Spatial dynamics has in many cases been invoked as a mechanism that can promote the evolution of coexistence and cooperation, although the precise conditions for this to occur have not yet been characterised. In an effort to address this question we have analyzed an alternative version of the theoretical game “war of attrition,” which exhibits unusual behavior: The well-mixed system exhibits quasistationary coexistence and a relaxation time that scales exponentially with the system size, while the spatial system shows a relaxation time that is considerably smaller and scales with a power $\alpha \approx 1.4$ of the system size. Further, the spatial system exhibits a first-order phase transition in the strategy distribution at a consolation prize of $k\approx 1/3$. Close to this point the relaxation time diverges with an exponent $\gamma \approx 1.2$. This analysis shows that the effect of space is highly dependent on the type of game considered.

We revisit two known models of deterministically driven ratchets, which exhibit high energetic efficiency, with the goal to uncover similarities and differences in the principles of their operation. Both the models rely on adiabaticity of the potential change process, however, the adiabaticity that we deal with in the two cases is of different types, slow and fast. It is shown that in the former (latter) case the drift velocity is an even (odd) functional of the potential, with the notable consequence that for the adiabatically slow driven ratchet the necessary symmetry breaking occurs only due to time-dependent parametric perturbations, while the spatial asymmetry of the potential is a mandatory condition for the adiabatically fast driven ratchet to operate. To treat energetic characteristics, the models are restated in terms of traveling potential ratchets. With such an approach, we find that in these cases (i) the conditions of high energetic efficiency to be reached are similar, and (ii) the symmetry properties of the kinetic coefficients are different. Based on our results, a strategy for designing efficient Brownian motors is suggested.

A system of ideal gas is switched from an initial equilibrium state to a final state not necessarily in equilibrium, by varying a macroscopic control variable according to a well-defined protocol. The distribution of work performed during the switching process is obtained. The equilibrium free energy difference, $\Delta F$, is determined from the work fluctuation relation. Some of the work values in the ensemble shall be less than $\Delta F$. We term these as ones that “violate” the second law of thermodynamics. A fluctuating lattice Boltzmann model has been employed to carry out the simulation of the switching experiment. Our results show that the probability of violation of the second law increases with the increase of switching time $\left(\tau \right)$ and tends to one-half in the reversible limit of $\tau \to \infty$.

We analyze the nonequilibrium steady states (NESS) of a one-dimensional harmonic chain of $N$ atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile defined through the local kinetic energy $T\left(j\right)\equiv \langle p_j^2\rangle /m_j$ oscillates with period two in the bulk of the system. Depending on boundary conditions, either the heavier or the lighter particles in the bulk are hotter. We obtain explicit integral expressions for the bulk temperature profile and steady state current in the limit $N\to \infty$. These depend on whether $N$ is odd or even. We also study similar temperature oscillations in the NESS of systems with noise in the dynamics. These die out as $N\to \infty$.

We investigate the effects of adsorbed films on the attenuative properties of loose granular media occupying a finite-sized rigid container that is open at the top. We measure the effective mass, $\tilde{M}\left(\omega \right)$, of loose tungsten particles prepared under two different sets of conditions: (i) We lightly coat tungsten grains with a fixed volume fraction of silicone oil (polydimethylsiloxane, PDMS), where the liquid viscosity is varied for individual realizations, and (ii) in the other set of experiments we vary the humidity. On a theoretical level, we are able to decompose the effective mass into a sum over the contributions from each of the normal modes of the granular medium. Our results indicate that increasing either the PDMS viscosity or the humidity, as the case may be, markedly increases the damping rate of each normal mode relevant to our measurements. However, there is appreciable damping even in the absence of any macroscopic film. With a notable exception in the case of the highest humidity in the humidity-controlled experiments, all the relevant modes are weakly damped in the sense of a microscopic theory based on damped contact forces between rigid particles.

Using molecular dynamics simulations, disorder trapping associated with solidification is studied for the (100), (110), and (111) growth directions in the $B2$ NiAl ordered alloy compound. At the high interface velocities studied we observe pronounced disorder and defect trapping, i.e., the formation of antisite defects and vacancies in the crystal at higher than equilibrium concentrations upon rapid solidification. The vacancies are located primarily on the Ni sublattice and the majority of antisite defects are Ni atoms on the Al sublattice, while the concentration of Al on the Ni sublattice is negligibly small. The defect concentration is found to increase in an approximately linear relationship with increasing the interface velocity. Further there is no significant anisotropy in the defect concentrations for different interface orientations. Our results suggest that the currently available models of disorder trapping should be extended to include both antisite defects and vacancies.

We derive an approximate analytic expression for the structure factor of equilibrium, thermal composition fluctuations in an ordered lamellar mesophase. In order to test the validity of the equation, we perform a series of stochastic simulations using an established model of block copolymer ordering and demonstrate that the equation fits the simulation data with zero adjustable fit parameters over a reasonably wide range of system and simulation parameters.

