Tipping phenomena in complex systems represent abrupt transitions in the system behavior due to incremental changes in parameters. Here, we report the emergence of an abrupt transition from an oscillatory to a death state in coupled limit cycle oscillators with higher-order repulsive interactions. This transition contrasts with the typical continuous transitions observed with pairwise repulsive links. It is notable that higher-order interactions introduce more complexity to the system dynamics, thereby leading to the transition to the death state at lower coupling strengths compared to pairwise coupled systems. Importantly, there exists a sudden revival of the oscillation from the death state with increasing the pairwise coupling strength despite the detrimental effect of pairwise couplings. The results are also robust for nonidentical systems. Furthermore, the analytical determination of the critical coupling strength for the tipping point aligns closely with the results obtained from numerical simulations.

A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework of learning through this kind of plasticity, capable of taking into account several features of the connectivity and pattern of activity of biological neural networks, including probability distributions of neuron firing rates, selectivity of the responses of single neurons to multiple stimuli, probabilistic connection rules, and noisy stimuli. More importantly, it describes the effects of stabilization, pruning, and reorganization of synaptic connections. This framework is used to compute the values of some relevant quantities used to characterize the learning and memory capabilities of the neuronal network in training and testing procedures as the number of training patterns and other model parameters vary. The results are then compared with those obtained through simulations with firing-rate-based neuronal network models.

The statics of the Fredrickson-Andersen model (FAM) of the liquid-glass transition is solved on the Bethe lattice (BL). The kinetic constraints of the FAM imply on the BL an ergodicity-breaking transition to a (glassy) phase where a fraction of spins of the system is permanently blocked, and the remaining “free” spins become nontrivially correlated. We compute several observables of the ergodicity-broken phase, such as the self-overlap, the configurational entropy, and the spin-glass susceptibility, and we compare the analytical predictions with numerical experiments. The cavity equations that we obtain allow us to define algorithms for fast equilibration and accelerated dynamics. We find that at variance with spin-glass models, the correlations inside a state do not exhibit a critical behavior.

The amplitude of a two-dimensional Ornstein-Uhlenbeck colored noise process evolves according to the one-dimensional Rayleigh process. This is a general model for the random amplitude fluctuations of a quasicycle, i.e., of a noise-induced oscillation around an equilibrium with complex eigenvalues in physical and biological systems. We consider the probability density of time intervals during which the amplitude is either below or above a fixed threshold. The statistics of such first return times (FRTs) are of particular interest in neuroscience to characterize brain rhythm power excursions known as bursts, as well as avalanches and other branching processes. In contrast with the density of first passage times computed using Fokker-Planck theory between a start point and a different endpoint, the density of FRTs is non-normalizable. A recently proposed technique reframes the problem using an expansion of the Fokker-Planck eigenfunctions along with a correction to the normalization. Analytical expressions for the FRT density for the Rayleigh process are shown to be in good agreement with those computed from numerical realizations over a wide range of parameters, both for trajectories above and below threshold. Special care is required to evaluate the theory above threshold due to the crowded roots of the Tricomi confluent hypergeometric function. The results provide insight into the statistics of threshold crossing times in quasicycles generally, and in the stochastic Wilson-Cowan neural equations in particular. Surprisingly, FRTs are governed by a single meta-parameter $\mathrm{\Delta }$ given by the ratio of the noise strength and the linear stability coefficient. We find the universal property that the mean FRT is invariant to the ratio of threshold to $\sqrt{\mathrm{\Delta }}$. The FRT density further exhibits exponential behavior over medium to long timescales, and mixtures of exponentials at shorter FRTs, thereby establishing the absence of strict power-law scaling in these threshold-crossing statistics.

The self-consistent inclusion of plasma effects in opacity calculations is a significant modeling challenge. As density increases, such effects can no longer be treated perturbatively. Building on a a recently published model that addresses this challenge, we calculate opacities of oxygen at solar interior conditions. The new model includes the effects of treating the free electrons consistently with the bound electrons, and the influence of free electron energy and entropy variations are explored. It is found that, relative to a state-of-the-art-model that does not include these effects, the bound free opacity of the oxygen plasmas considered can increase by 10%.

A lattice Boltzmann (LB) scheme for a level-set equation is proposed to capture interface and is coupled with the LB model for incompressible fluid to simulate immiscible two-phase flows. The reinitialization of a level-set field is achieved directly by adding a source term to LB equation, which avoids solving an additional partial differential equation as required in traditional level-set methods. Compared to the classical phase-field lattice Boltzmann method, the proposed approach demonstrates significantly reduced errors in solving interface motion and deformation. Furthermore, GPU parallel computation is implemented for the level-set lattice Boltzmann method (LS-LBM) to enhance computational efficiency. To validate the LS-LBM, it is employed to simulate four benchmark problems: static droplet, layered Poiseuille flow, rising bubble, and Rayleigh-Taylor instability. Numerical results show that LS-LBM exhibits good stability, accuracy and high efficiency, demonstrating its feasibility for accurate simulations of immiscible two-phase flows, even with large density ratios or high Reynolds numbers.

