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  • 1. Bögli, Sabine
    et al.
    Brown, B. Malcolm
    Marletta, Marco
    Tretter, Christiane
    Stockholm University, Faculty of Science, Department of Mathematics. Universität Bern, Switzerland.
    Wagenhofer, Markus
    Guaranteed resonance enclosures and exclosures for atoms and molecules2014In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 470, no 2171, article id 20140488Article in journal (Refereed)
    Abstract [en]

    In this paper, we confirm, with absolute certainty, a conjecture on a certain oscillatory behaviour of higher auto-ionizing resonances of atoms and molecules beyond a threshold. These results not only definitely settle a more than 30 year old controversy in Rittby et al. (1981 Phys. Rev. A 24, 1636-1639 (doi: 10.1103/PhysRevA.24.1636)) and Korsch et al. (1982 Phys. Rev. A 26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)), but also provide new and reliable information on the threshold. Our interval-arithmetic-based method allows one, for the first time, to enclose and to exclude resonances with guaranteed certainty. The efficiency of our approach is demonstrated by the fact that we are able to show that the approximations in Rittby et al. (1981 Phys. Rev. A 24, 1636-1639 (doi:10.1103/PhysRevA.24.1636)) do lie near true resonances, whereas the approximations of higher resonances in Korsch et al. (1982 Phys. Rev. A 26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)) do not, and further that there exist two new pairs of resonances as suggested in Abramov et al. (2001 J. Phys. A 34, 57-72 (doi:10.1088/0305-4470/34/1/304)).

  • 2. Liu, Jun Jie
    et al.
    Qin, Yangzong
    Bar Dolev, Maya
    Celik, Yeliz
    Wettlaufer, J. S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Braslavsky, Ido
    Modelling the influence of antifreeze proteins on three dimensional ice crystal melt shapes using a geometric approach2012In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 468, no 2147, p. 3311-3322Article in journal (Refereed)
    Abstract [en]

    The melting of pure axisymmetric ice crystals has been described previously by us within the framework of so-called geometric crystal growth. Non-equilibrium ice crystal shapes evolving in the presence of hyperactive antifreeze proteins (hypAFPs) are experimentally observed to assume ellipsoidal geometries ('lemon' or 'rice' shapes). To analyse such shapes, we harness the underlying symmetry of hexagonal ice I-h and extend two-dimensional geometric models to three-dimensions to reproduce the experimental dissolution process. The geometrical model developed will be useful as a quantitative test of the mechanisms of interaction between hypAFPs and ice.

  • 3.
    Mancarella, Francesco
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Style, Robert W.
    Wettlaufer, John S.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Oxford, UK; Yale University, USA.
    Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids2016In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 472, no 2189, article id 20150853Article in journal (Refereed)
    Abstract [en]

    Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when R/L less than or similar to 100. When R < 3L/2 (R = 3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.

  • 4. Martinez-Franco, Raquel
    et al.
    Sun, Junliang
    Stockholm University, Faculty of Science, Department of Materials and Environmental Chemistry (MMK).
    Sastre, German
    Yun, Yifeng
    Stockholm University, Faculty of Science, Department of Materials and Environmental Chemistry (MMK).
    Zou, Xiaodong
    Stockholm University, Faculty of Science, Department of Materials and Environmental Chemistry (MMK).
    Moliner, Manuel
    Corma, Avelino
    Supra-molecular assembly of aromatic proton sponges to direct the crystallization of extra-large-pore zeotypes2014In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 470, no 2166Article in journal (Refereed)
    Abstract [en]

    The combination of different experimental techniques, such as solid C-13 and H-1 magic-angle spinning NMR spectroscopy, fluorescence spectroscopy and powder X-ray diffraction, together with theoretical calculations allows the determination of the unique structure directing the role of the bulky aromatic proton sponge 1,8-bis(dimethylamino)naphthalene (DMAN) towards the extra-large-pore ITQ-51 zeolite through supra-molecular assemblies of those organic molecules.

  • 5. Subramaniyam, N. P.
    et al.
    Donges, Jonathan F.
    Stockholm University, Faculty of Science, Stockholm Resilience Centre.
    Hyttinen, J.
    Signatures of chaotic and stochastic dynamics uncovered with epsilon-recurrence networks2015In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 471, no 2183, article id 20150349Article in journal (Refereed)
    Abstract [en]

    An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, e-recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global e-recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rossler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global e-recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high noise levels and short data lengths. Furthermore, e-recurrence network analysis of the real-world epileptic data revealed the capability of these network measures in capturing dynamical transitions using short window sizes. e-recurrence network analysis is a powerful method in uncovering the signatures of chaotic and stochastic dynamics based on the geometrical properties of time series.

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