Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry preserving parameterization schemes   Methods for the design of physical parameterization schemes that possess
certain invariance properties are discussed. These methods are based on
different techniques of group classification and provide means to determine
expressions for unclosed terms arising in the course of averaging of nonlinear
differential equations. The demand that the averaged equation is invariant with
respect to a subalgebra of the maximal Lie invariance algebra of the unaveraged
equation leads to a problem of inverse group classification which is solved by
the description of differential invariants of the selected subalgebra. Given no
prescribed symmetry group, the direct group classification problem is relevant.
Within this framework, the algebraic method or direct integration of
determining equations for Lie symmetries can be applied. For cumbersome
parameterizations, a preliminary group classification can be carried out. The
methods presented are exemplified by parameterizing the eddy vorticity flux in
the averaged vorticity equation. In particular, differential invariants of
(infinite dimensional) subalgebras of the maximal Lie invariance algebra of the
unaveraged vorticity equation are computed. A hierarchy of normalized
subclasses of generalized vorticity equations is constructed. Invariant
parameterizations possessing minimal symmetry extensions are described and a
restricted class of invariant parameterization is exhaustively classified. The
physical importance of the parameterizations designed is discussed.

31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con