In phase-separated active fluids, the Ostwald process can go into reverse, leading to either microphase separation or bubbly phase separation. We show that the latter is formed of two macroscopic regions that are occupied by the homogeneous fluid and by the microphase separated one. Within the microphase-separated fluid, the relative rate of the Ostwald process, coalescence, and nucleation determines whether the size distribution of mesoscopic domains is narrowly peaked or displays a broad range of sizes before attaining a cutoff independent of system size. Our results are obtained via large-scale simulations of a minimal field theory for active phase separation and reproduced by an effective model in which the degrees of freedom are the locations and sizes of the microphase-separated domains.

We investigate the onset of quantum thermalization in a system governed by the Jahn-Teller Hamiltonian, which describes the interaction between a single spin and two bosonic modes. We find that the Jahn-Teller model exhibits a finite-size quantum phase transition between the normal phase and two types of super-radiant phase when the ratios of spin-level splitting to each of the two bosonic frequencies grow to infinity. We test the prediction of the eigenstate thermalization hypothesis in the Jahn-Teller model. We show that the expectation value of the spin observable quickly approaches its long-time average value. We find that the distance between the diagonal ensemble average and the microcanonical ensemble average of the spin observable decreases with the effective thermodynamic parameter. Furthermore, we show that the mean time fluctuations of the spin observable are small and are inversely proportional to the effective system dimension.

We introduce an aggregation process that begins with equal concentrations of positively and negatively “charged” monomers. Oppositely charged monomers merge to form neutral dimers. These dimers are the seeds for subsequent aggregation events in which neutral clusters of necessarily even mass join irreversibly to form neutral aggregates of ever-increasing size. In the mean-field approximation with mass independent reaction rates, we solve for the reaction kinetics and show that the concentration of clusters of mass $k, c_k\left(t\right)$, asymptotically scales as $A_k/t$, with $A_k$ having a nontrivial dependence on $k$. We also investigate the phenomenon of gelation in charged aggregation when the reaction rate equals the product of the two incident cluster masses. Finally, we generalize our model to the case of three and more types of monomers.

The image charge (IC) effect is a fundamental problem in electrostatics. However, proper treatment at the continuum level for many-ion systems, such as electrolyte solutions or ionic liquids, remains an open theoretical question. Here, we demonstrate and systematically compare the IC effects under metal and dielectric boundary conditions (BCs), based on a renormalized Gaussian-fluctuation theory. Our calculations for a simple 1:1 symmetric electrolyte in the point-charge approximation show that the double-layer structure, capacitance, and interaction forces between like-charged plates depend strongly on the types of boundaries, even in the weak-coupling regime. Like-charge attraction is predicted for both metal and dielectric BCs. Finally, we comment on the effects of a dielectrically saturated solvent layer on the metal surface. We provide these results to serve as a baseline for comparison with more realistic molecular dynamics simulations and experiments.

This paper reports a phase transition in coupled three-dimensional limit-cycle oscillators with an adaptive coupling. We reveal that the multiple-cluster rhythmic states emerge when natural frequencies of oscillators follow uniform distribution (case I), but disappear for Gaussian distribution (case II). Furthermore, as the coupling strength $K$ increases, two first-order phase transitions occur sequentially. When $K\to 0^{+}$, an inevitable and nonhysteretic discontinuous phase transition occurs. For $K>0$, another discontinuous phase transition with a hysteresis loop emerges, and its occurrence depends on the width of the natural frequency distribution. From the microscopic perspective of the system, there are double switches between suppression and revival of oscillations as $K$ varies in case I, but only one switch occurs in case II. Theoretical analyses of the incoherent states and the fixed points are given, which can be accurately verified by numerical simulations. This paper provides insights into our understanding of high-dimensional oscillators and their variants.

We obtained the full set of multiparameter vector beating soliton solutions for Manakov equations in both focusing and defocusing cases. Based on exact solutions, physical spectra of beating solitons are calculated analytically. It is found that the spectra of moving beating solitons are asymmetric relative to the sign change of the frequency. In contrast, the static beating solitons have symmetric spectra. We also study the second-order vector beating soliton solutions with either equal or unequal velocities. Numerical simulations confirmed the validity of our exact solutions.

A system is called antifragile when damage acts as a constructive element improving the performance of a global function. In this paper, we analyze the emergence of antifragility in the movement of random walkers on networks with modular structures or communities. The random walker hops considering the capacity of transport of each link, whereas the links are susceptible to random damage that accumulates over time. We show that in networks with communities and high modularity, the localization of damage in specific groups of nodes leads to a global antifragile response of the system improving the capacity of stochastic transport to more easily reach the nodes of a network. Our findings give evidence of the mechanisms behind antifragile response in complex systems and pave the way for their quantitative exploration in different fields.

