Showing papers in "Journal of Statistical Mechanics: Theory and Experiment in 2009"
TL;DR: This paper starts from the definition of a modularity function, given by Newman to evaluate the goodness of network community decompositions, and extends it to the more general case of directed graphs with overlapping community structures.
Abstract: Complex network topologies present interesting and surprising properties, such as community structures, which can be exploited to optimize communication, to find new efficient and context-aware routing algorithms or simply to understand the dynamics and meaning of relationships among nodes. Complex networks are gaining more and more importance as a reference model and are a powerful interpretation tool for many different kinds of natural, biological and social networks, where directed relationships and contextual belonging of nodes to many different communities is a matter of fact. This paper starts from the definition of a modularity function, given by Newman to evaluate the goodness of network community decompositions, and extends it to the more general case of directed graphs with overlapping community structures. Interesting properties of the proposed extension are discussed, a method for finding overlapping communities is proposed and results of its application to benchmark case-studies are reported. We also propose a new data set which could be used as a reference benchmark for overlapping community structures identification.
438 citations
TL;DR: In this article, the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson) is studied.
Abstract: We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr ρAn for any integer n is calculated as the four-point function of twist fields of a particular type and the final result is expressed in a compact form in terms of the Riemann–Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.
381 citations
TL;DR: A social network of cities is built that consists of communications between 571 cities in Belgium that is characterized by a gravity model: the communication intensity between two cities is proportional to the product of their sizes divided by the square of their distance.
Abstract: We analyze the anonymous communication patterns of 2.5 million customers of a Belgian mobile phone operator. Grouping customers by billing address, we build a social network of cities that consists of communications between 571 cities in Belgium. We show that inter-city communication intensity is characterized by a gravity model: the communication intensity between two cities is proportional to the product of their sizes divided by the square of their distance.
300 citations
TL;DR: In this paper, a new topological invariant, persistent homology, is determined and presented as a parameterized version of a Betti number in simplicial complexes constructed from complex networks.
Abstract: Long-lived topological features are distinguished from short-lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and presented as a parameterized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent topological attributes, shown to be related to the robust quality of networks, also reflect the deficiency in certain connectivity properties of networks. Random networks, networks with exponential connectivity distribution and scale-free networks were considered for homological persistency analysis.
200 citations
TL;DR: In this paper, a time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends.
Abstract: A time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time evolution cannot be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, with the result that chains of length of the order of n≈100 spins are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. A previously conjectured relation between quantum chaos and normal transport is re-confirmed with high accuracy for much larger systems.
188 citations
TL;DR: In this article, a method to derive the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz is presented.
Abstract: We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin–spin correlation function of the XXZ Heisenberg spin- 1/2 chain (with magnetic field) in the disordered regime as well as to the density–density correlation function of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.
180 citations
TL;DR: In this paper, the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated from its linear transformation under the assumption that the number of non-zero elements of x is typically limited to ρN (0≤ρ≤1).
Abstract: We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated from its linear transformation under the assumption that the number of non-zero elements of x is typically limited to ρN (0≤ρ≤1). Problems of this type can be solved by minimizing a cost function with respect to the Lp-norm , subject to the constraints under an appropriate condition. For several values of p, we assess a typical case limit αc(ρ), which represents a critical relation between α = P/N and ρ for successfully reconstructing the original vector by the minimization for typical situations in the limit while keeping α finite, utilizing the replica method. For p = 1, αc(ρ) is considerably smaller than its worst case counterpart, which has been rigorously derived in the existing literature on information theory.
180 citations
TL;DR: In this paper, the entanglement entropy of a block of contiguous spins in excited states of spin chains was studied in the XY model in a transverse field and the XXZ Heisenberg spin chain.
Abstract: We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling.
176 citations
TL;DR: Torquato and Stillinger as discussed by the authors derived an upper bound on the asymptotic coefficient governing local volume fraction fluctuations in terms of the corresponding quantity describing the variance in the local number density (i.e., number variance).
