It is well known that wave collapses can emerge from the focusing one-dimensional (1D) Majda-McLaughlin-Tabak (MMT) model as a result of modulational instability. However, how these wave collapses affect the spectral properties and statistics of the wave field has not been adequately studied. We undertake this task by simulating the forced-dissipated 1D MMT model over a range of forcing amplitudes. Our results show that when the forcing is weak, the spectrum agrees well with the prediction by wave turbulence theory with few collapses in the field. As the forcing strength increases, we see an increase in the occurrence of collapses, together with a transition from a power-law spectrum to an exponentially decaying spectrum. Through a spectral decomposition, we find that the exponential spectrum is dominated by the wave collapse component in the nonintegrable MMT model, which is in analogy to a soliton gas in integrable turbulence.

Symmetries are ubiquitous in science, aiding theoretical comprehension by discerning patterns in mathematical models and natural phenomena. This work introduces a method for assessing the extent of symmetry within a time series. We explore both microscopic and macroscopic features extracted from a recurrence plot. By analyzing the statistics of small recurrence matrices, our approach delves into microscale dynamics, facilitating the identification of symmetric time series segments through diagonal macroscale structures on a recurrence plot. We validate our approach by successfully quantifying involution symmetries for three-dimensional dynamical models, specifically, order-2 rotational symmetry in the Lorenz '63 model, and inversion symmetry in the Chua circuit. Our quantifier also detects symmetry breaking in the modified Lorenz model for El Niño phenomenon. The method can be applied in a versatile manner, not only to three-dimensional trajectories but also to univariate time series. Symmetry quantification in time series is promising for enhancing dynamical system modeling and profiling.

We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of the process in an explicit form by introducing integral nonlocal memory term into conditional probability function. We start from an expression for the conditional transition probability function describing additive multistep binary random chain and show that the telegraph processes can be considered as continuous-time interpolations of discrete-time dichotomous random sequences. An equation involving the memory function and the two-point correlation function of the telegraph process is analytically obtained. This integral equation defines the correlation properties of the processes with given memory functions. It also serves as a tool for solving the inverse problem, namely for generation of a telegraph process with a prescribed pair correlation function. We obtain analytically the correlation functions of the telegraph processes with two exactly solvable examples of memory functions and support these results by numerical simulations of the corresponding telegraph processes.

Amorphous solids are viscoelastic. They dissipate energy when deformed at finite rate and finite temperature. We here use analytic theory and molecular simulations to demonstrate that linear viscoelastic dissipation can be directly related to the static and dynamic properties of the fundamental vibrational excitations of an amorphous system. We study ultrastable glasses that do not age, i.e., that remain in stable minima of the potential energy surface at finite temperature. Our simulations show four types of vibrational modes, which differ in spatial localization, similarity to plane waves and vibrational lifetimes. At frequencies below the Boson peak, the viscoelastic response can be split into contributions from plane-wave and quasilocalized modes. We derive a parameter-free expression for the viscoelastic storage and loss moduli for both of these modes. Our results show that the dynamics of microscopic dissipation, in particular the lifetimes of the modes, determine the viscoelastic response only at high frequency. Quasilocalized modes dominate the linear viscoelastic response at intermediate frequencies below the Boson peak.

Based on the mesoscopic scale, the lattice Boltzmann method (LBM) with an enthalpy-based model represented in the form of distribution functions is widely used in the liquid-solid phase transition process of energy storage materials due to its direct and relatively accurate characterization of the presence of latent heat of solidification. However, since the enthalpy distribution function itself contains the physical properties of the material, these properties are transferred along with the enthalpy distribution function during the streaming process. This leads to deviations between the enthalpy-based model when simulating the phase transition process of different materials mixed and the actual process. To address this issue, in this paper, we construct an enthalpy-based model for different types of materials. For multiple materials, various forms of enthalpy distribution functions are employed. This method still uses the form of enthalpy distribution functions for collisions and streaming processes among the same type of substance, while for heat transfer between different materials, it avoids the direct transfer of enthalpy distribution functions and instead applies a source term to the enthalpy distribution functions, characterizing the heat transfer between different materials through the energy change before and after mixing based on the temperature. To verify the accuracy of the method proposed in this paper, a detailed solidification model for two different materials is constructed using the example of water droplets solidifying in air, and the results are compared with experimental outcomes. The results of the simulation show that the model constructed in this paper is largely in line with the actual process.

