Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Processes Crossing from Ballistic to Fractional Diffusion
  with Memory: Exact Results   We address the now classical problem of a diffusion process that crosses over
from a ballistic behavior at short times to a fractional diffusion (sub- or
super-diffusion) at longer times. Using the standard non-Markovian diffusion
equation we demonstrate how to choose the memory kernel to exactly respect the
two different asymptotics of the diffusion process. Having done so we solve for
the probability distribution function (pdf) as a continuous function which
evolves inside a ballistically expanding domain. This general solution agrees
for long times with the pdf obtained within the continuous random walk approach
but it is much superior to this solution at shorter times where the effect of
the ballistic regime is crucial.

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The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess