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arXiv2013

Biased and greedy random walks on two-dimensional lattices with quenched randomness: the "greedy" ant within a disordered environment

The principle characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here, the disorder allows for negative edge-weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization (ACO) heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter rho that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of rho for different bias strengths B is put under scrutiny. Upon tuning rho, the probability to find such a feasible lattice walk increases from zero to one. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point rho_c, resulting from numerically exact and "static" simulations in terms of the NWP model can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

cond-mat.dis-nn↗

arXiv2013

Pattern formation in individual-based systems with time-varying parameters

We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models. Similar to the well-known Kibble-Zurek scenario of defect formation, large-scale patterns are generated when model parameters are varied slowly, whereas fast sweeps produce a large number of small domains. The symmetry breaking is triggered by intrinsic noise, originating from the discrete dynamics at the micro-level. Based on a linear-noise approximation, we calculate the characteristic length scale of these patterns. We demonstrate the applicability of this approach in a simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and a model of cell differentiation. Our theoretical estimates are confirmed in simulations. In further numerical work, we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.

cond-mat.stat-mech↗

arXiv2013

Analytical Calculation of Four-Point Correlations for a Simple Model of Cages Involving Numerous Particles

Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter sigma) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the two-particle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to three-dimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.

cond-mat.stat-mech↗

arXiv2013

Counting metastable states in a kinetically constrained model using a patch repetition analysis

We analyse metastable states in the East model, using a recently-proposed patch-repetition analysis based on time-averaged density profiles. The results reveal a hierarchy of states of varying lifetimes, consistent with previous studies in which the metastable states were identified and used to explain the glassy dynamics of the model. We establish a mapping between these states and configurations of systems of hard rods, which allows us to analyse both typical and atypical metastable states. We discuss connections between the complexity of metastable states and large-deviation functions of dynamical quantities, both in the context of the East model and more generally in glassy systems.

cond-mat.stat-mech↗

arXiv2013

Local immobilization of particles in mass transfer described by the equation of the Jeffreys type

We consider the equation of the Jeffreys type as the basic one in three different models of mass transfer, namely, the Jeffreys type and two-phase models, and the $D_1$ approximation to the linear Boltzmann equation. We study two classic 1 + 1D problems in the framework of each model. The first problem is the transfer of a substance initially confined in a point. The second problem is the transfer of a substance from a stationary point source. We calculate the mean-square displacement (MSD) for the solutions of the first problem. The temporal behaviour of the MSD in the framework of the first and third models is found to be the same as that in the Brownian motion described by the standard Langevin equation. Besides, we find a remarkable phenomenon when a portion of the substance does not move.

cond-mat.stat-mech↗

arXiv2013

Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation

There are several examples which show that the critical exponents can be dependent on initial condition of the system. In such situations, there are many systems where various issues related to the universal behavior e.g. existence of universality, splitting of universality class, scaling violation, whether the initial dependence should persist even after sufficiently long time or is a transient effect, the reasons for such features, etc. are not yet quite clear. In this article, with the simple example of conserved lattice gas (CLG) model, we investigate such issues and clearly show that under certain situations the asymptotic decay exponents are in fact dependent on the initial condition of the system. We show that such effect arises because of existence of two competing time scales, and identify the initial conditions which capture the universal features of the system.

cond-mat.stat-mech↗

arXiv2013

Information driven current in a quantum Maxwell demon

We describe a minimal model of a quantum Maxwell demon obeying Hamiltonian dynamics. The model is solved exactly, and we analyze its steady-state behavior. We find that writing information to a quantum memory induces a probability current through the demon, which is the quantum analog of the classical Maxwell demon's action. Our model offers a simple and pedagogical paradigm for investigating the thermodynamics of quantum information processing.

cond-mat.stat-mech↗

arXiv2013

Non-equilibrium steady state and induced currents of a mesoscopically-glassy system: interplay of resistor-network theory and Sinai physics

We introduce an explicit solution for the non-equilibrium steady state (NESS) of a ring that is coupled to a thermal bath, and is driven by an external hot source with log-wide distribution of couplings. Having time scales that stretch over several decades is similar to glassy systems. Consequently there is a wide range of driving intensities where the NESS is like that of a random walker in a biased Brownian landscape. We investigate the resulting statistics of the induced current $I$. For a single ring we discuss how $sign(I)$ fluctuates as the intensity of the driving is increased, while for an ensemble of rings we highlight the fingerprints of Sinai physics on the $abs(I)$ distribution.

