Urban outputs often scale superlinearly with city population. A difficulty in understanding the mechanism of this phenomenon is that different outputs differ considerably in their scaling behaviors. Here, we formulate a physics-based model for the origin of superlinear scaling in urban outputs by treating human interaction as a random process. Our model suggests that the increased likelihood of finding required collaborations in a larger population can explain this superlinear scaling, which our model predicts to be non-power-law. Moreover, the extent of superlinearity should be greater for activities that require more collaborators. We test this model using a novel dataset for seven crime types and find strong support.

A cell must sense extracellular and intracellular fluctuations and respond appropriately to survive for optimal cellular functioning. Accordingly, a cell builds up biochemical networks which can transduce information of extracellular and intracellular fluctuations accurately. We consider a generic two-step cascade as a model gene regulatory network containing three regulatory proteins S, X, and Y connected as $\mathrm{S}\to \mathrm{X}\to \mathrm{Y}$. The intermediate node X is a stochastic variable, acts as an obstacle, and impedes the information flow from S to Y. We quantify the information that is restricted by X using the tools of information theory and term this as restricted information. In this context, we further propose two measurable quantities, restricted efficiency and information transfer efficiency. The former determines how efficiently X restricts the upstream information coming from S, while the latter computes the efficiency of X to pass the upstream information toward Y. We also quantify the information that is being uniquely transferred from X to Y, which determines the extent of the ability of X to act as a source of information. Our analysis shows that when the signal strength (or mean population of S, $\langle s\rangle$) is low, the intermediate X can carry forward the upstream information reliably as well, as it acts as a better source of information, thereby increasing the fidelity of the network. But at the high signal strength, X restricts most of the upstream information, and its ability to act as a source of information gets reduced. This leads to a loss of fidelity of the network.

A defense mechanism in epithelial tissue can mechanically eliminate abnormal cells by contracting the cell boundary or area via actomyosin activity. From numerical simulations of the vertex dynamics model and approximate analytical solutions based on deviations from the ground state, here we derived general conditions for mechanical cell elimination (MCE) occurring via cell contraction. In particular, we found that MCE is realized by saddle-node bifurcation in a wide parameter range, and that the size of the eliminated cell is almost constant at the bifurcation point, suggesting the existence of an intrinsic threshold cell area for MCE.

We investigate the thermohydrodynamic lubrication of the Lennard-Jones (LJ) fluid in plain wall channels by using a molecular-dynamics simulation. It is found that the LJ fluid solidifies near the wall when the viscous heating of the LJ fluid in the bulk regime is sufficiently large. The thickness of the solidified layer increases with the channel width. Thus, a long-range-ordered crystal-like structure forms near the wall in high-speed lubrication when the channel width is large. The mechanism of this counterintuitive solidification is investigated from both macroscopic and microscopic points of view. It is elucidated that the LJ molecules are densely confined in the vicinity of the wall due to the macroscopic mass and heat transport in the bulk regime. In this densely confined regime, the fluid molecules form a crystal-like structure, which is similar to that of the wall molecules, via direct molecular interaction. Band formation is also observed in the solidified region when the channel width is sufficiently large.

Extreme events that arise spontaneously in chaotic dynamical systems often have an adverse impact on the system or the surrounding environment. As such, their mitigation is highly desirable. Here, we introduce a control strategy for mitigating extreme events in a turbulent shear flow. The controller combines a probabilistic prediction of the extreme events with a deterministic actuator. The predictions are used to actuate the controller only when an extreme event is imminent. When actuated, the controller only acts on the degrees of freedom that are involved in the formation of the extreme events, exerting minimal interference with the flow dynamics. As a result, the attractors of the controlled and uncontrolled systems share the same chaotic core (containing the nonextreme events) and only differ in the tail of their distributions. We propose that such adaptive low-dimensional controllers should be used to mitigate extreme events in general chaotic dynamical systems, beyond the shear flow considered here.

