An innovative approach for determining the grinding media system of ball mill based on grinding kinetics and linear superposition principle

2021 ◽  
Vol 378 ◽  
pp. 172-181
Author(s):  
Jianwen Yu ◽  
Yonghong Qin ◽  
Peng Gao ◽  
Yuexin Han ◽  
Yanjun Li
Keyword(s):  
Ball Mill ◽  
Superposition Principle ◽  
Innovative Approach ◽  
Linear Superposition ◽  
Media System ◽  
Grinding Media ◽  
Linear Superposition Principle ◽  
Grinding Kinetics

The Multiple Exp-Function Method and the Linear Superposition Principle for Solving the (2+1)-Dimensional Calogero–Bogoyavlenskii–Schiff Equation

2015 ◽  
Vol 70 (9) ◽  
pp. 775-779 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Function Method ◽  
Superposition Principle ◽  
Solitary Wave Solutions ◽  
Linear Superposition ◽  
Wave Solutions ◽  
Linear Superposition Principle

AbstractIn this article, the multiple exp-function method and the linear superposition principle are employed for constructing the exact solutions and the solitary wave solutions for the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. With help of Maple and by using the multiple exp-method, we can get exact explicit one-wave, two-wave, and three-wave solutions, which include one-soliton-, two-soliton-, and three-soliton-type solutions. Furthermore, we apply the linear superposition principle to find n-wave solutions of the CBS equation. Two cases with specific values of the involved parameters are plotted for each two-wave and three-wave solutions.

scholarly journals Mass Transfer from Penetrations in Waste Containers

1987 ◽  
Vol 112 ◽  
Author(s):  
C. Pescatore ◽  
C. Sastre
Keyword(s):  
Steady State ◽  
Superposition Principle ◽  
Localized Corrosion ◽  
Waste Form ◽  
Linear Superposition ◽  
Waste Container ◽  
Linear Superposition Principle ◽  
Correct Application ◽  
Radionuclide Release ◽  
Multiple Holes

AbstractRecent studies have indicated that localized corrosion of a relatively small area of a waste container may impair the containment function to such an extent that larger releases may be possible than from the bare waste form. This would take place when a large number of holes coexist on the container while their concentration fields do not interact significantly with each other. After performing a steady state analysis of the release from a hole, it is shown that much fewer independent holes can coexist on a container surface than previously estimated. The calculated radionuclide release from multiple independent holes must be changed accordingly. Previous analyses did not proceed to a correct application of the linear superposition principle. This resulted in unacceptable physical conclusions and undue strain on the performance assessment necessary for a container licensing procedure. The paper also analyzes the steady state release from penetrations of finite length and whose concentration fields interact with one another. The predicted release from these penetrations is lower than the previously calculated release from holes of zero thickness. It is concluded here that the steady-state release from multiple holes on a waste container can not exceed the release from the bare waste form and that multiple perforations need not be a serious liability to container performance.

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