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Journal articleGarcia Millan R, Pruessner G, Pickering L, et al., 2018,
Correlations and hyperuniformity in the avalanche size of the Oslo Model
, Europhysics Letters: a letters journal exploring the frontiers of physics, Vol: 122, ISSN: 1286-4854Certain random processes display anticorrelations resulting in local Poisson-like disorder and global order, where correlations suppress fluctuations. Such processes are called hyperuniform. Using a map to an interface picture we show via analytic calculations that a sequence of avalanche sizes of the Oslo model is hyperuniform in the temporal domain with the minimal exponent $\lambda=0$ . We identify the conserved quantity in the interface picture that gives rise to the hyperuniformity in the avalanche size. We further discuss the fluctuations of the avalanche size in two variants of the Oslo model. We support our findings with numerical results.
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Journal articleNesbitt D, Pruessner G, Lee C, 2017,
Edge instability in incompressible planar active fluids
, Physical Review E, Vol: 96, ISSN: 1539-3755Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014)], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.
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Journal articleWillis G, Pruessner G, 2017,
Spatio-temporal correlations in the Manna model in one, three and five dimensions
, International Journal of Modern Physics B, Vol: 32, ISSN: 0217-9792Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d
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Journal articleFallesen T, Roostalu J, Duellberg C, et al., 2017,
Ensembles of Bidirectional Kinesin Cin8 Produce Additive Forces in Both Directions of Movement
, Biophysical Journal, Vol: 113, Pages: 2055-2067, ISSN: 0006-3495Most kinesin motors move in only one direction along microtubules. Members of the kinesin-5 subfamily were initially described as unidirectional plus-end-directed motors and shown to produce piconewton forces. However, some fungal kinesin-5 motors are bidirectional. The force production of a bidirectional kinesin-5 has not yet been measured. Therefore, it remains unknown whether the mechanism of the unconventional minus-end-directed motility differs fundamentally from that of plus-end-directed stepping. Using force spectroscopy, we have measured here the forces that ensembles of purified budding yeast kinesin-5 Cin8 produce in microtubule gliding assays in both plus- and minus-end direction. Correlation analysis of pause forces demonstrated that individual Cin8 molecules produce additive forces in both directions of movement. In ensembles, Cin8 motors were able to produce single-motor forces up to a magnitude of ∼1.5 pN. Hence, these properties appear to be conserved within the kinesin-5 subfamily. Force production was largely independent of the directionality of movement, indicating similarities between the motility mechanisms for both directions. These results provide constraints for the development of models for the bidirectional motility mechanism of fission yeast kinesin-5 and provide insight into the function of this mitotic motor.
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Journal articleRochester C, Sartor A, Pruessner G, et al., 2017,
"One dimensional" double layer. The effect of size asymmetry of cations and anions on charge-storage in ultranarrow nanopores-an Ising model theory
, RUSSIAN JOURNAL OF ELECTROCHEMISTRY, Vol: 53, Pages: 1165-1170, ISSN: 1023-1935We develop a statistical mechanical theory of charge storage in quasi-single-file ionophilic nanopores with pure room temperature ionic liquid cations and anions of different size. The theory is mapped to an extension of the Ising model exploited earlier for the case of cations and anions of the same size. We calculate the differential capacitance and the stored energy density per unit surface area of the pore. Both show asymmetry in the dependence on electrode potential with respect to the potential of zero charge, related to the difference in the size of the ions, which will be interesting to investigate experimentally. It also approves the increase of charge storage capacity via obstructed charging, which in these systems emerges for charging nanopores with smaller ions.
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Journal articleWei N, Pruessner G, 2016,
Comment on “Finite-size scaling of survival probability in branching processes”
, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 94, ISSN: 2470-0045R. Garcia-Millan et al. [Phys. Rev. E 91, 042122 (2015)] reported a universal finite-size scaling form of the survival probability in discrete time branching processes. In this comment, we generalize the argument to a wide range of continuous time branching processes. Owing to the continuity, the resulting differential (rather than difference) equations can be solved in closed form, rendering some approximations by R. Garcia-Millan et al. superfluous, although we work along similar lines. In the case of binary branching, our results are in fact exact. Demonstrating that discrete time and continuous time models have their leading order asymptotics in common, raises the question to what extent corrections are identical.
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Journal articleLee CF, Pruessner G, 2016,
Percolation mechanism drives actin gels to the critically connected state
, Physical Review E, Vol: 93, ISSN: 1539-3755Cell 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.
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Journal articlePruessner 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 articleDhar D, Pruessner G, Expert P, et al., 2016,
Directed Abelian sandpile with multiple downward neighbors
, Physical Review E, Vol: 042107, ISSN: 1539-3755We 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.
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Journal articleRochester CC, Kondrat S, Pruessner G, et 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: 1932-7447We 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.
