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DDC: 500 × Subject: mathematical model ×

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    Topological data analysis of contagion maps for examining spreading processes on networks
    ([London] : Nature Publishing Group UK, 2015) Taylor, Dane; Klimm, Florian; Harrington, Heather A.; Kramár, Miroslav; Mischaikow, Konstantin; Porter, Mason A.; Mucha, Peter J.
    Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges—for example, due to airline transportation or communication media—allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct ‘contagion maps’ that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.
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    Enhancing laser beam performance by interfering intense laser beamlets
    ([London] : Nature Publishing Group UK, 2019) Morace, A.; Iwata, N.; Sentoku, Y.; Mima, K.; Arikawa, Y.; Yogo, A.; Andreev, A.; Tosaki, S.; Vaisseau, X.; Abe, Y.; Kojima, S.; Sakata, S.; Hata, M.; Lee, S.; Matsuo, K.; Kamitsukasa, N.; Norimatsu, T.; Kawanaka, J.; Tokita, S.; Miyanaga, N.; Shiraga, H.; Sakawa, Y.; Nakai, M.; Nishimura, H.; Azechi, H.; Fujioka, S.; Kodama, R.
    Increasing the laser energy absorption into energetic particle beams represents a longstanding quest in intense laser-plasma physics. During the interaction with matter, part of the laser energy is converted into relativistic electron beams, which are the origin of secondary sources of energetic ions, γ-rays and neutrons. Here we experimentally demonstrate that using multiple coherent laser beamlets spatially and temporally overlapped, thus producing an interference pattern in the laser focus, significantly improves the laser energy conversion efficiency into hot electrons, compared to one beam with the same energy and nominal intensity as the four beamlets combined. Two-dimensional particle-in-cell simulations support the experimental results, suggesting that beamlet interference pattern induces a periodical shaping of the critical density, ultimately playing a key-role in enhancing the laser-to-electron energy conversion efficiency. This method is rather insensitive to laser pulse contrast and duration, making this approach robust and suitable to many existing facilities.
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    Network-induced multistability through lossy coupling and exotic solitary states
    ([London] : Nature Publishing Group UK, 2020) Hellmann, Frank; Schultz, Paul; Jaros, Patrycja; Levchenko, Roman; Kapitaniak, Tomasz; Kurths, Jürgen; Maistrenko, Yuri
    The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. For these, the ongoing transition to distributed renewable energy sources leads to a proliferation of dynamical actors. The desynchronisation of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a leading topic in power grid research. Here we uncover that, when taking into account physical losses in the network, the back-reaction of the network induces new exotic solitary states in the individual actors and the stability characteristics of the synchronous state are dramatically altered. These effects will have to be explicitly taken into account in the design of future power grids. We expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.