International Journal of Mathematics and Computational Science

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Unusual Frequency Distribution Function Shape Generated by Particles Making Brownian Walk Along Line With Monotone Increasing Friction

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[01]
Vladimir A. Dobrynskii, Institute for Metal Physics of N. A. S. U., Kiev, Ukraine.

With aid of computer simulation it is studied a 1-dimensional frequency distribution function of the particles which make forced oscillations along the y-axis and noise-excited Brownian walks along the x-axis on the plane exhibiting spatially non-linear non-homogeneous friction. The particle oscillations and their Brownian walks appear due to a joint action both of simple harmonic (sinusoidal) force and impulse noise. It is stated that the frequency distribution function depends very much on the starting point that the particles begin their movement and the given point position variation changes its form sometimes so much that its different visible shapes look as the ones of absolutely different frequency distribution functions which do yield by means of distinctly different ordinary differential equation systems. Thus we reveal a phenomenon of visible “disintegration” of the one-peak frequency distribution function into the two-peak one having the deepest pit between the peaks.

Frequency Distribution Function, Brownian Particle Walk, Impulse Noise

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