Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double Well Potential Function and Its Optimization in The n-dimensional
  Real Space -- Part I   A special type of multi-variate polynomial of degree 4, called the double
well potential function, is studied. When the function is bounded from below,
it has a very unique property that two or more local minimum solutions are
separated by one local maximum solution, or one saddle point. Our intension in
this paper is to categorize all possible configurations of the double well
potential functions mathematically. In part I, we begin the study with deriving
the double well potential function from a numerical estimation of the
generalized Ginzburg-Landau functional. Then, we solve the global minimum
solution from the dual side by introducing a geometrically nonlinear measure
which is a type of Cauchy-Green strain. We show that the dual of the dual
problem is a linearly constrained convex minimization problem, which is mapped
equivalently to a portion of the original double well problem subject to
additional linear constraints. Numerical examples are provided to illustrate
the important features of the problem and the mapping in between.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph