Higher-order dynamics are essential for maintaining species diversity in ecological systems. In this paper, we examine how intraspecific competition affects interspecific interactions within spatially embedded hyperlattice frameworks. We thoroughly analyze their impact on conserving biodiversity by including higher-order competitive processes. Extensive numerical simulations show that increased higher-order competition significantly boosts biodiversity, even with higher mobility. The snapshot analyses further identify four distinct spatial patterns resulting from species interactions: regular pattern formation, two-species dominance, spiral wave structures, and single-species dominance. These results emphasize the key role of higher-order competitive interactions in shaping and stabilizing ecological diversity.

The standard Axelrod model of cultural dissemination, based on discrete cultural traits, exhibits a nonequilibrium phase transition but is inherently limited by its inability to continuously probe the critical behavior. We address this limitation by investigating a generalized Axelrod model that employs continuous cultural traits confined to the interval $[0,1]$. This model utilizes a similarity threshold $d$ that serves as a continuous control parameter representing cultural tolerance. This framework allows for a robust quantitative analysis of the model's critical properties and its dynamics under cultural drift (copying noise). For this quantitative characterization, we primarily focus on the case of $F=2$ cultural features. For the perfect copying scenario, we precisely locate the critical threshold $d_c$, which separates the disordered (fragmented) and ordered (polarized) phases. Through finite-size scaling, we find that the mean domain density vanishes continuously at $d_c$ with the exponent $\beta =1/3$. Simultaneously, the largest domain fraction displays a surprising discontinuous jump at $d_c$. We find that the finite-size effects in the critical region are governed by the exponent $\nu =2$ for both the continuous and discontinuous transitions. Under imperfect copying, persistent noise introduces a powerful selective pressure on the trait space, leading to the emergence of two symmetry-related attractors at the trait values $d$ and $1-d$. However, these noise-induced attractors prove fragile in the thermodynamic limit, becoming unstable at large lattice sizes, which directly accounts for the observed failure of the dynamics to freeze under sustained cultural drift. This suggests that in large, continuously evolving societies, true cultural convergence is highly unlikely, leading instead to sustained fragmentation and nonstationary dynamics where cultural domains never fully stabilize.

We propose a generalized degree-biased random walk model (GDBRW) for scale-free networks, where transition probabilities inversely depend on source and target node degrees via tunable exponents $\alpha$ and $\beta$. We derive equilibrium probability distributions using a continuum approach and simulate exploration times across diverse network densities. The GDBRW model significantly boosts exploration efficiency in sparse networks, outperforming the traditional popularity-driven random walk. Through a detailed analysis of fallbacks—localized oscillations where the walker immediately returns to the previously visited node—we demonstrate that our model effectively suppresses hub-leaf trapping motifs. This symmetry-driven suppression of fallbacks explains the improved coverage efficiency and establishes GDBRW as a robust and efficient exploration strategy for scale-free networks, particularly in low-connectivity regimes.

Prediction of chaotic dynamical systems remains a fundamental challenge, primarily due to their extreme sensitivity to initial conditions and the coexistence of multiscale temporal dynamics. Although traditional Reservoir Computing (RC) and its delayed-feedback extension (DRC) have demonstrated promising performance in chaotic system prediction, they often struggle to capture the complex multiscale features present in such systems. To address these limitations, a Hybrid MultiScale Delayed Reservoir Computing framework (HyMS-DRC) is proposed. This approach integrates standard RC and delayed-feedback RC in a parallel multiscale architecture, where state fusion enhances the representation of dynamics across different temporal scales and mitigates memory fading in long-horizon prediction. We systematically evaluate HyMS-DRC on three canonical chaotic systems—Double Scroll, Lorenz, and Rössler—and compare it against RC, DRC, MultiScale Reservoir Computing (MS-RC), and MultiScale Delayed-Feedback Reservoir Computing (MS-DRC). Experimental results demonstrate that HyMS-DRC consistently achieves superior forecasting performance, attaining the lowest normalized root-mean-square errors (NRMSEs) of 0.0089, 0.0137, and 0.0662, and the longest valid prediction times of approximately 27.85, 24.29, and 22.37 on the three systems, respectively. Furthermore, long-term statistical analyses confirm that HyMS-DRC robustly reconstructs the attractor geometry and accurately reproduces the power spectral distribution, indicating excellent generalization and modeling capability for complex nonlinear dynamics. These findings highlight that combining multiscale structures with delayed feedback significantly enhances temporal memory and feature representation in reservoirs, enabling accurate and robust long-term prediction of chaotic systems.

Complex networks provide powerful tools for analyzing and understanding the intricate structures present in various systems, including natural language. Here, we analyze topology of growing word-adjacency networks constructed from Chinese and English literary works written in different periods. Unconventionally, instead of considering dictionary words only, we also include punctuation marks as if they were ordinary words. Our approach is based on two arguments: (1) punctuation carries genuine information related to emotional state, allows for logical grouping of content, provides a pause in reading, and facilitates understanding by avoiding ambiguity, and (2) our previous works have shown that punctuation marks behave like words in a Zipfian analysis and, if considered together with regular words, can improve authorship attribution in stylometric studies. We focus on a functional dependence of the average shortest path length $L\left(N\right)$ on a network size $N$ for different epochs and individual novels in their original language as well as for translations of selected novels into the other language. We approximate the empirical results with a growing network model and obtain satisfactory agreement between the two. We also observe that $L\left(N\right)$ behaves asymptotically similar for both languages if punctuation marks are included but becomes sizably larger for Chinese if punctuation marks are neglected.

The formation processes of highly ionized plasma channels (filaments), with an electron concentration of $N_e\sim {10}^{18}–{10}^{19}{\mathrm{cm}}^{-3}$, in a pulsed nanosecond discharge in air at a pressure of 100–760 Torr are investigated. The studies are carried out for millimeter-sized gaps with a point cathode and flat anode. It is established that explosive processes at the cathode give rise to the emergence of an ionization wave propagating toward the anode with a velocity of $\sim {10}^6–{10}^7$ cm/s and initiating the development of highly ionized filaments. The wave's propagation velocity is practically independent of the air pressure. At pressures 400–760 Torr, the ionization wave front is unstable and splits into numerous microchannels with typical diameters of $\sim 20\mu \mathrm{m}$ and electron concentrations $N_e=(1–5)\times {10}^{19}{\mathrm{cm}}^{-3}$. The microchannel formation ceases to be observed when the air pressure decreases from 400 to 300 Torr, whereas the discharge development occurs mainly through the development of a uniform highly ionized plasma filament. A decrease in pressure entails the drop in the maximum values of electron concentrations, which, however, are close to the values corresponding to complete ionization. Theoretical estimates of characteristic filamentation times are presented together with the analysis of the possible mechanism responsible for generating plasma with a high degree of ionization. The findings can be helpful in refining the models of plasma-chemical kinetics and the formation mechanisms of a system of highly ionized microchannels in high-pressure discharges at nanosecond times.

In this work, we investigate the relationship between the Seebeck coefficient $\left(\mathcal{S}\right)$, and the differential entropy per particle $(\mathrm{DEP}, s)$, as a tool for characterizing charge carriers in two-dimensional systems. Using armchair silicene nanoribbons as a model platform, we analyze how both quantities and their ratio depend on chemical potential at room temperature. While the Seebeck coefficient captures transport properties through the energy dependence of the electronic transmission, the DEP is directly connected to the system's electronic entropy, offering a direct thermodynamic alternative for estimating $\mathcal{S}$. We evaluate these transport-thermodynamic properties considering diverse ribbon widths, defining metallic and semiconducting regimes. We find both quantities $\mathcal{S}$ and $s$, are highly interconnected within the ribbon's band gap energy region, and their ratio $s/\mathcal{S}$ converges to the elementary charge $e$ across that energy window, fulfilling the Kelvin formula $\mathcal{S}=s/e$. On the contrary, $s/\mathcal{S}$ is undefined for gapless ribbons in the energy window of the first transmission channel. These results establish the ratio between the DEP and the Seebeck coefficient as a reliable and complementary probe for the determination of the elementary charge, and to identify the cleanness of electronic band gaps as $s/\mathcal{S}$ matches with $e$.

