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    Core-Core Dynamics in Spin Vortex Pairs

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    We investigate magnetic nano-pillars, in which two thin ferromagnetic nanoparticles are separated by a nanometer thin nonmagnetic spacer and can be set into stable spin vortex-pair configurations. The 16 ground states of the vortex-pair system are characterized by parallel or antiparallel chirality and parallel or antiparallel core-core alignment. We detect and differentiate these individual vortex-pair states experimentally and analyze their dynamics analytically and numerically. Of particular interest is the limit of strong core-core coupling, which we find can dominate the spin dynamics in the system. We observe that the 0.2 GHz gyrational resonance modes of the individual vortices are replaced with 2-6 GHz range collective rotational and vibrational core-core resonances in the configurations where the cores form a bound pair. These results demonstrate new opportunities in producing and manipulating spin states on the nanoscale and may prove useful for new types of ultra-dense storage devices where the information is stored as multiple vortex-core configurations

    The t-core of an s-core

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    We consider the tt-core of an ss-core partition, when ss and tt are coprime positive integers. Olsson has shown that the tt-core of an ss-core is again an ss-core, and we examine certain actions of the affine symmetric group on ss-cores which preserve the tt-core of an ss-core. Along the way, we give a new proof of Olsson's result. We also give a new proof of a result of Vandehey, showing that there is a simultaneous ss- and tt-core which contains all others

    Core TuLiP

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    We propose CoreTuLiP - the core of a trust management language based on Logic Programming. CoreTuLiP is based on a subset of moded logic programming, but enjoys the features of TM languages such as RT; in particular clauses are issued by different authorities and stored in a distributed manner. We present a lookup and inference algorithm which we prove to be correct and complete w.r.t. the declarative semantics. CoreTuLiP enjoys uniform syntax and the well-established semantics and is expressive enough to model scenarios which are hard to deal with in RT
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