In diluted lattices, cooperation is often enhanced at specific densities, particularly near the percolation threshold for stochastic updating rules. However, the replicator rule, despite being probabilistic, does not follow this trend. We find that this anomalous behavior is caused by structures formed by holes and defectors, which prevent some agents from experiencing fluctuations, thereby restricting the free flow of information across the network. As a result, the system becomes trapped in a frozen state, though this can be disrupted by introducing perturbations. Finally, we provide a more quantitative analysis of the relationship between the percolation threshold and cooperation, tracking its development within clusters of varying sizes and demonstrating how the percolation threshold shapes the fundamental structures of the lattice.

In this paper we perform a thorough numerical study of structural and spectral properties of hyperbolic random geometric graphs (HRGs) $G(n,\rho ,\alpha ,\zeta )$ by means of a random matrix theory (RMT) approach. HRGs are formed by distributing $n$ nodes in a Poincaré disk of fixed radius $\rho$; the radial node distribution is characterized by the exponent $\alpha$ and $\zeta$ controls the curvature of the embedding space. Specifically, we report and analyze average structural properties [by means of the number of nonisolated vertices $V_x\left(G\right)$, topological indices, and clustering coefficients] and average spectral properties [by means of standard RMT measures: the ratio between consecutive eigenvalue spacings $r_{\mathbb{R}}\left(G\right)$, the ratio between nearest- and next-to-nearest-neighbor eigenvalue distances $r_{\mathbb{C}}\left(G\right)$, and the inverse participation ratio and the Shannon entropy $S\left(G\right)$ of the eigenvectors]. Even though HRGs are, in general, more elaborated than Euclidean random geometric graphs, we show that both types of random graphs share important average properties, namely: (i) $\langle V_x\left(G\right)\rangle$ is a simple function of the average degree $\langle k\rangle , \langle V_x\left(G\right)\rangle \approx n[1-exp(-\gamma \langle k\rangle )]$, while (ii) properly normalized $\langle r_{\mathbb{R}}\left(G\right)\rangle , \langle r_{\mathbb{C}}\left(G\right)\rangle$ and $\langle S\left(G\right)\rangle$ scale with the parameter $\xi \propto \langle k\rangle n^{\delta }$. Here, $\gamma \equiv \gamma (\alpha /\zeta ), \delta \equiv \delta (\alpha /\zeta )$, and $\langle ·\rangle$ is the average over a graph ensemble.

Substrate-based cell motility is crucial for biological processes, and heterogeneity in the physical properties of the substrate can influence the outcomes of these processes. We demonstrate numerically the impact of different adhesion strengths on one substrate, achieved by adjusting the drag coefficients of different regions on the substrate, on cellular dynamics. We observed that, given the same initial cell location relative to the interface between two regions with different adhesion strengths, the behavior of a cell differs depending on whether it is initially a static cell or a stationary moving cell. Furthermore, we also introduced external stimulation to the cell. The cellular motility behavior around the interface can also be affected by adjusting the magnitude, range, and duration of the external stimulation.

A class of shell models is proposed where the shell variables are defined on a recurrent sequence of integer wave numbers such as the Fibonacci or the Padovan series or their variations, including a sequence made of square roots of Fibonacci numbers rounded to the nearest integer. Considering the simplest model, which involves only local interactions, the interaction coefficients can be generalized in such a way that the inviscid invariants, such as energy and helicity, can be conserved even though there is no exact self-similarity. It is shown that these models basically have identical features with standard shell models and produce the same power-law spectra, similar spectral fluxes, and analogous deviation from self-similar scaling of the structure functions, implying comparable levels of turbulent intermittency. Such a formulation potentially opens up the possibility of using shell models, or their generalizations along with discretized regular grids such as those found in direct numerical simulations, as either diagnostic tools or subgrid models. It also allows us to develop models where the wave-number shells can be interpreted as sparsely decimated sets of wave numbers over an initially regular grid. In addition to conventional shell models with local interactions that result in forward cascade, a particular a helical shell model with long-range interactions is considered on a similarly recurrent sequence of wave numbers, corresponding to the Fibonacci series, and found to result in the usual inverse cascade.

A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. In recent years, classical non-Markovian wave-particle entities that materialize as walking droplets have been shown to exhibit various hydrodynamic quantum analogs, including quantization in a harmonic potential by displaying few coexisting limit cycle orbits. By considering a truncated-memory stroboscopic pilot-wave model of the system in the low dissipation regime, we obtain a classical harmonic oscillator perturbed by oscillatory nonconservative forces that display countably infinite coexisting limit-cycle states, also known as megastability. Using averaging techniques in the low-memory regime, we derive analytical approximations of the orbital radii, orbital frequency and Lyapunov energy function of this megastable spectrum, and further show average energy conservation along these quantized states. Our formalism extends to a general class of self-excited oscillators and can be used to construct megastable spectrum with different energy-frequency relations.

An open quantum system interacting with a heat bath at a given temperature is expected to reach the mean force Gibbs (MFG) state as a steady state. The MFG state is given by tracing out the bath degrees of freedom from the equilibrium Gibbs state of the total system plus bath. When the interaction between the system and the bath is not negligible, it is different from the usual system Gibbs state obtained from the system Hamiltonian only. Using the path integral method, we present the exact MFG state for a coupled system of quantum harmonic oscillators in contact with multiple thermal baths at the same temperature. We develop a nonperturbative method to calculate the covariances with respect to the MFG state. By comparing them with those obtained from the system Gibbs state, we find that the effect of coupling to the bath decays exponentially as a function of the distance from the system-bath boundary. This is similar to the skin effect found recently for a quantum spin chain interacting with an environment. Using the exact results, we also investigate the ultrastrong coupling limit where the coupling between the system and the bath gets arbitrarily large and makes a connection with the recent result found for a general quantum system.

As is well known, one-dimensional spin systems with short-range interactions cannot undergo a phase transition at finite temperature. However, in many 1D Ising spin models with frustration, at a certain crossover point, the thermodynamic quantities show anomalies that resemble such a transition W. Yin [Phys. Rev. Res. 6, 013331 (2024)]. Recently, Yin [Phys. Rev. Res. 6, 013331 (2024)] has shown, using decorated ladders as an example, that a one-dimensional Ising model can be arbitrarily close to the genuine phase transition. Using the transfer matrix method and real space renormalization group technique, we find that crossover resembling a phase transition accompanied by gigantic specific heat can also occur in two-dimensional systems. We consider coupled Ising spin chains with a zig-zag structure and a four-spin $j_4$ interaction, which allows us to control the temperature at which the spins become unbound in the model with short-range interactions. The crossover point is defined by two parameters: the crossover temperature $t=t^{*}$ and the crossover interaction $j_4=j_4^{*}$, and occurs when the temperature at which the effective interaction between the spin subsystems zeros out coincides with the temperature at which the spins become unbound. In systems in which a genuine phase transition occurs at the critical temperature $t=t_c$, there are two possibilities: if $t_c>t^{*}$ the system undergoes a sequence of three phase transitions with a reentrant transition to disordered phase, while for $t_c<t^{*}$ the phase transition is preceded by the considered crossover. We study the key role in the appearance of anomalies in the thermodynamic quantities of the four-spin interactions which are suspected to have a significant impact on the properties of magnetic two-dimensional lattices, but possible also on the construction of social systems modeling the phenomenon of social validation or peer pressure.

Strategies aimed at reducing the negative effects of long-term uncertainty and risk are common in biology, game theory, and finance, even if they entail a cost in terms of mean benefit. Here, we focus on the single mutant's invasion of a finite resident population subject to fluctuating environmental conditions. Thus, the game-theoretical model we analyze integrates environmental and demographic randomness, i.e., the two leading sources of stochasticity and uncertainty. We use simulations and mathematical analysis to study if and when strategies that either increase or reduce payoff variance across environmental states can enhance the mutant fixation probability. Variance aversion implies that the mutant pays insurance in terms of mean payoff to avoid worst-case scenarios. Variance-prone or gambling strategies, on the other hand, entail specialization, allowing the mutant to capitalize on transient favorable conditions, leading to a series of “boom-and-bust” cycles. Our analyses elucidate how the rate of change of environmental conditions and the shape of the probability distribution of possible states affect the possible most convenient strategies. We discuss how our results relate to the bet-hedging theory, which aims to reduce fitness variance rather than payoff variance. We also describe the analogies and differences between these similar yet distinct approaches.

We consider the critical relaxation of the Ising model, the so-called model A, and study its operator product expansion. Within perturbation theory, we focus on the operator product expansions of the two-point function and the response function. At the fixed point, we normalize the coefficients and the scaling variables so that the result displays universality. The role of the fluctuation-dissipation theorem is also discussed, and it is shown that it provides nonperturbative relations among the operator product expansion coefficients. Finally, the large $N$ limit is considered.

Static and dynamic stress changes in the Earth's crust induced by an earthquake typically trigger other earthquakes. Identifying such aftershocks is an important step in seismic hazard assessment but has remained challenging, especially in cases involving natural fluid migration or anthropogenic fluid injections, which can occur with varying time scales and/or episodically, leading to strong temporal variations in earthquake occurrences. Here, we demonstrate analytically and numerically that earthquake catalogs without triggering can lead to spurious Omori-Utsu and productivity relations for the commonly used nearest-neighbor declustering method. However, we show that the robustness of the Omori-Utsu exponent on newly introduced parameters of the method allows one to determine whether, indeed, aftershocks are present. For a natural swarm catalog, which lacks a clear distinction between triggered and background events, we find that the catalog is dominated by aftershocks.

Transfer entropy (TE) is a widely used tool for quantifying causal relationships in stochastic dynamical systems. Traditionally, TE and its conditional variants are applied pairwise between dynamic variables to infer these relationships. However, identifying key drivers in such systems requires a measure of the causal influence exerted by each component on the entire system. I propose using outgoing transfer entropy (OutTE), the transfer entropy from a given variable to the collection of remaining variables, to quantify the causal influence of the variable on the rest of the system. Conversely, the incoming transfer entropy (InTE) is also defined to quantify the causal influence received by a component from the rest of the system. Since OutTE and InTE involve transfer entropy between univariate and multivariate time series, naive estimation methods can result in significant errors, especially when the number of variables is large relative to the number of samples. To address this, I introduce a novel estimation scheme that computes outgoing and incoming TE only between significantly interacting partners. The feasibility and effectiveness of this approach are demonstrated using synthetic data and real oral microbiota data. The method successfully identifies the bacterial species known to be key players in the bacterial community, highlighting its potential for uncovering causal drivers in complex systems.

We present a numerical model to study time-averaged acoustic radiation force and microstreaming around an elastic sphere immersed within an acoustically actuated viscoelastic fluid. We employ a perturbation approach to systematically identify limiting regimes where the viscoelastic fluid can be approximated as a purely viscous fluid at the acoustic and mean time scales. Unlike existing numerical models, we account for microstreaming and fluid elasticity contributions to the radiation force. We elucidate the inherent assumptions within reduced expressions considered in prior numerical models and highlight the divergence between the acoustic radiation force obtained from the reduced and general expressions. We also discuss numerical considerations to ensure the invariance of the acoustic radiation force with the choice of integration surface by recasting the time-averaged mass balance equation in terms of Stokes drift. Our results reveal that the acoustic radiation force exhibits a peak value for an optimal relaxation time, and both the peak acoustic radiation force and the optimal relaxation time increase with increasing polymer viscosity. The results also highlight the significant contribution of fluid elasticity to the radiation force and invalidate the previously employed reduced acoustic radiation force expressions for general viscoelastic regime.

Conservation laws are of great theoretical and practical interest. We describe an alternative approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is a unique approach based on kernel methods instead of neural networks which leads to lower computational costs and requires a lower amount of training data. We propose the use of an “indeterminate” form of kernel ridge regression where the labels still have to be found by additional conditions. We use a simple approach minimizing the length of the coefficient vector to discover a single conservation law.

We describe a custom-built device that is capable of superimposing triaxial unsteady magnetic fields on a sample at the same time that its microstructure is visualized using a high-speed camera and its rheological properties are measured with a commercial rheometer. The device reaches field strengths up to $5 \mathrm{kA}·{\mathrm{m}}^{-1}$, frequencies up to 4 kHz, and its functionality is evaluated by testing magnetorheological fluids under steady shear flow and field transients. Striking differences are found at small Mason numbers by changing the field configuration.

The present work investigates the effect of using six different particle shapes of equal volume on the discharge process of a rectangular silo with adjustable width, equipped with a flat bottom orifice opening of varying size. We find that the discharge rate decreases with the increasing aspect ratio of the particles for both lentil-shaped (oblate) and rice-shaped (prolate ellipsoidal) particles and macaroni-shaped particles show the lowest discharge rate among all the particle shapes. In addition, the silo width influences the discharge in such a way that the rates at which different particle shapes flow out from the system become more distinguishable at smaller silo widths. We observe that the velocity profile near the orifice opening becomes narrower and less sharp with increasing aspect ratio for both lentil- and rice-shaped particles. Moreover, the silo width does not have a significant influence on the velocity profile very near to the orifice, but, its influence becomes more noticeable with increasing height within the silo.

Gas discharge physics is particularly helpful to study many spectacular aspects of atmospheric electricity, e.g., lightning and sprite streamers. However, the observations of double-headed streamers (DHS) in nature—formed after the breakdown—remain an open question. Considering that the topic of DHS has been studied exclusively through theoretical and numerical models, this Letter presents the very first experimental model of DHS. Here, a primary plasma jet device operated at ground pressure is used to ignite a DHS in laboratory-scale experiments. This fundamental experimental model employs a noble gas flow (helium or neon) that expands freely and mixes with ambient air. The growth of the positive and the negative head was observed to originate from an isolated ionized column, directly confirming the previously published theoretical study. The high predictability and stability of the discharge allow advanced characterization diagnostics such as the Stark effect from which the electric field was measured along the discharge axis. This investigation indicates that a DHS can ignite in subbreakdown conditions and reveals the crucial role of the preionization phase. The consistency of these findings with some modeling studies on the topic will shed light on fundamental elementary processes in atmospheric electricity.

Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an affirmative answer. Specifically, we explore the Bak, Tang, and Wiesenfeld (BTW) and Manna sandpile models as instances of percolation transitions from disordered to ordered phases. To facilitate this analysis, we introduce the concept of drop density—a continuously adjustable control variable that quantifies the average number of particles added to a site. By tuning this variable, we observe a transition in the sandpile from a subcritical to a critical phase. Additionally, we define the scaled size of the largest avalanche occurring from the beginning of the sandpile as the order parameter for the self-organized critical transition and analyze its scaling behavior. Furthermore, we calculate the correlation length exponent and note its divergence as the critical point is approached. The finite-size scaling analysis of the avalanche size distribution works quite well at the critical point of the BTW sandpile.

We provide analytical expressions for the second virial coefficients of various hard, convex, monoaxial solids of revolution in higher-dimensional Euclidean spaces. Therefore, the rotation-averaged mutual excluded volume per particle is calculated employing the Brunn-Minkowski theorem using quermassintegrals of the respective shape. In addition to geometries without singularities in their surface curvature, so far unknown quermassintegrals for geometries with singularities in their surface curvature, such as hyperlenses and hypercones, are calculated. Studying the influence of the detailed particle shape, the second virial coefficients are analyzed in four dimensions depending on the aspect ratio $\nu$. These analytical expressions are extended to arbitrary-dimensional Euclidean spaces. The resulting virial coefficients are compared to available data for analogs in two and three dimensions. For hard hyperspheroids, the universal parity $B_2^{*}\left(\nu \right)=B_2^{*}\left({\nu }^{-1}\right)$ of the reduced second virial coefficient with respect to the aspect ratio $\nu$ is proven. Unlike other geometric shapes, the excluded volume of hyperspherocylinders in any dimension solely depends on at most three quermassintegrals.

Giant diffusion, where the diffusion coefficient of a Brownian particle in a periodic potential with an external force is significantly enhanced by the external force, is a nontrivial nonequilibrium phenomenon. We propose a simple stochastic model of giant diffusion, which is based on a biased continuous-time random walk (CTRW) with flight time. By introducing a flight time representing traversal dynamics, we derive the diffusion coefficient using renewal theory and demonstrate its universal peak behavior under various periodic potentials, especially in low-temperature regimes. Giant diffusion is universally observed in the sense that there is a peak of the diffusion coefficient for any tilted periodic potentials and the degree of the diffusivity is greatly enhanced especially for low-temperature regimes. The biased CTRW models with flight times are applied to diffusion under three tilted periodic potentials. Furthermore, the temperature dependence of the maximum diffusion coefficient and the external force that attains the maximum are presented for diffusion under a tilted sawtooth potential.