Recently it has been shown how to construct quantum analogs of classical stochastic processes by replacing random “which path” decisions with appropriately chosen superpositions. The resulting quantum processes are typically generating and destroying coherence at similar rates. Here we use this scheme to generate a large class of self-contained quantum extensions of a classical Markov chain process using symmetry operations. We show that the relaxation processes unfold very differently for the different quantum extensions. This is supported by monitoring the coherence, the probability of reaching the equilibrium, the decay of the number of domain walls, and the purity. We study the relation between the coherence measure based on the L1 norm and the speed of the relaxation process. For the coherence measure, we find that the finite-size scaling exists, where the corresponding critical exponents are different for short and long times.

We investigate the work done on finite quantum systems initially in an energy-diagonal ensemble when subjected to Haar-random unitary operations. On average, the system's energy shifts toward the infinite-temperature value, effectively equalizing the energy distribution. This suggests that states with energy above the infinite-temperature value serve as a resource for work extraction. This trend becomes typical in large systems as fluctuations vanish. Numerical simulations for a spin model illustrate this behavior. Similar trends arise from unitary quenches when the quench Hamiltonian satisfies the Eigenstate Thermalization Hypothesis together with additional spectral conditions such as nondegeneracy and flatness, showing that these properties are sufficient to reproduce Haar-typical energy equalization.

We revisit the irreversibility of the pendulum with time-dependent angular frequency, considered in a classical paper by K. Husimi. He introduced a parameter that measures the adiabaticity of a process utilizing an adiabatic invariant for the equation of motion of the pendulum. With this adiabaticity parameter, Husimi showed the irreversibility of the pendulum for a cyclic process, which is reminiscent of the Planck principle in thermodynamics, based on the microscopic mechanics. In this study, we generalize the argument by Husimi to a damped pendulum with friction, and highlight the role of conservation of a phase-space area on the Husimi's adiabaticity parameter. Moreover, we also investigate the second law of thermodynamics and its generalization for a general noncyclic process as well as a cyclic process, and elucidate how the Husimi's adiabaticity parameter impacts this law. In particular, for a general noncyclic process, we show the law of entropy nondecrease for the pendulum without friction by using the property of the Husimi's adiabaticity parameter.

Nickel-like ions have a metastable level (${3d}^{9}4s {{}^{3}D}_3$) that decays exclusively by a magnetic octupole ($M3$) transition. We earlier have measured the lifetime of this level in isotopically pure Ni-like Xe ions and have shown how hyperfine interaction modifies the lifetime. We now demonstrate how this long-lived level enables multistep ionization of Ni-like ions at much lower energies than the usual single-step ionization limit, even at the relatively low densities of our electron beam ion trap. Time-resolved and energy-varying observations of ${\mathrm{Xe}}^{26+}$ (Ni-like) and ${\mathrm{Xe}}^{27+}$ (Co-like) in an electron beam ion trap indicate the notable influence of the metastable level on the charge balance in a plasma. The interpretation of our observations is helped by collisional-radiative modeling with hybrid models based on the Flexible Atomic Code, which furthermore enables quantification.

Janus colloidal particles have spin vectors normal to their Janus equator and resulting spin-orientational order that differs from the orientational order considered in traditional models of hexatic melting. Based on imaging their monolayers experimentally, we describe their topological spin defects and show that the Berezinskii-Kosterlitz-Thouless model describes their orientational order when spin orientations are driven into two dimensions by an external AC electric field. This is nontrivial, as the model assumes isotropic nearest-neighbor interactions, which is not the case for this system. These experiments reveal the predictive power of this idealized model beyond the strict validity of its assumptions.

