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Let π : P → M n be a principal G-bundle, and let L : J 1 P → Λ n (M) be a G-invariant Lagrangian density. We obtain the Euler-Poincaré equations for the reduced Lagrangian l defined on C(P), the bundle of connections on P .
Ultra-small magnetic nanoparticles consisting of NiCo and FeNi alloys enclosed within graphitic shells (NiCo/G and FeNi/G) have been synthesized. The particles, which retained the face centered cubic (fcc) symmetry of the original bulk metals, together with the graphitic coating were characterized by means of aberration corrected scanning transmission… (More)
Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle.… (More)
FeCo-alloy graphite-coated nanoparticles with mean particle diameter under 8 nm have been synthesized following a CVD carbon-deficient method. The superior magnetic properties of FeCo-alloy nanoparticles makes them good candidates to be used as magnetic filler in magneto-polymer composites. Thanks to the protective effect of the graphite shell, FeCo… (More)