In online social dynamics, a robust scale invariance appears as a key feature of collaborative efforts that lead to new social value. The underlying empirical data thus offers a unique opportunity to study the origin of self-organized criticality (SOC) in social systems. In contrast to physical systems in the laboratory, various human attributes of the actors play an essential role in the process along with the contents (cognitive, emotional) of the communicated artifacts. As a prototypical example, we consider the social endeavor of knowledge creation via Questions and Answers (Q&A). Using a large empirical data set from one of such Q&A sites and theoretical modeling, we reveal fundamental characteristics of SOC by investigating the temporal correlations at all scales and the role of cognitive contents to the avalanches of the knowledge-creation process. Our analysis shows that the universal social dynamics with power-law inhomogeneities of the actions and delay times provides the primary mechanism for self-tuning towards the critical state; it leads to the long-range correlations and the event clustering in response to the external driving by the arrival of new users. In addition, the involved cognitive contents (systematically annotated in the data and observed in the model) exert important constraints that identify unique classes of the knowledge-creation avalanches. Specifically, besides determining a fine structure of the developing knowledge networks, they affect the values of scaling exponents and the geometry of large avalanches and shape the multifractal spectrum. Furthermore, we find that the level of the activity of the communities that share the knowledge correlates with the fluctuations of the innovation rate, implying that the increase of innovation may serve as the active principle of self-organization. To identify relevant parameters and unravel the role of the network evolution underlying the process in the social system under consideration, we compare the social avalanches to the avalanche sequences occurring in the field-driven physical model of disordered solids, where the factors contributing to the collective dynamics are better understood.

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Self-propulsion (SP) is a main feature of active particles (AP), such as bacteria or biological micromotors, distinguishing them from passive colloids. A renowned consequence of SP is accumulation at static interfaces, even in the absence of hydrodynamic interactions. Here we address the role of SP in the interaction between AP and a moving semipermeable membrane. In particular, we implement a model of noninteracting AP in a channel crossed by a partially penetrable wall, moving at a constant velocity $c$. With respect to both the cases of passive colloids with $c>0$ and AP with $c=0$, the AP with finite $c$ show enhancement of accumulation in front of the obstacle and experience a largely increased drag force. This effect is understood in terms of an effective potential localised at the interface between particles and membrane, of height proportional to $c\tau /\xi$, where $\tau$ is the AP's reorientation time and $\xi$ the width characterizing the surface's smoothness ($\xi \to 0$ for hard core obstacles). An approximate analytical scheme is able to reproduce the observed density profiles and the measured drag force, in very good agreement with numerical simulations. The effects discussed here can be exploited for automatic selection and filtering of AP with desired parameters.

We numerically study the local stress distribution within athermal, isotropically stressed, mechanically stable, packings of bidisperse frictionless disks above the jamming transition in two dimensions. Considering the Fourier transform of the local stress, we find evidence for algebraically increasing fluctuations in both isotropic and anisotropic components of the stress tensor at small wave numbers, contrary to recent theoretical predictions. Such increasing fluctuations imply a lack of self-averaging of the stress on large length scales. The crossover to these increasing fluctuations defines a length scale ${\ell }_0$, however, it appears that ${\ell }_0$ does not vary much with packing fraction $\varphi$, nor does ${\ell }_0$ seem to be diverging as $\varphi$ approaches the jamming ${\varphi }_J$. We also find similar large length scale fluctuations of stress in the inherent states of a quenched Lennard-Jones liquid, leading us to speculate that such fluctuations may be a general property of amorphous solids in two dimensions.

The resuspension and dispersion of particles occur in industrial fluid dynamic processes as well as environmental and geophysical situations. In this paper, we experimentally investigate the ability to fluidize a granular bed with a vertical gradient of temperature. Using laboratory experiments with a localized heat source, we observe a large entrainment of particles into the fluid volume beyond a threshold temperature. The buoyancy-driven fluidized bed then leads to the transport of solid particles through the generation of particle-laden plumes. We show that the destabilization process is driven by the thermal conductivity inside the granular bed and demonstrate that the threshold temperature depends on the thickness of the granular bed and the buoyancy number, i.e., the ratio of the stabilizing density contrast to the destabilizing thermal density contrast.

We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is described by a power law distribution over a finite range. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers' strength, in the limit of equal load sharing an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers, and the usual decreasing size effect of heterogeneous materials is restored only beyond a characteristic size. We show analytically that the extreme order statistics of fibers' strength is responsible for this peculiar behavior. Analyzing the results of computer simulations we deduce a scaling form which describes the dependence of the macroscopic strength of fiber bundles on the parameters of microscopic disorder over the entire range of system sizes.