We construct perturbation series for the $q$th moment of eigenfunctions of various critical random-matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region $q<1/2$. Our findings allow one to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dimensions ${\Delta }_q={\Delta }_{1-q}$, recently conjectured for critical models where an analog of the metal-insulator transition takes place. It is known that this relation is verified at leading order in the weak multifractality regime. Our results thus indicate that this symmetry holds in both limits of small and large coupling constant. For general values of the coupling constant we present careful numerical verifications of this symmetry relation for different critical random-matrix ensembles. We also present an example of a system closely related to one of these critical ensembles, but where the symmetry relation, at least numerically, is not fulfilled.

Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The distinctive scaling properties of the model at criticality, however, strongly suggest that it should belong to a different universality class than ordinary percolation. Here we introduce a generalization of the product rule that reveals the effect of nonlocality on the critical behavior of the percolation process. Precisely, pairs of unoccupied bonds are chosen according to a probability that decays as a power law of their Manhattan distance, and only that bond connecting clusters whose product of their sizes is the smallest becomes occupied. Interestingly, our results for two-dimensional lattices at criticality shows that the power-law exponent of the product rule has a significant influence on the finite-size scaling exponents for the spanning cluster, the conducting backbone, and the cutting bonds of the system. In all three cases, we observe a clear transition from ordinary to (nonlocal) explosive percolation exponents.

The problem addressed is the identification of cooperating agents based on correlations created as a result of the joint action of these and other agents. A systematic method for using correlations beyond second moments is developed. The technique is applied to a didactic example, the identification of alphabet letters based on correlations among the pixels used in an image of the letter. As in this example, agents can belong to more than one cluster. Moreover, the identification scheme does not require that the patterns be known ahead of time.

We study a dense colloidal suspension confined between two quasiparallel glass plates as a model system for a supercooled liquid in confined geometries. We directly observe the three-dimensional Brownian motion of the colloidal particles using laser scanning confocal microscopy. The particles form dense layers along the walls, but crystallization is avoided as we use a mixture of two particle sizes. A normally liquidlike sample, when confined, exhibits slower diffusive motion. Particle rearrangements are spatially heterogeneous, and the shapes of the rearranging regions are strongly influenced by the layering. These rearranging regions become more planar upon confinement. The wall-induced layers and changing character of the spatially heterogeneous dynamics appear strongly connected to the confinement-induced glassiness.

Amoeboid cells such as Dictyostelium discoideum and Madin-Darby canine kidney cells show the non-Brownian dynamics of migration characterized by the superdiffusive increase of mean-squared displacement. In order to elucidate the physical mechanism of this non-Brownian dynamics, a computational model is developed which highlights a group of inhibitory molecules for actin polymerization. Based on this model, we propose a hypothesis that inhibitory molecules are sent backward in the moving cell to accumulate at the rear of cell. The accumulated inhibitory molecules at the rear further promote cell locomotion to form a slow positive feedback loop of the whole-cell scale. The persistent straightforward migration is stabilized with this feedback mechanism, but the fluctuation in the distribution of inhibitory molecules and the cell shape deformation concurrently interrupt the persistent motion to turn the cell into a new direction. A sequence of switching behaviors between persistent motions and random turns gives rise to the superdiffusive migration in the absence of the external guidance signal. In the complex environment with obstacles, this combined process of persistent motions and random turns drives the simulated amoebae to solve the maze problem in a highly efficient way, which suggests the biological advantage for cells to bear the non-Brownian dynamics.

We present event distributions for the polymer translocation obtained by extensive Langevin dynamics simulations. Such distributions have not been reported previously and they provide new understanding of the stochastic characteristics of the process. We extract at a high length scale resolution distributions of polymer segments that continuously traverse through a nanoscale pore. The obtained log-normal distributions together with the characteristics of polymer translocation suggest that it is describable as a multiplicative stochastic process. In spite of its clear out-of-equilibrium nature the forced translocation is surprisingly similar to the unforced case. We find forms for the distributions almost unaltered with a common cut-off length. We show that the individual short-segment and short-time movements inside the pore give the scaling relations $\tau \sim N^{\alpha }$ and $\tau \sim f^{-\beta }$ for the polymer translocation.

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the method has still been missing so far. Here, we interpret an $\varepsilon$-recurrence network as a discrete subnetwork of a “continuous” graph with uncountably many vertices and edges corresponding to the system's attractor. This step allows us to show that various statistical measures commonly used in complex network analysis can be seen as discrete estimators of newly defined continuous measures of certain complex geometric properties of the attractor on the scale given by $\varepsilon$. In particular, we introduce local measures such as the $\varepsilon$-clustering coefficient, mesoscopic measures such as $\varepsilon$-motif density, path-based measures such as $\varepsilon$-betweennesses, and global measures such as $\varepsilon$-efficiency. This new analytical basis for the so far heuristically motivated network measures also provides an objective criterion for the choice of $\varepsilon$ via a percolation threshold, and it shows that estimation can be improved by so-called node splitting invariant versions of the measures. We finally illustrate the framework for a number of archetypical chaotic attractors such as those of the Bernoulli and logistic maps, periodic and two-dimensional quasiperiodic motions, and for hyperballs and hypercubes by deriving analytical expressions for the novel measures and comparing them with data from numerical experiments. More generally, the theoretical framework put forward in this work describes random geometric graphs and other networks with spatial constraints, which appear frequently in disciplines ranging from biology to climate science.

