We show that for a large range of approach velocities and over a large interval of stabilizing cubic cross-coupling between counterpropagating waves, a collision of stationary pulses leads to a partial annihilation of pulses via a spontaneous breaking of symmetry. This result arises for coupled cubic-quintic complex Ginzburg-Landau equations for traveling waves for sufficiently large values of the stabilizing cubic cross-coupling and for large enough approach velocities of the pulses. Briefly, we show in addition that the collision of counterpropagating pulses in a system of two coupled cubic Ginzburg-Landau equations with nonlinear gradients (Raman effect) might also lead to partial annihilation, indicating that this breaking of symmetry is generic. Systems of experimental interest include surface reactions, convective onset, biosolitons, and nonlinear optics.

Metastable reverse-phase droplets are calculated by renormalization-group theory by evaluating the magnetization of a droplet under magnetic field, matching the boundary condition with the reverse phase and noting whether the reverse-phase magnetization sustains. The maximal metastable droplet size and the discontinuity across the droplet boundary are thus calculated as a function of temperature and magnetic field for the Ising model in three dimensions. The method also yields hysteresis loops for finite systems, as function of temperature and system size.

Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive rule systems and statistical learning to explain our ability to learn new concepts from just a few examples. The aim of most of these studies is to reveal the underlying language structuring these representations and providing a general substrate for thought. However, describing a model of thought that is fixed once trained is against the extensive literature that shows how experience shapes concept learning. Here, we ask about the plasticity of these symbolic descriptive languages. We perform a concept learning experiment that demonstrates that humans can change very rapidly the repertoire of symbols they use to identify concepts, by compiling expressions that are frequently used into new symbols of the language. The pattern of concept learning times is accurately described by a Bayesian agent that rationally updates the probability of compiling a new expression according to how useful it has been to compress concepts so far. By portraying the language of thought as a flexible system of rules, we also highlight the difficulties to pin it down empirically.

We systematically investigate the thermal Hall effect in a Lorentz gas model with rotating circular scatterers; the rotating scatterers play a role similar to the magnetic field. The modified Lorentz gas model is a normal thermal transport system that satisfies Fourier law: the thermal conductivity is independent of the model length. We find that the intensity of the Hall effect changes its sign when the rotating direction of disks changes and it is independent of the magnitude of longitudinal temperature difference and only dependent of the average longitudinal temperature: it decreases with increasing the average temperature, especially at low angular velocity. The thermal Hall effect found in the modified Lorentz gas will help us understand the mechanism of the thermal Hall system and provide guidance for the application of the thermal Hall effect.

Hydrogen absorption by Pd exhibits hysteresis loops (provided the temperature is not too high) and represents one of the classical examples of first-order phase transitions in metals. Experiments indicate that addition of even a small amount of Au is able to suppress hysteresis. From this perspective, we analyze the energetics of hydrogen in a Pd-Au alloy by using extensive density-functional-theory (DFT) calculations. The dependence of the hydrogen binding energy on the number ($n$) of Au atoms forming an adsorption site is found to be appreciably nonlinear. With the DFT input for statistical calculations, we reproduce special features of the hydrogen absorption isotherms and explain the rapid decrease of the corresponding critical temperature with increasing Au fraction. The key factor here is that the phase transition is related primarily to absorption in sites formed only by Pd. With increasing Au amount, the fraction of such sites rapidly decreases, the distance between H atoms located there becomes on average larger, the interaction between them becomes weaker, and accordingly the driving force for the phase transition decreases. It is of interest that all these effects can be illustrated by taking only the configurations with $n\le 2$ into account. This means that in the context under consideration the fine details of the dependence of the hydrogen binding energy on $n$ are in fact not too important.

The information theoretic measure known as mutual information is widely used as a way to quantify the similarity of two different labelings or divisions of the same set of objects, such as arises, for instance, in clustering and classification problems in machine learning or community detection problems in network science. Here we argue that the standard mutual information, as commonly defined, omits a crucial term which can become large under real-world conditions, producing results that can be substantially in error. We derive an expression for this missing term and hence write a corrected mutual information that gives accurate results even in cases where the standard measure fails. We discuss practical implementation of the new measure and give example applications.