cond-mat.stat-mech↗

arXiv2014

Jammed lattice sphere packings

We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.

cond-mat.stat-mech↗

arXiv2014

Collective behavior of penetrable self-propelled rods in two dimensions

Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays. The properties of such systems depend both on their dimensionality and the interactions between their particles. We introduce a model for self-propelled rods in two dimensions that interact via a separation-shifted Lennard-Jones potential. Due to the finite potential barrier, the rods are able to cross. This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can occasionally escape to the third dimension in order to pass each other. Our quasi-two-dimensional self-propelled particles describe a class of active systems that encompasses microswimmers close to a wall and filaments propelled on a substrate. Using Monte Carlo simulations, we first determine the isotropic-nematic transition for passive rods. Using Brownian dynamics simulations, we characterize cluster formation of self-propelled rods as a function of propulsion strength, noise, and energy barrier. Contrary to rods with an infinite potential barrier, an increase of the propulsion strength does not only favor alignment but also effectively decreases the potential barrier that prevents crossing of rods. We thus find a clustering window with a maximum cluster size at medium propulsion strengths.

cond-mat.soft↗

arXiv2013

Avalanche localization and crossover scaling in amorphous plasticity

We perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long-range quadrupolar elastic interactions. We show that as the external stress increases towards the yielding phase transition, the scaling behavior of the avalanches crosses over from mean-field theory to a different universality class. This behavior is associated with strain localization, which significantly depends on the short-range properties of the interaction kernel.

cond-mat.soft↗

arXiv2013

Network Growth with Arbitrary Initial Conditions: Analytical Results for Uniform and Preferential Attachment

This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes selected uniformly at random, and preferential attachment, when probabilities are assigned proportional to the degrees of the existing nodes. We consider the cases of single and multiple links being formed by each newly-introduced node. The initial conditions are arbitrary, that is, the solution depends on the degree distribution of the initial graph which is the substrate of the growth. Previous work in the literature focuses on the asymptotic state, that is, when the number of nodes added to the initial graph tends to infinity, rendering the effect of the initial graph negligible. Our contribution provides a solution for the expected degree distribution as a function of time, for arbitrary initial condition. Previous results match our results in the asymptotic limit.

cond-mat.stat-mech↗

arXiv2013

Statistical Mechanics of Multi-Edge Networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos variables and those where they account for discrete, distinguishable events, which we call multi-edge networks. In this work we face this problem introducing multi-edge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multi-edges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multi-edge processes. The implications of these results are important as many real agent based problems mapped onto graphs require of this treatment for a proper characterization of its collective behavior.

physics.soc-ph↗

arXiv2013

Percolation of a general network of networks

Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of $n$ classic Erdős-Rényi (ER) networks, where each network depends on the same number $m$ of other networks, i.e., a random regular network of interdependent ER networks. In contrast to a \emph{treelike} NetONet in which the size of the largest connected cluster (mutual component) depends on $n$, the loops in the RR NetONet cause the largest connected cluster to depend only on $m$. We also analyzed the extremely vulnerable feedback condition of coupling. In the case of ER networks, the NetONet only exhibits two phases, a second order phase transition and collapse, and there is no first phase transition regime unlike the no feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when $q$ is large and second order phase transition when $q$ is small. Our results can help in designing robust interdependent systems.

physics.soc-ph↗

arXiv2013

The circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer

We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or 2D vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small noise amplitudes, scaling behavior is only of the latter type. Large noise is also seen to renormalize the bare physical parameters of the ring, akin to analogous parameter renormalization for equilibrium 3D membranes. Our results bear particular importance on the relation between relevant universality classes of scale-invariant systems in two dimensions.

cond-mat.stat-mech↗

arXiv2014

Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations

We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.

cond-mat.stat-mech↗

arXiv2014

Kosterlitz-Thouless and Potts transitions in a generalized XY model

We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso {\it et al} [PRL 106(2011)067202]. Using finite size scaling and focusing on the $q=3$ case, we locate the transitions between the paramagnetic (P), the nematic-like (N) and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the 3-states Potts universality class.

cond-mat.stat-mech↗

arXiv2014

Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, {Phys. Rev. Lett.} \textbf{105}, 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.

cond-mat.stat-mech↗