On Idempotent D-Norms

Replacing the spectral measure by a random vector \bfZ allows the representation of a max-stable distribution on $\R^d$ with standard negative margins via a norm, called \emph{$D$-norm}, whose generator is \bfZ. The set of $D$-norms can be equipped with a commutative multiplication type operation, making it a semigroup with an identity element. This multiplication leads to idempotent $D$-norms. We characterize the set of idempotent $D$-norms. Iterating the multiplication provides a track of $D$-norms, whose limit exists and is again a $D$-norm. If this iteration is repeatedly done on the same $D$-norm, then the limit of the track is idempotent.Comment: 17 page

Structural transformation and localization during simulated nanoindentation of a non-crystalline metal film

A simulation study demonstrates that localization can arise as the result of the breakdown of stable quasi-crystal-like atomic configurations. Samples produced at elevated quench rates and via more energetic processes contain a lower fraction of such configurations and exhibit significantly less pronounced localization and shorter spacing between bands. In the samples produced by the lowest quench rates localization is accompanied by the amorphization of material with initially quasi-crystal-like medium range order. This result is of particular significance in light of recent experimental evidence of local quasi-crystal order in the most stable of the bulk metallic glasses.Comment: 13 pages, 3 figure