The yielding transition of amorphous solids is a phase transition with a special type of universality. Critical exponents and scaling relations have been defined and proposed near the yield stress. We show here that, even in the initial stage of shear far below the yield stress, the stress-strain curve of amorphous solids also shows critical scaling with universal exponents. The key point is to remove the elastic part of the strain, and the shear stress exhibits a sublinear scaling with the plastic strain. We show how this critical scaling is related to the finite size effect of the minimum strain to trigger the first plastic avalanche after a quench. We point out that this sublinear scaling between the stress and the plastic strain implies the divergence of a high-order shear modulus. A scaling relation is derived between two exponents characterizing the stress-strain curve and the density distribution of the local stabilities, respectively. We test the critical scaling of the stress-strain curve using both mesoscopic and atomistic simulations and get satisfying agreement in two and three dimensions.

A parallel direct-forcing fictitious domain method is employed to perform fully resolved numerical simulations of turbulent channel flow laden with finite-size particles. The effects of the particle-fluid density ratio on the turbulence modulation in the channel flow are investigated at the friction Reynolds number of 180, the particle volume fraction of $0.84\%$, and the particle-fluid density ratio ranging from 1 to 104.2. The results show that the variation of the flow drag with the particle-fluid density ratio is not monotonic, with a larger flow drag for the density ratio of 10.42, compared to those of unity and 104.2. A significant drag reduction by the particles is observed for large particle-fluid density ratios during the transient stage, but not at the statistically stationary stage. The intensity of particle velocity fluctuations generally decreases with increasing particle inertia, except that the particle streamwise root-mean-square velocity and streamwise-transverse velocity correlation in the near-wall region are largest at the density ratio of the order of 10. The averaged momentum equations are derived with the spatial averaging theorem and are used to analyze the mechanisms for the effects of the particles on the flow drag. The results indicate that the drag-reduction effect due to the decrease in the fluid Reynolds shear stress is counteracted by the drag-enhancement effect due to the increase in the total particle stress or the interphase drag force for the large particle-inertia case. The sum of the total Reynolds stress and particle inner stress contributions to the flow drag is largest at the density ratio of the order of 10, which is the reason for the largest flow drag at this density ratio. The interphase drag force obtained from the averaged momentum equation (the balance theory) is significantly smaller than (but agrees qualitatively with) that from the empirical drag formula based on the phase-averaged slip velocity for large density ratios. For the neutrally buoyant case, the balance theory predicts a positive interphase force on the particles arising from the negative gradient of the particle inner stress, which cannot be predicted by the drag formula based on the phase-averaged slip velocity. In addition, our results show that both particle collision and particle-turbulence interaction play roles in the formation of the inhomogeneous distribution of the particles at the density ratio of the order of 10.

Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016)] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing holographic boundary distributions. The main ingredient of the Markov chain Monte Carlo sampler is the invariance under dilation. This paper presents a generalization to higher dimensions with the critical 3D Ising model. This leads to numerical estimations of a subset of the CFT data—scaling weights and structure constants—through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 036].

We develop an analytical statistical-mechanical model for hydrophobic solvation in water. In this three-dimensional Mercedes-Benz–like model, two neighboring waters have three possible interaction states: a radial van der Waals interaction, a tetrahedral orientation-dependent hydrogen-bonding interaction, or no interaction. Nonpolar solutes are modeled as van der Waals particles of different radii. The model is sufficiently simple that we can calculate the partition function and thermal and volumetric properties of solvation versus temperature, pressure, and solute radius. Predictions are in good agreement with results of Monte Carlo simulations. And their trends agree with experiments on hydrophobic solute insertion. The theory shows that first-shell waters are more highly structured than bulk waters, because of hydrogen bonding, and that that structure melts out faster with temperature than it does in bulk waters. Because the theory is analytical, it can explore a broad range of solvation properties and anomalies of water, at minimal computational expense.

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social networks, acquaintance networks, and scientific citation networks, where duplication mechanisms play a major role. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network, forming a link to the mother node, and with probability $p$ to each one of its neighbors. The degree distribution of the resulting network turns out to follow a power-law distribution, thus the ND network is a scale-free network. To calculate the DSPL we derive a master equation for the time evolution of the probability $P_t(L=\ell )$, $\ell =1,2,\cdots$, where $L$ is the distance between a pair of nodes and $t$ is the time. Finding an exact analytical solution of the master equation, we obtain a closed form expression for $P_t(L=\ell )$. The mean distance ${\langle L\rangle }_t$ and the diameter ${\mathrm{\Delta }}_t$ are found to scale like $lnt$, namely, the ND network is a small-world network. The variance of the DSPL is also found to scale like $lnt$. Interestingly, the mean distance and the diameter exhibit properties of a small-world network, rather than the ultrasmall-world network behavior observed in other scale-free networks, in which ${\langle L\rangle }_t\sim lnlnt$.

In this work, we explore the spatial structure of built zones and green areas in diverse western cities by analyzing the probability distribution of areas and a coefficient that characterize their respective shapes. From the analysis of diverse datasets describing land lots in urban areas, we found that the distribution of built-up areas and natural zones in cities obey inverse power laws with a similar scaling for the cities explored. On the other hand, by studying the distribution of shapes of lots in urban regions, we are able to detect global differences in the spatial structure of the distribution of land. Our findings introduce information about spatial patterns that emerge in the structure of urban settlements; this knowledge is useful for the understanding of urban growth, to improve existing models of cities, in the context of sustainability, in studies about human mobility in urban areas, among other applications.