The diffusive behavior of small entities is strongly influenced by the flow of the surrounding medium, a phenomenon ubiquitous in both natural and artificial environments. In this study, we investigate the transport characteristics of inertial active Brownian particles (ABPs) in a microfluidic channel under a Poiseuille flow. The interplay between the inertia of the particles and the imposed fluid flow leads to interesting diffusive behaviors. For instance, in the overdamped regime ($m\to 0$), particles exhibit a negative average velocity $\langle v\rangle$ due to upstream movement. As $m$ increases, particles tend to move along the flow direction with an increase in $\langle v\rangle$ in the positive direction, exhibiting a maximum at optimal $m$, and diminish for higher $m$ values. The effective diffusion coefficient $D_{\mathrm{eff}}$ also shows a peak at this optimal $m$. Interestingly, at higher $m$ values, $D_{\mathrm{eff}}$ decreases with increasing the noise strength. The self-propelled velocity of the particles further enhances the upstream movement. Furthermore, the rotation rate of the particles also contributes positively to the upstream motion, enhancing the diffusion of the particles by many orders in the limit of higher $m$. This study reveals that inertia not only modifies swimmer-flow interactions but also enables the emergence of new dynamical regimes, where mass-dependent trajectories can be harnessed for selective control. Such control holds promise for mass-based particle separation in precisely engineered environments and laboratory-on-a-chip devices for technological applications.

For spatial evolutionary games, a potential can be derived if the interaction is described by two-player, two-strategy, symmetric games that yield thermodynamical behavior for a suitable dynamical rule. Here, we show the existence of a potential for two-strategy group interactions in which the players with identical strategies receive equal payoffs. This type of group interaction includes some extended versions of the public goods game. Some peculiar consequences of these group interactions are illustrated in a simple model in which the players are located at the sites of a square lattice with periodic boundary conditions. This five-player group interaction supports the formation of striplike arrangements of the two strategies. Monte Carlo simulations, however, indicate the existence of many other ground states and the relevance of frustration in shaping the macroscopic behavior when the effect of noise is taken into consideration.

Immiscible two-phase flow in porous media occurs in many processes, such as enhanced oil recovery (EOR), as well as oil spill and soil remediation. These processes involve a fluid displacing another immiscible fluid within the confines of a heterogeneous porous structure. The invasion pattern generally remains the same under constant conditions but can also evolve over time in the presence of surfactants, which alter the interfacial tension (IFT) and surface wettability. The dynamics under such conditions extend beyond the usual way in which such immiscible displacement is modeled. Here, we develop a time-dependent pore network model (PNM) to simulate the effects of surfactant-induced IFT reduction on immiscible displacement driven by constant inlet pressure, with pressure drops across the network calculated using a random resistor network and mass conservation equations. Node-specific flux and velocity are derived using the Hagen-Poiseuille equation, and surfactant adsorption is modeled using the Langmuir isotherm, capturing its impact on fluid-fluid and solid-fluid interfaces within the invaded path. Since the evolution of the invasion pattern comprises the cooperative mechanisms of surfactant mass transfer to the interfaces and the resulting changes in capillary and Laplace pressures, we employ two strategies to quantify this complex feedback behavior: mass transfer based, introducing a mass transfer timescale, and Laplace pressure based, scaling with the inlet pressure. Results reveal that heavy-tailed pore throat distribution accelerates the onset of secondary invasions, which enhances the dominance of Laplace pressure. As the distribution becomes more symmetric or Gaussian, mass transfer becomes the dominant mechanism. This interplay highlights the intricate balance between mass transfer and capillary effects in governing the spatiotemporal evolution of immiscible fluid invasion.

The paper presents a theoretical study of the dynamic magnetic response of an ensemble of interacting superparamagnetic nanoparticles with aligned easy magnetization axes, subjected to both static (dc) and alternating (ac) magnetic fields simultaneously. Such a system traditionally models soft magnetosensitive composites synthesized from liquid dispersions of magnetic nanoparticles in a strong static magnetic field, followed by the solidification of the liquid matrix. The investigation was carried out by numerically solving the Fokker-Planck-Brown equation using a modified mean-field theory that accounts for dipole-dipole interactions between particles at the level of pair correlations. It is shown that the system's dynamics are determined by the competition between the magnetic anisotropy energy, the interaction of magnetic moments with external fields, and the dipole-dipole interactions. The key spectral characteristics of the dynamic susceptibility are analyzed, namely, the low-frequency value of the real part of the susceptibility, and the value and position of the maximum of the imaginary part. A nonmonotonic regime was observed for one of these characteristics, activated when the ac and dc fields exceed critical values. Based on the numerical data, approximating formulas are proposed that relate the spectral characteristics to the amplitude of the ac field, the intensity of the dc field, and the material parameters. On one hand, these relations are in demand for optimizing the synthesis of magnetosensitive composites for biomedicine and sensing, as they allow predicting the intervals of increase and decrease in dynamic susceptibility depending on the intensity of the ac or dc fields. On the other hand, these relations can be used to determine the magnetic anisotropy constant of the magnetic filler particles from experimental measurements of the dynamic susceptibility.