Abstract: Hyperuniform point patterns are characterized by vanishing infinite-wavelength density fluctuations and encompass all crystal structures, certain quasiperiodic systems, and special disordered point patterns (Torquato and Stillinger 2003 Phys. Rev. E 68 041113). This paper generalizes the notion of hyperuniformity to include also two-phase random heterogeneous media. Hyperuniform random media do not possess infinite-wavelength volume fraction fluctuations, implying that the variance in the local volume fraction in an observation window decays faster than the reciprocal window volume as the window size increases. For microstructures of impenetrable and penetrable spheres, we derive an upper bound on the asymptotic coefficient governing local volume fraction fluctuations in terms of the corresponding quantity describing the variance in the local number density (i.e., number variance). Extensive calculations of the asymptotic number variance coefficients are performed for a number of disordered (e.g., quasiperiodic tilings, classical 'stealth' disordered ground states, and certain determinantal point processes), quasicrystal, and ordered (e.g., Bravais and non-Bravais periodic systems) hyperuniform structures in various Euclidean space dimensions, and our results are consistent with a quantitative order metric characterizing the degree of hyperuniformity. We also present corresponding estimates for the asymptotic local volume fraction coefficients for several lattice families. Our results have interesting implications for a certain problem in number theory.
154 citations
TL;DR: A metric is proposed that assumes that a maximal clique only belongs to one community, and it is proved that the optimization of the metric on the original network is equivalent to the optimizing of Newman's modularity on the maximalClique network.
Abstract: It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem. Instead of assuming that one node can only belong to one community, our metric assumes that a maximal clique only belongs to one community. In this way, the overlaps between communities are allowed. To identify the overlapping community structure, we construct a maximal clique network from the original network, and prove that the optimization of our metric on the original network is equivalent to the optimization of Newman's modularity on the maximal clique network. Thus the overlapping community structure can be identified through partitioning the maximal clique network using any modularity optimization method. The effectiveness of our metric is demonstrated by extensive tests on both artificial networks and real world networks with a known community structure. The application to the word association network also reproduces excellent results.
132 citations
TL;DR: In this paper, an adaptive detrending algorithm and critically assessing the effectiveness of Fourier truncation in eliminating the 11-year cycle was proposed, which showed that the values of the fractal scaling exponents obtained by Movahed et al. are artifacts of the filtering algorithm that they used.
Abstract: Multifractal theory provides an elegant statistical characterization of many complex dynamical variations in Nature and engineering. It is conceivable that it may enrich characterization of the sun's magnetic activity and its dynamical modeling. Recently, on applying Fourier truncation to remove the 11-year cycle and carrying out multifractal detrended fluctuation analysis of the filtered sunspot time series, Movahed et al reported that sunspot data are characterized by multifractal scaling laws with the exponent for the second-order moment, h(2), being 1.12. Moreover, they think the filtered sunspot data are like a fractional Brownian motion process with anti-persistent long-range correlations characterized by the Hurst parameter H = h(2)−1 = 0.12. By designing an adaptive detrending algorithm and critically assessing the effectiveness of Fourier truncation in eliminating the 11-year cycle, we show that the values of the fractal scaling exponents obtained by Movahed et al are artifacts of the filtering algorithm that they used. Instead, sunspot data with the 11-year cycle properly filtered are characterized by a different type of multifractal with persistent long-range correlations characterized by H≈0.74.
TL;DR: In this article, the authors show that integrability can be used to characterize quantum quenches, using a model of fermions with pairing interactions (Richardson's model).
Abstract: Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from both the vanishing timescale of the quench event, which can thus create arbitrarily high energy modes, and its non-local nature, which curtails the utility of local excitation bases. We here show that nonperturbative methods based on integrability can prove sufficiently powerful to completely characterize quantum quenches: we illustrate this using a model of fermions with pairing interactions (Richardson's model). The effects of simple (and multiple) quenches on the dynamics of various important observables are discussed. Many of the features that we find are expected to be universal to all kinds of quench situations in atomic physics and condensed matter.
TL;DR: In this article, the existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, such as forest-fires or earthquake automata, is scrutinized.
Abstract: The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, such as forest-fires or earthquake automata, is scrutinized in this paper. By using three different levels of description—(i) a simple mean field, (ii) a more detailed mean-field description in terms of a (self-organized) branching processes, and (iii) a full stochastic representation in terms of a Langevin equation—it is shown on general grounds that non-conserving dynamics does not lead to bona fide criticality. Contrary to the case for conserving systems, a parameter, which we term the 're-charging' rate (e.g. the tree-growth rate in forest-fire models), needs to be fine-tuned in non-conserving systems to obtain criticality. In the infinite-size limit, such a fine-tuning of the loading rate is easy to achieve, as it emerges by imposing a second separation of timescales but, for any finite size, a precise tuning is required to achieve criticality and a coherent finite-size scaling picture. Using the approaches above, we shed light on the common mechanisms by which 'apparent criticality' is observed in non-conserving systems, and explain in detail (both qualitatively and quantitatively) the difference with respect to true criticality obtained in conserving systems. We propose to call this self-organized quasi-criticality (SOqC). Some of the reported results are already known and some of them are new. We hope that the unified framework presented here will help to elucidate the confusing and contradictory literature in this field. In a forthcoming paper, we shall discuss the implications of the general results obtained here for models of neural avalanches in neuroscience for which self-organized scale-invariance in the absence of conservation has been claimed.
