scholarly journals A simple moment model to study the effect of diffusion on the coagulation of nanoparticles due to Brownian motion in the free molecule regime

2012 ◽  
Vol 16 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Wenxi Wang ◽  
Qing He ◽  
Nian Chen ◽  
Mingliang Xie
Keyword(s):  
Method Of Moments ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Particle Coagulation ◽  
Average Volume ◽  
One Dimensional ◽  
The One ◽  
And Diffusion ◽  
Dimensional Domain ◽  
Series Expansion Method

In the study a simple model of coagulation for nanoparticles is developed to study the effect of diffusion on the particle coagulation in the one-dimensional domain using the Taylor-series expansion method of moments. The distributions of number concentration, mass concentration, and particle average volume induced by coagulation and diffusion are obtained.

scholarly journals Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yang Zhao ◽  
De-Fu Cheng ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Derivative ◽  
Series Expansion ◽  
Present Method ◽  
Expansion Method ◽  
One Dimensional ◽  
Local Fractional Derivative ◽  
Simple Tool ◽  
Fractional Schrödinger Equations ◽  
The One ◽  
Series Expansion Method

The local fractional Schrödinger equations in the one-dimensional Cantorian system are investigated. The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.

scholarly journals High concentration Brownian coagulation in jet flow using two enhancement formulations

2012 ◽  
Vol 16 (5) ◽  
pp. 1519-1523
Author(s):  
Pei-Feng Lin ◽  
Di-Chong Wu ◽  
Ze-Fei Zhu
Keyword(s):  
Volume Fraction ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
High Volume ◽  
Jet Flow ◽  
High Concentration ◽  
Brownian Coagulation ◽  
Planar Jet ◽  
Ultra Fine Particle ◽  
The One

Ultra-fine particle coagulation by Brownian motion at high concentration in planar jet flow is simulated. A Taylor-Series Expansion Method of Moments is employed to solve the particle general dynamic equation. The volume fraction gets high value, very closes to that at the nozzle exit. As the vortex pairing develops, the high volume fraction region rolls out and mixes with the low value region. The enhancement factor given by Trzeciak et al. will be less than one at some specific outer positions, which seems to be less accurate than the one given by Heine et al.

scholarly journals Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ai-Min Yang ◽  
Xiao-Jun Yang ◽  
Zheng-Biao Li
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Expansion Method ◽  
Cantor Sets ◽  
Diffusion Equations ◽  
And Diffusion ◽  
Series Expansion Method

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

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.

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