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  • Journal article
    Piovani D, Grujic J, Jensen HJ, 2016,

    Linear stability theory as an early warning sign for transitions in high dimensional complex systems

    , Journal of Physics A - Mathematical and Theoretical, Vol: 49, ISSN: 1751-8113

    We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation, we are able to construct a good early-warning indicator of the transitions occurring intermittently.

  • Journal article
    Lee CF, Pruessner G, 2016,

    Percolation mechanism drives actin gels to the critically connected state

    , Physical Review E, Vol: 93, ISSN: 1539-3755

    Cell motility and tissue morphogenesis depend crucially on the dynamic remodelling of actomyosinnetworks. An actomyosin network consists of an actin polymer network connected by crosslinkerproteins and motor protein myosins that generate internal stresses on the network. A recent discoveryshows that for a range of experimental parameters, actomyosin networks contract to clusterswith a power-law size distribution [Alvarado J. et al. (2013) Nature Physics 9 591]. Here, weargue that actomyosin networks can exhibit robust critical signature without fine-tuning becausethe dynamics of the system can be mapped onto a modified version of percolation with trapping(PT), which is known to show critical behaviour belonging to the static percolation universalityclass without the need of fine-tuning of a control parameter. We further employ our PT model togenerate experimentally testable predictions.

  • Journal article
    Pruessner G, Lee CF, 2016,

    Comment on "Anomalous Discontinuity at the Percolation Critical Point of Active Gels"

    , Physical Review Letters, Vol: 116, ISSN: 1079-7114
  • Journal article
    Dhar D, Pruessner G, Expert P, Christensen K, Zachariou Net al., 2016,

    Directed Abelian sandpile with multiple downward neighbors

    , Physical Review E, Vol: 042107, ISSN: 1539-3755

    We study the directed Abelian sandpile model on a square lattice, with K downward neighborsper site, K > 2. The K = 3 case is solved exactly, which extends the earlier known solution forthe K = 2 case. For K > 2, the avalanche clusters can have holes and side-branches and are thusqualitatively different from the K = 2 case where avalanche clusters are compact. However, we findthat the critical exponents for K > 2 are identical with those for the K = 2 case, and the largescale structure of the avalanches for K > 2 tends to the K = 2 case.

  • Journal article
    Broga KM, Viegas E, Jensen HJ, 2016,

    Model analysis of the link between interest rates and crashes

    , Physica A - Statistical Mechanics and Its Applications, Vol: 457, Pages: 225-238, ISSN: 0378-4371

    We analyse the effect of distinct levels of interest rates on the stability of the financial network under ourmodelling framework. We demonstrate that banking failures are likely to emerge early on under sustainedhigh interest rates, and at much later stage - with higher probability - under a sustained low interest ratescenario. Moreover, we demonstrate that those bank failures are of a different nature: high interest ratestend to result in significantly more bankruptcies associated to credit losses whereas lack of liquidity tends tobe the primary cause of failures under lower rates.

  • Journal article
    Rochester CC, Kondrat S, Pruessner G, Kornyshev AAet al., 2016,

    Charging Ultra-nanoporous Electrodes with Size-asymmetric Ions Assisted by Apolar Solvent

    , The Journal of Physical Chemistry C, Vol: 120, Pages: 16042-16050, ISSN: 1932-7447

    We develop a statistical theory of charging quasi single-file pores with cations and anions of different sizes as well as solvent molecules or voids. This is done by mapping the charging onto a one-dimensional Blume–Emery–Griffith model with variable coupling constants. The results are supported by three-dimensional Monte Carlo simulations in which many limitations of the theory are lifted. We explore the different ways of enhancing the energy storage which depend on the competitive adsorption of ions and solvent molecules into pores, the degree of ionophilicity and the voltage regimes accessed. We identify new solvent-related charging mechanisms and show that the solvent can play the role of an “ionophobic agent”, effectively controlling the pore ionophobicity. In addition, we demonstrate that the ion-size asymmetry can significantly enhance the energy stored in a nanopore.

  • Journal article
    Yan X, Minnhagen P, Jensen HJ, 2016,

    The likely determines the unlikely

    , Physica A - Statistical Mechanics and Its Applications, Vol: 456, Pages: 112-119, ISSN: 0378-4371

    We point out that the functional form describing the frequency of sizes of events in complexsystems (e.g. earthquakes, forest fires, bursts of neuronal activity) can be obtained from maximallikelihood inference, which, remarkably, only involve a few available observed measures such asnumber of events, total event size and extremes. Most importantly, the method is able to predictwith high accuracy the frequency of the rare extreme events. To be able to predict the few, oftenbig impact events, from the frequent small events is of course of great general importance. For adata set of wind speed we are able to predict the frequency of gales with good precision. We analyseseveral examples ranging from the shortest length of a recruit to the number of Chinese characterswhich occur only once in a text.

  • Journal article
    Nekovar S, Pruessner G, 2016,

    A field-theoretic approach to the Wiener Sausage

    , Journal of Statistical Physics, Vol: 163, Pages: 604-641, ISSN: 0022-4715

    The Wiener Sausage, the volume traced out by a sphere attachedto a Brownian particle, is a classical problem in statistics and mathematicalphysics. Initially motivated by a range of field-theoretic, technical questions,we present a single loop renormalised perturbation theory of a stochasticprocess closely related to the Wiener Sausage, which, however, proves to beexact for the exponents and some amplitudes. The field-theoretic approach isparticularly elegant and very enjoyable to see at work on such a classic problem.While we recover a number of known, classical results, the field-theoretictechniques deployed provide a particularly versatile framework, which allowseasy calculation with different boundary conditions even of higher momentaand more complicated correlation functions. At the same time, we provide ahighly instructive, non-trivial example for some of the technical particularitiesof the field-theoretic description of stochastic processes, such as excludedvolume, lack of translational invariance and immobile particles. The aim ofthe present work is not to improve upon the well-established results for theWiener Sausage, but to provide a field-theoretic approach to it, in order togain a better understanding of the field-theoretic obstacles to overcome.

  • Journal article
    Watkins NW, Pruessner G, Chapman SC, Crosby NB, Jensen HJet al., 2016,

    25 Years of Self-organized Criticality: Concepts and Controversies

    , Space Science Reviews, Vol: 198, Pages: 3-44, ISSN: 1572-9672

    Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers.

  • Journal article
    Watkins NW, Pruessner G, Chapman SC, Crosby NB, Jensen HJet al., 2016,

    Erratum to: 25 Years of Self-organized Criticality:Concepts and Controversies

    , Space Science Reviews, Vol: 198, Pages: 45-45, ISSN: 1572-9672

    Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers.

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