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  • Journal article
    Bothe M, Pruessner G, 2021,

    Doi-Peliti field theory of free Active Ornstein-Uhlenbeck Particles

    , Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, ISSN: 1539-3755
  • Journal article
    Pruessner G, Garcia-Millan R, 2021,

    Run-and-tumble motion in a harmonic potential: field theory and entropy production

    , Journal of Statistical Mechanics: Theory and Experiment, ISSN: 1742-5468
  • Journal article
    Nesbitt D, Pruessner G, Lee CF, 2021,

    Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method

    , New Journal of Physics, Vol: 23, ISSN: 1367-2630

    The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting these systems are a common set of symmetries and conservation laws, defining dry active fluids as a class of physical system. Many interesting behaviours have been observed at high densities, which remain difficult to simulate due to the computational demand. Here, we show how two-dimensional dry active fluids in a dense regime can be studied using a simple modification of the lattice Boltzmann method. We apply our method on a model that exhibits motility-induced phase separation, and an active model with contact inhibition of locomotion, which has relevance to collective cell migration. For the latter, we uncover multiple novel phase transitions: two first-order and one potentially critical. We further support our simulation results with an analytical treatment of the hydrodynamic equations obtained via the Chapman-Enskog coarse-graining procedure.

  • Journal article
    Amarteifio S, Fallesen T, Pruessner G, Sena Get al., 2021,

    A random-sampling approach to track cell divisions in time-lapse fluorescence microscopy

    , Plant Methods, Vol: 17, ISSN: 1746-4811

    BackgroundParticle-tracking in 3D is an indispensable computational tool to extract critical information on dynamical processes from raw time-lapse imaging. This is particularly true with in vivo time-lapse fluorescence imaging in cell and developmental biology, where complex dynamics are observed at high temporal resolution. Common tracking algorithms used with time-lapse data in fluorescence microscopy typically assume a continuous signal where background, recognisable keypoints and independently moving objects of interest are permanently visible. Under these conditions, simple registration and identity management algorithms can track the objects of interest over time. In contrast, here we consider the case of transient signals and objects whose movements are constrained within a tissue, where standard algorithms fail to provide robust tracking.ResultsTo optimize 3D tracking in these conditions, we propose the merging of registration and tracking tasks into a registration algorithm that uses random sampling to solve the identity management problem. We describe the design and application of such an algorithm, illustrated in the domain of plant biology, and make it available as an open-source software implementation. The algorithm is tested on mitotic events in 4D data-sets obtained with light-sheet fluorescence microscopy on growing Arabidopsis thaliana roots expressing CYCB::GFP. We validate the method by comparing the algorithm performance against both surrogate data and manual tracking.ConclusionThis method fills a gap in existing tracking techniques, following mitotic events in challenging data-sets using transient fluorescent markers in unregistered images.

  • Journal article
    Cocconi L, Kuhn-Regnier A, Neuss M, Sendova-Franks AB, Christensen Ket al., 2021,

    Reconstructing the Intrinsic Statistical Properties of Intermittent Locomotion Through Corrections for Boundary Effects

  • Journal article
    Christensen K, Cocconi L, Sendova-Franks AB, 2021,

    Animal intermittent locomotion: a null model for the probability of moving forward in bounded space.

    , Journal of Theoretical Biology, Vol: 510, Pages: 1-19, ISSN: 0022-5193

    We present a null model to be compared with biological data to test for intrinsic persistence in movement between stops during intermittent locomotion in bounded space with different geometries and boundary conditions. We describe spatio-temporal properties of the sequence of stopping points r1,r2,r3,… visited by a Random Walker within a bounded space. The path between stopping points is not considered, only the displacement. Since there are no intrinsic correlations in the displacements between stopping points, there is no intrinsic persistence in the movement between them. Hence, this represents a null-model against which to compare empirical data for directional persistence in the movement between stopping points when there is external bias due to the bounded space. This comparison is a necessary first step in testing hypotheses about the function of the stops that punctuate intermittent locomotion in diverse organisms. We investigate the probability of forward movement, defined as a deviation of less than 90° between two successive displacement vectors, as a function of the ratio between the largest displacement between stops that could be performed by the random walker and the system size, α=Δℓ/Lmax. As expected, the probability of forward movement is 1/2 when α→0. However, when α is finite, this probability is less than 1/2 with a minimum value when α=1. For certain boundary conditions, the minimum value is between 1/3 and 1/4 in 1D while it can be even lower in 2D. The probability of forward movement in 1D is calculated exactly for all values 0<α⩽1 for several boundary conditions. Analytical calculations for the probability of forward movement are performed in 2D for circular and square bounded regions with one boundary condition. Numerical results for all values 0<α⩽1 are presented for several boundary conditions. The cases of rectangle and ellipse are also considered and an approximate model of

