We demonstrate that standard delay systems with a linear instantaneous and a delayed nonlinear term show weak chaos, asymptotically subdiffusive behavior, and weak ergodicity breaking if the nonlinearity is chosen from a specific class of functions. In the limit of large constant delay times, anomalous behavior may not be observable due to exponentially large crossover times. A periodic modulation of the delay causes a strong reduction of the effective dimension of the chaotic phases, leads to hitherto unknown types of solutions, and the occurrence of anomalous diffusion already at short times. The observed anomalous behavior is caused by nonhyperbolic fixed points in function space.

Returning walks on a lattice are sequences of moves that start at a given lattice site and return to the same site after $n$ steps. Determining the total number of returning walks of a given length $n$ is a typical graph-theoretical problem with connections to lattice models in statistical and condensed matter physics. We derive analytical expressions for the returning walk numbers on the 11 two-dimensional Archimedean lattices by developing a connection to the theory of Bloch energy bands. We benchmark our results through an alternative method that relies on computing the moments of adjacency matrices of large graphs, whose construction we explain explicitly. As condensed matter physics applications, we use our formulas to compute the density of states of tight-binding models on the Archimedean lattices and analytically determine the asymptotics of the return probability. While the Archimedean lattices provide a sufficiently rich structure and are chosen here for concreteness, our techniques can be generalized straightforwardly to other two- or higher-dimensional Euclidean lattices.

Polyadic (or higher-order) interactions can significantly impact the dynamics of interacting particle systems. However, previous studies have often assumed group sizes to be relatively small. In this work, we examine the influence of multiscale polyadic group interactions, where some groups are small and others are very large. We consider two paradigmatic examples, an SIS-epidemic and the adaptive voter model. On the level of the mean field, we specifically discuss the impact of the multiscale polyadic interactions on equilibrium dynamics and phase transitions. For the SIS-epidemic model, we find a region of bistability that protects the disease-free state over a wide range beyond the classical epidemic threshold from a significant outbreak. For the adaptive voter model, we show that multiscale polyadic interactions can stabilize the network or increase the convergence rate to an unbiased equilibrium.

We present a minimally invasive method for probing the mechanical properties of soft-walled microchannels by analyzing the bifurcations in the periodic motion of a magnetically actuated microrobot. Under oscillatory magnetic excitation, the microrobot undergoes transitions, including grazing and fold bifurcations, during wall interactions that are highly sensitive to local stiffness and damping. Experiments and numerical continuation reveal consistent bifurcation shifts across channels of varying compliance, enabling mechanical characterization through frequency-dependent response. A piecewise-smooth dynamical model incorporating fluid damping and compliant boundaries captures the observed behaviors. This bifurcation-based approach leverages dynamic signatures to provide a sensitive method for mechanical sensing in simplified confined environments. It lays the groundwork for future extensions towards applications in tissue diagnostics, vascular health monitoring, and soft material characterization.

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we consider the challenging problem of multiplicative structural alterations and asymmetrical interaction coupling. We introduce a framework to approximate the averaged response at each network node for general structural alterations, including non-normal and asymmetrical ones. Our findings indicate that both the asymmetry and non-normality of the structural alterations impact the global and local responses at different orders in time. We propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration.

Understanding the principles of self-organized motion in active materials can provide valuable insights into complex biological phenomena such as collective cell migration and bacterial locomotion. Furthermore, the ability to control and manipulate the motion of soft materials through stimuli opens up exciting possibilities for the design of novel soft robots capable of autonomous movement and adaptation. Here, we report the superhelical self-propulsion of a model Belousov-Zhabotinsky (BZ) self-oscillating gel in three-dimensional space driven by scroll waves under gradient illumination. A Transition from planar epicyclic locomotion to superhelical and irregular locomotion is obtained in nonilluminated and illuminated media, respectively. By increasing the illumination gradient, the wave dynamics becomes unstable and both ends of the wave filament drift randomly, causing three-dimensional irregular locomotion. The simulated locomotion can be fit with a two-frequency superhelix, similar to the locomotion trajectories of entities such as Euglena gracilis, sperm cells, and Chlamydomonas reinhardtii.