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Journal articleNekovar S, Pruessner G, 2016,
A field-theoretic approach to the Wiener Sausage
, Journal of Statistical Physics, Vol: 163, Pages: 604-641, ISSN: 0022-4715The 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.
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Journal articleWatkins NW, Pruessner G, Chapman SC, et al., 2016,
25 Years of Self-organized Criticality: Concepts and Controversies
, Space Science Reviews, Vol: 198, Pages: 3-44, ISSN: 1572-9672Introduced 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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Journal articleWatkins NW, Pruessner G, Chapman SC, et al., 2016,
Erratum to: 25 Years of Self-organized Criticality:Concepts and Controversies
, Space Science Reviews, Vol: 198, Pages: 45-45, ISSN: 1572-9672Introduced 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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Journal articleAschwanden MJ, Crosby NB, Dimitropoulou M, et al., 2016,
25 Years of Self-Organized Criticality: Solar and Astrophysics
, Space Science Reviews, Vol: 198, Pages: 47-166, ISSN: 1572-9672Shortly after the seminal paper “Self-Organized Criticality: An explanation of 1/f noise” by Bak et al. (1987), the idea has been applied to solar physics, in “Avalanches and the Distribution of Solar Flares” by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.
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Journal articleRochester CC, Pruessner G, Kornyshev AA, 2015,
Statistical mechanics of 'Unwanted Electroactuation' in nanoporous supercapacitors
, Electrochimica Acta, Vol: 174, Pages: 978-984, ISSN: 0013-4686Nanoporous electrodes have the potential to increase the surface electrode interfacial area and the stored energy density of a supercapacitor. However, structural deformation of the electrode can become apparent when the size of the pore is comparable to the size of a charging ion. After many cycles this could cause wear and degradation. We present a theoretical study of this ‘Unwanted Electroactuation’ in a carbon electrode wetted with an ionic liquid. We incorporate changes of the carbon-carbon bond length due to electrochemical doping of the pore walls and steric effects related to counterion insertion into the pore via a modified Ising model of charge storage. When considering the total electrode deformation these effects either complement or compete with each other, depending on the polarisation of the electrode. Our model shows qualitative agreement with the features of the experimentally observed expansion caused by variation of electrode potential.
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Journal articleWillis G, Pruessner G, Keelan J, 2015,
Minimalistic real-space Renormalization of 4x4 Ising and Potts Models in two dimensions
, Frontiers in Physics, Vol: 3, ISSN: 2296-424XWe introduce and discuss a real-space renormalization group (RSRG) procedure on verysmall lattices, which in principle does not require any of the usual approximations, e.g., acut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carriedout numerically on very small lattices (4×4 to 2×2) and implemented for the Ising Modeland the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of thecorrelation length exponent and the magnetization exponent are typically within 3–7% ofthe exact values. The 4-state Potts Model generates a third magnetic exponent, whichseems to be unknown in the literature. A number of questions about the meaning ofcertain exponents and the procedure itself arise from its use of symmetry principles andits application to the q = 5 Potts Model.
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Journal articleMcAteer RTJ, Aschwanden MJ, Dimitropoulou M, et al., 2015,
25 Years of self-organized criticality: numerical detection methods
, Space Science Reviews, Vol: 198, Pages: 217-266, ISSN: 1572-9672The detection and characterization of self-organized criticality (SOC), in bothreal and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basicautocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numericalmethods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expandingfield of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.
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Journal articleFont-Clos F, Pruessner G, Moloney NR, et al., 2015,
The perils of thresholding
, New Journal of Physics, Vol: 17, ISSN: 1367-2630The thresholding of time series of activity or intensity is frequently used to define and differentiateevents. This is either implicit, for example due to resolution limits, or explicit, in order to filter certainsmall scale physics from the supposed true asymptotic events. Thresholding the birth–death process,however, introduces a scaling region into the event size distribution, which is characterized by anexponent that is unrelated to the actual asymptote and is rather an artefact of thresholding. As a result,numerical fits of simulation data produce a range of exponents, with the true asymptote visible only inthe tail of the distribution. This tail is increasingly difficult to sample as the threshold is increased. Inthe present case, the exponents and the spurious nature of the scaling region can be determinedanalytically, thus demonstrating the way in which thresholding conceals the true asymptote. Theanalysis also suggests a procedure for detecting the influence of the threshold by means of a datacollapse involving the threshold-imposed scale.
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Conference paperPruessner G, 2015,
Predictions and correlations in self-organised criticality
, Pages: 3-12, ISSN: 0930-8989Whether Self-Organised Criticality (SOC) can be used as a tool for prediction of events and event sizes has been subject to quite some debate in the past. While conflicting opinions about predictability have been put forward, there has always been widespread agreement that strong correlations exist in SOC. The following brief review summarises some insights from the study of correlations in SOC models.
