08 Fakultät Mathematik und Physik

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Institute: search.filters.UBSInstitut.Fakultät Mathematik und Physik (Institutsübergreifend)Subject: search.filters.subject.530

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    Entropy by neighbor distance as a new measure for characterizing spatiotemporal orders in microscopic collective systems
    (2023) Fu, Yulei; Wu, Zongyuan; Zhan, Sirui; Yang, Jiacheng; Gardi, Gaurav; Kishore, Vimal; Malgaretti, Paolo; Wang, Wendong
    Collective systems self-organize to form globally ordered spatiotemporal patterns. Finding appropriate measures to characterize the order in these patterns will contribute to our understanding of the principles of self-organization in all collective systems. Here we examine a new measure based on the entropy of the neighbor distance distributions in the characterization of collective patterns. We study three types of systems: a simulated self-propelled boid system, two active colloidal systems, and one centimeter-scale robotic swarm system. In all these systems, the new measure proves sensitive in revealing active phase transitions and in distinguishing steady states. We envision that the entropy by neighbor distance could be useful for characterizing biological swarms such as bird flocks and for designing robotic swarms.
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    Fractional calculus for distributions
    (2024) Hilfer, Rudolf; Kleiner, Tillmann
    Fractional derivatives and integrals for measures and distributions are reviewed. The focus is on domains and co-domains for translation invariant fractional operators. Fractional derivatives and integrals interpreted as -convolution operators with power law kernels are found to have the largest domains of definition. As a result, extending domains from functions to distributions via convolution operators contributes to far reaching unifications of many previously existing definitions of fractional integrals and derivatives. Weyl fractional operators are thereby extended to distributions using the method of adjoints. In addition, discretized fractional calculus and fractional calculus of periodic distributions can both be formulated and understood in terms of -convolution.