This article presents a Monte Carlo study on bond percolation in distorted square and triangular lattices. The distorted lattices are generated by dislocating the sites from their regular positions. The amount and direction of the dislocations are random, but can be tuned by the distortion parameter $\alpha$. Once the sites are dislocated, the bond lengths $\delta$ between the nearest neighbors change. A bond can only be occupied if its bond length is less than a threshold value called the connection threshold $d$. It is observed that when the connection threshold is greater than the lattice constant (assumed to be 1), the bond percolation threshold $p_{\mathrm{b}}$ always increases with distortion. For $d\le 1$, no spanning configuration is found for the square lattice when the lattice is distorted, even very slightly. On the other hand, the triangular lattice not only spans for $d\le 1$, it also shows a decreasing trend for $p_{\mathrm{b}}$ in the low-$\alpha$ range. These variation patterns have been linked with the average coordination numbers of the distorted lattices. A critical value $d_{\mathrm{c}}$ for the connection threshold has been defined as the value of $d$ below which no spanning configuration can be found, even after occupying all the bonds satisfying the connection criterion $\delta \le d$. The behavior of $d_{\mathrm{c}}\left(\alpha \right)$ is markedly different for the two lattices.

Systems that are driven by a randomly timed, external protocol can seemingly violate the second law of thermodynamics. We show that this thermodynamic paradox is resolved if the outcome of the random time is stored in a memory device. Specifically, we show that the average work required to erase the memory is always larger than the average work gained from the protocol. We also discuss concrete setups that measure random times directly without continuous monitoring. Taken together, this paper discusses the relationship between temporal information and thermodynamics. This framework is relevant for external protocols employing random times, such as stochastic resetting protocols and cyclically driven heat engines that use randomly timed protocols.

We study the impact of dimension on the radiative transfer (i.e., thermal x-ray transport) through the nonscattering random medium within the coupling of radiation to material. To this purpose, our approach is based on the direct numerical simulations (DNSs) combined with developed analytical models. Systematic calculations for 29 different sets of physical parameters show two- and three-dimensional transport results are similar, while a remarkable problem-dependent difference is observed in most cases between one and two dimensions, which are explicitly analyzed by using the dimension compression method. Furthermore, we find a good scaling law with respect to the effective optical thickness, thereby we propose an analytical model to predict the impact of dimension and a good agreement with DNS results is identified. In addition, we develop a simple formula to account for the maximum dimensional effect when the materials' opacity contrast is infinitely large. Our work provides a clear physical picture and predictable analytical models for the influence of dimension on the radiative transfer in the thermally participating random media.

Qubits in planar quantum disks can be controlled using magnetic fields. This provides a practical mechanism for qubit reset during operation. Then, the question arises: What reset protocol is the optimal one in terms of least dissipated heat? To answer this question, we solve the Euler-Lagrange equation for the dissipation rate of Zeeman disks with both soft and hard confinement. Exploiting the conserved Hamilton function reduces the complexity from solving nonlinear differential equations to purely algebraic ones. We also discuss practical constraints imposed by the maximal achievable drive. Finally, an approximate analytical protocol is devised and shown to be highly accurate.

The apparent contradiction between time-reversible microscopic dynamics and irreversible macroscopic behavior remains a cornerstone challenge in statistical mechanics. Traditional probabilistic models attribute entropy growth to systems evolving toward macrostates with more accessible microstates, yet they often fail to explain the mechanistic origins of irreversibility. We introduce map entropy, which reframes entropy growth as a structural consequence of any irreversible process that disperses energy into translational degrees of freedom. Through state-space transitions, it alters the configuration manifold via changes in particle number or momentum, expanding or pruning accessible microstates, consistent with Boltzmann's relation $(S=k_{B}ln\mathrm{\Omega })$, and unifies insights from nonequilibrium thermodynamics, reaction kinetics, and information theory. By applying map entropy to mechanical processes, chemical reactions, computational erasure, entropy of mixing, thermodynamic equilibration, and paradoxes such as Maxwell's demon, we demonstrate its predictive power and experimental testability, reframing the second law as a structural law rather than a statistical tendency.

