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Simulation model of the fractal patterns in ionic conducting polymer films

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Amir S., Mohamed N., Hashim Ali S.

Open Physics

2010

vol. 8

issue 1

150-156

Normally polymer electrolyte membranes are prepared and studied for applications in electrochemical devices. In this work, polymer electrolyte membranes have been used as the media to culture fractals. In order to simulate the growth patterns and stages of the fractals, a model has been identified based on the Brownian motion theory. A computer coding has been developed for the model to simulate and visualize the fractal growth. This computer program has been successful in simulating the growth of the fractal and in calculating the fractal dimension of each of the simulated fractal patterns. The fractal dimensions of the simulated fractals are comparable with the values obtained in the original fractals observed in the polymer electrolyte membrane. This indicates that the model developed in the present work is within acceptable conformity with the original fractal.

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α

100%

Jumarie G.

Open Physics

2008

vol. 6

issue 3

737-753

In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E α(hαDx α)f(x) where E α() denotes the Mittag-Leffler function, and D x α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.

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2 Open Physics

1 2010

1 2008

1 Amir S.

1 Hashim Ali S.

1 Jumarie G.

1 Mohamed N.

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Simulation model of the fractal patterns in ionic conducting polymer films

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α