scholarly journals On the behaviour of solutions of the two-cell cubic autocatalator reaction model

2008 ◽  
Vol 44 ◽  
pp. 1 ◽  
Author(s):  
H. I. Abdel-Gawad ◽  
K. M. Saad
Keyword(s):  
Reaction Model ◽  
Cubic Autocatalator

scholarly journals A cubic autocatalator chemical reaction model with limit cycle analysis and consistency preserving discretization

2021 ◽  
Vol 87 (2) ◽  
pp. 441-462
Author(s):  
Qamar Din ◽  
◽  
Muhammad Sajjad Shabir ◽  
Muhammad Asif Khan
Keyword(s):  
Chemical Reaction ◽  
Discrete Time ◽  
Continuous System ◽  
Reaction Model ◽  
Qualitative Properties ◽  
Time Model ◽  
Interior Equilibrium ◽  
Chemical Reaction Model ◽  
Scheme Analysis ◽  
Cubic Autocatalator

This article deals with the study of some qualitative properties of a cubic autocatalator chemical reaction model. Particularly, we obtain a dynamically consistent cubic autocatalator discrete-time model by applying a nonstandard difference scheme. Analysis of the existence of equilibria and their stability is carried out. It is proved that a continuous system undergoes the Hopf bifurcation at its interior equilibrium, whereas the discrete-time version undergoes Neimark-Sacker bifurcation at its interior fixed point. Moreover, numerical simulation is provided to strengthen our theoretical discussion.

scholarly journals Bifurcation analysis of a discrete-time four-dimensional cubic autocatalator chemical reaction model with coupling through uncatalysed reactant

2021 ◽  
Vol 87 (2) ◽  
pp. 415-439
Author(s):  
Muhammad Salman Khan ◽  
Keyword(s):  
Fixed Point ◽  
Chemical Reaction ◽  
Discrete Time ◽  
Hybrid Control ◽  
Continuous System ◽  
Reaction Model ◽  
Dimensional System ◽  
Chemical Reaction Model ◽  
Cubic Autocatalator ◽  
Positive Fixed Point

In this manuscript, we discuss a four-dimensional cubic autocatalator chemical reaction model in continuous form. We investigate the existence of one and only positive fixed point and then we have obtained some parametric conditions for local stability of continuous system by using Routh-Hurwitz stability criteria. Moreover, we discretize the four-dimensional continuous cubic autocatalator chemical reaction model by using Euler’s forward method and then by using a nonstandard difference scheme we obtained a consistent discrete-time counterpart of four-dimensional cubic autocatalator chemical reaction model. Parametric conditions for local asymptotic stability of one and only positive fixed point of obtained system are also discussed. It is shown that the obtained system experiences the Neimark-Sacker bifurcation at one and only positive fixed point by using a general standard for Neimark-Sacker bifurcation. The discrete-time counterpart of genuine four-dimensional system displays chaotic dynamics at different standards of bifurcation parameter. Furthermore, the control of Neimark-Sacker bifurcation and chaos is also deliberated by using a generalized hybrid control scheme, which is based on parameter perturbation and feedback control. Finally, some numerical examples are given to strengthen our theoretical results.

Intensification of cooling in a batch reactor with an exothermic reaction by nonisothermal control in stable pseudostationary states

1984 ◽  
Vol 49 (11) ◽  
pp. 2566-2578 ◽  
Author(s):  
Josef Horák ◽  
Petr Beránek ◽  
Dagmar Maršálková
Keyword(s):  
Batch Reactor ◽  
Exothermic Reaction ◽  
Reaction Model ◽  
Order Reaction ◽  
Zero Order ◽  
Coolant Temperature ◽  
Inlet Temperature ◽  
Adaptive Parameter ◽  
Zero Order Reaction ◽  
Set Up

An algorithm is set up and tested for the temperature control of a batch reactor consisting in jump changes in the inlet temperature of entering coolant. This temperature is so chosen that its difference from the temperature of the reaction mixture is near the highest difference at which the stable pseudostationary state of the system still exists. For the prediction of the new coolant inlet temperature, a zero-order reaction model is used with an adaptive parameter estimated from the experimentally established value of the maximum of the reaction mixture overheating at the previous coolant temperature.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

Gas Cell Infrared and Attenuated Total Reflection Infrared Spectroscopic Studies for Organic–Inorganic Interactions in Adsorption of Fulvic Acid on the Goethite Surface Generating Carbon Dioxide

