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

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

Abelian Manna model in three dimensions and below

The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the the coefficients of an \epsilon-expansion. Rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices.Comment: 6 pages, 3 figures, 6 tables, submitted to PR

Comment on “Finite-size scaling of survival probability in branching processes”

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

Exact solution of a boundary tumbling particle system in one dimension

We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by exploiting an elegant underlying structure of the perturbation theory. We calculate the particle densities, currents and variance as well as characteristics of the boundary tumbling. The analytical findings, in agreement with Monte-Carlo simulations, show how the particle densities are linked to the scale of diffusive fluctuations at the boundaries. The generality of our approach suggests it could be readily applied to similar problems described by Fokker-Planck equations containing localised reaction terms

Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes

We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose formalism. This field theory treats interactions and the effect of external, possibly self-correlated noise in a perturbation about a Markovian process, thereby providing a systematic, diagrammatic approach to extreme events. We apply the formalism to Brownian Motion and calculate its survival probability distribution subject to self-correlated noise

Edge instability in incompressible planar active fluids

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

A solvable non-conservative model of Self-Organized Criticality

We present the first solvable non-conservative sandpile-like critical model of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345 (1998)] that a lack of conservation in the microscopic dynamics of an SOC-model can be compensated by introducing an external drive and thereby re-establishing criticality. The model shown is critical for all values of the conservation parameter. The analytical derivation follows the lines of Broeker and Grassberger [H.-M. Broeker and P. Grassberger, Phys. Rev. E 56, 3944 (1997)] and is supported by numerical simulation. In the limit of vanishing conservation the Random Neighbor Forest Fire Model (R-FFM) is recovered.Comment: 4 pages in RevTeX format (2 Figures) submitted to PR

Synchronization by small time delays

AbstractSynchronization is a phenomenon observed in all of the living and in much of the non-living 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 integrate-and-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

Broken scaling in the Forest Fire Model

We investigate the scaling behavior of the cluster size distribution in the Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical simulations, partly on (massively) parallel machines. It turns out that simple scaling is clearly violated, as already pointed out by Grassberger [P. Grassberger, J. Phys. A: Math. Gen. 26, 2081 (1993)], but largely ignored in the literature. Most surprisingly the statistics not seems to be described by a universal scaling function, and the scale of the physically relevant region seems to be a constant. Our results strongly suggest that the DS-FFM is not critical in the sense of being free of characteristic scales.Comment: 9 pages in RevTEX4 format (9 figures), submitted to PR