The modulation and control of oscillatory phenomena in complex systems are essential with implications across biological, physical, neural, and engineered systems. Beyond pairwise interactions, higher-order networks have emerged as a valid framework for modeling complex systems, capturing interactions that simultaneously occur among three or more units. However, the influence of higher-order interactions on amplitude death (AD) behavior in complex networks remains poorly understood. Here, we investigate the phenomenon of AD in complex networks featuring delayed coupling across first-order, second-order, and combined interaction schemes. Employing a dimensionality reduction approach, we simplify the high-dimensional system and analytically derive the boundaries of the AD region from the resulting low-dimensional system. Numerical simulations are performed to validate the theoretical framework. Our results indicate that both the coupling strengths of the first-order and second-order interactions, as well as the network topologies, can significantly modulate the oscillatory behavior. The results demonstrate that an increase in either first-order or second-order strength reduces the AD region and promotes two distinct transition processes: a sequential transition from oscillation to AD and back to oscillation or a direct transition from the AD state to oscillatory dynamics. Furthermore, increased connection density enhances oscillatory dynamics, while sparser connectivity promotes the occurrence of the AD state. These findings offer insights into how higher-order interactions shape oscillatory dynamics in complex network architectures.

We present a case study of how the topology of temporal networks affects their ability to synchronize. Specifically, we investigate chaotic pendula coupled through two distinct topologies of temporal networks: small-world and random. Both temporal networks evolve from a nearest-neighbor ring structure with identical edge-rewiring probabilities and timescales. The chaotic pendula are initialized with the same distribution of initial conditions. Here, the edge-rewiring probability refers to the likelihood that one endpoint of an edge is disconnected and then reconnected to a different, randomly chosen node—with self-connections and duplicate edges excluded. The timescale denotes the interval between successive network-rewiring events. The objective is to determine which temporal topology (small-world or random) more effectively facilitates synchronization under the same edge-rewiring parameters. Our results show that synchronization occurs only when the edge-rewiring probability exceeds a critical threshold specific to each network type. For networks with short timescales, temporal random networks achieve synchronization at lower edge-rewiring probabilities and at a faster rate. In contrast, when edge-rewiring probabilities are higher, temporal small-world networks exhibit better synchronization performance over longer timescales. When the edge-rewiring probability reaches one, both network types exhibit comparable synchronization levels. Additionally, we analyze the synchronizability of these temporal networks at short timescales using the master-stability function and proposed the edge-variation rate for analyzing synchronizability at longer timescales. Both analytical approaches provide approximate predictions that align with our numerical results.

Understanding the statistical laws governing citation dynamics remains a fundamental challenge in network theory and the science of science. Citation networks typically exhibit in-degree distributions well approximated by log-normal distributions, yet also display power-law behavior in the high-citation regime—an apparent contradiction lacking a unified explanation. Here we identify a previously unrecognized phenomenon: The variance of the logarithm of citation counts per unit time follows a power law with respect to time ($t$) since publication, scaling as $t^H$, with $H$ constant. This discovery introduces a new challenge while simultaneously offering a crucial clue to resolving this discrepancy. We develop a stochastic model in which latent attention to publications evolves through a memory-driven process with cumulative advantage, modeled as fractional Brownian motion with Hurst parameter $H$ and volatility. We show that antipersistent fluctuations in attention ($H<1/2$) yield log-normal citation distributions, whereas persistent attention dynamics ($H>1/2$) favor heavy-tailed power laws, thus resolving the log-normal–power-law contradiction. Numerical simulations confirm both the $t^H$ law and the transition between regimes. Empirical analysis of arXiv e-prints indicates that the latent attention process is intrinsically antipersistent ($H\approx 0.13$). By linking memory effects and stochastic fluctuations in attention to broader network dynamics, our findings provide a unifying framework for understanding the evolution of collective attention in science and other attention-driven processes.

I investigate the formation of multiscale magnetic-field structures in a rotating, self-gravitating dusty plasma comprising electrons, ions, and charged dust grains. By incorporating the gravitomagnetic field, arising from mass currents in rotating astrophysical objects, into a three-component fluid model, I derive a triple-curl Beltrami equilibrium characterized by three distinct spatial scales. These scales emerge from the eigenvalues of a governing cubic equation, reflecting the combined effects of self-gravitation, rotation, and electromagnetic interactions. The model provides novel insights into the role of rotation and gravity in plasma self-organization, with potential implications for star and cluster formation in astrophysical environments. In particular, I estimate that centimeter-sized dust grains in dense rotating molecular clouds can experience gravitational and electromagnetic forces of comparable magnitude, significantly altering the equilibrium magnetic and flow-field profiles.

