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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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    ItemOpen Access
    Hydrogen adsorption on metal-organic frameworks
    (2011) Streppel, Barbara; Schütz, Gisela (Prof. Dr.)
    In this thesis hydrogen adsorption is measured in ten MOFs with pores ranging from 3.4A to 34A and ultra-high surface areas of up to 5000 m2/g. Adsorption and desorp- tion isotherms are measured in two different regimes. First, at temperatures between 77K and room temperature and pressure up to 2MPa. From these measurements the isosteric heat of adsorption is determined in dependence of the hydrogen uptake for the whole range important for technical application. Second, hydrogen adsorption is mea- sured at approximately 20K and pressure up to 0.1MPa. For this new measurement technique a cryostat was developed, tested and calibrated. Hydrogen adsorption at 20 K enables for the first time the determination of specific surface area and specific pore volume by hydrogen. From theoretical calculations there are indications that the specific surface area and specific pore volume depend on the gas used for the determination and that surface areas and pore volumes available for hydrogen are remarkably different from the surface area and pore volumes determined by nitrogen or argon adsorption. Therefore, for the characterization of hydrogen storage materials the surface area and pore volume should be determined by hydrogen adsorption which is done in this work for the first time. Furthermore, adsorbed hydrogen at 20 K is less mobile than at 77 K. Therefore, adsorp- tion sites with different adsorption energy in the framework are subsequently filled. This filling can be observed from steps in the low pressure isotherm. Similar observations have been made before for nitrogen at 77 K and argon at 87 K, but never for hydrogen. Finally the results of hydrogen storage experiments are discussed concerning the requirements for application in a tank system. This work on the relation of hydrogen storage properties to the structure of MOFs will enable tailored synthesis of optimized MOFs for hydrogen storage application.
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    ItemOpen Access
    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.