Characterizing the structural complexity of networks is a major challenging work in network science. However, a valid measure to quantify network complexity remains unexplored. Although the entropy of various network descriptors and algorithmic complexity have been selected in the previous studies to do it, most of these methods only contain local information of the network, so they cannot accurately reflect the global structural complexity of the network. In this paper, we propose a statistical measure to characterize network complexity from a global perspective, which is composed of the communicability sequence entropy of the network and the associated Jensen-Shannon divergence. We study the influences of the topology of the synthetic networks on the complexity measure. The results show that networks with strong heterogeneity, strong degree-degree correlation, and a certain number of communities have a relatively large complexity. Moreover, by studying some real networks and their corresponding randomized network models, we find that the complexity measure is a monotone increasing function of the order of the randomized network, and the ones of real networks are larger complexity-values compared to all corresponding randomized networks. These results indicate that the complexity measure is sensitive to the changes of the basic topology of the network and increases with the increase of the external constraints of the network, which further proves that the complexity measure presented in this paper can effectively represent the topological complexity of the network.

It has been recognized that multiplexes and interlayer degree correlations can play a crucial role in the resilience of many real-world complex systems. Here we introduce a multiplex pruning process that removes nodes of degree less than $k_i$ and their nearest neighbors in layer $i$ for $i=1,...,m$, and establish a generic framework of generalized $\mathbf{k}$-core ($G\mathbf{k}$-core) percolation over interlayer uncorrelated and correlated multiplex networks of $m$ layers, where $\mathbf{k}=(k_1,...,k_m)$ and $m$ is the total number of layers. $G\mathbf{k}$-core exhibits a discontinuous phase transition for all $\mathbf{k}$ owing to cascading failures. We have unraveled the existence of a tipping point of the number of layers, above which the $G\mathbf{k}$-core collapses abruptly. This dismantling effect of multiplexity on $G\mathbf{k}$-core percolation shows a diminishing marginal utility in homogeneous networks when the number of layers increases. Moreover, we have found the assortative mixing for interlayer degrees strengthens the $G\mathbf{k}$-core but still gives rise to discontinuous phase transitions as compared to the uncorrelated counterparts. Interlayer disassortativity on the other hand weakens the $G\mathbf{k}$-core structure. The impact of correlation effect on $G\mathbf{k}$-core tends to be more salient systematically over $\mathbf{k}$ for heterogenous networks than homogeneous ones.

Bootstrap percolation has been used to describe opinion formation in society and other social and natural phenomena. The formal equation of the bootstrap percolation may have more than one solution, corresponding to several stable fixed points of the corresponding iteration process. We construct a reversible bootstrap percolation process, which converges to these extra solutions displaying a hysteresis typical of discontinuous phase transitions. This process provides a reasonable model for fake news spreading and the effectiveness of fact checking. We show that sometimes it is not sufficient to discard all the sources of fake news in order to reverse the belief of a population that formed under the influence of these sources.

When a viscoelastic fluid, such as an aqueous polymer solution, flows through a porous medium, the fluid undergoes a repetitive expansion and contraction as it passes from one pore to the next. Above a critical flow rate, the interaction between the viscoelastic nature of the polymer and the pore configuration results in spatial and temporal flow instabilities reminiscent of turbulentlike behavior, even though the Reynolds number $\mathrm{Re}\ll 1$. To investigate whether this is caused by many repeated pore body–pore throat sequences, or simply a consequence of the converging (diverging) nature present in a single pore throat, we performed experiments using anionic hydrolyzed polyacrylamide (HPAM) in a microfluidic flow geometry representing a single pore throat. This allows the viscoelastic fluid to be characterized at increasing flow rates using microparticle image velocimetry in combination with pressure drop measurements. The key finding is that the effect, popularly known as “elastic turbulence,” occurs already in a single pore throat geometry. The critical Deborah number at which the transition in rheological flow behavior from pseudoplastic (shear thinning) to dilatant (shear thickening) strongly depends on the ionic strength, the type of cation in the anionic HPAM solution, and the nature of pore configuration. The transition towards the elastic turbulence regime was found to directly correlate with an increase in normal stresses. The topology parameter, $Q_f$, computed from the velocity distribution, suggests that the “shear thickening” regime, where much of the elastic turbulence occurs in a single pore throat, is a consequence of viscoelastic normal stresses that cause a complex flow field. This flow field consists of extensional, shear, and rotational features around the constriction, as well as upstream and downstream of the constriction. Furthermore, this elastic turbulence regime, has high-pressure fluctuations, with a power-law decay exponent of up to |−2.1| which is higher than the Kolmogorov value for turbulence of |−5/3|.

The dynamics of anisotropic nano- to micro scale colloidal particles in confined environments, either near neighboring particles or boundaries, is relevant to a wide range of applications. We utilized Brownian dynamics simulations to predict the translational and rotational fluctuations of a Janus sphere with a cap of nonmatching density near a boundary. The presence of the cap significantly impacted the rotational dynamics of the particle as a consequence of gravitational torque at experimentally relevant conditions. Gravitational torque dominated stochastic torque for a particle >1 μm in diameter and with a 20-nm-thick gold cap. Janus particles at these conditions sampled mostly cap-down or “quenched” orientations. Although the results summarized herein showed that particles of smaller diameter (<1 μm) with a thin gold coating (<5 nm) behave similarly to an isotropic particle, small increases in either particle diameter or coating thickness quenched the polar rotation of the particle. Histogram landscapes of the separation distance from the boundary and orientation observations of particles with larger diameters or thicker gold coatings were mostly populated with quenched configurations. Finally, the histogram landscapes were inverted to obtain the potential energy landscapes, providing a road map for experimental data to be interpreted.

We study phase transition in a binary system of monodisperse active and passive particles. The particles are initially randomly positioned inside a fixed boundary square enclosure. The active particles can move with their self-propulsion force. Whereas, the passive particles do not have any self-propulsion force, and they move by the spatial interactions with other particles. An alignment force in our discrete element model causes the emergence of collective milling motion. Without this alignment interaction, the particle system remains in a disordered phase. Whereas, the ordered milling phase is attained after achieving a minimum coordination among neighboring particles. The phase transition from disordered to ordered depends upon the relative effect of self-propulsion and the alignment, initial states of the particles, noise level, and the fraction of the active particles present in the system. The phase transition we observed is of first-order nature.

Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding of the kinematics of origami fold patterns. Here we study the configurations of non-Euclidean origami, folding structures with Gaussian curvature concentrated on the vertices, for arbitrary origami fold patterns. The kinematics of such structures depends crucially on the sign of the Gaussian curvature. As an application of our general results, we show that the configuration space of nonintersecting, oriented vertices with positive Gaussian curvature decomposes into disconnected subspaces; there is no pathway between them without tearing the origami. In contrast, the configuration space of negative Gaussian curvature vertices remains connected. This provides a new, and only partially explored, mechanism by which the mechanics and folding of an origami structure could be controlled.

The linear stability of a Newtonian liquid layer flowing down an inclined plane lined with a deformable linear elastic solid characterized by a continuously varying modulus is analyzed in this study. A low-wave-number asymptotic analysis is performed to obtain an analytical expression for the complex wavespeed which shows striking similarity with the earlier results of Sahu and Shankar [Sahu and Shankar, Phys. Rev. E 94, 013111 (2016)] for gravity-driven flow of Newtonian fluid past a solid bilayer having constant shear modulus (in each layer) lined on a rigid inclined plane. This shows that a deformable solid layer having a continuously varying shear modulus can be treated as a generalization of a system having multiple solid layers of constant shear modulus. Also, in the low-wave-number limit, we show that the stability of the free surface is governed by the value of effective shear modulus $G_{\mathrm{eff}}$, and not by the detailed spatial variation of the modulus. Here the effective shear modulus ($H/G_{\mathrm{eff}}={\int }_1^{1+H}1/[E_0+\overline{E}\left(z\right)]dz$, where $[E_0+\overline{E}\left(z\right)]$ represents the modulus gradient function) characterizes the overall modulus of the elastic solid, which is obtained by treating the continuous variation to be the limit of the arrangement of solid layers of infinitesimal thickness (each having a constant shear modulus) in a series. At finite wave numbers, we show that the free-surface and the liquid-solid interface become unstable as we increase the value of $\mathrm{\Gamma }$, where $\mathrm{\Gamma }$ indicates the ratio of viscous stresses in the fluid to elastic stresses in the solid. When the system is analysed for different types of spatial modulus variations, we find results similar to those of Gkanis and Kumar [Gkanis and Kumar, Phys. Rev. E 73, 026307 (2006)], i.e., when we have two different configurations of the shear modulus function that have the same spatially averaged modulus, but have different values at the interface, the system is more stable for the configuration having higher shear modulus at the liquid-solid interface. In a similar manner, when we examined systems having the same shear modulus at the liquid-solid interface and same average modulus, the more stable case is the one which has a higher value of shear modulus just below the interface. Thus the use of deformable solids with a depth-dependent modulus potentially offers more control in the passive manipulation of the instabilities.

A barotropic counterpart of the well-known convected vortex test case is rigorously derived from the Euler equations along with an athermal equation of state. Starting from a given velocity distribution corresponding to an intended flow recirculation, the athermal counterpart of the Euler equations are solved to obtain a consistent density field. The present initialization is assessed on a standard lattice Boltzmann solver based on the D2Q9 lattice. Compared to the usual isentropic initialization, a much lower spurious relaxation toward the targeted solution is observed, which is due to the spatial resolution rather than approximated macroscopic quantities. The amplitude of the spurious waves can be further reduced by including an off-equilibrium part in the initial distribution functions.

We obtain the phase diagram for the Blume-Capel model with the bimodal distribution for random crystal fields, in the space of three fields: temperature ($T$), crystal field ($\mathrm{\Delta }$), and magnetic field ($H$) on a fully connected graph. We find three different topologies for the phase diagram, depending on the strength of disorder. Three critical lines meet at a tricritical point only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first-order surface in the $H=0$ plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.

We propose a unified framework for both Shannon-Khinchin and Shore-Johnson axiomatic systems. We do it by rephrasing Shannon-Khinchine axioms in terms of generalized arithmetics of Kolmogorov and Nagumo. We prove that the two axiomatic schemes yield identical classes of entropic functionals—the Uffink class of entropies. This allows to re-establish the entropic parallelism between information theory and statistical inference that has seemed to be “broken” by the use of non-Shannonian entropies.

Bacteria living on surfaces use different types of motility mechanisms to move on the surface in search of food or to form microcolonies. Twitching is one such form of motility employed by bacteria such as Neisseria gonorrhoeae, in which the polymeric extensions known as type IV pili mediate its movement. Pili extending from the cell body adhere to the surface and pull the bacteria by retraction. The bacterial movement is decided by the two-dimensional tug-of-war among the pili attached to the surface. Natural surfaces on which these microcrawlers dwell are generally spatially inhomogeneous and have varying surface properties. Their motility is known to be affected by the topography of the surfaces. Therefore, it is possible to control bacterial movement by designing structured surfaces which can be potentially utilized for controlling biofilm architecture. In this paper, we numerically investigate the twitching motility in a two-dimensional corrugated channel. The bacterial movement is simulated by two different models: (a) a detailed tug-of-war model which extensively describe the twitching motility of bacteria assisted by pili and (b) a coarse-grained run-and-tumble model which depicts the motion of wide-ranging self-propelled particles. The simulation of bacterial motion through asymmetric corrugated channels using the above models show rectification. The bacterial transport depends on the geometric parameters of the channel and inherent system parameters such as persistence length and self-propelled velocity. In particular, the variation of the particle current with the geometric parameters of the microchannels shows that one can optimize the particle current for specific values of these parameters.

We investigate the mechanisms of opening-mode fracture initiation in granular media. The study is based on a simulation of grain-scale fluid-grain interactions through a coupled numerical approach in which the discrete element method is used to solve for the mechanics of a solid granular medium, and computational fluid dynamics is used to model fluid flow and drag forces. We present benchmark problems with analytical solutions and validate this numerical model against experiments on a viscous-drag-driven cavity in the literature. Additional simulation results show fracture initiation mechanisms in a random granular packing subjected to constant boundary stresses and to fluid injection with a localized source. The dimensionless variable $F_{\mathrm{s}}/F_{\mathrm{sk}}$ (ratio of seepage force $F_{\mathrm{s}}$ and skeletal force $F_{\mathrm{sk}}$) incorporates the impacts of physical properties and injection parameters including fluid viscosity, injection velocity, grain size, and effective stresses, and it has been used as a criterion separating regimes of fluid invasion and drag-driven fracture opening. Our simulation results show that $F_{\mathrm{s}}/F_{\mathrm{sk}}$ in combination with ${\tau }_1$ (ratio of diffusion time from hydromechanical coupling and injection time) serves as a prediction of fracture opening within granular packing. We suggest a simple criterion ($F_{\mathrm{s}}/F_{\mathrm{sk}}>1$ or ${\tau }_1>0.17$) that is valid for various types of granular media and injection conditions to determine if fracture opening will occur. Among other applications, this study is useful to predict the initiation and propagation of fractures in natural sediments.

Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological, and social systems. Here we apply first-passage analysis tools to investigate the properties and characteristics of random walkers in networks with different topology. Starting with the simplest two-dimensional square lattice, we modify its topology incrementally by randomly reconnecting links between sites. We characterize these networks by first-passage time from a significant number of random walkers without interaction, varying the departure and arrival locations. We also apply the concept of first-passage simultaneity, which measures the likelihood of two walkers reaching their destination together. These measures, together with the site occupancy statistics during the processes, allowed us to differentiate the studied networks, especially the random networks from the scale-free networks, by their navigability. We also show that small-world features can also be highlighted with the proposed technique.