We study the influence of angular momentum on the eigenvalue statistics of a two-dimensional quantum system with rotational symmetry composed of concentric Dirac-δ barriers inside an infinite circular well. Using the transfer-matrix method, we computed extensive ensembles of eigenvalues for different transmission probabilities, numbers of barriers, and angular quantum numbers $m$. The unfolded spectra were analyzed by level-spacing distributions, number variance, and eigenstate participation. As the transmission increases, the system undergoes a transition from Poisson to Gaussian-orthogonal-ensemble statistics, whereas the angular momentum modifies the fine structure of spectral correlations and eigenfunction delocalization. In particular, high $m$ values enhance the number variance and modulate level repulsion at low transmission. These findings show that even in rotationally symmetric systems, angular momentum acts as an internal parameter that subtly reshapes the signatures of quantum chaos in singular potentials.

Community detection is a central problem in complex network analysis, yet conventional algorithms often suffer from sensitivity to initialization, entrapment in local optima, and high computational costs. We propose a community detection framework based on multiagent reinforcement learning that integrates a reward function balancing intracommunity compactness and intercommunity separateness, an initialization strategy guided by node importance, and node embeddings trained via DeepWalk. Each community is assigned an independent detection agent that allocates nodes through a deep $Q$-learning network, enabling adaptive partitioning. The use of node importance and embedding distance improves candidate selection efficiency, while the $\epsilon$-greedy strategy and target network updates enhance global exploration and stability. Extensive experiments on multiple datasets demonstrate that the proposed method consistently outperforms baseline approaches, achieving more accurate and scalable community detection, particularly in large-scale networks.

In typical models of collective motion, each individual takes the average direction of multiple neighbors, resulting in the ordered movement of large flocks. Alternatively, interactions with only one random neighbor at a time can also lead to order, referred to as noise-induced order, but only in small flocks. Here, we propose a new model of collective movement in which individuals interact with a single random neighbor yet can produce order in large flocks. Our model consists of individuals who can also stop, inspired by the intermittent stop-and-go motion in real animals. We introduce a halting interaction in which an individual may stop upon encountering a neighbor moving in the opposite direction, rather than instantly aligning. Using mean-field deterministic and stochastic approximations for a one-dimensional version of the model, we show that persistent collective order emerges even in large flocks. This represents a different mechanism from conventional averaging-based order in large flocks or noise-induced ordering in small flocks. We confirm the mean-field predictions using individual-based simulations in both one and two dimensions. Our results highlight how incorporating a stopped state and halting interactions can generate new routes to order in collective movement.

Magnetically confined fusion plasmas exhibit predator-prey-like cyclic oscillations through the self-regulating interaction between drift-wave turbulence and zonal flow. To elucidate the detailed mechanism and causality underlying this phenomenon, we construct a simple stochastic predator-prey model that incorporates intrinsic fluctuations and analyze its statistical properties from an information-theoretic perspective. We first show that the model exhibits persistent fluctuating cyclic oscillations called quasicycles due to amplification of intrinsic noise. This result suggests the possibility that the previously observed periodic oscillations in a toroidal plasma are not limit cycles, but quasicycles, and that such quasicycles may be widely observed under various conditions. For this model, we further prove that information of the zonal flow is propagated to turbulence. This result suggests that turbulence behavior may be predictable to a certain extent based on zonal flow characteristics.

We have previously shown in model studies that rapid quenches of systems of monomers interacting to form polymer chains can fix nonequilibrium chemistries which could lead to the origin of life. We suggested that such quenching processes might have occurred at very high rates on early Earth, giving an efficient mechanism for natural sorting through enormous numbers of nonequilibrium chemistries from which those most likely to lead to life could be naturally selected. Taking account of kinetic barriers, we found good agreement between laboratory quenching experiments on solutions of amino acids and the resulting model. We also made a preliminary comparison between reported data on polypeptides sampled from emissions from smokers near ocean ridges and our model. However, that previous model assumed that the concentrations of all monomeric amino acids in the medium were the same whereas that is not the case in samples taken from ocean smokers. Here we take account of the heterogeneous concentrations of the amino acid monomers in the medium in the analysis of the smoker data and compare the results with the data on polypeptide concentrations found in the samples taken by a submersible in the Mariana Trough. Results are consistent with the hypothesis that smokers were the source of large and extremely diverse numbers of polypeptides in thermal disequilibrium which could incubate processes leading to life.