A national voting population, when segmented into groups such as, for example, different states, can yield a counterintuitive scenario in which the winner may not necessarily get the highest number of total votes. A recent example is the 2016 presidential election in the United States. We model the situation by using interacting opinion dynamics models, and we look at the effect of coarse graining near the critical points where the spatial fluctuations are high. We establish that the sole effect of coarse graining, which mimics the “winner take all” electoral college system in the United States, can give rise to finite probabilities of events in which a minority candidate wins even in the large size limit near the critical point. The overall probabilities of victory of the minority candidate can be predicted from the models, which indicate that one may expect more instances of minority candidate winning in the future.

For information diffusion in multiplex networks, the effect of interlayer contagion on spreading dynamics has been explored in different settings. Nevertheless, the impact of interlayer recovery processes, i.e., the transition of nodes to stiflers in all layers after they become stiflers in any layer, still remains unclear. In this paper, we propose a modified ignorant-spreader-stifler model of rumor spreading equipped with an interlayer recovery mechanism. We find that the information diffusion can be effectively promoted for a range of interlayer recovery rates. By combining the mean-field approximation and the Markov chain approach, we derive the evolution equations of the diffusion process in two-layer homogeneous multiplex networks. The optimal interlayer recovery rate that achieves the maximal enhancement can be calculated by solving the equations numerically. In addition, we find that the promoting effect on a certain layer can be strengthened if information spreads more extensively within the counterpart layer. When applying the model to two-layer scale-free multiplex networks, with or without degree correlation, similar promoting effect is also observed in simulations. Our work indicates that the interlayer recovery process is beneficial to information diffusion in multiplex networks, which may have implications for designing efficient spreading strategies.

Recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families. Specifically, two of these cell families have been shown to interact through a nonlocal chasing mechanism, which has previously been modeled using integro-differential equations. We extend this framework to include the experimentally observed fact that the cells often exhibit chiral movement, in that the cells chase, and run away, at angles different to the line connecting their centers. This framework is simplified through the use of multiple small limits leading to a coupled set of partial differential equations which are amenable to Fourier analysis. This analysis results in the production of dispersion relations and necessary conditions for a patterning instability to occur. Beyond the theoretical development and the production of new pattern planiforms we are able to corroborate the experimental hypothesis that the global pigmentation patterns can be dependent on the chirality of the chromatophores.

We study the rectification of a two-dimensional thermal gas in a channel of asymmetric dissipative walls. For an ensemble of smooth Lennard-Jones particles, our numerical simulations reveal a nonmonotonic dependence of the flux on the thermostat temperature, channel asymmetry, and particle density, with three distinct regimes. Theoretical arguments are developed to shed light on the functional dependence of the flux on the model parameters.

As is well known, confined fluid systems subject to forced vibrations produce mean flows, called in this context streaming flows. These mean flows promote an overall mass transport in the fluid that has consequences in the transport of passive scalars and surfactants, when these are present in a fluid interface. Such transport causes surfactant concentration inhomogeneities that are to be counterbalanced by Marangoni elasticity. Therefore, the interaction of streaming flows and Marangoni convection is expected to produce new flow structures that are different from those resulting when only one of these effects is present. The present paper focuses on this interaction using the liquid bridge geometry as a paradigmatic system for the analysis. Such analysis is based on an appropriate post-processing of the results obtained via direct numerical simulation of the system for moderately small viscosity, a condition consistent with typical experiments of vibrated millimetric liquid bridges. It is seen that the flow patterns show a nonmonotone behavior as the Marangoni number is increased. In addition, the strength of the mean flow at the free surface exhibits two well-defined regimes as the forcing amplitude increases. These regimes show fairly universal power-law behaviors.

An $XY$ model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range-order phase characterized by an algebraically decaying correlation function with the exponent $\eta =T/\left[2\pi J\right(p,\alpha \left)\right]$, nonlinearly dependent on the parameters $p$ and $\alpha$ that control the number of the higher-order terms and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of topological excitations (vortices) in changing the nature of the transition is discussed.

Barkhausen effect in ferromagnetic materials provides an excellent area for investigating scaling phenomena found in disordered systems exhibiting crackling noise. The critical dynamics is characterized by random pulses or avalanches with scale-invariant properties, power-law distributions, and universal features. However, the traditional Barkhausen avalanches statistics may not be sufficient to fully characterize the complex temporal correlation of the magnetic domain walls dynamics. Here we focus on the multifractal scenario to quantify the temporal scaling characteristics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films with thicknesses from 50 to 1000 nm. We show that the multifractal properties are dependent on film thickness, although they seem to be insensitive to the structural character of the materials. Moreover, we observe for the first time the vanishing of the multifractality in the domain walls dynamics. As the thickness is reduced, the multifractal behavior gives place to a monofractal one over the entire range of time scales. This reorganization in the temporal scaling characteristics of Barkhausen avalanches is understood as a universal restructuring associated to the dimensional crossover, from three- to two-dimensional magnetization dynamics.