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Abstract:We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the "rarefied gas" limit or the "molecular chaos" hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

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Global effort s around the world are focused on to discuss several health care strategies for minimizing the impact of the new coronavirus (COVID-19) on the community. As it is clear that this virus becomes a public health threat and spreading easily among individuals. Mathematical models with computational simulations are effective tools that help global effort s to estimate key transmission parameters and further improvements for controlling this disease. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates.This work reviews and develops some suggested models for the COVID-19 that can address important questions about global health care and suggest important notes. Then, we suggest an updated model that includes a system of differential equations with transmission parameters. Some key computational simulations and sensitivity analysis are investigated. Also, the local sensitivities for each model state concerning the model parameters are computed using three different techniques: non-normalizations, half normalizations, and full normalizations.Results based on the computational simulations show that the model dynamics are significantly changed for different key model parameters. Interestingly, we identify that transition rates between asymptomatic infected with both reported and unreported symptomatic infected individuals are very sensitive parameters concerning model variables in spreading this disease. This helps international effort s to reduce the number of infected individuals from the disease and to prevent the propagation of new coronavirus more widely on the community. Another novelty of this paper is the identification of the critical model parameters, which makes it easy to be used by biologists with less knowledge of mathematical modeling and also facilitates the improvement of the model for future development theoretically and practically.

In view of ecological concern and energy security, execution of refrigeration system should be enriched which can be done by improving the characteristics of working liquids. The nanoliquids have gained interest in industrial and engineering fields due to their outstanding thermophysical features. Researchers used nanoliquids as working liquid and detected substantial variations in thermal performance. In the present research work, our intention is to explore the impact of nonlinear thermal radiation and variable thermal conductivity on 3D flow of cross-nanofluid. Moreover, heat sink-source, chemical processes and activation energy are implemented. Zero mass flux relation with thermophoresis and Brownian motion mechanisms are scrutinized. The required system of ordinary ones is achieved by implementing appropriate transformations. The achieved system of ordinary ones is computed numerically by implementing bvp4c scheme. Graphs are plotted to explore the impact of various physical parameters on concentration, temperature and velocity fields. It is detected from obtained graphical data that thermophoresis and Brownian motion mechanisms significantly affect heat transport mechanism. Furthermore, graphical analysis reveals that concentration of cross-nanofluid enhances for augmented values of activation energy.