Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electron acceleration with improved Stochastic Differential Equation
  method: cutoff shape of electron distribution in test-particle limit   We develop a method of stochastic differential equation to simulate electron
acceleration at astrophysical shocks. Our method is based on It\^{o}'s
stochastic differential equations coupled with a particle splitting, employing
a skew Brownian motion where an asymmetric shock crossing probability is
considered. Using this code, we perform simulations of electron acceleration at
stationary plane parallel shock with various parameter sets, and studied how
the cutoff shape, which is characterized by cutoff shape parameter $a$, changes
with the momentum dependence of the diffusion coefficient $\beta$. In the
age-limited cases, we reproduce previous results of other authors,
$a\approx2\beta$. In the cooling-limited cases, the analytical expectation
$a\approx\beta+1$ is roughly reproduced although we recognize deviations to
some extent. In the case of escape-limited acceleration, numerical result fits
analytical stationary solution well, but deviates from the previous asymptotic
analytical formula $a\approx\beta$.

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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol