Granular materials exhibit complex transitions between solid-like and fluid-like states. Although natural granular particles typically have irregular shapes, the impact of particle angularity on granular flow remains poorly understood. Here, we demonstrate, through laboratory experiments and numerical simulations, that particle angularity controls vibrated granular flow. Highly angular particles sustain long-lived convective motion, whereas smoother (more rounded) particles rapidly form dense, solid-like structures that suppress fluidization. We further show that rolling resistance models commonly used in simulations fail to fully capture these angularity-driven effects. Our findings challenge standard simulation approaches and indicate that natural granular flows (e.g., landslides and planetary regolith) could be far more dynamic than predicted by spherical-particle approximations. This underscores the crucial but often underappreciated role of particle shape in granular physics.

Ratchet effects can appear for particles interacting with an asymmetric potential under ac driving or for a thermal system in which a substrate is periodically flashed. Here, we show that a different type of collective ratchet effect can arise for a pattern-forming system coupled to an asymmetric substrate when the interaction potential between the particles is periodically oscillated in order to cycle the system through different patterns. We consider particles with competing short-range attraction and long-range repulsion subjected to time-dependent oscillations of the ratio between the attractive and repulsive interaction terms, which causes the system to cycle periodically between crystal and bubble states. In the presence of the substrate, this system exhibits both a positive and a reversed ratchet effect, and we show that there is a maximum in the ratchet efficiency as a function of interaction strength, ac drive frequency, and particle density. Our results could be realized for a variety of pattern-forming systems on asymmetric substrates where the pattern type or particle interactions can be oscillated.

Magnetic thin films and two-dimensional (2D) arrays of magnetic nanoparticles exhibit unique physical properties that make them valuable for a wide range of technological applications. In such systems, dipolar interactions play a crucial role in determining their physical behavior. However, due to the anisotropic and long-range nature of dipolar interactions, conventional Monte Carlo (MC) methods face challenges in investigating these systems near criticality. In this study, we examine the critical behavior of a triangular lattice of XY dipoles using the optimized Tomita MC algorithm tailored for dipolar interactions. We employ two independent computational approaches to estimate the critical temperature and exponents: equilibrium MC simulations with histogram reweighting and the nonequilibrium relaxation method. Notably, both approaches demonstrate that this XY dipolar system might be in a new universality class very close to the 2D Ising universality class.

Fokker-Planck equations (forward Kolmogorov equations) describe the time evolution of probability densities from a given initial condition. For distributions over the real line, these evolution equations can sometimes be transformed into dynamics over the incomplete zeroth and first moments. We call this perspective the Lorenz dynamics of the system after the Lorenz curve description of distributions of wealth. This offers the benefit of presenting the dynamics over a compact domain. The integral transformation is motivated and then stated for a general class of Fokker-Planck equations. Following this, the transformed equation is solved for the heat equation and some variants thereof. Finally, some equations arising from the application of kinetic theory to idealized economic systems are transformed and analyzed in this new light.

We study the local entropy production rate and the local entropy flow in active systems composed of noninteracting run-and-tumble particles in a thermal bath. After providing generic time-dependent expressions, we focus on the stationary regime. Remarkably, in this regime the two entropies are equal and depend only on the distribution function and its spatial derivatives. We discuss in detail two case studies relevant to real situations. First, we analyze the case of space-dependent speed describing photokinetic bacteria, cosidering two different shapes of the speed, namely piecewise constant and sinusoidal. Finally, we investigate the case of external force fields, focusing on harmonic and linear potentials, which allow analytical treatment. In all investigated cases, we compare exact and approximated analytical results with numerical simulations.

In realistic neural circuits, both neurons and synapses are coupled in dynamics with separate time scales. The circuit functions are intimately related to these coupled dynamics. However, it remains challenging to understand the intrinsic properties of the coupled dynamics. Here, we develop the neuron-synapse coupled quasi-potential method to demonstrate how learning induces a qualitative change in the macroscopic behaviors of recurrent neural networks. We find that under the Hebbian learning, a large Hebbian strength will alter the nature of the chaos transition, from a continuous type to a discontinuous type, where the onset of chaos requires a smaller synaptic gain compared to the nonplastic counterpart network. In addition, our theory predicts that under feedback and homeostatic learning, the location and type of chaos transition are retained, and only the chaotic fluctuation is adjusted. Our theoretical calculations are supported by numerical simulations.

