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95/105= 0.91


1,1

The problem of short times for brownian motion and diffusion equation

doi: 10.6062/jcis.2013.04.03.0075

Authors

J. M. Silva, J. A. S. Lima and M. P. M. A. Baroni

Abstract

The studies on diffusive particles (immersed in a fluid or gas) which can be described by a parabolic diffusion equation usually leads to an infinite speed of propagation. In general, this apparent propagation speed is the result of neglecting the atomistic structure of matter and considering a frequency of finite collision. A favorable argument on this idea comes from the possibility that parabolic equations transmit signs with infinite speeds. In order to solve this difficulty, it is convenient to treat the problem from a point of view of a wave treatment. In the present paper, we presented a study on the hyperbolic differential equation describing the behavior of the brownian particle. In particular, when the numeric and exact solutions are compared the result privileges a finite speed of propagation.

Keywords

References

[1] P. Chatterjee, L. Hernquist and A. Loeb, “Phys. Rev. Lett.” 88, 121103 (2002).

[2] R. N. Mantegna and H. E. Stanley, "An introduction to econophysycs: Correlations and Complexity in Finance" , Cambridge-University Press, (2000).

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