TL;DR: In this paper, the authors derived the characteristic function for the joint measurement of the changes of two or more commuting observables upon an external forcing of a quantum system, in particular, the statistics of the internal energy, the exchanged heat and the work of a system that weakly couples to its environment.
Abstract: The characteristic function for the joint measurement of the changes of two or more commuting observables upon an external forcing of a quantum system is derived. In particular, the statistics of the internal energy, the exchanged heat and the work of a quantum system that weakly couples to its environment are determined in terms of the energy changes of the system and the environment due to the action of a classical, external force on the system. If the system and the environment initially are in a canonical equilibrium, the work performed on the system is shown to satisfy the Tasaki–Crooks theorem and the Jarzynski equality.
TL;DR: In this paper, a method for estimating the cross-correlation Cxy(τ ) of long-range correlated series x(t )a ndy(t), at varying lags τ and scales n,i s was proposed.
Abstract: A method for estimating the cross-correlation Cxy(τ ) of long-range correlated series x(t )a ndy(t), at varying lags τ and scales n ,i s proposed. For fractional Brownian motions with Hurst exponents H1 and H2, the asymptotic expression for Cxy(τ ) depends only on the lag τ (wide-sense stationarity) and scales as a power of n with exponent H1 + H2 for τ → 0. The method is illustrated on: (i) financial series, to show the leverage effect; (ii) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.
TL;DR: A method by which stochastic processes are mapped onto complex networks is introduced and it is demonstrated that the time series can be reconstructed with high precision by means of a simple random walk on their corresponding networks.
Abstract: We introduce a method by which stochastic processes are mapped onto complex networks. As examples, we construct the networks for such time series as those for free-jet and low-temperature helium turbulence, the German stock market index (the DAX), and white noise. The networks are further studied by contrasting their geometrical properties, such as the mean length, diameter, clustering, and average number of connections per node. By comparing the network properties of the original time series investigated with those for the shuffled and surrogate series, we are able to quantify the effect of the long-range correlations and the fatness of the probability distribution functions of the series on the networks constructed. Most importantly, we demonstrate that the time series can be reconstructed with high precision by means of a simple random walk on their corresponding networks.
TL;DR: In this paper, the distribution of the partition functions for a class of one-dimensional random energy models with logarithmically correlated random potential, above and at the glass transition temperature, was derived based on an analytical continuation of the Selberg integral.
Abstract: We compute the distribution of the partition functions for a class of one-dimensional random energy models with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian free field (2D GFF) along various planar curves. Our method extends the recent analysis of Fyodorov and Bouchaud (2008 J. Phys. A: Math. Theor. 41 372001) from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a duality relation satisfied by the suitable generating function of free energy cumulants in the high temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2D GFF on the [0,1] interval. We provide numerical checks of the circular case and the interval case and discuss universality and various extensions. The relevance to the distribution of the length of a segment in Liouville quantum gravity is noted.
TL;DR: In this article, a pair of Brownian particles are coupled to a thermal bath at temperatures T 1 and T 2 and the information flow nullifies at equilibrium, and its efficiency is defined as the ratio of the flow to the total entropy production in the system.
Abstract: A basic task of information processing is information transfer (flow). Here we study a pair of Brownian particles each coupled to a thermal bath at temperatures T1 and T2. The information flow in such a system is defined via the time-shifted mutual information. The information flow nullifies at equilibrium, and its efficiency is defined as the ratio of the flow to the total entropy production in the system. For a stationary state the information flows from higher to lower temperatures, and its efficiency is bounded from above by (max[T1,T2])/(|T1−T2|). This upper bound is imposed by the second law and it quantifies the thermodynamic cost for information flow in the present class of systems. It can be reached in the adiabatic situation, where the particles have widely different characteristic times. The efficiency of heat flow—defined as the heat flow over the total amount of dissipated heat—is limited from above by the same factor. There is a complementarity between heat and information flow: the set-up which is most efficient for the former is the least efficient for the latter and vice versa. The above bound for the efficiency can be (transiently) overcome in certain non-stationary situations, but the efficiency is still limited from above. We study yet another measure of information processing (transfer entropy) proposed in the literature. Though this measure does not require any thermodynamic cost, the information flow and transfer entropy are shown to be intimately related for stationary states.
