-order in time. A strategy is devised in order to improve its speed of convergence by means of an extrapolation method that is coupled to the PageRank algorithm. Some numerical examples are given.

scholarly journals Comments on “Homotopy Perturbation Method for Solving Reaction-Diffusion Equations”

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Afgan Aslanov
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Diffusion Type ◽  
Homotopy Perturbation ◽  
False Conclusion ◽  
Correct Form

The paper entitled“Homotopy perturbation method for solving reaction diffussion equation”contains some mistakes and misinterpretations along with a false conclusion. Applying the homotopy perturbation method (HPM) in an incorrect manner, the authors have drawn the false conclusion that this approach is efficient for reaction-diffusion type of equation. We show that HPM in the proposed form is not efficient in most cases, and hence, we will introduce the correct form of HPM.

scholarly journals Calculation of the apparent Michaelis constant for biosensors using reaction-diffusion equations

2014 ◽  
Vol 55 ◽  
Author(s):  
Pranas Katauskis ◽  
Feliksas Ivanauskas ◽  
Sigitas Laukevičius
Keyword(s):  
Mathematical Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Michaelis Constant ◽  
Amperometric Biosensors ◽  
The Relationship

The relationship between the apparent Michaelis constant and the diffusion module for one and two-layer biosensors is studied using a mathematical model describing action of the amperometric biosensors.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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