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Continuous Time Random Walk: Difference between revisions
→Fractional Differential Equations
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<ref>[http://link.aps.org/doi/10.1103/PhysRevE.71.011111 R. Sánchez, B.A. Carreras, and B.Ph. van Milligen, ''Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations'', Phys. Rev. E '''71''' (2005) 011111]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevE.71.011111 R. Sánchez, B.A. Carreras, and B.Ph. van Milligen, ''Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations'', Phys. Rev. E '''71''' (2005) 011111]</ref> | ||
The fluid limit is the limit of large scales and long times, i.e., ignoring fine detail. | The fluid limit is the limit of large scales and long times, i.e., ignoring fine detail. | ||
In order to proceed, it is necessary to make an assumption regarding the shape of the distributions appearing in the kernel ''K''. Invoking the Generalized Limit Theorem for the sums of random variables, | |||
<ref>B. V. Gnedenko and A. N. Kolmogorov, ''Limit Distributions or Sums of Independent Random Variables'', Addison-Wesley, Reading, MA (1954)</ref> | |||
these distributions are taken to be Lévy distributions. This choice allows modelling both | |||
[[Non-diffusive transport|sub- and super-diffusive transport]], and in the appropriate limit, standard ("Fickian") transport is recovered. | |||
== References == | == References == | ||
<references /> | <references /> | ||