A key quantity describing the dynamics of complex systems is the first-passage time (FPT). The statistical properties of FPT depend on the specifics of the underlying system dynamics. We present a unified approach to account for the diversity of statistical behaviors of FPT observed in real-world systems. We find three distinct regimes, separated by two transition points, with fundamentally different behavior for FPT as a function of increasing strength of the correlations in the system dynamics: stretched exponential, power-law, and saturation regimes. In the saturation regime, the average length of FPT diverges proportionally to the system size, with important implications for understanding electronic delocalization in one-dimensional correlated-disordered systems.

In this work, we present a novel analytical model for tracer dispersion in laminar flow through porous media. Based on a straightforward physical argument, it describes the generic behavior of dispersion over a wide range of Péclet numbers (exceeding eight orders of magnitude). In particular, the model accurately captures the intermediate scaling behavior of longitudinal dispersion, obviating the need to subdivide the dispersional behavior into a number of disjunct regimes or using empirical power-law expressions. The analysis also suggests the possible existence of a new material property, the critical Péclet number, reflecting the mesoscale geometric properties of the microscopic pore structure.

The relationship between predator and prey plays an important role in ecosystem conservation. However, our understanding of the principles underlying the spatial distribution of predators and prey is still poor. Here we present a phase diagram of a predator-prey system and investigate the lattice formation in such a system. We show that the production of stable lattice structures depends on the limited diffusion or migration of prey as well as higher carrying capacity for the prey. In addition, when the prey's growth rate is lower than the birth rate of the predator, global prey lattice formation is initiated by microlattices at the center of prey spirals. The predator lattice is later formed in the predator spirals. But both lattice formations proceed together as the prey growth rate increases.

We have developed a simple model for pedestrians by dividing walking velocity into two parts, which are step size and pace of walking (number of steps per unit time). Theoretical analysis on pace indicates that rhythm that is slower than normal-walking pace in a low-density regime increases flow if the flow-density diagram is convex downward in a high-density regime. In order to verify this result, we have performed an experiment with real pedestrians and observed the improvement of flow in a congested situation using slow rhythm.

We study a system composed of two partially interdependent networks; when nodes in one network fail, they cause dependent nodes in the other network to also fail. In this paper, the percolation of partially interdependent networks under targeted attack is analyzed. We apply a general technique that maps a targeted-attack problem in interdependent networks to a random-attack problem in a transformed pair of interdependent networks. We illustrate our analytical solutions for two examples: (i) the probability for each node to fail is proportional to its degree, and (ii) each node has the same probability to fail in the initial time. We find the following: (i) For any targeted-attack problem, for the case of weak coupling, the system shows a second order phase transition, and for the strong coupling, the system shows a first order phase transition. (ii) For any coupling strength, when the high degree nodes have higher probability to fail, the system becomes more vulnerable. (iii) There exists a critical coupling strength, and when the coupling strength is greater than the critical coupling strength, the system shows a first order transition; otherwise, the system shows a second order transition.

Populations of mobile and communicating agents describe a vast array of technological and natural systems, ranging from sensor networks to animal groups. Here, we investigate how a group-level agreement may emerge in the continuously evolving network defined by the local interactions of the moving individuals. We adopt a general scheme of motion in two dimensions and we let the individuals interact through the minimal naming game, a prototypical scheme to investigate social consensus. We distinguish different regimes of convergence determined by the emission range of the agents and by their mobility, and we identify the corresponding scaling behaviors of the consensus time. In the same way, we rationalize also the behavior of the maximum memory used during the convergence process, which determines the minimum cognitive/storage capacity needed by the individuals. Overall, we believe that the simple and general model presented in this paper can represent a helpful reference for a better understanding of the behavior of populations of mobile agents.

We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

We have elucidated the effect of statistical asymmetry on the directed current in Smoluchowski-Feynman ratchets driven by chaotic noise. Based on the inhomogeneous Smoluchowski equation and its generalized version, we arrive at analytical expressions of the directed current that includes a source term. The source term indicates that statistical asymmetry can drive the system further away from thermodynamic equilibrium, as exemplified by the constant flashing, the state-dependent, and the tilted deterministic Smoluchowski-Feynman ratchets, with the consequence of an enhancement in the directed current.

