Multifactor Uncertain Chemical Reaction Equation

2022 ◽  
Author(s):  
Han Tang
Keyword(s):  
Differential Equation ◽  
Chemical Reaction ◽  
Half Life ◽  
Reaction Pathways ◽  
Uncertain Differential Equation ◽  
Reaction Equation ◽  
Moment Estimation ◽  
Multiple Reactions ◽  
Parallel Reactions ◽  
Generalized Moment

The previous uncertain chemical reaction equation describes the time evolution of single reactions. But in many practical cases, a substance is consumed by several different reaction pathways. For the above considerations, this paper extends the discussion to multiple reactions. Specifically, by taking the decomposition of C2H5OH as an example, parallel reactions with one reactant are analyzed with the multifactor uncertain differential equation. The derived equation is called the multifactor uncertain chemical reaction equation. Following that, the parameters in the multifactor uncertain chemical reaction equation are estimated by the generalized moment estimation. Based on the multifactor uncertain chemical reaction equation, half-life of reaction is investigated. Finally, a numerical example is presented to illustrate the usefulness of the multifactor uncertain chemical reaction equation.

scholarly journals Uncertain Chemical Langevin Equation

2020 ◽  
Author(s):  
Han Tang ◽  
Xiangfeng Yang
Keyword(s):  
Differential Equation ◽  
Chemical Kinetics ◽  
Langevin Equation ◽  
Half Life ◽  
Reaction Rate ◽  
Rate Of Change ◽  
Uncertain Differential Equation ◽  
Important Research ◽  
Chemical Langevin Equation

Reaction rate is a particularly important research object in chemical kinetics, and it is a measure of the rate of change of reactants. In order to illustrate and clarify the evolution of number of a substance involved in the reaction, this paper derives the uncertain chemical Langevin equation based on uncertain differential equation. Using the actual observations, one can estimate the parameters presented in the uncertain chemical Langevin equation. As an application, half-life of reaction is investigated. Finally, a paradox for the stochastic chemical Langevin equation is given.

Parameter estimation in multifactor uncertain differential equation

2021 ◽  
pp. 1-14
Author(s):  
Nan Zhang ◽  
Yuhong Sheng ◽  
Jing Zhang ◽  
Xiaoli Wang
Keyword(s):  
Differential Equation ◽  
Parameter Estimation ◽  
Research Direction ◽  
Estimation Methods ◽  
Uncertain Differential Equation ◽  
Method Of Moment ◽  
Unknown Parameters ◽  
Moment Estimation ◽  
Parameter Estimation Methods ◽  
Important Research Direction

In uncertainty theory, parameter estimation of uncertain differential equation is a very important research direction. The parameter estimation of multifactor uncertain differential equation needs to be solved. Multifactor uncertain differential equation is a differential equation driven by multiple Liu processes. The paper introduces two methods to solve the unknown parameters of the multifactor uncertain differential equation, they are the method of moment estimation and the method of least squares estimation. Several numerical examples are used to illustrate the proposed parameter estimation methods.

Chemical reaction and thermal radiation effects on magnetohydrodynamics flow of Casson–Williamson nanofluid over a porous stretching surface

2021 ◽  
pp. 095440892110253
Author(s):  
Pooja P Humane ◽  
Vishwambhar S Patil ◽  
Amar B Patil
Keyword(s):  
Differential Equation ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Radiation Effects ◽  
Physical Mechanism ◽  
Reaction Parameter ◽  
Stretching Surface ◽  
Injection Parameter ◽  
Chemical Reaction Parameter ◽  
Porous Stretching Surface

The flow of Casson–Williamson fluid on a stretching surface is considered for the study. The movement of fluid is examined under the effect of external magnetic field, thermal radiation and chemical consequences. The model is formed by considering all the physical aspects responsible for the physical mechanism. The formed mathematical model (partial differential equation) is numerically solved after transforming it into an ordinary one (ordinary differential equation) via similarity invariants. The physical mechanism for velocity, temperature, and concentration is examined through the associated parameters like radiation index, Williamson and Casson parameter, suction/injection parameter, porosity index, and chemical reaction parameter.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

scholarly journals A Numerical Study of Chemical Reaction in a Nanofluid Flow Due to Rotating Disk in the Presence of Magnetic Field

2021 ◽  
Author(s):  
Muhammad Ramzan ◽  
Poom Kumam ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan ◽  
Wasim Jamshed
Keyword(s):  
Differential Equation ◽  
Radial Velocity ◽  
Chemical Reaction ◽  
Axial Velocity ◽  
Numerical Study ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Partial Differential ◽  
Suction Parameter ◽  
Matlab Programming

Abstract In this paper, a numerical study of MHD steady flow due to the rotating disk with chemical reaction was explored. Effect of different parameters such as Schmidt number, chemical reaction parameter, Prandtl number, Suction parameter, heat absorption/generation parameter, Nano-particle concentration, Reynold number, Magnetic parameter, skin friction, shear stress, temperature distribution, Nusselt number, mass transfer rate, radial velocity, axial velocity, and tangential velocity was analyzed and discussed. For the simplification of non-linear partial differential equations (PDEs) into the nonlinear ordinary differential equation (ODEs), the method of Similarity transformation was employed, and the resulting partial differential equation was solved by using finite difference method through MATLAB programming. This work's remarkable finding is that with the expansion of nanoparticle concentration radial velocity, tangential velocity and temperature of the fluid was enhanced but reverse reaction for axial velocity. Furthermore, the present results are found to be in excellent agreement with previously published work.

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