Fitting two different materials is a versatile methodology in manufacturing complex structures. One of the canonical models for fitting is the snap-fit model, in which flexible materials and rigid structures are assembled by pushing their interlocking components together. The assembly via snap-fit is often accompanied by large deformations of flexible structures and abrupt force drops, highlighting the role of elasticity, geometry, and contact friction. Despite several model studies revealing fundamental mechanics for snap-fit, the current snap-fit design relies on prototyping and empirical rules. In this paper, we analyze a snap-fit model in which a naturally curved beam slips into a rigid hole. We construct an analytical model based on the theory of elastica with contact friction and demonstrate that its predictions are in excellent quantitative agreement with both simulations and experiments. We find three distinct sliding modes: folding, pinning, and unfolding. The classification is systematically organized in a phase diagram based on the geometric parameters of the shells and the hole. Our study complements existing approaches by providing a predictive framework for contact-based structures that involve friction, elasticity, and geometry, and sheds light on a unified understanding of the interactions between an elastic and a rigid body.

Reservoir observers provide a data-driven approach to the inference of unmeasured variables from observed ones for nonlinear dynamical systems. While previous studies have demonstrated wide applicability, their performance may vary considerably with different input variables, even compromising reliability in the worst cases. To enhance the performance of inference, we integrate residual calibration and attention mechanism into the reservoir observer design. The residual calibration module leverages information from the estimation residuals to refine the observer output, and the attention mechanism exploits the temporal dependencies of the data to enrich the representation of reservoir internal dynamics. Experiments on typical chaotic systems demonstrate that our method substantially improves inference accuracy, especially for the worst cases resulting from the traditional reservoir observers. We also invoke the notion of transfer entropy to explain the reason for the input-dependent observation discrepancy and the effectiveness of the proposed method.

This work introduces a parametric simulation-free reduced-order model for incompressible flows undergoing a Hopf bifurcation, leveraging the parametrization method for invariant manifolds. Unlike data-driven approaches, this method operates directly on the governing equations, eliminating the need for full-order simulations. The proposed model is computed at a single value of the bifurcation parameter yet remains valid over a range of values. The approach systematically constructs an invariant manifold and embedded dynamics, providing an accurate and efficient reduction of the original system. The ability to capture precritical steady states, the bifurcation point, and postcritical limit cycle oscillations is demonstrated by a strong agreement between the reduced-order model and full-order simulations, while achieving significant computational speedup.

Controlling nonlinear effects in $\mu$– and nanoelectromechanical systems is essential for unlocking their full potential in sensing, signal processing, and frequency control. In this study, we develop a voltage-dependent Hamiltonian framework for a nanoelectromechanical resonator with two strongly coupled vibrational modes, representative of a nanostring platform. The mode frequencies and couplings of the system are tuned electrostatically using a dc voltage, which also controls the strength of the interactions. Our theoretical model reproduces the experimentally observed avoided crossing in the absence of an ac drive and generates tunable frequency-comb spectra when a parametric drive is applied. By scanning the dc voltage, we generate a phase diagram that links comb formation and sharp regime boundaries to underlying bifurcations, multistability, and attractor switching. Phase-resolved diagnostics based on a Kuramoto order parameter, together with autocorrelation and Poincaré analyses, quantify coherence and critical slowing down near these transitions. We further explore the relationship between nonlinear coupling, parametric excitation, and stability transitions within a single device of experimental relevance and establish a dynamical framework for engineering nanoelectromechanical resonators that offer enhanced tunability, functionality, and a predictive link to experimental outcomes.

Minimal conditions for dynamical stability refer to the necessary criteria that system parameters must meet to ensure its response to disturbances remains bounded over time. Lyapunov and Kapitza stability criteria are classical examples that have led to major technological advances and fundamental insights in physics. Here, we establish new minimal stability conditions for systems whose potential energy curvature varies periodically in time, extending Kapitza stabilization to what we term optimal dynamical stabilization. Using optimal control theory, we determine the minimal time-periodic stiffness required to stabilize a linear mass-spring system and validate our predictions with model experiments. When the potential curvature alternates between negative and positive values, the set of modulation functions ensuring optimal stability becomes discrete and is governed by eigenvalue problems mathematically analogous to those describing quantum bound states in one-dimensional potential wells. These findings deepen our understanding of dynamical systems and lay the foundation for promising new passive stabilization techniques in applied physics.

