Browsing by Author "Veselic, Ivan"

Now showing 1 - 4 of 4
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    Mini-Workshop: L2-Spectral Invariants and the Integrated Density of States
    (Zürich : EMS Publ. House, 2006) Lenz, Daniel; Schick, Thomas; Veselic, Ivan
    L2 -spectral invariants play an increasingly important role in the analysis of infinite geometric objects allowing for the action of a group. Typical such objects are covering spaces like Riemannian manifolds and graphs. The aim is to understand the group and the geometry of the object. The associated L2 -invariants can all be derived from the integrated density of states —also known as spectral distribution function— of a suitable geometrically induced equivariant Laplacian. On the other hand, the integrated density of states is also a most prominent quantity in the study of Laplacians with
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    Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence
    (Zürich : EMS Publ. House, 2009) Veselic, Ivan
    The mini-workshop was devoted to the spectral analysis of random Schr¨dinger-type operators. While this topic has been intensively studo ied by physicists and mathematicians for several decades, more recently there has been particular attention devoted to models where the random parameters enter the model in a non-monotone or non-linear way. Most of the established methods applied for random operators, in fact, hinge on the presence of monotonicity w. r. t. randomness. Thus the treatment of non-monotone models forces a deeper analysis of the structure of random Hamiltonians and, in particular, the interplay of the kinetic and the potential energy parts.
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    Mini-Workshop: Multiscale and Variational Methods in Material Science and Quantum Theory of Solids
    (Zürich : EMS Publ. House, 2007) Chenchiah, Isaac; Veselic, Ivan; Zimmer, Johannes
    This workshop brought together 18 scientists from three different mathematical communities: (i) random Schrödinger operators, (ii) quantum mechanics of interacting atoms, and (iii) mathematical materials science. Several underlying themes were identified and addressed: variational principles, homogenisation techniques, thermodynamic limits, spectral theory, and dynamic and stochastic aspects.
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    Ocean rogue waves and their phase space dynamics in the limit of a linear interference model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Birkholz, Simon; Brée, Carsten; Veselic, Ivan; Demircan, Ayhan; Steinmeyer, Günter
    We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.