We theoretically study the impact of coherent intermode coupling on the nonlinear dynamics of two counterpropagating modes in a Kerr microcavity driven by symmetric counterpropagating pumps, focusing on the realization of stationary and oscillatory states with broken symmetry. Notably, the symmetry-breaking threshold for positive intermode coupling coefficients $\beta$ grows sharply, while for negative $\beta$ the threshold first decreases, reaches a minimum, and then gradually increases as $\left|\beta \right|$ increases. We show that the system exhibits robust and self-similar behavior with symmetry breaking and symmetry restoring in stationary regimes for a fairly wide range of negative $\beta$ and pump powers. The model with real positive and negative $\beta$ covers all possible cases in which spontaneous symmetry breaking can occur. We also demonstrate that diverse oscillatory regimes are observable only within a very narrow range of small $\left|\beta \right|$ and these regimes are highly sensitive to $\beta$. Therefore, when utilizing oscillatory regimes, even weak intermode coupling should not be neglected and requires careful attention. These findings have applications in the development of ultrasensitive miniature sensors, as well as other devices employing spontaneous symmetry breaking.

The linear or nonlinear nature of a dynamical system is often evaluated by applying nonlinearity tests to an experimental time series that is typically the only observable output of the system. The most widely used nonlinearity test is the method of surrogates: a set of linear time series that replicate the properties of the experimental time series, specifically the marginal distribution and the autocorrelation function. This set of surrogates represents the null hypothesis of linearity, and can be created by several techniques. However, these techniques typically require some degree of manipulation in the frequency domain that often produces correlations in the Fourier phases leading to undesired nonlinear correlations in the surrogates. Here, we present a nonlinearity test that does not rely on generating surrogates, therefore avoiding the problem of spurious nonlinearities in the null hypothesis. Our approach uses the autocorrelation function of the time series under assessment to statistically determine whether the observed correlations could arise from a linear Gaussian time series that has been reversibly transformed into the experimental time series. If so, the experimental time series is considered linear; if not, it is considered nonlinear. We have applied the test to several well known models of linear and nonlinear time series, obtaining excellent results in both cases.

Using a delay differential equation model for a two-section semiconductor laser, we have found a new bifurcation scenario leading to stable mode-locked operation with normal dispersion properties of the light travel. The pulse profile is asymmetric, with a slower leading edge and a negative chirp. We classify the parameter space in which this regime exists as a Busse balloon and describe its boundaries.

We investigate the dynamics of the Ikeda map in the conservative limit, where it is represented as a two-dimensional area-preserving map governed by two control parameters, $\theta$ and $\varphi$. We demonstrate that the map can be interpreted as a composition of a rotation and a translation of the state vector. In the integrable case ($\varphi =0$), the map reduces to a uniform rotation by angle $\theta$ about a fixed point, independent of initial conditions. For $\varphi \ne 0$, the system becomes nonintegrable, and the rotation angle acquires a coordinate dependence. The resulting rotation number profile exhibits extrema as a function of position, indicating the formation of shearless barriers. We analyze the emergence, persistence, and breakup of these barriers as the control parameters vary.

Fisher's classical debt-deflation model outlined a sequence of events governing the positive feedback in economic downturns. This theory has been formative for modern economic policy, including the 2008 crisis. However, few quantitative models have been developed to incorporate positive feedback in cyclic economic dynamics. Here we present an agent-based model in which companies compete by adjusting wages, and workers probabilistically choose employers based on the wage offered. Despite omitting debt, unemployment, and other features in Fisher's model, the model generates endogenous inflation-deflation cycles, irregularly recurring recessions, and clustered bankruptcies. These dynamics emerge from feedback between wage growth, consumer demand, and company fragility, where high wages increase purchasing power but also raise vulnerability to shocks. The model qualitatively reproduces several empirical patterns, including inflation volatility, recession periods and durations, and asymmetric asset returns, though it diverges in firm size distributions and mortality rates. Our results demonstrate that complex macroeconomic behavior can arise from simple, wage-driven interactions alone.

Time-varying group interactions constitute the building blocks of many complex systems. The framework of temporal hypergraphs makes it possible to represent them by taking into account the higher-order and temporal nature of the interactions. However, the corresponding datasets are often incomplete and/or limited in size and duration, and surrogate time-varying hypergraphs able to reproduce their statistical features constitute interesting substitutions, especially to understand how dynamical processes unfold on group interactions. Here we introduce a temporal hypergraph model, the Emerging Activity Temporal Hypergraph (EATH), which can be fed by parameters measured in a dataset and create synthetic datasets with similar properties. In the model each node has an independent underlying activity dynamic, and the overall system activity emerges from the nodes' dynamics, with temporal group interactions resulting from both the activity of the nodes and memory mechanisms. We first show that the EATH model can generate surrogate hypergraphs of several empirical datasets of face-to-face interactions, mimicking temporal and topological properties at the node and hyperedge level. We also showcase the possibility to use the resulting synthetic data in simulations of higher-order contagion dynamics, comparing the outcome of such process on original and surrogate datasets. Finally, we illustrate the flexibility of the model, which can generate synthetic hypergraphs with tunable properties: as an example, we generate “hybrid” temporal hypergraphs, which mix properties of different empirical datasets. Our work opens several perspectives, from the generation of synthetic realistic hypergraphs describing contexts where data collection is difficult to a deeper understanding of dynamical processes on temporal hypergraphs.