We investigate the role of contrarians in a recently proposed weighted-influence variant of the $q$-voter model. In this framework, nonunanimous influence groups affect the focal agent through weighted contributions governed by a bias parameter $p$. We extend this setting by introducing a fraction $\alpha$ ($\alpha >0$) of contrarians, defined as agents who systematically oppose the prevailing influence irrespective of whether the group is unanimous or divided. Analytical mean-field calculations and Monte Carlo simulations reveal that the final states of the system are governed by simple phase boundaries: regions of positive and negative majority separated by the lines $p=1/2$ and $\alpha =1/2$, with equally-mixed states confined to these boundaries. While low contrarian densities are insufficient to overturn the bias, higher values of $\alpha$ systematically drive the system closer to a balanced coexistence of opinions, though exact parity is prevented by the presence of bias $p$. We further analyze the temporal relaxation of opinions and extract the characteristic time scales of convergence. Our findings highlight how contrarians, acting as structured nonconformists, can suppress consensus and maintain opinion diversity, while internal biases ultimately hinder a perfectly even split.

Experimental evidence indicates that intracellular chloride concentration regulates the excitation–inhibition (EI) balance, yet the mechanisms by which activity-dependent chloride dynamics drive seizure evolution and stage transitions remain unclear. We present a conductance-based neuronal network in which EI balance emerges from chloride homeostasis via channel-mediated influx and transporter-mediated extrusion. We show that the fraction of inhibitory synaptic conductance contributing to channel-mediated influx acts as a control parameter that organizes seizure dynamics into distinct stages–preictal, ictal-tonic, and ictal-clonic–distinguished by characteristic amplitude and frequency signatures. Decreasing this fraction shortens ictal activity and suppresses seizure initiation, whereas high fraction promotes the emergence of ictal-tonic and ictal-clonic stages and spiral-wave dynamics, rendering seizure dynamics largely insensitive to inhibition. At intermediate values, seizures bypass the ictal–tonic stage and emerge directly as the ictal–clonic stage. Moreover, joint variation of fractions with synaptic strengths reveals that recurrent excitation expands the tonic–clonic seizure, while recurrent inhibition prolongs preictal states and suppresses ictal-clonic activity.

We develop the Kazantsev theory of small-scale dynamo generation at small Prandtl numbers near the generation threshold and restore the concordance between the theory and numerical simulations: the theory predicted a power-law decay below the threshold, while simulations demonstrate exponential decay. We show that the exponential decay is temporary and owes its existence to the flattening of the velocity correlator at large scales. This effect corresponds to the existence of a long-living virtual level in the corresponding Schrödinger-type equation. We also find the critical Reynolds number, the increment of growth or decay above and under the threshold and the time of exponential decrease under the threshold; we express them in terms of the quantitative characteristic properties of the velocity correlator, which makes it possible to compare the results with the data of different simulations.

In this paper, we present a numerical approach to simulate the condensation and evaporation processes of capillary bridges within granular materials. The formation and dynamics of capillary bridges are captured using a phase-field-based framework implemented within the Lattice Boltzmann Method (LBM) to solve the Allen-Cahn and Navier-Stokes equations, while evaporation and condensation processes accounted for local changes in position of the capillary interfaces. Our model captures the emergence of hysteresis as a result of irreversible geometric transitions—such as bridge coalescence and snap-off—without prescribing any constitutive relation between suction and saturation degrees. This change in capillary regimes arises naturally from the interface dynamics and is not solved by the LBM. In particular, we can capture and analyze the discontinuities in capillary forces, when capillary bridges merge or split within small elementary assemblies of three or four spherical particles. Having validated our numerical results for the above elementary assemblies, a polydispersed granular assembly composed of 1000 spherical grains is next addressed. Our simulations capture well-known condensation and evaporation hysteresis phenomenon while offering the possibility to inspect the underlying topology of air and water clusters for the same water saturation along different hydraulic paths.

The extraction of spatiotemporal coherence in high-dimensional, chaotic, nonlinear dynamical systems, such as turbulent flows, remains a fundamental challenge in physics, mathematics, and engineering. In this work, we employ Shannon transfer entropy (TE) to identify causally coherent motions in a zero-pressure-gradient turbulent boundary layer (TBL). This causality metric, rooted in information theory, enables the identification of sources and targets in dynamical systems using the corresponding time series. However, TE requires sophisticated tuning of various hyperparameters, such as the Markovian order of the source ($m$), which can spatially vary in wall-bounded turbulent flow. Here, we present an adaptive tuning and discuss the influence of $m$ across different TBLs. We introduce the concept of causally coherent structures (CCS), i.e., coherent structures interpreted as spatiotemporal patterns of causality. Moreover, the net transfer entropy flux is also utilized to identify boundary layer locations acting either as sources or targets. The standard viscous, logarithmic, and outer layers are characterized by information fluxes, highlighting, for example, dominant top-down interactions between the inner and outer layers, analogously to the classical energy cascade. This work extends techniques previously employed in the literature, such as correlation and spectral analysis, and presents an approach that is inherently general and applicable to a wide range of chaotic dynamical systems, with applications in cognitive sciences, systems biology and finance.