Fractional heterogeneous telegraph processes are considered in the framework of telegrapher's equations accompanied by memory effects. The integral decomposition method is developed for the rigorous treating of the problem. Exact solutions for the probability density functions and the mean squared displacements are obtained. A relation between the fractional heterogeneous telegrapher's equation and the corresponding Langevin equation has been established in the framework of the developed subordination approach. The telegraph process in the presence of stochastic resetting has been studied, as well. An exact expression for both the nonequilibrium stationary distributions/states and the mean squared displacements are obtained.

The Domany-Kinzel (DK) model encompasses several types of nonequilibrium phase transitions, depending on the selected parameters. We apply supervised, semisupervised, and unsupervised learning methods to studying the phase transitions and critical behaviors of the $(1+1)$-dimensional DK model. The supervised and the semisupervised learning methods permit the estimations of the critical points, the spatial and temporal correlation exponents, concerning labeled and unlabeled DK configurations, respectively. Furthermore, we also predict the critical points by employing principal component analysis and autoencoder. The PCA and autoencoder can produce results in good agreement with simulated stationary particle number density.

We introduce an autocatalytic aggregation model in which the rate at which two clusters merge is controlled by the third “catalytic” cluster, whose mass must equal the mass of one of the reaction partners. The catalyst is unaffected by the joining event and can participate in or catalyze subsequent reactions. This model is meant to mimic the self-replicating reactions that occur in models for the origin of life. We solve the kinetics of catalytic coagulation for the case of mass-independent reaction rates and show that the total cluster density decays as $t^{-1/3}$, while the density of clusters of fixed mass decays as $t^{-2/3}$. These behaviors contrast with the corresponding $t^{-1}$ and $t^{-2}$ scalings for classic aggregation. We extend our model to mass-dependent reaction rates, to situations where only “magic” mass clusters can catalyze reactions, and to include steady monomer input.

We study numerically a family of surface growth models that are known to be in the universality class of the Kardar-Parisi-Zhang equation when driven by uncorrelated noise. We find that, in the presence of noise with power-law temporal correlations with exponent $\theta$, these models exhibit critical exponents that differ both quantitatively and qualitatively from model to model. The existence of a threshold value for $\theta$ below which the uncorrelated fixed point is dominant occurs for some models but not for others. In some models the dynamic exponent $z\left(\theta \right)$ is a smooth decreasing function, while it has a maximum in other cases. Despite all models sharing the same symmetries, critical exponents turn out to be strongly model dependent. Our results clearly show the fragility of the universality class concept in the presence of long-range temporally correlated noise.

We study the synergy between disorder (phenomenologically modeled by the introduction of Riesz fractional derivative in the corresponding Schrödinger equation) and spin-orbit coupling (SOC) on the exciton spectra in two-dimensional (2D) semiconductor structures. We demonstrate that the joint impact of “fractionality” and SOC considerably modifies the spectrum of corresponding “ordinary” (i.e., without fractional derivatives) hydrogenic problem, leading to the non-Poissonian statistics of the adjacent level distance distribution. The latter fact is strong evidence of the possible emergence of quantum chaotic features in the system. Using analytical and numerical arguments, we discuss the possibilities to control the above chaotic features using the synergy of SOC, Coulomb interaction, and “fractionality,” characterized by the Lévy index $\mu$.

In this study, we simulate breath figures that are evolving two-dimensional assemblies of droplets on a substrate. We focus on the Voronoi/Shannon entropy of these figures, which quantifies the order related to the coordination number of droplets. We show that the Voronoi entropy of the complete breath figure pattern converges to a value that is the one of a randomly distributed point system. Conversely, the subset containing exclusively large droplets of the breath figure exhibits significantly lower entropy than that obtained for all droplets. Using molecular dynamics simulations, we show that coalescence events in breath figures induce the same Voronoi entropy as that caused by repulsive interactions in a bidimensional atomic system.

Consciousness within the brain hinges on the synchronized activities of millions of neurons, but the mechanism responsible for orchestrating such synchronization remains elusive. In this study we employ cavity quantum electrodynamics to explore entangled biphoton generation through cascade emission in the vibration spectrum of C-H bonds within the lipid molecules' tails. The results indicate that the cylindrical cavity formed by a myelin sheath can facilitate spontaneous photon emission from the vibrational modes and generate a significant number of entangled photon pairs. The abundance of C-H bond vibration units in neurons can therefore serve as a source of quantum entanglement resources for the nervous system. These findings may offer insight into the brain's ability to leverage these resources for quantum information transfer, thereby elucidating a potential source for the synchronized activity of neurons.