  • Journal article
    Walter B, Pruessner G, Salbreux G, 2021,

    First passage time distribution of active thermal particles in potentials

    , Physical Review Research, Vol: 3, Pages: 013075 – 1-013075 – 22, ISSN: 2643-1564

    We introduce a perturbative method to calculate all moments of thefirst-passage time distribution in stochastic one-dimensional processes whichare subject to both white and coloured noise. This class of non-Markovianprocesses is at the centre of the study of thermal active matter, that isself-propelled particles subject to diffusion. The perturbation theory aboutthe Markov process considers the effect of self-propulsion to be small comparedto that of thermal fluctuations. To illustrate our method, we apply it to thecase of active thermal particles (i) in a harmonic trap (ii) on a ring. Forboth we calculate the first-order correction of the moment-generating functionof first-passage times, and thus to all its moments. Our analytical results arecompared to numerics.

  • Journal article
    Cocconi L, de Gennes M, Salbreux G, 2021,

    Strip it out and build it back! Engineering a morphogen gradient

    , TheScienceBreaker, Vol: 07
  • Journal article
    Cocconi L, Garcia Millan R, Zhen Z, Buturca B, Pruessner Get al., 2020,

    Entropy production in exactly solvable systems

    , Entropy: international and interdisciplinary journal of entropy and information studies, Vol: 22, Pages: 1-33, ISSN: 1099-4300

    The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.

  • Journal article
    Bordeu Weldt I, Garcin C, Habib SJ, Pruessner Get al., 2020,

    Effective potential description of the interaction between single stem cells and localized ligands

    , Physical Review X, Vol: 10, Pages: 041022 – 1-041022 – 18, ISSN: 2160-3308

    Cell signalling is essential for cell fate determination and tissue patterning. As signalling ligandsare presented to the receiving cell, they are recruited and recognised by the cell membrane as to elicita biological response and to pattern multicellular tissues. Cells can accumulate and transport theseligands, which results in an emergent organisation of the ligands' spatial distribution. To study thisorganisation, we make use of a simpli ed experimental setup, in which single mouse embryonic stemcells (mESCs) can interact with immobilized ligands. We introduce a two species age-dependentcorrelation function that allows the description and quanti cation of the spatio-temporal dynamicsof single cell-ligand interactions. Through the analysis of mESC data and numerical simulations weshow that cells act as e ective force- eld generators, perturbing and organising their environment.This organisation, captured in the form of an ageing e ective potential, is an emergent property ofthe population of single cells interacting with randomly distributed localized ligands.

  • Journal article
    Stapornwongkul KS, de Gennes M, Cocconi L, Salbreux G, Vincent J-Pet al., 2020,

    Patterning and growth control in vivo by an engineered GFP gradient

    , SCIENCE, Vol: 370, Pages: 321-+, ISSN: 0036-8075
  • Journal article
    Pausch J, Garcia-Millan R, Pruessner G, 2020,

    Time‐dependent branching processes: a model of oscillating neuronal avalanches

    , Scientific Reports, Vol: 10, Pages: 1-17, ISSN: 2045-2322

    Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existenceof a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinarycontinuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronalactivity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing theextinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, wederive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitativecomparison to available experimental results.

  • Journal article
    Hiratsuka T, Bordeu I, Pruessner G, Watt FMet al., 2020,

    Regulation of ERK basal and pulsatile activity control proliferation and exit from the stem cell compartment in mammalian epidermis.

    , Proceedings of the National Academy of Sciences of USA, Vol: 117, Pages: 17796-17807, ISSN: 0027-8424

    Fluctuation in signal transduction pathways is frequently observed during mammalian development. However, its role in regulating stem cells has not been explored. Here we tracked spatiotemporal ERK MAPK dynamics in human epidermal stem cells. While stem cells and differentiated cells were distinguished by high and low stable basal ERK activity, respectively, we also found cells with pulsatile ERK activity. Transitions from Basalhi-Pulselo (stem) to Basalhi-Pulsehi, Basalmid-Pulsehi, and Basallo-Pulselo (differentiated) cells occurred in expanding keratinocyte colonies and in response to differentiation stimuli. Pharmacological inhibition of ERK induced differentiation only when cells were in the Basalmid-Pulsehi state. Basal ERK activity and pulses were differentially regulated by DUSP10 and DUSP6, leading us to speculate that DUSP6-mediated ERK pulse down-regulation promotes initiation of differentiation, whereas DUSP10-mediated down-regulation of mean ERK activity promotes and stabilizes postcommitment differentiation. Levels of MAPK1/MAPK3 transcripts correlated with DUSP6 and DUSP10 transcripts in individual cells, suggesting that ERK activity is negatively regulated by transcriptional and posttranslational mechanisms. When cells were cultured on a topography that mimics the epidermal-dermal interface, spatial segregation of mean ERK activity and pulses was observed. In vivo imaging of mouse epidermis revealed a patterned distribution of basal cells with pulsatile ERK activity, and down-regulation was linked to the onset of differentiation. Our findings demonstrate that ERK MAPK signal fluctuations link kinase activity to stem cell dynamics.