Porous media are ubiquitous in both nature and engineering applications. Therefore, their modeling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of this type of medium, obtaining its subregion (s) such as 2D images or several small areas can be feasible. Therefore, reconstructing whole images from limited information is a primary technique in these types of cases. Given data in practice cannot generally be determined by users and may be incomplete or only partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we propose a deep-learning-based framework for reconstructing full images from their much smaller subareas. In particular, conditional generative adversarial network is utilized to learn the mapping between the input (a partial image) and output (a full image). To ensure the reconstruction accuracy, two simple but effective objective functions are proposed and then coupled with the other two functions to jointly constrain the training procedure. Because of the inherent essence of this ill-posed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus enabling the network to provide multiple candidate outputs. Our method is extensively tested on a variety of porous materials and validated by both visual inspection and quantitative comparison. It is shown to be accurate, stable, and even fast ($\sim 0.08$ s for a $128\times 128$ image reconstruction). The proposed approach can be readily extended by, for example, incorporating user-defined conditional data and an arbitrary number of object functions into reconstruction, while being coupled with other reconstruction methods.

Fractional Brownian motion is a widely used stochastic process that is particularly suited to model anomalous diffusion. We focus on capturing the mean and variance of fractional Brownian motion reflected at level 0. As explicit expressions or numerical techniques are not available, we base our analysis on Monte Carlo simulation. Our main findings concern closed-form approximations of the mean and variance, with a near-perfect fit.

Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators—at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the cross-correlation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the mean-field fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the cross-correlation, at both super- and subcritical coupling.

This paper introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannon's mutual information, and introduces the O-information as a metric that is capable of characterizing synergy- and redundancy-dominated systems. The O-information is a symmetric quantity, and can assess intrinsic properties of a system without dividing its parts into “predictors” and “targets.” We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we present an exploration on the relevance of statistical synergy in Baroque music scores.

We consider the process of chemical erosion of a porous medium infiltrated by a reactive fluid in a thin-front limit, in which the width of the reactive front is negligible with respect to the diffusive length. We show that in the radial geometry the advancing front becomes unstable only if the flow rate in the system is sufficiently high. The existence of such a stable region in parameter space is in contrast to the Saffman-Taylor instability in radial geometry, where for a given flow rate the front always eventually becomes unstable, after reaching a certain critical radius. We also examine the similarities between the reactive-infiltration instability and the similar instability in the heat transfer, which is driving the formation of star-like patterns on frozen lakes.

Spatially localized invariant solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations [Schneider, Gibson, and Burke, Phys. Rev. Lett. 104, 104501 (2010)]. We demonstrate the mechanism by which these snaking solutions originate from well-known periodic states of the Taylor-Couette system. They are formed by a localized slug of wavy-vortex flow that emerges from a background of Taylor vortices via a modulational sideband instability. This mechanism suggests a close connection between pattern-formation theory and Navier-Stokes flow.

Chains of particles coupled through anharmonic interactions and subject to non-Gaussian baths can exhibit paradoxical outcomes such as heat currents flowing from colder to hotter reservoirs. Aiming to explore the role of generic nonharmonicities in mediating the contributions of non-Gaussian fluctuations to the direction of heat propagation, we consider a chain of power-law oscillators, with interaction potential $V\left(x\right)\propto {\left|x\right|}^{\alpha }$, subject to Gaussian and Poissonian baths at its ends. Performing numerical simulations and addressing heuristic considerations, we show that a deformable potential has bidirectional control over heat flux.