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Journal articleGastner MT, Markou N, Pruessner G, et al., 2014,
Opinion Formation Models on a Gradient
, PLOS One, Vol: 9, ISSN: 1932-6203Statistical physicists have become interested in models of collective social behaviorsuch as opinion formation, where individuals change their inherently preferredopinion if their friends disagree. Real preferences often depend on regional culturaldifferences, which we model here as a spatial gradient g in the initial opinion. Thegradient does not only add reality to the model. It can also reveal that opinionclusters in two dimensions are typically in the standard (i.e., independent)percolation universality class, thus settling a recent controversy about a nonconsensusmodel. However, using analytical and numerical tools, we also present amodel where the width of the transition between opinions scales !g{1=4, not!g{4=7 as in independent percolation, and the cluster size distribution isconsistent with first-order percolation.
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Journal articlePruessner G, Cheang S, Jensen HJ, 2014,
Synchronization by small time delays
, Physica A: Statistical Mechanics and its Applications, Vol: 420, Pages: 8-13, ISSN: 1873-2119Synchronization is a phenomenon observed in all of the living and in much of the nonliving world, for example in the heart beat, Huygens’ clocks, the flashing of fireflies and the clapping of audiences. Depending on the number of degrees of freedom involved, different mathematical approaches have been used to describe it, most prominently integrateand-fire oscillators and the Kuramoto model of coupled oscillators. In the present work, we study a very simple and general system of smoothly evolving oscillators, which continue to interact even in the synchronized state. We find that under very general circumstances, synchronization generically occurs in the presence of a (small) time delay. Strikingly, the synchronization time is inversely proportional to the time delay.
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Journal articleRubin KJ, Pruessner G, Pavliotis GA, 2014,
Mapping multiplicative to additive noise
, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113- Author Web Link
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- Citations: 9
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Journal articleRochester CC, Lee AA, Pruessner G, et al., 2013,
Interionic Interactions in Conducting Nanoconfinement
, CHEMPHYSCHEM, Vol: 14, Pages: 4121-4125, ISSN: 1439-4235- Author Web Link
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- Citations: 38
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Book chapterPruessner G, 2013,
SOC computer simulations + SOC Laboratory Experiments
, Self-Organized Criticality Systems, Editors: Aschwanden -
Journal articlePruessner G, 2013,
THE AVERAGE AVALANCHE SIZE IN THE MANNA MODEL AND OTHER MODELS OF SELF-ORGANIZED CRITICALITY
, INTERNATIONAL JOURNAL OF MODERN PHYSICS B, Vol: 27, ISSN: 0217-9792- Author Web Link
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- Citations: 5
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Book chapterPruessner G, 2013,
A field theory for self-organised criticality
, Springer Proceedings in Complexity, Pages: 79-86Although self-organised criticality has been introduced more than two decades ago, its theoretical foundations remain somewhat elusive: How does it work? What is its link to ordinary critical phenomena? How can exponents be calculated systematically? Does it actually exist at all? In the following a field theory is introduced that addresses these questions. In contrast to previous attempts, this field theory is not phenomenological, or based on symmetry arguments. Rather, it is based on the microscopic dynamics of the Manna Model. Exponents can be calculated in an ϵ-expansion perturbatively in a systematic way. Above the upper critical dimension, the field theory becomes (asymptotically) exact, allowing immediate comparison to numerical results.
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Book chapterPruessner G, 2012,
Probability densities in complex systems, measuring
, Computational Complexity: Theory, Techniques, and Applications, Pages: 2267-2285, ISBN: 9781461417996Article Outline: Glossary Definition of the Subject Introduction Simulation Techniques Scaling Histogram Data Representation Future Directions Bibliography
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BookPruessner G, 2012,
Self-Organised Criticality
, Publisher: Cambridge University Press, ISBN: 9780521853354Giving a detalied overview of the subject, this book takes in the results and methods that have arisen since the term self-organised criticality was coined twenty years ago.
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Journal articleHoai NH, Pruessner G, 2012,
Abelian Manna model in three dimensions and below
, PHYSICAL REVIEW E, Vol: 85, ISSN: 1539-3755- Author Web Link
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- Citations: 14
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BookPruessner G, 2012,
Self-organised criticality: Theory, models and characterisation
, ISBN: 9780521853354Giving a detalied overview of the subject, this book takes in the results and methods that have arisen since the term self-organised criticality was coined twenty years ago. Providing an overview of numerical and analytical methods, from their theoretical foundation to the actual application and implementation, the book is an easy access point to important results and sophisticated methods. Starting with the famous Bak-Tang-Wiesenfeld sandpile, ten key models are carefully defined, together with their results and applications. Comprehensive tables of numerical results are collected in one volume for the first time, making the information readily accessible to readers. Written for graduate students and practicing researchers in a range of disciplines, from physics and mathematics to biology, sociology, finance, medicine and engineering, the book gives a practical, hands-on approach throughout. Methods and results are applied in ways that will relate to the reader's own research.
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