TL;DR: In this paper, the eigenvectors of the modified transition matrix of the Bethe ansatz were analyzed and the results obtained by de Gier and Essler were recovered and a physical interpretation of the exceptional points were given.
Abstract: The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation function of the current can be obtained as well by diagonalizing a modified transition matrix, which is still integrable: the spectrum of this new matrix can also be described in terms of Bethe roots for special values of the parameters. However, due to the algebraic framework used to write the Bethe equations in previous works, the nature of the excitations and the full structure of the eigenvectors remained unknown. This paper explains why the eigenvectors of the modified transition matrix are physically relevant, gives an explicit expression for the eigenvectors and applies it to the study of atypical currents. It also shows how the coordinate Bethe ansatz developed for the excitations leads to a simple derivation of the Bethe equations and of the validity conditions of this ansatz. All the results obtained by de Gier and Essler are recovered and the approach gives a physical interpretation of the exceptional points. The overlap of this approach with other tools such as the matrix ansatz is also discussed. The method that is presented here may be not specific to the asymmetric exclusion process and may be applied to other models with open boundaries to find similar exceptional points.
TL;DR: In this paper, the authors investigated the structure and evolution of the Brazilian airport network (BAN) as regards several quantities: routes, connections, passengers and cargo, and showed that its structure is dynamic, with changes in relative relevance of some airports and routes.
Abstract: The aviation sector is profitable, but sensitive to economic fluctuations, geopolitical constraints and governmental regulations. As for other means of transportation, the relation between origin and destination results in a complex map of routes, which can be complemented with information associated with the routes themselves, for instance, frequency, traffic load and distance. The theory of networks provides a natural framework for investigating the dynamics on the resulting structure. Here, we investigate the structure and evolution of the Brazilian airport network (BAN) as regards several quantities: routes, connections, passengers and cargo. Some structural features are in accordance with previous results for other airport networks. The analysis of the evolution of the BAN shows that its structure is dynamic, with changes in the relative relevance of some airports and routes. The results indicate that the connections converge to specific routes. The network shrinks at the route level but grows in number of passengers and amount of cargo, which more than doubled during the period studied.
TL;DR: In this article, the authors study the Deffuant et al model for continuous-opinion dynamics under the influence of noise and derive the master equation of this process, which is used to derive approximate conditions for the transition between opinion clusters and the disordered state.
Abstract: We study the Deffuant et al model for continuous-opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending on a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order–disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The master equation analysis is compared with direct Monte Carlo simulations. We find that the master equation and the Monte Carlo simulations do not always agree due to finite-size-induced fluctuations that we analyze in some detail.
TL;DR: In this article, the authors consider the case where the zero-temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single-particle modes and show that the temperature broadening of the lineshape exhibits a pronounced asymmetry and a shift of the maximum upward in energy.
Abstract: We consider the finite-temperature frequency and momentum-dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero-temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single-particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the lineshape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ('temperature-dependent gap'). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.
TL;DR: This work addresses the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an Ultimatum Game in complex networks and discusses the emergence of fairness in the different settings and network topologies.
Abstract: We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an Ultimatum Game in complex networks. Specifically, players of three types are considered: (a) empathetic, whose aspiration levels, and offers, are equal, (b) pragmatic, who do not distinguish between the different roles and aim to obtain the same benefit, and (c) agents whose aspiration levels, and offers, are independent. We analyze the asymptotic behavior of pure populations with different topologies using two kinds of strategic update rules: natural selection, which relies on replicator dynamics, and social penalty, inspired by the Bak–Sneppen dynamics, in which players are subject to a social selection rule penalizing not only the less fit individuals, but also their first neighbors. We discuss the emergence of fairness in the different settings and network topologies.
TL;DR: In this paper, the Taylor expansion method was extended to establish equivalent partial differential equations of DDH lattice Boltzmann schemes at an arbitrary order of accuracy for thermal and linear fluid models in one to three dimensions.
Abstract: In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive formally the associated dynamical equations for classical thermal and linear fluid models in one to three space dimensions. We use this approach to adjust relaxation parameters in order to enforce fourth order accuracy for thermal model and diffusive relaxation modes of the Stokes problem. We apply the resulting scheme for numerical computation of associated eigenmodes and compare our results with analytical references.
TL;DR: In this article, the exact block entanglement in the XXZ spin chain at Δ = −1/2 was studied and the moments of the reduced density matrix and its spectrum were derived.
