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Mechanism of metallurgical coke gasification in CO2 and H2O using a reaction-diffusion model

CHEMICAL ENGINEERING JOURNAL 2025年 512卷

作者： Wang, Ai Rish, Salman Khoshk Jenkins, David R. Tahmasebi, Arash Univ Newcastle Newcastle Inst Energy & Resources NIER BHP Ctr Sustainable Steelmaking Res Callaghan NSW 2308 Australia

Hydrogen-enriched blast furnace can lower CO2 emissions in ironmaking, however, H2O generated during the process may react deleteriously with metallurgical coke, leading to accelerated structural degradation. A transient reaction-diffusion model was developed to investigate the gasification mechanism of cokes of varying strength, in either CO2 or H2O reaction environments. The model was validated by experimental mass loss over time produced using TGA and over radius measured using micro-CT imaging techniques. This led to improved accuracy compared with previous coke gasification models in the literature. Coke mass loss rate in H2O was significantly higher than CO2, and the reaction rate was lower for cokes with higher strength, regardless of gas type. When coke was reacted with CO2, the mass loss occurred more uniformly with depth into lumps, while in H2O a greater mass loss was observed near the coke surface. The reaction rate constant in H2O was typically 3.5 times greater than CO2. The initial effective diffusivity of H2O was also higher than CO2 (approximately 1.9 times). Compared to CO2, during the coke reaction with H2O, the local reactivity of carbon plays a more dominant role than gas diffusion. The developed model was used to predict the gasification behaviour of a 50 mm lump. Compared with CO2, greater mass loss at the surface of larger lumps in H2O led to shrinkage in size, while the core of the lumps remained less reacted.

关键词： Hydrogen blast furnace Coke gasification mechanism CO2 and H2O reaction reaction-diffusion model Coke size

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Analysis of a general reaction-diffusion model using Lie symmetries and conservation laws

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JOURNAL OF MATHEMATICAL CHEMISTRY 2025年第2期63卷 419-434页

作者： Saez-Martinez, Sol Univ Cadiz Dept Math Avda Univ Cadiz10 Puerto Real 11519 Spain

Turing's model to explains the formation of patterns in morphogenesis considered a system of chemicals, termed morphogens, that react and diffuse through tissues. These reaction-diffusion systems can start homogeneously but later develop patterns due to instabilities triggered by random disturbances. Building on this foundation, Kepper realized the Chlorite-Iodide Malonic-Acid reaction, an example of an oscillatory reaction in a homogeneous solution that forms spatial patterns in a non-homogeneous environment. This work led to further studies, such as the Lengyel-Epstein reaction-diffusion model, which describes the dynamics of chemical concentrations of activator and inhibitor species. This paper extends these classical models by investigating a general reaction-diffusion system through the lens of Lie symmetries. We analyze the system using Lie point symmetry generators and Lie symmetry groups, enabling us to reduce the equations via these symmetries. Furthermore, we compute the conservation laws for the general reaction-diffusion model using the multipliers approach, involving dependent variables, independent variables, and their derivatives up to a certain order. By applying various symmetry groups, we derive new solutions from known ones, offering deeper insights into the dynamics of pattern formation in biological systems.

关键词： reaction-diffusion model Symmetries Partial differential equations Conservation laws

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Structure of positive solutions for a reaction-diffusion model with additional food and protection zone

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2025年第1期542卷

作者： Wang, Jingjing Jia, Yunfeng Xian Univ Finance & Econ Sch Math Xian 710100 Shaanxi Peoples R China Shaanxi Normal Univ Sch Math & Stat Xian 710062 Shaanxi Peoples R China

The additional food and protection zone provided to predator and prey respectively are introduced into a reaction-diffusion predation model with nonlinear functional response in this paper. We mainly concentrate on the combined effects of additional food and protection zone on the existence and uniqueness of solution for the model. It is shown that, compared with the models with classical Beddington-DeAngelis functional response, the integration of additional food and protection zone into Beddington-DeAngelis functional response causes the model to produce new critical values for the existence of positive solutions. Moreover, we derive that the model permits a unique positive solution when the strength of mutual interference among predators or the quantity of additional food is large, where, the effect of quantity of additional food on the positive solution is a new finding. The results shed light on that the combination of additional food and protection zone is an effective and environmentally-friendly strategy in preserving biodiversity. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： reaction-diffusion model Additional food Protection zone Positive solution Existence

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Application of a reaction-diffusion model with different incidence rates: COVID-19 strains evolution

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NONLINEAR DYNAMICS 2024年第23期112卷 21533-21561页

作者： Lu, Fangzheng Tu, Yunbo Meng, Xinzhu Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China

