Continuous Time Random Walk: Difference between revisions

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== Fractional Differential Equations ==
== Fractional Differential Equations ==


For certain specific choices of the single-particle step distribution (more restricted than the restrictions needed to derive a Master Equation), the resulting evolution equation for the particle density can be written in the form of a Fractional Differential Equation (FDE).
While the Master Equation corresponds to a CTRW in the limit of many particles, the
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, i.e., ignoring fine detail.


== References ==
== References ==
<references />
<references />

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