We use three-dimensional dissipative particle dynamics to study binary fluids undergoing the reversible reaction $A\rightleftharpoons B$ concurrent with phase separation. The interplay between reaction-induced mixing and interfacial segregation drives the system into nonequilibrium steady states with finite domains. Symmetric reaction rates ($k^f=k^b$) lead to a steady domain size $R\left(t\right)$, while asymmetric rates induce a crossover from bicontinuous networks to droplet morphologies and then saturation in the asymptotic limit. We characterize these domains using correlation functions and growth laws, $R\left(t\right)\sim t^{\theta }$, where $\theta \simeq 1$ and $2/3$ indicate hydrodynamic growth. Growth saturates at a domain size $R_s\sim k^{-\alpha }$ with $\alpha \simeq 1/3$, consistent with scaling predictions and prior studies of reaction-controlled coarsening. Thus, the chemical reaction acts as a competing relaxation channel that gradually shifts the system off criticality, regulates coarsening pathways, and ultimately arrests coarsening.

We present a unified theory of critical finite-size scaling for lattice statistical-mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results for linear and branched polymers, multicomponent spin systems, and percolation. Both short-range and long-range interactions are included. The universal finite-size scaling is inherited from the scaling of the system unwrapped to the infinite lattice. We also present conjectures for universal scaling profiles for the susceptibility and two-point function plateau in a critical window. For free boundary conditions, the universal scaling has been proven to apply at a pseudocritical point for hierarchical spins, and we conjecture that this holds generally.

Random graphs offer a useful mathematical representation of a variety of real-world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical moments. In this investigation we elaborate on a generalization of the former where link probabilities are conditioned on the appearance of other links, corresponding to the introduction of interactions in an effective generalized statistical mechanical formalism. When restricted to the simplest nontrivial case of pairwise interactions, one can derive a closed form renormalization group transformation for maximum coordination number two on the corresponding line graph. Higher coordination numbers do not admit exact closed form renormalization group transformations, a feature that paraphrases the usual absence of exact transformations in two or more dimensional lattice systems. We introduce disorder and study the induced renormalization group flow on its probability assignments, highlighting its formal equivalence to time reversed anisotropic drift diffusion on the statistical manifold associated with the effective Hamiltonian. We discuss the implications of our findings, stressing the long wavelength irrelevance of certain classes of pairwise conditioning on random graphs, and conclude with possible applications. These include modeling the scaling behavior of preferential effects on social networks, opinion dynamics, and reinforcement effects on neural networks, as well as how our findings offer a systematic framework to deal with data limitations in inference and reconstruction problems.

In RNA world scenarios, pools of RNA oligomers form strongly interacting, dynamic systems, which enable molecular evolution. In such pools, RNA oligomers hybridize and dehybridize, ligate, and break, ultimately generating longer RNA molecules, which may fold into catalytically active ribozymes. A key process for the elongation of RNA oligomers is templated ligation, which can occur when two RNA strands are adjacently hybridized onto a template strand. Detailed simulations of the dynamics in RNA pools involve a large variety of possible sequences and reactions. Here we develop a reduced description of these complex dynamics within the space of sequence motifs. We then explore to what extent our reduced description can capture the behavior of detailed simulations that account for the full dynamics in the space of RNA strands. Towards this end, we project the dynamics into a motif space, which accounts only for the abundance of all possible four-nucleotide motifs. A system of ordinary differential equations describes the dynamics of those motifs. Its control parameters are effective rate constants for reactions in motif space, which we obtain from the rate constants for the processes underlying the full dynamics in the space of RNA strands. We find that these reduced motif space dynamics indeed capture important aspects of the informational dynamics of RNA pools in sequence space. This approach could also provide a framework to rationalize and interpret features of the sequence dynamics observed in experimental systems.

The impact between a spherical shell (a table-tennis ball, in practice) and a compliant silicone surface is studied. Experimentally, the potential for achieving higher reflected angular velocity on a compliant surface compared to a rigid one is explored with special attention given to the roles of friction and of the soft substrate deformability. Additionally, local observations of the contact region and potential buckling of the spherical shell are pursued. In normal incidence, the main effect of the soft substrate on the rebound is a decrease in the coefficient of restitution of the linear velocity and an increase in the duration of contact, without a clear dependence on the substrate thickness. In addition, by observing the shell geometry at contact it was found that the shell flattening prior to its buckling is smaller on a soft surface than that observed on a rigid surface. In oblique incidence, the introduction of a soft layer clearly increases the ability of the substrate to transfer spin to the spherical shell, with a significant dependence on the layer thickness. A mechanical model incorporating linear elasticity of the surface shows a good correlation with the latter experimental results.