Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thin-walled cylindrical shells, which are particularly ubiquitous in living systems, such as rod-shaped bacteria. However, tubular biological structures are often pressurized, and the knowledge of the mechanical response upon bending in this scenario is limited. In this work, we use a computational model to study the mechanical response and the deformations as a result of bending pressurized tubes. In addition, we develop a model inspired by tension-field theory to analytically describe the mechanical behavior before and after the wrinkling transition. Furthermore, we investigate the development and evolution of wrinkle patterns beyond the instability, showing different wrinkled configurations. We discover the existence of a multiwavelength mode following the purely sinusoidal wrinkles and anticipating the kinked configuration of the tube.

Several interesting and important natural processes are the manifestation of the interplay of nonlinearity and fluctuations. Stochastic resonance is one such mechanism and is crucial to explain many physical, chemical, and biological processes, as well as having huge technological importance. The general setup to describe stochastic resonance considers two states. Recently, it has been unveiled that it is necessary to consider the intrinsic fluctuations related to the two different states of the system are different in interpreting certain fundamental natural processes, such as glacial-interglacial transitions in Earth's ice age. This also has significance in developing advantageous technologies. However, until now, there has been no general theory describing stochastic resonance in terms of the transition rate between the two states and their probability distribution function while considering different noise amplitudes or fluctuation characteristics of these two states. The development of this fundamental theory is attempted in the present research work. As a first step, a relevant approximation is used in which the system is considered within the adiabatic limit. The analytical derivations are corroborated by numerical simulation results. Furthermore, a semianalytical theory is proposed for the definite system without any approximations as the exact analytical solution is not achievable. This semianalytical theory is found to replicate the results obtained from the Brownian dynamics simulation study for previously known quantifiers for stochastic resonance which are estimated in the present context for the system with state-dependent diffusion.

Spatiotemporal distribution of urban population is crucial to understand the structure and dynamics of cities. Most studies, however, have focused on the microscopic structure of cities such as their few most crowded areas. In this work, we investigate the macroscopic structure of cities such as their clusters of highly populated areas. To do this, we analyze the spatial distribution of urban population and its intraday dynamics in Seoul and Helsinki with a percolation framework. We observe that the growth patterns of the largest clusters in the real and randomly shuffled population data are significantly different, and highly populated areas during the daytime are denser and form larger clusters than highly populated areas during the nighttime. An analysis of the cluster-size distributions at percolation criticality shows that their power-law exponents during the daytime are lower than those during the nighttime, indicating that the spatial distributions of urban population during daytime and nighttime fall into different universality classes. Finally measuring the area-perimeter fractal dimension of the collection of clusters demonstrates that the fractal dimensions during the daytime are higher than those during the nighttime, indicating that the perimeters of clusters during the daytime are rougher than those during the nighttime. Our findings suggest that even the same city can have qualitatively different spatial distributions of population over time, and propose a way to quantitatively compare the macrostructure of cities based on population distribution data.

A large literature has investigated the stability of the synchronous solution over a chaotic or periodic time evolution, for an arbitrary network of coupled oscillators. Delays may affect the dynamics of an uncoupled oscillator or node-to-node coupling. An important result is that in the presence of small perturbations about the synchronous solution there is a maximum Lyapunov exponent that determines asymptotic stability. However, different regions of a chaotic or periodic attractor have different transverse reactivities, which measure the transient growth of the norm of the perturbations. Knowledge about the reactive characterization of an attractor can be used to implement a control action only when needed and achieve synchronization efficiently, i.e., by reducing the amount of control used. In this paper we consider arbitrary networks of coupled lasers in the presence of self-feedback delay and laser-to-laser communication delays and successfully implement an efficient synchronization strategy, based on knowledge about the reactivity of the attractor.

The brain needs to perform time-critical computations to ensure survival. A potential solution lies in the nonlocal, distributed computation at the whole-brain level made possible by criticality and amplified by the rare long-range connections found in the brain's unique anatomical structure. This nonlocality can be captured by the mathematical structure of Schrödinger's wave equation, which is at the heart of the complex harmonics decomposition (CHARM) framework that performs the necessary dimensional manifold reduction able to extract nonlocality in critical spacetime brain dynamics. Using a large neuroimaging dataset of over 1000 people, CHARM captured the critical, nonlocal and long-range nature of brain dynamics and the underlying mechanisms were established using a precise whole-brain model. Equally, CHARM revealed the significantly different critical dynamics of wakefulness and sleep. Overall, CHARM is a promising theoretical framework for capturing the low-dimensionality of the complex network dynamics observed in neuroscience and provides evidence that networks of brain regions rather than individual brain regions are the key computational engines of critical brain dynamics.

A quasi-irrotational approximation for the linear Rayleigh-Taylor instability in elastic solids with finite thickness has been developed for the case in which the slab is in contact with a rigid wall. The approximation yields simple but still reasonably accurate expressions for the instability growth rate. They have the same character as the completely irrotational approximations already developed for semi-infinite media, and they recover its results in the limit for very thick slabs. The model is applied to an analysis of the boundary of stability and the boundary for the elastic to plastic transition in elastic-plastic media. The approach allows for consideration of the presence of a viscous fluid beneath the elastic-plastic slab, extending previous results for ideal fluids.

A hybrid kinetic-fluid model is used to study plasma stratification in alternating current (ac) discharges in noble gases at low plasma densities. Self-consistent coupled solutions of a nonlocal kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained for a positive column and the entire discharge with near-electrode sheaths. Standing striations are obtained for the reduced values of electric fields, $E/p$, corresponding to the inelastic energy balance of electrons in a range of driving frequencies. An analog of Novak's law, $\mathrm{\Lambda }\approx {\varepsilon }_1/\left(e\langle E\rangle \right)$ (striation length $\mathrm{\Lambda }$ proportional to the excitation threshold of atoms ${\varepsilon }_1$ and inversely proportional to the mean square root of the electric field $\langle E\rangle$, where $e$ is the electron charge), is observed in simulations, indicating the nonlocal nature of standing striations in ac discharges at low plasma densities. Stratified plasma operates in a dynamic regime for various driving frequencies. In this regime, ions respond to the time-averaged electric field, whereas electrons react to the instantaneous electric field. The disparity of time scales between ambipolar diffusion, which occurs at the ion time scale, and electron kinetics in the coordinate-energy phase space, which occurs at the free electron diffusion time scale, produces complicated fluxes in the phase space (due to electron heating, energy loss in collisions, and ionization processes) that are responsible for the stratification. Our paper emphasizes the need for the kinetic approach to analyze stratification phenomena in ac discharge of noble gases. It promotes an efficient method for the kinetic treatment of electrons that is an alternative to the commonly used particle-in-cell method.

Understanding the statistical mechanics of low-energy excitations in structural glasses has been the focus of extensive research efforts in the past decades due to their key roles in determining the low-temperature mechanical and transport properties of these intrinsically nonequilibrium materials. While it is established that glasses feature low-energy nonphononic excitations that follow a non-Debye vibrational density of states, we currently lack a well-founded theory of these fundamental objects and their vibrational spectra. A recent theory—that builds on the so-called heterogeneous-elasticity theory (HET) and its extensions—provides explicit predictions for the scaling of the low-frequency tail of the nonphononic spectrum of glasses, the localization properties of the vibrational modes that populate this tail, and its connections to glass formation history and to the form of the distribution of weak microscopic (interatomic) stresses. Here, we employ computer models of structural glasses to quantitatively test these predictions. Our findings do not support the HET's predictions regarding the nature and statistics of low-energy excitations in glasses, highlighting the need for additional theoretical developments.

