Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.

The effect of the contaminant emission rate on the velocity field and contaminant distribution with the presence of an obstacle in a large space

In the industrial field, the prediction of the contaminant gas distribution is very meaningful. However, when the leakage is high, not only the contaminant distribution will not follow the pattern of the original flowfield, but the contaminant buoyancy or negative buoyancy will affect the flowfield conversely. In this study, we focus on the effect of the contaminant emission rate on the velocity field and contaminant distribution with an obstacle in a large space by means of CFD simulation. Two leaking positions and five emission rates of the source have been taken into consideration. When the emission rate is high enough, the flowfield structure will be altered and new vortexes will appear. The contaminant dimensionless concentration distribution is totally different from the low-emission-rate conditions. The flammable region becomes significant, which leads to the potential risk of explosion.

Adsorption capacity of chosen sandy ground with respect to contaminants relocating with groundwater

One of the most important problems concerning contaminant transport in the ground is the problem related to the definition of parameters characterizing the adsorption capacity of ground for the chosen contaminants relocating with groundwater. In this paper, for chloride and sulfate indicators relocating in sandy ground, the numerical values of retardation factors (Ra) (treated as average values) and pore groundwater velocities with adsorption (ux/Ra) (in micro-pore ground spaces) are taken into consideration. Based on 2D transport equation the maximal dimensionless concentration values (C*max c) in the chosen ground cross-sections were calculated. All the presented numerical calculations are related to the unpublished measurement series which was marked in this paper as: October 1982. For this measurement series the calculated concentration values are compared to the measured concentration ones (C*max m) given recently to the author of this paper. In final part of this paper the parameters characterizing adsorption capacity (Ra, ux/Ra) are also compared to the same parameters calculated for the two earlier measurement series. Such comparison also allowed for the estimation of a gradual in time depletion of adsorption capacity for the chosen sandy ground.

Description and Verification of the Contaminat Transport Models in Groundwater (Theory And Practice)

This paper presents a general overview of 2D mathematical models for both the inorganic and the organic contaminants moving in an aquifer, taking into consideration the most important processes that occur in the ground. These processes affect, to a different extent, the concentration reduction values for the contaminants moving in a groundwater. In this analysis, the following processes have been taken into consideration: reversible physical non-linear adsorption, chemical and biological reactions (as biodegradation/biological denitrification) and radioactive decay (for moving radionuclides). Based on these 2D contaminant transport models it has been possible to calculate numerically the dimensionless concentration values with and without all the chosen processes in relation to both the chosen natural site (piezometers) and the chosen contaminants.In this paper, it has also been possible to compare all the numerically calculated concentration values to the measured concentration ones (in the chosen earlier piezometers) in relation to both the new unpublished measurement series of May 1982 and the new set of parameters used in these 2D contaminant transport models (as practical verification of these models).

A note on the small-time development of the solution to a coupled, nonlinear, singular reaction-diffusion system

In this paper, we consider a coupled, nonlinear, singular (in the sense that the reaction terms in the equations are not Lipschitz continuous) reaction-diffusion system, which arises from a model of fractional order chemical autocatalysis and decay, with positive initial data. In particular, we consider the cases when the initial data for the the dimensionless concentration of the autocatalyst, β, is of (a) O(x−λ) or (b) O(e−σ x) at large x (dimensionless distance), where σ > 0 and λ are constants. While initially the dimensionless concentration of the reactant, α, is identically unity, we establish, by developing the small-t (dimensionless time) asymptotic structure of the solution, that the support of β(x, t) becomes finite in infinitesimal time in both cases (a) and (b) above. The asymptotic form for the location of the edge of the support of β as t → 0 is given in both cases.