  • Journal article
    Gcina M, Luca C, Pruessner G, Moloney Net al., 2020,

    Dynamically accelerated cover times

    , Physical Review Research, Vol: 2, Pages: 023421 – 1-023421 – 9, ISSN: 2643-1564

    Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d≥3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to “accelerate” or “decelerate” upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1/fα Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d>3, our results for acceleration in d=3 challenge the current understanding of the role of correlations in the cover time problem.

  • Working paper
    Amarteifio S, Fallesen T, Pruessner G, Sena Get al., 2020,

    A fuzzy-registration approach to track cell divisions in time-lapse fluorescence microscopy

    , Publisher: bioRxiv


  • Journal article
    Bordeu Weldt I, Amarteifio S, Garcia Millan R, Walter B, Wei N, Pruessner Get al., 2019,

    Volume explored by a branching random walk on general graphs

    , Scientific Reports, Vol: 9, ISSN: 2045-2322

    Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding---the branching random walk (BRW)---is required. Despite its wide range of applications, the properties of the volume explored by the BRW so far remained elusive, with exact results limited to one dimension. Here we present analytical results, supported by numerical simulations, on the scaling of the volume explored by a BRW in the critical regime, the onset of epidemics, in general environments. Our results characterise the spreading dynamics on regular lattices and general graphs, such as fractals, random trees and scale-free networks, revealing the direct relation between the graphs' dimensionality and the rate of propagation of the viral process. Furthermore, we use the BRW to determine the spectral properties of real social and metabolic networks, where we observe that a lack of information of the network structure can lead to differences in the observed behaviour of the spreading process. Our results provide observables of broad interest for the characterisation of real world lattices, tissues, and networks.

  • Journal article
    Wei N, Pruessner G, 2019,

    Critical density of the Abelian Manna model via a multitype branching process

    , Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 100, Pages: 1-6, ISSN: 1539-3755

    A multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the Abelian Manna model. This branching process incorporates partially the spatiotemporal correlations of the activity, which are essential for the dynamics, in particular in low dimensions. An analytical expression for the critical density in arbitrary dimensions is derived, which significantly improves the results over mean-field theories, as confirmed by comparison to the literature on numerical estimates from simulations. The method can easily be extended to lattices and dynamics other than those studied in the present work.

  • Journal article
    Pausch J, Pruessner G, 2019,

    Is actin filament and microtubule growth reaction- or diffusion-limited?

    , Journal of Statistical Mechanics: Theory and Experiment, Vol: 2019, ISSN: 1742-5468

    Inside cells of living organisms, actin filaments and microtubules selfassemble and dissemble dynamically by incorporating actin or tubulin from the cell plasma or releasing it into their tips’ surroundings. Such reaction-diffusion systems can show diffusion- or reaction-limited behaviour. However, neither limit explains the experimental data: while the offset of the linear relation between growth speed and bulk tubulin density contradicts the diffusion limit, the surprisingly large variance of the growth speed rejects a pure reaction limit. In this article, we accommodate both limits and use a Doi-Peliti field-theory model to estimate how diffusive transport is perturbing the chemical reactions at the filament tip. Furthermore, a crossover bulkdensity is predicted at which the limiting process changes from chemical reactions to diffusive transport. In addition, we explain and estimate larger variances of the growth speed.

  • Journal article
    Duarte D, Amarteifio S, Ang H, Kong IY, Ruivo N, Pruessner G, Hawkins ED, Lo Celso Cet al., 2019,

    Defining the in vivo characteristics of acute myeloid leukemia cells behavior by intravital imaging

    , Immunology and Cell Biology, Vol: 97, Pages: 229-235, ISSN: 0818-9641

    The majority of acute myeloid leukemia (AML) patients have a poor response to conventional chemotherapy. The survival of chemoresistant cells is thought to depend on leukemia-bone marrow (BM) microenvironment interactions, which are not well understood. The CXCL12/CXCR4 axis has been proposed to support AML growth but was not studied at the single AML cell level. We recently showed that T-cell acute lymphoblastic leukemia (T-ALL) cells are highly motile in the BM; however, the characteristics of AML cell migration within the BM remain undefined. Here, we characterize the in vivo migratory behavior of AML cells and their response to chemotherapy and CXCR4 antagonism, using high-resolution 2-photon and confocal intravital microscopy of mouse calvarium BM and the well-established MLL-AF9-driven AML mouse model. We used the Notch1-driven T-ALL model as a benchmark comparison and AMD3100 for CXCR4 antagonism experiments. We show that AML cells are migratory, and in contrast with T-ALL, chemoresistant AML cells become less motile. Moreover, and in contrast with T-ALL, the in vivo exploratory behavior of expanding and chemoresistant AML cells is unaffected by AMD3100. These results expand our understanding of AML cells-BM microenvironment interactions, highlighting unique traits of leukemia of different lineages.

