Mathematical Model Of Chemical Reaction Research Articles

Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions-Two Illustrative Examples.

Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamics-based theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with the entropic inequality (the second law of thermodynamics) are illustrated. The theory illustrated here can be viewed as a tool for verifying and generalizing traditional mass-action kinetics by means of modern non-equilibrium thermodynamics, which is able to deal also with such rather problematic cases.

Исследование и редуцирование математической модели химической реакции методом Соболя

Исследование и редуцирование математической модели химической реакции методом Соболя

The Kinetic Model of n‐Decane Oxidation in the Presence of Inhibitory Composition

ABSTRACTThis article addresses mathematical modeling of the reaction of inhibited organic compounds oxidation. It was proposed to solve the inverse problems of chemical kinetics by using the index method of constrained global minimization of the deviation between the calculated and experimental data. This approach allows us to use more complete information about the chemical process which, in its turn, reduces the range of possible solutions, narrows down the domain of uncertainty, and improves the quality of mathematical model of chemical reactions. The index method was applied to solving inverse kinetic problem for the reaction of n‐decane oxidation in the presence of a p‐oxydiphenylamine/n‐decyl alcohol inhibitory composition.

The Network Operator Method for Identifications of Chemical Reactions

A problem of identification of mathematical model of chemical reaction is considered. Mathematical model in the form of ODE is obtained from the experimental data of concentrations changes during the reaction process. To solve the identification problem we use a numerical network operator method that allows finding structure and parameters of mathematical expression presented as an integer matrix. The network operator method uses evolutionary search algorithms. A numerical example of identification for the chemical generation singlet oxygen reaction is given.

Numeric simulation of the formation of hexagonal nanoscale structure arrays in anodic aluminum oxide

Formation of hexagonal periodic nanoscale structures at the surface of aluminum oxide is considered in the present paper. The mathematical model of chemical reactions at metal-oxide and oxide/electrolyte interfaces is described. A weak nonlinear approximation near the instability threshold results in the two-dimensional Kuramoto-Sivashinsky equation. The solution of this equation provides the same regular hexagonal nanoscale structure arrays that are observed in physical experiments. The two-stage complex Rosenbrock scheme developed by the author is applied for the numerical simulation of this problem in the present paper. The high accuracy O(τ4) and L1 stability, along with the relative simplicity of the method, make it possible to use a conventional PC to perform the calculations.

Positive solutions for singular semilinear elliptic systems

We establish existence results for singular semilinear elliptic systems on bounded domains with homogeneous Dirichlet boundary conditions. The systems considered are the paradigmatic mathematical models of chemical reactions, morphogenesis (singular Gierer-Meinhardt system) and population dynamics. In these systems the operator need not be in divergence form and the systems need not be cooperative. The results have been obtained by the method of sub and supersolutions (appropriately modified) and Schauder's fixed point theorem. Some uniqueness results have been obtained extending a "concavity" argument used for a single equation. We extend some existence results to general elliptic operators and more general nonlinearities and we prove existence for systems that have not been considered in the literature.

Mathematical model of chemical reactions in polydisperse porous media

The recursive mathematical model of the porous media is developed, in which the structure of a porous macroparticle is represented as a system of finer porous particles (microparticles), each of which in turn also consists of a next level system of porous microparticles, etc. The porous structure of microparticles of each level is described by a model of chaotically located spheres. This recursive model is used for developing a mathematical model of chemical reaction in the porous media describing speeds of reagent supply to a reactionary surface as a function of internal structure of a particle, diffusion resistance of microparticles of various levels being accounted. Calculations of a high-temperature pyrolysis process of methane in the porous carbonized samples of wood are carried out. Satisfactory agreement with experimental data is received.

Systems Modeling of Nonequilibrium Chemical Reactions Using STELLA

Understanding mathematical models of chemical reactions is central to the fields of geology, geochemistry, and contaminant hydrogeology. Unfortunately, many students struggle with understanding the relations between the mathematics and the physical reality. Even upper-level undergraduate students often misunderstand fundamental concepts such as chemical equilibrium. To address the question of how to provide students with strong conceptual and quantitative reinforcement of systems in general and how to better understand chemical reactions in particular, we developed an exercise using STELLA to model a sorption-reaction system. STELLA enables students to build dynamic systems graphically from a physically based conceptual model independent of the governing differential equations. Using their STELLA models, students can gain insights into the system, observe relationships among model parameters and results, and discover new insights into what chemical equilibrium means and implies. Students can also explore their STELLA models to discover connections to the mathematical representation, thereby gaining a deeper appreciation of the mathematics behind the model and ultimately strengthening their mathematical skills.

Law of Large Numbers and Central Limit Theorem for Linear Chemical Reactions with Diffusion

Two mathematical models of chemical reactions with diffusion for a single reactant in a one-dimensional volume are compared, namely, the deterministic and the stochastic models. The deterministic model is given by a partial differential equation, the stochastic one by a space-time jump Markov process. By the law of large numbers the consistency of the two models is proved. The deviation of the stochastic model from the deterministic model is estimated by a central limit theorem. This limit is a distribution-valued Gauss-Markov process and can be represented as the mild solution of a certain stochastic partial differential equation.

Mathematical models of chemical reactions

Mathematical models of chemical reactions

Mathematical models of chemical reactions

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The Computer Control of Arc Furnace and Its Mathematical Model

The control of refining period of arc furnace steelmaking especially its mathematical model is explained.As an example of the mathematical model of chemical reaction, the modellings of oxygen blowing of stainless steel, one is based on the diffusion rate limitting and the other is based on the equilibrium relation are explained. And end point carbon control at Jones & Laughline Steel Corp. is explained.A bath temperature model of continuous-fed prereduced iron pellet is explained as an example of thermal model and an example of procedure of dynamic model drawing up.The total steelmaking control system executed at Reisholz's is explained.