Amber is a unique example of a fragile glass that has been extensively aged below its glass transition temperature, thus reaching a state that is not accessible under normal experimental conditions. We studied the medium-range order of Baltic amber by x-ray diffraction (XRD) at high pressures. The pressure dependences of the low-angle XRD intensity between 0 and 5 ${\mathrm{\AA }}^{-1}$ were measured from 0 to 7.3 GPa by the energy-dispersive XRD. The first diffraction peak at 1.1 ${\mathrm{\AA }}^{-1}$ and ambient pressure has a doublet structure consisting of the first sharp diffraction peak (FSDP) at 1.05 ${\mathrm{\AA }}^{-1}$ and the second feature at 1.40 ${\mathrm{\AA }}^{-1}$. The peak position and the width of the FSDP increase as the pressure increases, while the intensity of the FSDP decreases. Below $P_0=2.4$ GPa, the rapid increase of the FSDP peak position was observed, while above $P_0$, the gradual increase was observed. Below $P_0$, voids and holes in a relatively low-density state are suppressed, whereas above $P_0$, the suppression becomes mild. Such a change suggests the crossover from the low- to high-density state at $P_0$. There is a close correlation between the pressure dependence of XRD and previously reported sound velocity results. The correlation between the mean-square fluctuation of the shear modulus on the nanometer scale and fragility in amber and other glass formers is also discussed.

This study investigates the (longitudinal) thermodynamic and structural characteristics of single-file confined square-well and square-shoulder disks by employing a mapping technique that transforms the original system into a one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard statistical-mechanical techniques, exact results are derived for key properties, including the equation of state, internal energy, radial distribution function, and structure factor. The asymptotic behavior of the radial distribution function is explored, revealing structural changes in the spatial correlations. Additionally, exact analytical expressions for the second virial coefficient are presented. The theoretical results for the thermodynamic and structural properties are validated by our Monte Carlo simulations.

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equations for the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., $f\left(v_y\right)$ or $f\left(v_{\perp }\right)$. The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. The quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counterexamples, as in leukocyte coordination (where signaling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signaling. Our method is able to infer the strength of couplings and fields, but also the time required by the couplings to completely transfer information among the units. We demonstrate the validity of our approach providing excellent results on synthetic datasets of non-Markovian trajectories generated by the Heisenberg-Kuramoto and Vicsek models equipped with delayed interactions. As a proof of concept, we also apply the method to experiments on dendritic migration, where matching equal-time correlations results in a significant information loss.

An important working hypothesis to investigate brain activity is whether it operates in a critical regime. Recently, maximum-entropy phenomenological models have emerged as an alternative way of identifying critical behavior in neuronal data sets. In the present paper, we investigate the signatures of criticality from a firing rate-based maximum-entropy approach on data sets generated by computational models, and we compare them to experimental results. We found that the maximum entropy approach consistently identifies critical behavior around the phase transition in models and rules out criticality in models without phase transition. The maximum-entropy-model results are compatible with results for cortical data from urethane-anesthetized rats data, providing further support for criticality in the brain.

We study the dynamics of a classical circuit corresponding to a discrete-time version of the kinetically constrained East model. We show that this classical “Floquet-East” model displays pre-transition behavior which is a dynamical equivalent of the hydrophobic effect in water. For the deterministic version of the model, we prove exactly (i) a change in scaling with size in the probability of inactive space-time regions (akin to the “energy-entropy” crossover of the solvation free energy in water), (ii) a first-order phase transition in the dynamical large deviations, (iii) the existence of the optimal geometry for local phase separation to accommodate space-time solutes, and (iv) a dynamical analog of “hydrophobic collapse.”

Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities $p<1$ of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on $p$ and with diffusion exponents that depend on the dimensions of matrix $\left(E\right)$ and fractal $\left(D_F\right)$ as $\nu =1/(2+D_F-E)$. This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for $p\lesssim {10}^{-3}$ and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.

In this Letter, the single-element Maxwell model is generalized with respect to the wave vector and extended with a correction function that measures the reduced viscous response. This model has only two free parameters and avoids the attenuation-frequency locking present in the original model. Through molecular simulations it is shown that the model satisfactory predicts the transverse dynamics of the binary Lennard-Jones system at different temperatures, as well as water and toluene at ambient conditions. The correction function shows that the viscous response is significantly reduced compared to the predictions of the original Maxwell model and that there exists a characteristic length scale of minimum dissipation.