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Conditions for Translation and Scaling Invariance of the Neutron Diffusion Equation. (arXiv:1810.04658v1 [math.AP])
来源于:arXiv
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 wor 查看全文>>