Bivariate Taylor-series expansion method of moment for particle population balance equation in Brownian coagulation

2017 ◽  
Vol 114 ◽  
pp. 94-106 ◽  
Author(s):  
Jiang Zhi ◽  
Shen Jie ◽  
Lu Zhiming
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Balance Equation ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Population Balance Equation ◽  
Method Of Moment ◽  
Brownian Coagulation ◽  
Particle Population ◽  
Series Expansion Method

scholarly journals The asymptotic stability of the Taylor-series expansion method of moment model for Brownian coagulation

2018 ◽  
Vol 22 (4) ◽  
pp. 1651-1657
Author(s):  
Mingliang Xie ◽  
Tingting Kong ◽  
Jin Li ◽  
Jiang Lin
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Perturbation Equation ◽  
Method Of Moment ◽  
Brownian Coagulation ◽  
Asymptotic Stable ◽  
The Stability ◽  
Series Expansion Method

In the present study, the linear stability of population balance equation due to Brownian motion is analyzed with the Taylor-series expansion method of moment. Under certain conditions, the stability of the Taylor-series expansion method of moment model is reduced to a well-studied problem involving eigenvalues of matrices. Based on the principle of dimensional analysis, the perturbation equation is solved asymptotically. The results show that the Taylor-series expansion method of moment model is asymptotic stable, which implies that the asymptotic solution is uniqueness, and supports the self-preserving size distribution hypothesis theoretically.

Rationalize the irrational and fractional expressions in nonlinear analysis

2016 ◽  
Vol 30 (04) ◽  
pp. 1650068 ◽  
Author(s):  
Yongfeng Yang ◽  
Tingdong Jiang ◽  
Zhong Ren ◽  
Junyao Zhao ◽  
Zheng Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Series Expansion ◽  
Taylor Series ◽  
Impact Force ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Stochastic Bifurcation ◽  
Bifurcation And Chaos ◽  
Integral Process ◽  
Series Expansion Method

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

scholarly journals The Fundamental Aspects of TEMOM Model for Particle Coagulation due to Brownian Motion—Part II: In the Continuum Regime

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
He Qing ◽  
Xie Mingliang
Keyword(s):  
Taylor Series Expansion ◽  
Expansion Method ◽  
Order Moment ◽  
Method Of Moment ◽  
Brownian Coagulation ◽  
Theoretical System ◽  
The Relationship ◽  
Expansion Point ◽  
The Continuum ◽  
Series Expansion Method

The fundamental aspects of the Taylor-series expansion method of moment (TEMOM) model proposed to model the aerosol population balance equation due to Brownian coagulation in the continuum regime is shown in this study, such as the choice of the expansion pointu, the relationship between asymptotic behavior and analytical solution, and the error of the high-order moment equations. All these analyses will contribute to the buildup of the theoretical system of the TEMOM model.

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