COVID-19 is continuously evolving, and the JN.1 strain has become the primary prevalent strain in the world. This paper focuses on the JN.1 strain and establishes a two-strain reaction-diffusion model with different incidence rates. In this paper, the saturation incidence rate is used to describe the individual's fear of the JN.1 strain. First, we discuss the well-posedness with positivity and boundedness, obtain the reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_reaction-diffusion model$$\end{document}, and study the long-term behavior of the solution, including extinction, uniform persistence, local stability and global asymptotical stability. Second, we discretize the continuous system using the NSFD method and explore the well-posedness of the discrete system. Third, we use the method of sensitivity analysis to reveal the effect of parameters on the basic reproduction number. Susceptible individuals are more easily infected as the spatial diffusion coefficient increases. Besides, it is beneficial to form herd immunity. Moreover, this research reveals the evolution trend of COVID-19: the virus infection rate continuously increases while the mortality rate caused by the virus decreases after increases, tending to 0 since the beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} strain. The final result of the SARS-CoV-2 continued evolution is a higher infection rate and lower mortality rate, consistent with the long-term evolution trend of the virus.

关键词： COVID-19 evolution reaction-diffusion model Discrete system Global asymptotic stability Sensitivity analysis

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Influence of Human Behavior on COVID-19 Dynamics Based on a reaction-diffusion model

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QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 2023年第3期22卷 1-26页

作者： Zhi, Shun Niu, Hong-Tao Su, You-Hui Han, Xiaoling Shenyang Univ Technol Sch Sci Shenyang 110870 Liaoning Peoples R China Xuzhou Univ Technol Sch Math & Stat Xuzhou 221018 Jiangsu Peoples R China Northwest Normal Univ Coll Math & Stat Lanzhou 730070 Gansu Peoples R China

To investigate the influence of human behavior on the spread of COVID-19, we propose a reaction-diffusion model that incorporates contact rate functions related to human behavior. The basic reproduction number R-0 is derived and a threshold-type result on its global dynamics in terms of R-0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R-0 = 1;while there exists a positive stationary solution and the disease is uniformly persistent if R-0 > 1. By the numerical simulations of the analytic results, we find that human behavior changes may lower infection levels and reduce the number of exposed and infected humans.

关键词： reaction-diffusion model COVID-19 Human behavior change Basic reproduction number

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reaction-diffusion model to describe biodiesel production using lipase encapsulated in ZIF-8

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FUEL 2022年 311卷 122630-122630页

作者： Al-Mansouri, Reem Du, Wei Al-Zuhair, Sulaiman UAE Univ Chem & Petr Engn Dept Al Ain 15551 U Arab Emirates Tsinghua Univ Dept Chem Engn Beijing 100084 Peoples R China UAE Univ Natl Water & Energy Ctr Al Ain 15551 U Arab Emirates

Lipase has successfully been encapsulated into hexagonal zeolitic imidazolate frameworks (ZIF-8) for use in biodiesel production. It was shown that the lipase encapsulation did not have a significant effect on the morphology, surface properties and crystallinity. The effects of methanol ratio, temperature, oil concentration and water content, on the biodiesel production yield and rate of reaction, were tested. The highest yield was obtained at a methanol ratio and temperature of 6:1 and 40 degrees C, respectively, and a drop was observed by increasing both. It was also shown that the yield decreased with the increase in water content. The activity and stability of the immobilized lipase in ZIF-8 by encapsulation was compared to that immobilized by surface adsorption. Although the adsorbed lipase on ZIF-8 showed higher activity, the stability of the encapsulated one was higher. At methanol ratio of 12:1, the encapsulated lipase in ZIF-8 maintained 83% residual activity after 5 cycles, compared to only 34% attained by the adsorbed lipase at the same conditions. The experimental results were used to determine the kinetics parameters of modified Ping Pong Bi Bi model, and the accuracy of the prediction were compared to those obtained by the Michaelis Menten model. To gain a better insight into how the reaction occurs inside the ZIF-8 crystal with encapsulated lipase, a diffusion-reaction model was developed and numerically solved. The results clearly show that the substrate did not diffuse deeply into the crystal, which further confirmed the mass transfer limitation that resulted in the lower activity of the encapsulated lipase as compared to the adsorbed one. The developed numerical model can be applied to any diffusion-reaction systems.

关键词： Biodiesel Zeolite imidazolate framework Lipase Finite difference reaction-diffusion model

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A numerical efficient splitting method for the solution of HIV time periodic reaction-diffusion model having spatial heterogeneity

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2023年 609卷

作者： Raza, Nauman Arshed, Saima Bakar, Abu Shahzad, Aamir Inc, Mustafa Univ Punjab Dept Math Quaid E Azam Campus Lahore Pakistan Firat Univ Sci Fac Dept Math TR-23119 Elazig Turkey China Med Univ Dept Med Res Taichung 40402 Taiwan

This study examines a novel reaction-diffusion model for the existence and treatment of acquired immunodeficiency syndrome. This model is a spatial extension of the recent HIV model and human immunodeficiency viruses cause this disorder. The most significant barrier to eradicating this virus is latency and the virus' subsequent viral reservoir in CD4+ T cells. A nonstandard operator splitting strategy is proposed to approximate the solution of the time-periodic reaction-diffusion model. The main advantages of employing this approach over other techniques are its low computational costs, high accuracy and ease of implementation. The results are truly solid and match those available in the literature. The nature of the solution for the threshold parameter is demonstrated graphically using numerical results. Finally, the M-matrix theory and the positivity of the proposed scheme are discussed.(c) 2022 Elsevier B.V. All rights reserved.