  • Journal article
    Reijne A-M, Bordeu I, Pruessner G, Sena Get al., 2018,

    Linear stability analysis of morphodynamics during tissue regeneration in plants

    , Journal of Physics D: Applied Physics, Vol: 52, Pages: 1-9, ISSN: 0022-3727

    One of the key characteristics of multicellular organisms is the ability to establish and maintain shapes, or morphologies, under a variety of physical and chemical perturbations. A quantitative description of the underlying morphological dynamics is a critical step to fully understand the self-organising properties of multicellular systems. Although many powerful mathematical tools have been developed to analyse stochastic dynamics, rarely these are applied to experimental developmental biology.Here, we take root tip regeneration in the plant model system Arabidopsis thaliana as an example of robust morphogenesis in living tissue, and present a novel approach to quantify and model the relaxation of the system to its unperturbed morphology. By generating and analysing time-lapse series of regenerating root tips captured with confocal microscopy, we are able to extract and model the dynamics of key morphological traits at cellular resolution. We present a linear stability analysis of its Markovian dynamics, with the stationary state representing the intact root in the space of morphological traits. This analysis suggests the intriguing co-existence of two distinct temporal scales during the process of root regeneration in Arabidopsis.We discuss the possible biological implications of our specific results, and suggest future experiments to further probe the self-organising properties of living tissue.

  • Journal article
    Garcia Millan R, Pausch J, Walter B, Pruessner Get al., 2018,

    Field-theoretic approach to the universality of branching processes

    , Physical Review E, Vol: 98, ISSN: 1539-3755

    Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival probability, expected avalanche duration, the so-called avalanche shape, the n-point correlation function, and the probability density function of the total avalanche size. Previous studies have shown universality in certain observables of branching processes using probabilistic arguments; however, a comprehensive description is lacking. We derive the field theory that describes the process and demonstrate how to use it to calculate the relevant observables and their scaling to leading order in time, revealing the universality of the moments of the population size. Our results explain why the first and second moment of the offspring distribution are sufficient to fully characterize the process in the vicinity of criticality, regardless of the underlying offspring distribution. This finding implies that branching processes are universal. We illustrate our analytical results with computer simulations.

  • Journal article
    Jensen HJ, Pazuki RH, Pruessner G, Tempesta Pet al., 2018,

    Statistical mechanics of exploding phase spaces: ontic open systems

    , Journal of Physics A: Mathematical and Theoretical, Vol: 51, ISSN: 1751-8113

    The volume of phase space may grow super-exponentially ('explosively') with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.

  • Journal article
    Garcia Millan R, Pruessner G, Pickering L, Christensen Ket 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: 1286-4854

    Certain 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.

  • Journal article
    Corral A, Garcia-Millan R, Moloney NR, Font-Clos Fet al., 2018,

    Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects

    , PHYSICAL REVIEW E, Vol: 97, ISSN: 2470-0045
  • Journal article
    Nesbitt D, Pruessner G, Lee C, 2017,

    Edge instability in incompressible planar active fluids

    , Physical Review E, Vol: 96, ISSN: 1539-3755

    Interfacial 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.

  • Journal article
    Willis 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: 0217-9792

    Although 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

  • Journal article
    Fallesen T, Roostalu J, Duellberg C, Pruessner G, Surrey Tet al., 2017,

    Ensembles of Bidirectional Kinesin Cin8 Produce Additive Forces in Both Directions of Movement

    , Biophysical Journal, Vol: 113, Pages: 2055-2067, ISSN: 0006-3495

    Most 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.

  • Journal article
    Rochester C, Sartor A, Pruessner G, Kornyshev AAet 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: 1023-1935

    We 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.

  • Journal article
    Wei 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: 2470-0045

    R. 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.

  • Journal article
    Corral A, Garcia-Millan R, Font-Clos F, 2016,

    Exact derivation of a finite-size scaling law and corrections to scaling in the geometric galton-watson process

    , PLoS ONE, Vol: 11, Pages: 1-17, ISSN: 1932-6203

    The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary.

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