Abstract: We carry out a systematic study of the exact block entanglement in the XXZ spin chain at Δ = −1/2. We present the first analytic expressions for reduced density matrices for n spins in a chain of length L (for n≤6 and arbitrary but odd L) for a truly interacting model. The entanglement entropy and the moments of the reduced density matrix and its spectrum are then easily derived. We explicitly construct the 'entanglement Hamiltonian' as the logarithm of this matrix. Exploiting the degeneracy of the ground state, we find the scaling behavior of the entanglement of the zero-temperature mixed state.
TL;DR: In this article, the authors discuss the well known Einstein and the Kubo fluctuation-dissipation relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution.
Abstract: We discuss the well known Einstein and the Kubo fluctuation-dissipation relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multivariate linear Langevin model, which includes dynamics with memory, is used as a treatable example to show how the usual relations are recovered only in particular cases. This study brings to the fore the ambiguities of a check of the FDR done without knowing the significant degrees of freedom and their coupling. An analogous scenario emerges in the dynamics of diluted shaken granular media. There, the correlation between position and velocity of particles, due to spatial inhomogeneities, induces violation of usual FDRs. The search for the appropriate correlation function which could restore the FDR can be more insightful than a definition of 'non-equilibrium' or 'effective temperatures'.
TL;DR: In this article, the authors present a brief overview of the recent investigations aimed at understanding features of stochastic dynamics under the influence of Levy white noise perturbations, and find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.
Abstract: A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the above mentioned properties of 'Gaussianity' and 'whiteness' of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Levy walks, so called Levy flights correspond to the class of Markov processes which can still be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Levy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed at understanding features of stochastic dynamics under the influence of Levy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.
TL;DR: In this paper, a flood fill dynamic potential field method is used to simulate the movement of a large crowd of pedestrians around a corner, where during the filling process the value of a field cell is not increased by 1, but by a larger value, if it is occupied by an agent.
Abstract: When a large group of pedestrians moves around a corner, most pedestrians do not follow the shortest path, which is to stay as close as possible to the inner wall, but try to minimize the travel time. For this they accept to move on a longer path with some distance to the corner, to avoid large densities and by this succeed in maintaining a comparatively high speed. In many models of pedestrian dynamics the basic rule of motion is often either 'move as far as possible toward the destination' or—reformulated—'of all coordinates accessible in this time step move to the one with the smallest distance to the destination'. On top of this rule modifications are placed to make the motion more realistic. These modifications usually focus on local behavior and neglect long-ranged effects. Compared to real pedestrians this leads to agents in a simulation valuing the shortest path a lot better than the quickest. So, in a situation such as the movement of a large crowd around a corner, one needs an additional element in a model of pedestrian dynamics that makes the agents deviate from the rule of the shortest path. In this work it is shown how this can be achieved by using a flood fill dynamic potential field method, where during the filling process the value of a field cell is not increased by 1, but by a larger value, if it is occupied by an agent. This idea may be an obvious one: however, the tricky part—and therefore in a strict sense the contribution of this work—is (a) to minimize unrealistic artifacts, as naive flood fill metrics deviate considerably from the Euclidean metric and in this respect yield large errors, (b) do this with limited computational effort and (c) keep agents' movement at very low densities unaltered.
TL;DR: In this paper, the distribution of the time-integrated current in an exactly solvable toy model of heat conduction was studied analytically and numerically, and a relation between system statistics at the end of a large deviation event and for intermediate times was revealed.
Abstract: We study the distribution of the time-integrated current in an exactly solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and the system statistics during a large deviation event. In this way we unveil a relation between system statistics at the end of a large deviation event and for intermediate times. The mid-time statistics is independent of the sign of the current, a reflection of the time-reversal symmetry of microscopic dynamics, while the end-time statistics does depend on the current sign, and also on its microscopic definition. We compare our exact results with simulations based on the direct evaluation of large deviation functions, analyzing the finite-size corrections of this simulation method and deriving detailed bounds for its applicability. We also show how the Gallavotti–Cohen fluctuation theorem can be used to determine the range of validity of simulation results.
TL;DR: In this paper, the authors investigated the stochastic extinction processes in a class of epidemic models, motivated by the process of natural disease extinction in epidemics, and examined the rate of extinction as a function of disease spread.
Abstract: We investigate the stochastic extinction processes in a class of epidemic models. Motivated by the process of natural disease extinction in epidemics, we examine the rate of extinction as a function of disease spread. We show that the effective entropic barrier for extinction in a susceptible?infected?susceptible epidemic model displays scaling with the distance to the bifurcation point, with an unusual critical exponent. We make a direct comparison between predictions and numerical simulations. We also consider the effect of non-Gaussian vaccine schedules, and show numerically how the extinction process may be enhanced when the vaccine schedules are Poisson distributed.