2021 ◽  
pp. 000370282199121
Author(s):  
Yuki Nakaya ◽  
Satoru Nakashima ◽  
Takahiro Otsuka
Keyword(s):  
Carbon Dioxide ◽  
Activation Energy ◽  
Fulvic Acid ◽  
Spectroscopic Studies ◽  
Reaction Model ◽  
Total Reflection ◽  
Attenuated Total Reflection ◽  
Gas Cell ◽  
Rate Determining Step ◽  
Ir Spectroscopic

The generation of carbon dioxide (CO2) from Nordic fulvic acid (FA) solution in the presence of goethite (α-FeOOH) was observed in FA–goethite interaction experiments at 25–80 ℃. CO2 generation processes observed by gas cell infrared (IR) spectroscopy indicated two steps: the zeroth order slower CO2 generation from FA solution commonly occurring in the heating experiments of the FA in the presence and absence of goethite (activation energy: 16–19 kJ mol–1), and the first order faster CO2 generation from FA solution with goethite (activation energy: 14 kJ mol–1). This CO2 generation from FA is possibly related to redox reactions between FA and goethite. In situ attenuated total reflection infrared (ATR-IR) spectroscopic measurements indicated rapid increases with time in IR bands due to COOH and COO– of FA on the goethite surface. These are considered to be due to adsorption of FA on the goethite surface possibly driven by electrostatic attraction between the positively charged goethite surface and negatively charged deprotonated carboxylates (COO–) in FA. Changes in concentration of the FA adsorbed on the goethite surface were well reproduced by the second order reaction model giving an activation energy around 13 kJ mol–1. This process was faster than the CO2 generation and was not its rate-determining step. The CO2 generation from FA solution with goethite is faster than the experimental thermal decoloration of stable structures of Nordic FA in our previous report possibly due to partial degradations of redox-sensitive labile structures in FA.

scholarly journals Langmuir Adsorption Kinetics in Liquid Media: Interface Reaction Model

ACS Omega ◽  
2021 ◽  
Author(s):  
Md Akhtarul Islam ◽  
Myisha Ahmed Chowdhury ◽  
Md. Salatul Islam Mozumder ◽  
Md. Tamez Uddin
Keyword(s):  
Adsorption Kinetics ◽  
Interface Reaction ◽  
Reaction Model ◽  
Liquid Media ◽  
Langmuir Adsorption

scholarly journals Isothermal Kinetic Analysis of the Thermal Decomposition of Wood Chips from an Apple Tree

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 195
Author(s):  
Ivan Vitázek ◽  
Martin Šotnar ◽  
Stella Hrehová ◽  
Kristína Darnadyová ◽  
Jan Mareček
Keyword(s):  
Thermal Decomposition ◽  
Apple Tree ◽  
Combustion Process ◽  
Reaction Model ◽  
Wood Chips ◽  
Small Scale ◽  
Exponential Factor ◽  
Air Atmosphere ◽  
First Order Chemical Reaction ◽  
Isothermal Kinetic

The thermal decomposition of wood chips from an apple tree is studied in a static air atmosphere under isothermal conditions. Based on the thermogravimetric analysis, the values of the apparent activation energy and pre-exponential factor are 34 ± 3 kJ mol−1 and 391 ± 2 min−1, respectively. These results have also shown that this process can be described by the rate of the first-order chemical reaction. This reaction model is valid only for a temperature range of 250–290 °C, mainly due to the lignin decomposition. The obtained results are used for kinetic prediction, which is compared with the measurement. The results show that the reaction is slower at higher values of degree of conversion, which is caused by the influence of the experimental condition. Nevertheless, the obtained kinetic parameters could be used for the optimization of the combustion process of wood chips in small-scale biomass boilers.

scholarly journals Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach

2021 ◽  
Vol 5 (2) ◽  
pp. 51
Author(s):  
Ashraf M. Tawfik ◽  
Mohamed Mokhtar Hefny
Keyword(s):  
Molecular Species ◽  
Transport Model ◽  
Mean Square Displacement ◽  
Telegraph Equation ◽  
Reaction Model ◽  
Simulation Techniques ◽  
Experimental Works ◽  
The Mean ◽  
Classical Transport ◽  
Fractional Reaction

In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time.

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