Boolean networks are discrete dynamical systems in which the state (0 or 1) of each node is updated at each time $t$ to a state determined by the states at time $t-1$ of those nodes that have links to it. When these systems are used to model genetic control, the case of canalizing update rules is of particular interest. A canalizing rule is one for which a node state at time $t$ is determined by the state at time $t-1$ of a single one of its inputs when that inputting node is in its canalizing state. Previous work on the order-disorder transition in Boolean networks considered complex, nonrandom network topology. In the current paper we extend this previous work to account for canalizing behavior.

In this paper, stochastic resonance of an ensemble of coupled bistable systems driven by noise having an $\alpha$-stable distribution and nonhomogeneous coupling is investigated. The $\alpha$-stable distribution considered here is characterized by four intrinsic parameters: $\alpha \in (0,2]$ is called the stability parameter for describing the asymptotic behavior of stable densities; $\beta \in [-1,1]$ is a skewness parameter for measuring asymmetry; $\gamma \in (0,\infty )$ is a scale parameter for measuring the width of the distribution; and $\delta \in (-\infty ,\infty )$ is a location parameter for representing the mean value. It is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths. We show that the stability parameter $\alpha$ and the scale parameter $\gamma$ can be well selected to generate resonant effects in response to external signals. In addition, the interplay between the skewness parameter $\beta$ and the location parameter $\delta$ on the resonance effects is also studied. We further show that the asymmetry of a Lévy $\alpha$-stable distribution resulting from the skewness parameter $\beta$ and the location parameter $\delta$ can enhance the resonance effects. Both theoretical analysis and simulation are presented to verify the results of this paper.

Electrohydrodynamics in the presence of hydrophobic interactions in narrow confinements is traditionally represented from a continuum viewpoint by a Navier slip-based conceptual paradigm, in which the slip length carries the sole burden of incorporating the effects of substrate wettability on interfacial electromechanics, precluding any explicit dependence of the interfacial potential distribution on the substrate wettability. Here we show that this traditional way of treating electrokinetics-wettability coupling may lead to serious discrepancies in predicting the resultant transport characteristics as manifested through an effective zeta potential. We suggest that an alternative consistent description of the underlying physics through a free-energy-based formalism, in conjunction with considerations of hydrodynamic and electrical property variations consistent with the pertinent phase-field description, may represent the underlying consequences in a more rational manner, as compared to the traditional slip-based model coupled with a two-layer description. Our studies further reveal that the above discrepancies may not occur solely due to the slip-based route of representing the interfacial wettability, but may be additionally attributed to the act of “discretizing” the interfacial phase fraction distribution through an artificial two-layer route.

This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion $\kappa$ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent $\lambda$ with two times $\tau$ and $\tilde{\tau }$. The time $1/\lambda$ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time $t$, while $\tau$ measures it in the recent past before $t$, and $\tilde{\tau }$ in the early part of the trajectory. We show that the chemical speed scales like ${\kappa }^{1/2}$ and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

In this study, a new filter-matrix lattice Boltzmann (FMLB) model is proposed and extended to include incompressible thermal flows. A new equilibrium solution is found in the improved FMLB model, which is derived from the Hermite expansion. As a result, the velocity-dependent pressure is removed, which is an inherent defect of Somers's FMLB model. In addition, the improved model is extended to include incompressible thermal flows by introducing a class of temperature-distribution function for evaluating the temperature field. Two different temperature-distribution functions are discussed. The improved FMLB model and the temperature-evaluation equation are combined into one coupled model. Numerical simulations are performed on the two-dimensional (2D) lid-driven square cavity flow and the 2D natural convection flow in a square cavity using the improved FMLB model and the two coupled models, respectively. The numerical results of the 2D lid-driven square cavity flow show that the improved FMLB model is superior to the lattice Bhatnagar-Gross-Krook (LBGK) model in terms of both accuracy and stability. When compared with the multi-relaxation-time (MRT) model, the similar accuracy and slightly enhanced stability can be obtained by the improved model. The advantage of the improved model is that it no longer relies on difficult selection of the free parameters requested by the MRT model; in addition, the force term is already included in the collision operator of the improved model. In the case of 2D natural convection flow, the numerical results of the two present models are almost the same, and both exhibit good agreement with the benchmark solution.