We characterize the generation of flow vortices in nanoscale confinements under the combined effects of patterned surface charge density and substrate wettability. Using molecular dynamics simulations, we elucidate the effects of ion solvation and steric interactions toward influencing the resultant transport characteristics, which are otherwise difficult to resolve using classical electrokinetic theory. We also evaluate the velocity slip (local and global) as well as vorticity parameters, in an effort to assess the implications of the generated flow structure from a pseudocontinuum viewpoint. Results from the present study are expected to provide valuable insights on augmentation of nanoscale mixing.

A promising approach to the modeling of anomalous (non-Gaussian) dispersion in flow through heterogeneous porous media is the continuous-time random walk (CTRW) method. In such a formula on the waiting time distribution $\psi \left(t\right)$ is usually assumed to be given by $\psi \left(t\right)\sim t^{-1-\alpha }$, with $\alpha$ fitted to the experimental data. The exponent $\alpha$ is also related to the power-law growth of the mean-square displacement of the solute with the time $t$ $\langle R^2\left(t\right)\rangle \sim t^{\zeta }$. Invoking percolation and using a scaling analysis, we relate $\alpha$ to the geometrical exponents of percolation ($\nu$, $\beta$, and ${\beta }_B$) as well as the exponents $\mu$ and $e$ that characterize the power-law behavior of the effective conductivity and permeability of porous media near the percolation threshold. We then explain the cause of the nonuniversality of $\alpha$ in terms of the nonuniversality of $\mu$ and $e$ in continuum systems, and in percolation models with long-range correlations, and propose bounds for it. The results are consistent with the experimental data, both at the laboratory and field scales.

Capillary processes greatly influence vapor mediated transport dynamics and associated changes in liquid phase content of porous media. Rapid x-ray synchrotron tomography measurements were used to resolve liquid-vapor interfacial dynamics during evaporation and condensation within submillimetric pores forming between sintered glass bead samples subjected to controlled ambient temperature and relative humidity. Evolution of gas-liquid interfacial shapes were in agreement with predictions based on our analytical model for interfacial dynamics in confined wedge-shaped pores. We also compared literature experimental data at the nanoscale to illustrate the capability of our model to describe early stages of condensation giving rise to the onset of capillary forces between rough surfaces. The study provides high resolution, synchrotron-based observations of capillary evaporation-condensation dynamics at the pore scale as the confirmation of the pore scale analytical model for capillary condensation in a pore and enables direct links with evolution of macroscopic vapor gradients within a sintered glass bead sample through their effect on configuration and evolution of the local interfaces. Rapid condensation processes play a critical role in the onset of capillary-induced friction affecting mechanical behavior of physical systems and industrial applications.

We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may develop even in situations where separately the ratchet and the geometric restrictions do not give rise to particle motion. The combined rectification effects can lead to bidirectional transport depending on particle size, resulting in a different route for segregation. The reported mechanism can be used to control transport in mesostructures and nanodevices in which particles move in a reduced space.

The phase behavior of interacting rigid rods of length $k$ ($k$-mers) on two-dimensional square and triangular lattices has been studied by theoretical calculations in the framework of the lattice-gas model. The process was analyzed by comparing the dependence on coverage of the free energy per site of an isotropic submonolayer of interacting $k$-mers $f_{\mathrm{iso}}\left(\theta \right)$ with that corresponding to a fully aligned (nematic) system $f_{\mathrm{nem}}\left(\theta \right)$. The existence of an intersection point between the curves $f_{\mathrm{iso}}\left(\theta \right)$ and $f_{\mathrm{nem}}\left(\theta \right)$, which is indicative of the occurrence of an isotropic-nematic phase transition in the adlayer, allowed us to obtain the complete (temperature, coverage, $k$-mer size) phase diagram of the system.