A statistical thermodynamics description of particles having a set of spatially correlated states with statistical exclusion is developed. A general approximation for the density of states is presented from a state-counting ansatz recently introduced accounting for the multiple state exclusion statistical phenomena as a consequence of state spatial correlations. The multiple exclusion statistics is characterized by an exclusion correlation constant $g_c$ which is consistently determined within the formalism from proper thermodynamic limits. The analytical form of $g_c$ is given in terms of the Lambert function from the particle-lattice geometry. A generalized statistical distribution is obtained reducing to Haldane's statistics and Wu's distribution in the limiting case of particles on a set of spatially uncorrelated states. The problem of hard rods ($k$-mers) on a square lattice is studied with this formalism. From the entropy density dependence of the isotropic (I) and fully oriented nematic (N) phases, the approximation predicts two transitions, $\mathrm{I}\to \mathrm{N}$ and high-coverage $\mathrm{N}\to \mathrm{I}$ (disordered), only for $k\ge 7$ with the entropy at saturation matching to the known value from a Monte Carlo (MC) simulation. Critical coverage of both transitions is given for $k=7$ to $k=20$ in the first and second orders of approximations, in qualitative and quantitative agreement with results from MC simulations. State exclusion frequency $\mathit{e}\left(n\right)$ and exclusion average $\mathcal{G}\left(n\right)$ functions are introduced and given in terms of the chemical potential to obtain a thermodynamic characterization of the state exclusion evolution on density. Results of chemical potential and state exclusion are shown for ideal lattice gases of $k$-mers, squares, and rectangles on a square lattice. Analytical results are compared with fast-relaxation grand canonical MC simulations.

Statistical thermodynamics of particles having a spectrum of topological correlated states and observing statistical exclusion is developed to describe mixtures of species of arbitrary size and shape. A generalized statistical distribution is obtained through a configuration space ansatz recently introduced for single species accounting for the multiple exclusion statistical phenomena, where spatially correlated particle states can be simultaneously excluded by more than one particle. Statistical exclusion on a correlated states spectrum is characterized by exclusion statistical parameters ${\beta }_{cij}$ which are self-consistently determined within the multiple exclusion from thermodynamic boundary conditions. Self-exclusion and cross-exclusion frequency functions ${\mathit{e}}_{ij}\left(n\right)$ and average cumulative exclusion functions ${\mathcal{G}}_{ij}\left(n\right)$ are introduced to characterize the state exclusion spectrum as density varies. Haldane's statistics and Wu's distribution for statistically independent excluding species are recovered in the limit of uncorrelated states for single species as well as for mixtures of self- and cross-excluding species with constant mutual statistical exclusion. The multiple exclusion statistics formalism is applied to the $k$-mer problem on a square lattice rationalized as a mixture of two differently oriented self-excluding and cross-excluding pseudospecies. An isotropic-nematic and a high-density nematic-isotropic (disordered) phase transitions is predicted only for $k\ge 7$. The isotropic-nematic transition is continuum as expected, but the high-density transition results in a first-order one. The formalism provides phase coexistence lines and the chemical potential dependence of the low- and high-density branches in the nematic regime. The theoretical approach to lattice gases presented in this work offers a unique general framework applicable to mixtures of entropy-complex lattice gases. From this framework, $k$-mer phase transitions can be reproduced, and significant configuration features can be derived from the state exclusion spectrum functions.

We study the first-passage problem for a partially reactive target by $N$ identical diffusive particles in a finite $d$-dimensional space, laying a focus on the effects of the partial reactivity when searchers are initially excluded from the target region. By solving the Fokker-Planck equation, we obtain the mean first-passage time that exhibits a power-law dependence on the number of searchers as ${\tau }_N\sim N^{-\alpha }$, proving that the exponent $\alpha$ varies with dimensionality, reactivity, and the number of searchers, and specifying conditions in which crossovers between different exponents occur. We confirm the validity of our analytic results by performing Langevin dynamics simulations for various sets of system parameters.

