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Continuous Time Random Walk: Difference between revisions
→Fractional Differential Equations
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Fractional Differential Equation (FDE) corresponds to a Master Equation in the ''fluid limit''. | Fractional Differential Equation (FDE) corresponds to a Master Equation in the ''fluid limit''. | ||
<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, | The fluid limit is the limit of large scales and long times (of the solution ''n(x,t)'', not of the underlying transport mechanism). | ||
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, | 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, | ||