We investigate local persistence in five different models and their variants in the directed Ising (DI) universality class in one dimension. These models have right-left symmetry. We study Grassberger's models A and B. We also study branching and annihilating random walks with two offspring: the nonequilibrium kinetic Ising model and the interacting monomer-dimer model. Grassberger's models are updated in parallel. This is not the case in other models. We find that the local persistence exponent in all these models is unity or very close to it. A change in the mode of the update does not change the exponent unless the universality class changes. In general, persistence exponents are not universal. Thus it is of interest that the persistence exponent in a range of models in the DI class is the same. Excellent scaling behavior of finite-size scaling is obtained using exponents in the DI class in all models. We also study off-critical scaling in some models and DI exponents yield excellent scaling behavior. We further study graded persistence, which shows similar behavior. However, for a logistic map with delay, which also has the transition in the DI class, there is no transition from nonzero to zero persistence at the critical point. Thus the accompanying transition in persistence and universality of the persistence exponent hold when the underlying model has right-left symmetry.

We study solitary waves in a one-dimensional lattice of identical masses that are connected in series by nonlinear springs. The potential of each spring is nonconvex, where two disjoint convex regions, phase I and phase II, are separated by a concave, spinodal region. Consequently, the force-strain relation of the spring is nonmonotonous, which gives rise to a bistable behavior. Based on analytical treatment, with some approximations, combined with extensive numerical simulations, we are able to reveal important insights. For example, we find that the solitary-wave solution is indifferent to the energy barrier that separates the two energy wells associated with phase I and phase II, and that the shape of the wave can be described by means of merely two scalar properties of the potential of the springs, namely, the ratio of stiffness in phase II and phase I, and the ratio between the Maxwell's force and corresponding transition strain. The latter ratio provides a useful measure for the significance of the spinodal region. Linear stability of the solitary-wave solution is studied analytically using the Vakhitov-Kolokolov criterion applied to the approximate solutions obtained in the first part. These results are validated by numerical simulations. We find that the solitary-wave solution is stable provided that its velocity is higher than some critical value. It is shown that, practically, the solitary waves are stable for almost the entire range of possible wave velocities. This is also manifested in the interaction between two solitary waves or between a solitary wave and a wall (rigid boundary). Such interaction results in a minor change of height and shape of the solitary wave along with the formation of a trail of small undulations that follow the wave, as expected in a nonintegrable system. Even after a significant number of interactions the changes in the wave height and shape are minor, suggesting that the bistable chain may be a useful platform for delivering information over long distances, even concurrently with additional information (other solitary waves) passing through the chain.

Kinetic Monte Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy experiments. In parallel, simplified approaches such as limited mobility (LM) models characterized by a fixed diffusion length have been studied. Here we investigate an extended LM model to gain deeper insight into the role of diffusional processes concerning the growth morphology. Our model is based on the stochastic transition rules of the Das Sarma–Tamborena model but differs from the latter via a variable diffusion length. A first guess for this length can be extracted from the saturation value of the mean-squared displacement calculated from short KMC simulations. Comparing the resulting surface morphologies in the sub- and multilayer growth regime to those obtained from KMC simulations, we find deviations which can be cured by adding fluctuations to the diffusion length. This mimics the stochastic nature of particle diffusion on a substrate, an aspect which is usually neglected in LM models. We propose to add fluctuations to the diffusion length by choosing this quantity for each adsorbed particle from a Gaussian distribution, where the variance of the distribution serves as a fitting parameter. We show that the diffusional fluctuations have a huge impact on cluster properties during submonolayer growth as well as on the surface profile in the high coverage regime. The analysis of the surface morphologies on one- and two-dimensional substrates during sub- and multilayer growth shows that the LM model can produce structures that are indistinguishable to the ones from KMC simulations at arbitrary growth conditions.

A multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the Abelian Manna model. This branching process incorporates partially the spatiotemporal correlations of the activity, which are essential for the dynamics, in particular in low dimensions. An analytical expression for the critical density in arbitrary dimensions is derived, which significantly improves the results over mean-field theories, as confirmed by comparison to the literature on numerical estimates from simulations. The method can easily be extended to lattices and dynamics other than those studied in the present work.

Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size. However, the approach to the limiting behavior is remarkably slow. Thus, an understanding of the scaling and finite-size properties of fractal dimensions is essential. We present such a study for random matrix ensembles, and compare with two chaotic quantum systems—the kicked rotor and a spin chain. For random matrix ensembles we analytically obtain the finite-size dependence of the mean behavior of the multifractal dimensions, which provides a lower bound to the typical (logarithmic) averages. We show that finite statistics has remarkably strong effects, so that even random matrix computations deviate from analytic results (and show strong sample-to-sample variation), such that restoring agreement requires exponentially large sample sizes. For the quantized standard map (kicked rotor) the multifractal dimensions are found to follow the random matrix predictions closely, with the same finite statistics effects. For a XXZ spin-chain we find significant deviations from the random matrix prediction—the large-size scaling follows a system-specific path towards unity. This suggests that local many-body Hamiltonians are “weakly ergodic,” in the sense that their eigenfunction statistics deviate from random matrix theory.

We studied the evolution of cooperation in the framework of evolutionary game theory, implementing voluntary participation in the prisoner's dilemma. Although previous studies have tried to overcome the dilemma by introducing voluntary participation called a “loner,” the question of which strategies among various strategies including voluntary participation are adaptive under competitive circumstances is still an unsolved puzzle. Here we have developed a model that consists of all possible strategies using a one-period memory of past actions. This model enables us to analyze a “melting pot” of strategies, wherein several strategies interact and compete with each other. Our results revealed that one strategy, in which one escapes if a partner defects or cooperates if a partner becomes a loner, dominates and maintains cooperation in an alternating prisoner's dilemma game. However, the so-called “win-stay, lose-shift” strategy dominates in a simultaneous prisoner's dilemma game. Our simulations clearly show that voluntary participation in the prisoner's dilemma game works in the alternating situation rather than the simultaneous one.

We study theoretically the collective dynamics of particles driven by an optical vortex along a circular path. Phase equations of $N$ particles are derived by taking into account both hydrodynamic and repulsive interactions between them. For $N=2$, the particles attract with each other and synchronize, forming a doublet that moves faster than a singlet. For $N=3$ and 5, we find periodic rearrangement of doublets and a singlet. For $N=4$ and 6, the system exhibits either a periodic oscillating state or a stable synchronized state depending on the initial conditions. These results reproduce main features of previous experimental findings. We quantitatively discuss the mechanisms governing the nontrivial collective dynamics.

We generalize and then use a recently introduced formalism to study thermal fluctuations of atomic displacements in several two- and three-dimensional crystals. We study both close-packed and open crystals with multiatom bases. Atomic displacement fluctuations in a solid, once coarse grained over some neighborhood, may be decomposed into two mutually orthogonal components. In any dimension $d$ there are always $d^2$ affine displacements representing local strains and rotations of the ideal reference configuration. In addition, there exist a number of nonaffine localized displacement modes that cannot be represented as strains or rotations. The number of these modes depends on $d$ and the size of the coarse-graining region. All thermodynamic averages and correlation functions concerning the affine and nonaffine displacements may be computed within harmonic theory. We show that for compact crystals, such as the square and triangular crystals in $d=2$ and the simple body-centered-cubic and face-centered-cubic crystals in $d=3$, a single set of $d$-fold degenerate modes always dominates the nonaffine subspace and is separated from the rest by a large gap. These modes may be identified with specific precursor configurations that lead to lattice defects. In open crystals, such as the honeycomb and kagome lattices, there is no prominent gap, although soft nonaffine modes continue to be associated with known floppy modes representing localized defects. Higher-order coupling between affine and nonaffine components of the displacements quantifies the tendency of the lattice to be destroyed by large homogeneous strains. We show that this coupling is larger by almost an order of magnitude for open lattices as compared to compact ones. Deformation mechanisms such as lattice slips and stacking faults in close-packed crystals can also be understood within this framework. The qualitative features of these conclusions are expected to be independent of the details of the atomic interactions.