Active particles with a (magnetic) dipole moment are of interest for steering self-propelled motion but also result in novel collective effects due to their dipole-dipole interaction. Here systems of active dipolar particles are studied with Brownian dynamics simulations to systematically characterize the different patterns they form, specifically in the presence of an external (magnetic) field. The combination of three types of order—clustering, orientational alignment, and chain formation—is used to classify the patterns observed in these systems. In the presence of an external field, oriented chains and bands are found to be dominant. These structures show some similarities with columnar cluster seen in (passive) ferrofluids and display columnar spacing and number of lanes per cluster that both decrease with increasing field strength.

Intermittent locomotion represents a significant area of research. This type of motion can be exhibited by individual species or groups of species, contingent upon their morphology, environmental factors, and physiological requirements. In some instances, this phenomenon contributes to the enhancement of group dynamics within a system. Intermittent motion is not limited to living systems but can also be observed in inanimate active systems. Previous research has extensively documented that camphor-based systems can generate intermittent motion characterized by irregular movements interspersed with periods of stasis. This particular type of motion has been observed in both single-camphor disk and multiple-disk systems. However, the underlying mechanisms responsible for the intermittent motion remain elusive. Here we address this question using the combination of experimental and theoretical modeling. We visualize the dissolved, local concentration of camphor released by the disk in the liquid. The concentration field shows interesting dynamic patterns as it is advected by the ambient liquid within a confinement. Intermittent motion results from formation and opening of dynamic traps that set up the evolving camphor cloud. Moreover, our findings indicate that the size of the confinement and the rate of camphor release are the key factors governing this behavior. To validate our findings, we present a mathematical model that captures the dynamics of the surrounding camphor cloud. This model successfully reproduces the ability of the disk to switch between two distinct states: the "burst" and "pause." The feedback mechanism between the surrounding camphor cloud and the disk plays a crucial role in governing these transitions.

We analytically investigate a one-dimensional random sequential adsorption (RSA) model in which deposition probabilities are nonuniform and depend on the polarization state of the available intervals. Adsorbed segments behave as dipoles with two possible orientations, leading to orientation-dependent placement rules that combine stochastic selection with deterministic relaxation to energetically favorable positions. By generalizing the standard RSA integral equation to include polarization-dependent boundary conditions, we derive and solve uncoupled functional recurrences for the mean coverage, obtaining exact results for both deterministic and stochastic regimes. Furthermore, we compute the variance using the law of total variance, identifying distinct intracase and intercase contributions to the fluctuations. The model exhibits a continuous transition between steplike coverage profiles as the orientation probability varies, providing a tractable framework for studying interaction-driven nonuniform adsorption processes.

Recent studies have used the Lorentzian ansatz to obtain mean-field reductions of Izhikevich neuron networks, but these approaches stop short of connecting microscopic dynamics to synchrony measures. In this work, we construct an equivalent phase model for the Izhikevich neuron and apply the Ott-Antonsen ansatz to derive mean-field equations in terms of the Kuramoto order parameter. This provides governing equations for the evolution of synchrony in networks of Izhikevich neurons. We further demonstrate that the conformal mapping originally derived for quadratic integrate-and-fire neurons remains valid for the Izhikevich model, thereby extending the link between voltage–firing-rate and phase-based descriptions to a broader and more biologically realistic neuron class. Using this mapping, we challenge the common assumption that high firing rates indicate strong synchrony, and instead show that high-amplitude oscillations in firing rate are the true signature of synchrony. This result holds across excitatory and inhibitory populations and suggests that EEG and MEG spectral power could serve as noninvasive biomarkers of underlying neuronal synchrony. Together, these findings extend mean-field reduction techniques to richer neuronal models, strengthen the bridge between mathematical theory and experimental observables, and provide new insight into the relationship between firing activity and collective neural dynamics.