Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditions for Translation and Scaling Invariance of the Neutron
  Diffusion Equation   Lie group methods are applied to the time-dependent, monoenergetic neutron
diffusion equation in materials with spatial and time dependence. To accomplish
this objective, the underlying 2nd order partial differential equation (PDE) is
recast as an exterior differential system so as to leverage the isovector
symmetry analysis approach. Some of the advantages of this method as compared
to traditional symmetry analysis approaches are revealed through its use in the
context of a 2nd order PDE. In this context, various material properties
appearing in the mathematical model (e.g., a diffusion coefficient and
macroscopic cross section data) are left as arbitrary functions of space and
time. The symmetry analysis that follows is restricted to a search for
translation and scaling symmetries; consequently the Lie derivative yields
specific material conditions that must be satisfied in order to maintain the
presence of these important similarity transformations. The principal outcome
of this work is thus the determination of analytic material property functions
that enable the presence of various translation and scaling symmetries within
the time- dependent, monoenergetic neutron diffusion equation. The results of
this exercise encapsulate and generalize many existing results already
appearing in the literature. While the results contained in this work are
primarily useful as phenomenological guides pertaining to the symmetry behavior
of the neutron diffusion equation under certain assumptions, they may
eventually be useful in the construction of exact solutions to the underlying
mathematical model. The results of this work are also useful as a starting
point or framework for future symmetry analysis studies pertaining to the
neutron transport equation and its many surrogates.

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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg