The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural networks at a mean-field level, e.g., assuming large fully connected networks. Moreover, its stochastic counterpart allows one to study fluctuation-induced phenomena, such as avalanches. Here we revisit the stochastic Wilson-Cowan model paying special attention to the possible phase transitions between quiescent and active phases. We unveil eight possible types of such transitions, including continuous ones with scaling behavior belonging to known universality classes—such as directed percolation and tricritical directed percolation—as well as six distinct ones. In particular, we show that under some special circumstances, at a so-called “Hopf tricritical directed percolation” transition, rather unconventional behavior is observed, including the emergence of scaling breakdown. Other transitions are discontinuous and show different types of anomalies in scaling and/or exhibit mixed features of continuous and discontinuous transitions. These results broaden our knowledge of the possible types of critical behavior in networks of excitatory and inhibitory units and are, thus, of relevance to understanding avalanche dynamics in actual neuronal recordings. From a more general perspective, these results help extend the theory of nonequilibrium phase transitions into quiescent or absorbing states.

A semianalytic formula of the dynamic structure factor $S\left(k,\omega \right)$ for classical Debye solids over the entire wave-number $\left(k\right)$ and frequency (ω) range is constructed by taking into account multiphonon thermal diffuse scattering up to infinite order. The formula adopts Gaussian approximations to the spatial and time decay of the multiphonon part of the displacement correlation function. Numerical illustrations for isotropic polycrystals reveal that, as $k$ increases, sharp peaks due to one-phonon normal scattering in the hydrodynamic regime $(k\to 0)$ are replaced by diffuse spectra consisting of umklapp scattering and multiphonon continuum; approach toward the ideal-gas spectra in the large-$k$ limit is proven from analytic properties of the multiphonon term. When $k$ coincides with a Bragg reflection point, total thermal diffuse scattering $S_{\mathrm{TDS}}\left(k,\omega \right)$ exhibits a 1/ω divergence as $\omega \to 0$, which in turn gives rise to a logarithmic enhancement of the corresponding static structure factor $S_{\mathrm{TDS}}\left(k\right)$. Overall accuracy of the theory is confirmed through the exact zeroth-order frequency-moment sum rule between $S_{\mathrm{TDS}}\left(k,\omega \right)$ and $S_{\mathrm{TDS}}\left(k\right)$; agreement with the second-order sum rule is shown to be satisfactory except for the vicinity of the Debye cutoff region.

We report the effect on the phase transitional behavior of 8OCB liquid crystal (LC) doped with functionalized CdSe/ZnS quantum dots (QDs) in different concentrations. The temperature-dependent data of high-resolution optical birefringence and dielectric anisotropy are utilized to characterize the critical anomaly for both the isotropic-to-nematic ($I-N$) and nematic-to-smectic-$A$ ($N\text{−}\mathrm{Sm}A$) phase transitions. The obtained results reveal that the order parameter exponent $\left(\beta \right)$ for the pure LC is found to be $\beta =0.249$ and does not vary upon the inclusion of QDs in the pure matrix. It describes the weakly first-order characteristic of the $I-N$ phase transition for all the studied samples, which falls within the limit of the tricritical hypothesis. Conversely, depending on the range of the $N$ phase, we observed a nonuniversal nature of the specific heat capacity critical exponent $({\alpha }^{\prime }$) linked with the $N\text{−}\mathrm{Sm}A$ phase transition for all the studied samples. A relative comparison was made amongst the ${\alpha }^{\prime }$ values extracted from both the anisotropy data, and further, a theoretical relationship is established with these exponent values. The coupling strength among the $N$ and $\mathrm{Sm}A$ order parameters is determined using the optical birefringence data and discussed from the perspective of mutual interaction between the LC-QDs ligands. The results signify that a strong ligand-ligand interaction between neighboring QDs effectively reduces the $N$ range and slightly influences the $N\text{−}\mathrm{Sm}A$ phase transition.

Thin sheets respond to confinement by smoothly wrinkling or by focusing stress into small, sharp regions. From engineering to biology, geology, textiles, and art, thin sheets are packed and confined in a wide variety of ways, and yet fundamental questions remain about how stresses focus and patterns form in these structures. Using experiments and molecular dynamics simulations, we probe the confinement response of circular sheets, flattened in their central region and quasistatically drawn through a ring. Wrinkles develop in the outer, free region, then are replaced by a truncated cone, which forms in an abrupt transition to stress focusing. We explore how the force associated with this event, and the number of wrinkles, depend on geometry. Additional cones sequentially pattern the sheet until axisymmetry is recovered in most geometries. The cone size is sensitive to in-plane geometry. We uncover a coarse-grained description of this geometric dependence, which diverges depending on the proximity to the asymptotic $d$-cone limit, where the clamp size approaches zero. This paper contributes to the characterization of general confinement of thin sheets, while broadening the understanding of the $d$ cone, a fundamental element of stress focusing, as it appears in realistic settings.

Damped-driven systems are ubiquitous in science, however, the damping and driving mechanisms are often quite convoluted. This paper presents an experimental and theoretical investigation of a fluidic droplet on a vertically vibrating fluid bath as a damped-driven system. We study a fluidic droplet in an annular cavity with the fluid bath forced above the Faraday wave threshold. We model the droplet as a kinematic point particle in air and as inelastic collisions during impact with the bath. In both experiments and the model, the droplet is observed to chaotically change velocity with a Gaussian distribution. Finally, the statistical distributions from experiments and theory are analyzed. Incredibly, this simple deterministic interaction of damping and driving of the droplet leads to more complex Brownian-like and Levy-like behavior.

We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which $M$ candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other $M-1$ candidate edges are being discarded. These two rules are prototypical “explosive” percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., $M=2$. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with $M$ larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for $M$ from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed $M$.

We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain. This nonintegral form distinguishes the extended relation from previous relations expressed by integration over a frequency. To obtain this relation, we consider one-particle one-dimensional systems described by an overdamped Langevin equation with a force driving the system away from equilibrium. We assume a special property of the potential in the system. From this Langevin equation, we obtain the Fokker-Planck (FP) equation describing the time evolution of the distribution function of the particle. Using the FP equation, we calculate the responses of the particle velocity and heat current by applying time-dependent perturbations of the driving force and temperature. We express the extent of the FRR violation in terms of these responses with time correlation functions and expand them in powers of the FP operator. This reciprocal relation is valid far from equilibrium. One can also confirm this reciprocal relation through experiments with systems such as colloidal suspensions because the FRR violation can be experimentally observed.

In the present study the interaction of a sine-Gordon kink with a localized inhomogeneity is considered. In the absence of dissipation, the inhomogeneity considered is found to impose a potential energy barrier. The motion of the kink for near-critical values of velocities separating transmission from barrier reflection is studied. Moreover, the existence and stability properties of the kink at the relevant saddle point are examined and its dynamics is found to be accurately captured by effective low-dimensional models. In the case where there is dissipation in the system, below the threshold value of the current, a stable kink is found to exist in the immediate vicinity of the barrier. The effective particle motion of the kink is investigated obtaining very good agreement with the result of the original field model. Both one and two degree-of-freedom settings are examined with the latter being more efficient than the former in capturing the details of the kink motion.

We identify a class of trapping potentials in cubic nonlinear Schrödinger equations (NLSEs) that make them nonintegrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidistant energy spectra (e.g., the harmonic-oscillator trap), which give rise to a large number of resonances enhancing the nonlinearity. In a broad range of dynamical solutions, spanning the regimes in which the nonlinearity may be either weak or strong in comparison with the linear part of the NLSE, the power spectra are shaped as narrow (quasidiscrete), evenly spaced spikes, unlike generic truly continuous (ergodic) spectra. We develop an analytical explanation for the emergence of these spectral features in the case of weak nonlinearity. In the strongly nonlinear regime, the presence of such structures is tracked numerically by performing simulations with random initial conditions. Some potentials that prevent ergodicity in this manner are of direct relevance to Bose-Einstein condensates: they naturally appear in 1D, 2D, and 3D Gross-Pitaevskii equations (GPEs), the quintic version of these equations, and a two-component GPE system.

Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range $r_c$ which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync $\pi$ has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength ${\sigma }_r$ is very small for a fixed $r_c$ and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of $r_c$. For ${\sigma }_r=0$ and for sufficiently small values of $r_c$, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling ${\sigma }_a$ and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as ${\sigma }_a$ increases. These results are supported by simulations and animations added as supplemental materials.

The challenging problem of network reconstruction from dynamical data can in general be formulated as an optimization task of solving multiple linear equations. Existing approaches are of the two types: Point-by-point (PBP) and global methods. The local PBP method is computationally efficient, but the accuracies of its solutions are somehow low, while a global method has the opposite traits: High accuracy and high computational cost. Taking advantage of the network symmetry, we develop a novel framework integrating the advantages of both the PBP and global methods while avoiding their shortcomings: i.e., high reconstruction accuracy is guaranteed, but the computational cost is orders of magnitude lower than that of the global methods in the literature. The mathematical principle underlying our framework is block coordinate descent (BCD) for solving optimization problems, where the various blocks are determined by the network symmetry. The reconstruction framework is validated by numerical examples with a variety of network structures (i.e., sparse and dense networks) and dynamical processes. Our success is a demonstration that the general principle of exploiting symmetry can be extended to tackling the challenging inverse problem or reverse engineering of complex networks. Since solving a large number of linear equations is key to a plethora of problems in science and engineering, our BCD-based network reconstruction framework will find broader applications.

The assumption of constant population size is central in population genetics. It led to a large body of results that is robust to modeling choices and that has proven successful to understand evolutionary dynamics. In reality, allele frequencies and population size are both determined by the interaction between a population and the environment. Relaxing the constant-population assumption has two big drawbacks. It increases the technical difficulty of the analysis, and it requires specifying a mechanism for the saturation of the population size, possibly making the results contingent on model details. Here we develop a framework that encompasses a great variety of systems with an arbitrary mechanism for population growth limitation. By using techniques based on scale separation for stochastic processes, we are able to calculate analytically properties of evolutionary trajectories, such as the fixation probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three parameters related to the intergeneration timescale, the invasion fitness, and the carrying capacity of the strains. In other words, different systems, such as Lotka-Volterra or a chemostat model (contained in our framework), share the same evolutionary outcomes after a proper remapping of their parameters. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of invasion fitness.

The transport properties of colloidal particles in active liquids have been studied extensively. It has led to a deeper understanding of the interactions between passive and active particles. However, the phase behavior of colloidal particles in active media has received little attention. Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles. Our study reveals dynamic clustering of colloids in active media due to an interplay of activity and attractive effective potential between the colloids. The strength of the effective potential is set by the size ratio of passive particles to the active ones. As the relative size of the passive particles increases, the effective potential becomes stronger and the average size of the clusters grows. The simulations reveal a macroscopic phase separation at sufficiently large size ratios. We will discuss the effect of density fluctuations of active particles on the nature of effective interactions between passive ones.

We propose a simple active hydrodynamic model for the self-propulsion of a liquid droplet suspended in micellar solutions. The self-propulsion of the droplet occurs by spontaneous breaking of isotropic symmetry and is studied using both analytical and numerical methods. The emergence of self-propulsion arises from the slow dissolution of the inner fluid into the outer micellar solution as filled micelles. We propose that the surface generation of filled micelles is the dominant reason for the self-propulsion of the droplet. The flow instability is due to the Marangoni stress generated by the nonuniform distribution of the surfactant molecules on the droplet interface. In our model, the driving parameter of the instability is the excess surfactant concentration above the critical micellar concentration, which directly correlates with the experimental observations. We consider various low-order modes of flow instability and show that the first mode becomes unstable through a supercritical bifurcation and is the only mode contributing to the swimming of the droplet. The flow fields around the droplet for these modes and their combined effects are also discussed.

Nonlocal electron transport is important for understanding laser-target coupling for laser-direct-drive (LDD) inertial confinement fusion (ICF) simulations. Current models for the nonlocal electron mean free path in radiation-hydrodynamic codes are based on plasma-physics models developed decades ago; improvements are needed to accurately predict the electron conduction in LDD simulations of ICF target implosions. We utilized time-dependent density functional theory (TD-DFT) to calculate the electron stopping power (SP) in the so-called conduction-zone plasmas of polystyrene in a wide range of densities and temperatures relevant to LDD. Compared with the modified Lee-More model, the TD-DFT calculations indicated a lower SP and a higher stopping range for nonlocal electrons. We fit these electron SP calculations to obtain a global analytical model for the electron stopping range as a function of plasma conditions and the nonlocal electron kinetic energy. This model was implemented in the one-dimensional radiation-hydrodynamic code lilac to perform simulations of LDD ICF implosions, which are further compared with simulations by the standard modified Lee-More model. Results from these integrated simulations are discussed in terms of the implications of this TD-DFT-based mean-free-path model to ICF simulations.

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (Kardar-Parisi-Zhang equation). We solve these equations and find three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition.

We adopt the neural network (NN) flow method to study the Berezinskii-Kosterlitz-Thouless (BKT) phase transitions of the two-dimensional $q$-state clock model with $q\ge 4$. The NN flow consists of a sequence of the same units that proceed with the flow. This unit is a variational autoencoder trained by the data of Monte Carlo configurations in unsupervised learning. To gauge the difference among the ensembles of Monte Carlo configurations at different temperatures and the uniqueness of the ensemble of NN-flow states, we adopt the Jensen-Shannon divergence (JSD) as the information-distance measure “thermometer.” This JSD thermometer compares the probability distribution functions of the mean spin value of two ensembles of states. Our results show that the NN flow will flow an arbitrary spin state to some state in a fixed-point ensemble of states. The corresponding JSD of the fixed-point ensemble takes a unique profile with peculiar features, which can help to identify the critical temperatures of BKT phase transitions of the underlying Monte Carlo configurations.

Ubiquitous thermal conduction makes its force effect particularly important in diverse fields, such as electronic engineering and biochemistry. However, regulating thermal conduction force is still challenging due to two stringent restrictions. First, a temperature gradient is essential for inducing the force effect. Second, the force direction is fixed to the temperature gradient in a specific material. Here, we demonstrate that thermal conduction force can exist unexpectedly at a zero average temperature gradient in dielectric crystals. The wavelike feature of thermal conduction is considered, i.e., the second sound mode. Based on the momentum conservation law for phonon gases, we analyze thermal conduction force with the plane, zeroth-order Bessel, and first-order Bessel second sounds. Remarkably, the force direction is highly tunable to be along or against the second sound direction. These results provide valuable insights into thermal conduction force in those environments with temperature fluctuations, and they open up possibilities for practical applications in manipulating the local thermal conductivity of crystals.

Quantum Otto and Carnot engines have recently been receiving attention due to their ability to achieve high efficiencies and powers based on the laws of quantum mechanics. This paper discusses the theory, progress, and possible applications of quantum Otto and Carnot engines, such as energy production, cooling, and nanoscale technologies. In particular, we investigate a two-spin Heisenberg system that works as a substance in quantum Otto and Carnot cycles while exposed to an external magnetic field with both Dzyaloshinsky-Moriya and dipole-dipole interactions. The four stages of engine cycles are subject to analysis with respect to the heat exchanges that occur between the hot and cold reservoirs, alongside the work done during each stage. The operating conditions of the heat engine, refrigerator, thermal accelerator, and heater are all achieved. Moreover, our results demonstrate that the laws of thermodynamics are strictly upheld and the Carnot cycle produces more useful work than that of the Otto cycle.