关键词： HIV reaction-diffusion model Basic reproduction number Nonstandard operator splitting method Positivity

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Global dynamics of a nonlocal periodic reaction-diffusion model of bluetongue disease

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JOURNAL OF DIFFERENTIAL EQUATIONS 2021年 272卷 127-163页

作者： Li, Fuxiang Zhao, Xiao-Qiang China Univ Geosci Beijing Sch Sci Beijing 100083 Peoples R China Mem Univ Newfoundland Dept Math & Stat St John NF A1C 5S7 Canada

In this paper, we propose a nonlocal reaction-diffusion model of bluetongue disease with seasonality, spatial heterogeneous structure, and periodic extrinsic incubation period. We introduce the basic reproduction ratio R-0 for this model and show that the disease-free periodic solution is globally attractive if R-0 < 1, while the disease is uniformly persistent if R-0 > 1. Further, we obtain the global attractivity of the positive steady state in the case where all the coefficients are constants. Numerically, we study the bluetongue transmission in Corsica Island, France, and investigate the impact of some model parameters on R-0. We find that the disease risk may be underestimated if the spatial heterogeneity is ignored. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Bluetongue disease Periodic incubation period Basic reproduction ratio Noncompact solution maps reaction-diffusion model

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reaction-diffusion model-Based Research on Formation Mechanism of Neuron Dendritic Spine Patterns

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FRONTIERS IN NEUROROBOTICS 2021年 15卷 563682页

作者： Jia, Yiqing Zhao, Qili Yin, Hongqiang Guo, Shan Sun, Mingzhu Yang, Zhuo Zhao, Xin Nankai Univ Coll Artificial Intelligence Inst Robot & Automat Informat Syst Tianjin Peoples R China Nankai Univ Sch Med State Key Lab Med Chem Biol Tianjin Peoples R China

The pattern abnormalities of dendritic spine, tiny protrusions on neuron dendrites, have been found related to multiple nervous system diseases, such as Parkinson's disease and schizophrenia. The determination of the factors affecting spine patterns is of vital importance to explore the pathogenesis of these diseases, and further, search the treatment method for them. Although the study of dendritic spines is a hot topic in neuroscience in recent years, there is still a lack of systematic study on the formation mechanism of its pattern. This paper provided a reinterpretation of reaction-diffusion model to simulate the formation process of dendritic spine, and further, study the factors affecting spine patterns. First, all four classic shapes of spines, mushroom-type, stubby-type, thin-type, and branched-type were reproduced using the model. We found that the consumption rate of substrates by the cytoskeleton is a key factor to regulate spine shape. Moreover, we found that the density of spines can be regulated by the amount of an exogenous activator and inhibitor, which is in accordance with the anatomical results found in hippocampal CA1 in SD rats with glioma. Further, we analyzed the inner mechanism of the above model parameters regulating the dendritic spine pattern through Turing instability analysis and drew a conclusion that an exogenous inhibitor and activator changes Turing wavelength through which to regulate spine densities. Finally, we discussed the deep regulation mechanisms of several reported regulators of dendritic spine shape and densities based on our simulation results. Our work might evoke attention to the mathematic model-based pathogenesis research for neuron diseases which are related to the dendritic spine pattern abnormalities and spark inspiration in the treatment research for these diseases.

关键词： dendritic spine Turing instability reaction-diffusion model branching morphogenesis glioma

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Qualitative analysis on a reaction-diffusion model arising from population dynamics *

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APPLIED MATHEMATICS AND COMPUTATION 2022年 428卷

作者： Wang, Jingjing Jia, Yunfeng Li, Fangfang Shaanxi Normal Univ Sch Math & Stat Xi'an 710062 Shaanxi Peoples R China Northwestern Polytech Univ Sch Math & Stat Xi'an 710072 Shaanxi Peoples R China

To maintain biodiversity and ecological balance, studying population dynamics of species by establishing different mathematical models is quite important. In this paper, we deal with a reaction-diffusion predation model with mixed functional responses. We are mainly concerned with the coexistence of the species. We firstly give the long-time behaviors of parabolic dynamical system. Secondly, we consider the steady state system, including the priori estimate, existence, uniqueness and asymptotic stability of positive solutions to the system. The result shows that the coexistence of the species depends to a great extent on their intrinsic growth rates, diffusion situations and the predation pressure imposed to preys by predators. The uniqueness and stability results show that the functional response has important effects on the model, which is mainly reflected by the predation behavior of predators. Finally, some numerical simulations are presented to illustrate the theoretical results. (c) 2022 Elsevier Inc. All rights reserved.

关键词： reaction-diffusion model Coexistence Stability Uniqueness Fixed point index

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