We report a new mechanism through which extreme events with a dragon-king-like distribution emerge in a network of unidirectional ring of Hindmarsh-Rose bursting neurons interacting through chemical synapses. We establish and substantiate the fact that depending on the choice of initial conditions, the neurons are divided into different clusters. These clusters transit from a phase-locked state (antiphase) to phase synchronized regime with increasing value of the coupling strength. Before attaining phase synchronization, there exist some regions of the coupling strength where these clusters are phase synchronized intermittently. During such intermittent phase synchronization, extreme events originate in the mean field of the membrane potential. This mechanism, which we name as intermittent cluster synchronization, is proposed as the new precursor for the generation of emergent extreme events in this system. These results are also true for diffusive coupling (gap junctions). The distribution of the local maxima of the collective observable shows a long-tailed non-Gaussian while the interevent interval follows the Weibull distribution. The goodness of fit is corroborated using probability-probability plot and quantile-quantile plot. This intermittent phase synchronization becomes rarer and rarer with an increase in the number of clusters of initial conditions.

We demonstrate and analyze anomalous diffusion properties of point-like particles in a two-dimensional system with circular scatterers arranged in a square lattice and governed by smooth potentials, referred to as the square soft Lorentz gas. Our numerical simulations reveal a rich interplay of normal and anomalous diffusion depending on the system parameters. To describe diffusion in normal regimes, we develop a unit cell hopping model that, in the single-hop limit, recovers the Machta-Zwanzig approximation and converges toward the numerical diffusion coefficient as the number of hops increases. Anomalous diffusion is characterized by quasiballistic orbits forming Kolmogorov-Arnold-Moser islands in phase space, alongside a complex tongue structure in parameter space defined by the interscatterer distance and potential softness. The distributions of the particle displacement vector show notable similarities to both analytical and numerical results for a hard-wall square Lorentz gas, exhibiting Gaussian behavior in normal diffusion and long tails due to quasiballistic orbits in anomalous regimes. Our work thus provides a catalog of key dynamical system properties that characterize the intricate changes in diffusion when transitioning from hard billiards to soft potentials.

Cooperation is a self-organized collective behavior. It plays a significant role in the evolution of both ecosystems and human society. Reinforcement learning is different from imitation learning, offering a new perspective for exploring cooperation mechanisms. However, most existing studies with the public goods game (PGG) employ a self-regarding setup or are on pairwise interaction networks. Players in the real world, however, optimize their policies based not only on their histories but also on the histories of their coplayers, and the game is played in a group manner. In this work, we investigate the evolution of cooperation in the PGG under the other-regarding reinforcement learning evolutionary game on hypergraph by combining the $Q$-learning algorithm and evolutionary game framework, where other players' action history is incorporated and the game is played on hypergraphs. Our results show that as the synergy factor $\widehat{r}$ increases, the parameter interval divides into three distinct regions—the absence of cooperation, medium cooperation, and high cooperation—accompanied by two abrupt transitions in the cooperation level near ${\widehat{r}}_1^{*}$ and ${\widehat{r}}_2^{*}$, respectively. Interestingly, we identify regular and anticoordinated chessboard structures in the spatial pattern that positively contribute to the first cooperation transition but adversely affect the second. Furthermore, we provide a theoretical treatment for the first transition with an approximated ${\widehat{r}}_1^{*}$ and reveal that players with a long-sighted perspective and low exploration rate are more likely to reciprocate kindness with each other, thus facilitating the emergence of cooperation. Our findings contribute to understanding the evolution of human cooperation, where other-regarding information and group interactions are commonplace.

We analytically explore the dynamics of a charged active particle coupled to two thermal baths kept at two different temperatures in two dimensions. The particle is confined to an asymmetric harmonic potential and a magnetic field of constant magnitude is applied perpendicular to the plane of motion of the particle. For such a system, as opposed to a Brownian gyrator, the potential asymmetry and temperature gradient are not the key factors for the gyration, as long as finite activity and magnetic field are present. The system shows only a paramagnetic behavior in the absence of either potential asymmetry or temperature gradient. However, by tuning the temperature gradient or potential asymmetry, the system as a function of the duration of activity can exhibit paramagnetic, diamagnetic, or coexistence of both the phases. Interestingly, the magnetic moment vanishes for parameters for which the system possesses a nonequilibrium steady state and hence, a magnetic transition is observed through these nonmagnetic points. Further, when the system is suspended in a viscoelastic medium characterized by a finite memory, it exhibits a magnetic transition in the activity-memory parameter space through a nonmagnetic line. This nonmagnetic line is sensitive to temperature gradient and potential asymmetry. It interestingly forms a closed loop with a diamagnetic phase inside the loop and the entire regime outside as paramagnetic. This results in the emergence of a trapped diamagnetic phase existing only within a finite regime of activity-memory parameter space. This phase eventually disappears as the temperature gradient increases (or decreases) depending on the sign of the potential asymmetry. Moreover, it is observed that by tuning the system parameters, one can obtain zero magnetic moment even for parameter ranges that defy the equilibrium condition of the system.

