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Denoting the primitive of A by ζ, our choice of M guarantees that eiζ is a single valued function on M . This is the crucial observation that facilitates the analysis. It is here that we need the condition that the flux through every cycle of M is an odd integer times π. We can therefore define the new gauge v = e−iζ ψ. 48) where we introduced a weight w that models nonuniformities in the network thickness. The nonuniformity will enable us to investigate symmetry breaking even in single loops. Consider further the mapping G : M → M which sends every point to its corresponding point on the other copy of M .

Later on several papers applied the theoretical formulation developed by de Gennes and Alexander to micronetworks of varied geometric and topological characteristics (infinite networks, planar and spaJ. Berger and J. ): LNP m62, pp. 23–62, 2000. c Springer-Verlag Berlin Heidelberg 2000 24 J. I. Castro and A. ) obtaining results which are important not only because of the physics underlying them but also because of possible future applications. The de Gennes-Alexander theory was very successful in explaining the description of the second order phase transition between the normal and superconducting phases and is the subject of this review.

This is the crucial observation that facilitates the analysis. It is here that we need the condition that the flux through every cycle of M is an odd integer times π. We can therefore define the new gauge v = e−iζ ψ. 48) where we introduced a weight w that models nonuniformities in the network thickness. The nonuniformity will enable us to investigate symmetry breaking even in single loops. Consider further the mapping G : M → M which sends every point to its corresponding point on the other copy of M .

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