Loopy tensor networks have internal correlations that often make their compression inefficient. We show that even local bond optimization can make better use of the insight it has locally into relevant loop correlations. By cutting the bond, we define a set of states whose linear dependence can be used to truncate the bond dimension. The linear dependence is eliminated with zero modes of the states' metric tensor. The method is illustrated by a series of examples for the infinite pair-entangled projected state (iPEPS) and for the periodic matrix product state (pMPS) that occurs in the tensor renormalization group (TRG) step. In all examples, it provides better initial truncation errors than standard initialization.

Using molecular dynamics, this study investigates the local elastic properties of transverse shear deformation of lipid membranes. The analysis demonstrates that transverse shear deformation induces anisotropy in the local stress profile of the lipid bilayer, a phenomenon attributed to the Poynting effect. By analyzing the relationship between transverse shear stress and the induced anisotropy, the local transverse shear modulus is determined. From the local transverse shear modulus, several integral elastic parameters can be derived, including the monolayer tilt modulus, tilt–curvature coupling modulus, and curvature gradient modulus. The calculated tilt modulus values show good agreement with results from an independent analysis of lipid director fluctuations.

Granular materials exhibit complex behavior because of their nonequilibrium nature and dissipative mechanism. This study investigates the role of granular potential in bidisperse granular packings and its influence on thermodynamic properties such as entropy, compactivity, and density of states. Experimental tests using x-ray tomography were performed to examine the microstructure and volume fluctuations of bidisperse mixtures with varying composition ratios. Using a statistical mechanics approach and the fluctuation equation framework, the free-volume index and granular potential for an ensemble were quantified, revealing their direct correlation with packing structure and jamming behavior. The results show that granular potential significantly contributes to excess free volume, thereby influencing packing efficiency and stability. The findings offer insights into the implications of granular thermodynamics for natural and engineered systems, such as soil stability, landslides, and vascular flow regulation.

Recent studies of two-dimensional polydisperse disk systems have revealed a coordinated self-organization of cell stresses and shapes, with certain distributions collapsing onto a master form for many processes, size distributions, friction coefficients, and cell orders. Here we examine the effects of particle angularity on the indicators of self-organization, using simulations of bidisperse regular $N$ polygons and varying $N$ systematically. We find that the strong correlation between local cell stresses and orientations, as well as the collapses of the conditional distributions of scaled cell stress ratios to a master Weibull form for all cell orders $k$, is independent of angularity and friction coefficient. In contrast, increasing angularity makes the collapses of the conditional distributions sensitive to changes in the friction coefficient.

Membrane filtration is widely used in water treatment to remove foulants from contaminated water. Foulant buildup on the membrane occludes the area open for fluid flow, which impairs the efficiency of the filtration operation by decreasing the flux through the membrane. Backwashing (BW) is a strategy to restore the membrane, wherein clean water is processed backward through the membrane to dislodge attached foulants. We develop a Monte Carlo model to simulate constant-pressure forward filtration (FF) and BW through dead-end, flat-sheet membranes, with membrane fouling dominated by intermediate blocking. We validate our model against real-world experiments conducted with different foulant types and concentrations and run under different filtration conditions. Relying primarily on measurable physical parameters and employing easy-to-implement parameter fitting techniques as needed, we show good agreement between experimental data and numerical simulations. We extend these results to predict flux behavior in FF and BW when foulant properties or filtration conditions are varied. This model can be used to further investigate the impact of varying BW duration, frequency, and/or pressure on the rate of flux recovery.

Finding principles of nonequilibrium self-organization in dissipative quantum systems is an open problem. One example is the notion of quantum dissipative adaptation (QDA), that relates the transition probability between the ground states of a quantum system to the nonequilibrium work absorbed during the transition. However, QDA was originally derived with three-level systems in lambda ($\mathrm{\Lambda }$) configuration. Here, we consider a two-qubit model driven by single-photon pulses. We find that the absorbed work is generally related to the sum of $\mathrm{\Lambda }$-type transition probabilities, instead of the direct transition probability between the two ground states. Although this is equivalent to standard QDA in most scenarios, we find an exception whereby optimal self-organization is not accompanied by maximum work consumption. We show how quantum coherence leaves this kind of imprint in the energetics of self-organization in the present model.

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear dynamical system on networks. A graph convolution and attention-based neural network framework has been developed to identify the steady-state behavior of the linear dynamical system. We reveal that our trained model distinguishes the different states with high accuracy. Furthermore, we have evaluated model performance with real-world data. In addition, to understand the explainability of our model, we provide an analytical derivation for the forward and backward propagation of our framework.