We experimentally and computationally analyze impact-shock-induced stress wave propagation in packings of disordered flexible fibers. We find that dispersive wave propagation, associated with large stress attenuation, occurs much more prevalently in systems with larger fiber aspect ratios and moderate fiber flexibility. We trace these features to the microstructural properties of fiber contact chains and the energy-trapping abilities of deformable fibers. These findings provide insights into physics of the shock-impacted flexible fiber packings and open the way toward an improved granular-material-based damping technology.

Correlations of the displacement field in a two-dimensional model colloidal liquid are studied numerically and analytically. By calculating the displacement correlations and the shear strain correlations from the numerical data of particle simulations, the displacement field is shown to have nontrivial correlations, even in liquids that are only slightly glassy with the area fraction as low as $0.5$. It is suggested analytically and demonstrated numerically that the displacement correlations are more informative than the shear correlations: the former behaves logarithmically with regard to the spatial distance at shorter scales, while the corresponding information is missing from the shear correlations. The logarithmic behavior of the displacement correlations is interpreted as manifesting a long-lived aspect of the cage effect.

We investigate phase coexistence in a weakly stochastic reaction-diffusion system without assuming a continuum description. Concretely, for $(2N+1)$ diffusion-coupled vessels in which a chemical reaction exhibiting bistability occurs, we derive a condition for the phase coexistence in the limit $N\to \infty$. We then find that the phase coexistence condition depends on the rate of hopping between neighboring vessels. The conditions in the high- and low-hopping-rate limits are expressed in terms of two different potentials which are determined from the chemical reaction model in a single vessel.

Gács's coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables or probabilistic ensembles, rendering it applicable to settings arbitrarily far from equilibrium. For measure-preserving dynamical systems equipped with a Markovian coarse graining, we prove a number of fluctuation inequalities. These include algorithmic versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics. In general, the algorithmic entropy determines a system's actual capacity to do work from an individual state, whereas the Gibbs-Shannon entropy gives only the mean capacity to do work from a state ensemble that is known a priori.

Research on stochastic differential equations (SDEs) involving both additive and multiplicative noise has been extensive. In cases where the primary process is driven by a multiplicative stochastic process, additive white noise typically represents an intrinsic and unavoidable fast component. This applies to phenomena such as thermal fluctuations, inherent uncertainties in measurement processes, or rapid wind forcing in ocean dynamics. In this paper, we focus on an important class of such systems, particularly those characterized by linear drift and multiplicative noise, which have been extensively explored in the literature. In many existing studies, multiplicative stochastic processes are often treated as white noise. However, when considering colored multiplicative noise, the emphasis has usually been on characterizing the far tails of the probability density function (PDF), irrespective of the spectral properties of the noise. In the absence of additive noise and with a general colored multiplicative SDE, standard perturbation approaches lead to a second-order partial differential equation (PDE) known as the Fokker-Planck equation (FPE), consistent with Fick's law. In this paper, we reveal a significant deviation from this standard behavior when additive white noise is introduced. At the leading order of the stochastic process strength, perturbation approaches yield a third-order PDE, regardless of the white noise intensity. The breakdown of the FPE further indicates the breakdown of Fick's law. Additionally, we derive the explicit solution for the equilibrium PDF corresponding to this third-order PDE master equation. Through numerical simulations, we demonstrate significant deviations from results obtained using the FPE derived from Fick's law.