Anomalies observed in the neutron spectral shift of high-yield shots at the National Ignition Facility (NIF) suggest the presence of suprathermal ions [E. P. Hartouni et al., Nat. Phys. 19, 72 (2023)], implying that kinetic effects play a significant role in burning inertial confinement fusion (ICF) plasmas. Furthermore, recent measurements of reaction-in-flight (RIF) neutrons offer a direct probe of the stopping power in the burning fuel region of high-energy alpha particles and up-scattered fuel ions. We have developed the particle-in-cell code PICNIC, an exactly energy-conserving particle-in-cell Monte-Carlo collision (PIC-MCC) code to simulate the burn stage in ICF. We present results from 1D spherical simulations of NIF shot N210808, which was the first to exceed the Lawson criterion for laser fusion. We find that the suprathermal ions generated by large-angle Rutherford and nuclear elastic scattering (NES) with fusion alphas produce an alpha knock-on neutron (AKN) signal consistent with the extent and relative yield of the AKN spectrum identified in ignition experiments at the NIF. We also find that the inclusion of large-angle scattering physics does not explain the anomalously large spectral shift observed in the experiment.

Accurate modeling and generation of porous media structures are critical for understanding fluid transport, mechanical properties, and multiphysics behavior in natural and engineered materials. In this paper, we develop a generative framework that leverages latent diffusion models (LDMs) trained on porous media generated using stochastic simulation along with experimental data. The utilized stochastic model provides a computationally efficient method to produce high-resolution porous samples that preserve spatial correlation statistics derived from training images. These samples serve as a statistically controlled dataset to train a latent diffusion pipeline, which integrates a variational autoencoder for dimensionality reduction and a UNet denoiser for latent-space generation. The resulting LDM learns a powerful and data-driven prior over porous structures while preserving key statistical properties. We demonstrate that the model can unconditionally generate realistic porous media models that reflect the input spatial statistics while exhibiting improved visual diversity and generative fidelity. This hybrid approach offers a promising pathway for fast, scalable, and controllable porous media generation in data-scarce or simulation-heavy settings.

We investigate the crossover of critical behavior for the dynamic phase transition (DPT) in ferromagnetic thin films using Monte Carlo simulations of the kinetic Ising model, focusing on the scaling behavior of the dynamic order parameter under a time-dependent external magnetic field. Specifically, we study the transition of the critical behavior of such multilayer film systems from two-dimensional (2D) to three-dimensional (3D) as a function of the film thickness and the distance to the critical point, which enables dimensional crossover observations. Our results indicate that the effective critical exponents exhibit a clear transition in their scaling behavior, with thinner films showing 2D-like characteristics and thicker films displaying 3D-like behavior, for both the DPT and the thermodynamic phase transitions (TPT). Quantitatively, the crossover from 2D to 3D behavior occurs at larger film thicknesses for the DPT compared to the TPT, suggesting that DPT and TPT are governed by distinctly different length scales and underlying surface effects. These findings are in agreement with experimental observations in ultrathin Co films, where dynamic and thermodynamic critical exponents were found to differ. Therefore, our study provides an in-depth explanation for critical phenomena in thin-film ferromagnets driven by a time-dependent magnetic field. By comparing the dimensional crossover properties of both TPT and DPT, we present a comprehensive understanding of how thin-film geometry and surface effects influence the scaling laws and critical behavior in nonequilibrium systems.

The flows of tissues of epithelial cells often involve T1 transitions. These neighbor exchanges are irreversible rearrangements crossing an energy barrier. Here, by an exact geometric construction, I determine this energy barrier for general, isolated T1 transitions dominated by line tensions. I show how deviations from regular cell packing reduce this energy barrier, but find that line tension fluctuations increase it on average. By another exact construction, I prove that the nonlinear tensions in vertex models of tissues also resist T1 transitions. My results thus form the basis for coarse-grained understanding of cell neighbor exchanges for continuum descriptions of epithelia.