We consider the problem of electron transport in segregated conductor-insulator composites in which the conducting particles are connected to all others via tunneling conductances, thus forming a global tunneling-connected resistor network. Segregation is induced by the presence of large insulating particles, which forbid the much smaller conducting fillers from occupying uniformly the three-dimensional volume of the composite. By considering both colloidal-like and granular-like dispersions of the conducting phase, modeled respectively by dispersions in the continuum and in the lattice, we evaluate by Monte Carlo simulations the effect of segregation on the composite conductivity $\sigma$, and show that an effective-medium theory applied to the tunneling network reproduces accurately the Monte Carlo results. The theory clarifies that the main effect of segregation in the continuum is that of reducing the mean interparticle distances, leading to a strong enhancement of the conductivity. In the lattice-segregation case the conductivity enhancement is instead given by the lowering of the percolation thresholds for first and beyond-first nearest neighbors. Our results generalize to segregated composites the tunneling-based description of both the percolation and hopping regimes introduced previously for homogeneous disordered systems.

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.

When microbes compete for limited resources, they often engage in chemical warfare using bacterial toxins. This competition can be understood in terms of evolutionary game theory (EGT). We study the predictions of EGT for the bacterial “suicide bomber” game in terms of the phase portraits of population dynamics, for parameter combinations that cover all interesting games for two-players, and seven of the 38 possible phase portraits of the three-player game. We compare these predictions to simulations of these competitions in finite well-mixed populations, but also allowing for probabilistic rather than pure strategies, as well as Darwinian adaptation over tens of thousands of generations. We find that Darwinian evolution of probabilistic strategies stabilizes games of the rock-paper-scissors type that emerge for parameters describing realistic bacterial populations, and point to ways in which the population fixed point can be selected by changing those parameters.

Two-plasmon-decay (TPD) instability is investigated for conditions relevant for the shock-ignition (SI) scheme of inertial confinement fusion. Two-dimensional particle-in-cell simulations show that in a hot, large-scale plasma, TPD develops in concomitance with stimulated Raman scattering (SRS). It is active only during the first picosecond of interaction, and then it is rapidly saturated due to plasma cavitation. TPD-excited plasma waves extend to small wavelengths, above the standard Landau cutoff. The hot electron spectrum created by SRS and TPD is relatively soft, limited to energies below 100 keV, which should not be a danger for the fuel core preheat in the SI scenario.

Charged particle interaction with localized wave packets in a magnetic field is formulated using the canonical perturbation theory and the Lie transform theory. An electrostatic wave packet characterized by a wide range of group and phase velocities as well as spatial extent along and across the magnetic field is considered. The averaged changes in the momentum along the magnetic field, the angular momentum, and the guiding center position for an ensemble of particles due to their interaction with the wave packet are determined analytically. Both resonant and ponderomotive effects are included. For the case of a Gaussian wave packet, closed-form expressions include the dependency of the ensemble averaged particle momenta and guiding center position variations on wave packet parameters and particle initial conditions. These expressions elucidate the physics of the interaction which is markedly different from the well known case of particle interaction with plane waves and are relevant to a variety of applications ranging from space and astrophysical plasmas to laboratory and fusion plasmas, as well as accelerators and microwave devices.

In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

A simple model for the boarding of an airplane is studied. Passengers have reserved seats but enter the airplane in arbitrary order. Queues are formed along the aisle, as some passengers have to wait to reach the seats for which they have reservation. We label a passenger by the number of his or her reserved seat. In most cases the boarding process is much slower than for the optimal situation, where passenger and seat orders are identical. We study this dynamical system by calculating the average boarding time when all permutations of $N$ passengers are given equal weight. To first order, the boarding time for a given permutation (ordering) of the passengers is given by the number $s$ of sequences of monotonically increasing values in the permutation. We show that the distribution of $s$ is symmetric on $[1,N]$, which leads to an average boarding time $(N+1)/2$. We have found an exact expression for $s$ and have shown that the full distribution of $s$ approaches a normal distribution as $N$ increases. However, there are significant corrections to the first-order results, due to certain correlations between passenger ordering and the substrate (seat ordering). This occurs for some cases in which the sequence of the seats is partially mirrored in the passenger ordering. These cases with correlations have a boarding time that is lower than predicted by the first-order results. The large number of cases with reduced boarding times have been classified. We also give some indicative results on the geometry of the correlations, with sorting into geometry groups. With increasing $N$, both the number of correlation types and the number of cases belonging to each type increase rapidly. Using enumeration we find that as a result of these correlations the average boarding time behaves like $N^{\alpha }$, with $\alpha \simeq 0.69$, as compared with $\alpha =1.0$ for the first-order approximation.