We present a numerical study of multicommodity transport in a noisy, nonlinear network. The nonlinearity determines the dynamics of the edge capacities, which can be amplified or suppressed depending on the local current flowing across an edge. We consider network self-organization for three different nonlinear functions: For all three we identify parameter regimes where noise leads to self-organization into more robust topologies, that are not found by the sole noiseless dynamics. Moreover, the interplay between noise and specific functional behavior of the nonlinearity gives rise to different features, such as (i) continuous or discontinuous responses to the demand strength and (ii) either single or multistable solutions. Our study shows the crucial role of the activation function on noise-assisted phenomena.

Mutations provide variation for evolution to emerge. A quantitative analysis of how mutations arising in single individuals expand and possibly fixate in a population is essential for studying evolutionary processes. While it is intuitive to expect that a continuous influx of mutations will lead to a continuous flow of mutations fixating in a stable constant population, joint fixation of multiple mutations occur frequently in stochastic simulations even under neutral selection. We quantitatively measure and analyze the distribution of joint fixation events of neutral mutations in constant populations and discussed the connection with previous results. We propose a new concept, the mutation “waves,” where multiple mutations reach given frequencies simultaneously. We show that all but the lowest frequencies of the variant allele frequency distribution are dominated by single mutation “waves,” which approximately follow an exponential distribution in terms of size. Consequently, large swaths of empty frequencies are observed in the variant allele frequency distributions, with a few frequencies having numbers of mutations far in excess of the expected average values over multiple realizations. We quantify the amount of time each frequency is empty of mutations and further show that the discrete mutation waves average out to a continuous distribution named as the wave frequency distribution, the shape of which is predictable based on few model parameters.

We study the electrostatic energy of binary ionic mixtures (BIMs) in the form of Coulomb crystals with the main focus on ordered crystals. We consider 15 different binary bcc-like lattices, accurately calculate their electrostatic energies, and approximate them by a unified equation. These results extend those available in the literature. A detailed comparison with selected previous results is made, particularly, using previous calculations in the linear mixing rule approximation. The case of disordered BIMs is also outlined. The results are expected to be useful for exploring multicomponent Coulomb systems in compact stars, laboratory plasmas, and technological applications.

Coupled optical cavities provide one of the simplest possible schemes to engineer the interaction of bosonic modes. This paper investigates a two-mode model where, in addition to the usual mode coupling, the presence of an amplification term associated to one of the modes triggers an unexpectedly rich dynamical scenario. The resulting nontrivial model is diagonalized by implementing the dynamical-algebra method, a group-theoretic approach which allows one to determine the stability diagram of the model Hamiltonian in terms of the two mode frequencies for given values of the interaction and amplification parameters. The mode interaction significantly modifies the simple amplification effect of the noninteracting model causing the separation of the unstable domain (where the amplification takes place) into two subdomains, one of which is stable, features no amplification effect, and exhibits an extension controlled by the interaction parameter. The analysis of stability properties is corroborated by the fully analytic study of the energy spectrum which exhibits the transition from a discrete to a continuous structure whenever the system undergoes the transition from a stable region to an unstable region where the amplification effect occurs. This scenario is further confirmed by the calculation of the time evolution of the mode populations.

Finding the source of an epidemic is important, because correct source identification can help to stop a budding epidemic or prevent new ones. We investigate the backward equations of the $N$-intertwined mean-field approximation susceptible-infectious-susceptible (SIS) process. The backward equations allow us to trace the epidemic back to its source on networks of sizes up to at least $N=1500$. Additionally, we show that the source of the “more realistic” Markovian SIS model cannot feasibly be found, even in a “best-case scenario,” where the infinitesimal generator $Q$, which completely describes the epidemic process and the underlying contact network, is known. The Markovian initial condition $s\left(0\right)$, which reveals the epidemic source, can be found analytically when the viral state vector $s\left(t\right)$ is known at some time $t$ as $s\left(0\right)=s\left(t\right)e^{-Qt}$. However, $s\left(0\right)$ can hardly be computed, except for small times $t$. The numerical errors are largely due to the matrix exponential $e^{-Qt}$, which is severely ill-behaved.

We consider an active, stochastic microscopic model of particles suspended in a fluid and show that the coarse-grained description of this model renders odd viscoelasticity. The particles are odd dumbbells, each featuring a robotic device as the bead, which exhibits a particular torque response. We show that this model can be macroscopically treated as a viscoelastic fluid, analytically calculate the coefficients of the corresponding viscoelastic model, and corroborate the results using molecular dynamics simulations. This study provides a unified analytical framework for several experimental and numerical setups designed to elucidate odd effects in fluids.