We show that the emergence of systemic risk in complex systems can be understood from the evolution of functional networks representing interactions inferred from fluctuation correlations between macroscopic observables. Specifically, we analyze the long-term collective dynamics in the New York Stock Exchange, the largest financial market in the world, for almost a century and show that periods marked by systemic crisis are associated with emergence of frustration. This is indicated by the loss of structural balance in the networks of interaction between stocks. Moreover, the mesoscopic organization of the networks during these periods exhibits prominent core-periphery organization. This suggests an increased degree of coherence in the collective dynamics of the system, which is reinforced by our observation of the transition to delocalization in the dominant eigenmodes when the systemic risk builds up. While frustration has been associated with phase transitions in physical systems such as spin glasses, its role as a signal for systemic risk buildup leading to severe crisis as shown here provides a novel perspective into the dynamical processes leading to catastrophic failures in complex systems.

The phenomenon of phase synchronization of oscillatory systems, arising out of feedback coupling is ubiquitous across physics and biology. In noisy, complex systems, one generally observes transient epochs of synchronization followed by nonsynchronous dynamics. How does one guarantee that the observed transient epochs of synchronization are arising from an underlying feedback mechanism and not from some peculiar statistical properties of the system? This question is particularly important for complex biological systems, where the search for a nonexistent feedback mechanism may turn out to be an enormous waste of resources. In this article, we propose a null model for synchronization, motivated by expectations on the dynamical behavior of biological systems, to provide a quantitative measure of the confidence with which one can infer the existence of a feedback mechanism based on observation of transient synchronized behavior. We demonstrate the application of our null model to the phenomenon of gait synchronization in free-swimming nematodes, Caenorhabditis elegans.

A subgrid-scale (SGS) model for large-eddy simulation (LES) of compressible isotropic turbulence is constructed by using a data-driven framework. An artificial neural network (ANN) based on local stencil geometry is employed to predict the unclosed SGS terms. The input features are based on the first-order and second-order derivatives of filtered velocity and temperature which appear in the second-order Taylor approximation of the SGS stress and heat flux. It is shown that the proposed ANN-7 model performs better than the gradient model in the a priori test. The correlation coefficient is larger and the relative error is smaller for ANN-7 model as compared to those of the gradient model in the a priori test. In an a posteriori analysis, the performance of ANN-7 model shows advantage over the dynamic Smagorinsky model and dynamic mixed model in the prediction of spectra and structure functions of velocity and temperature, and instantaneous flow structures. Artificial neural network is a promising tool for understanding the physical fundamentals of SGS unclosed terms with further improvement.

It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some exponent $h<1$ (i.e., not necessarily differentiable) at small scales. Different methods have already been proposed to explore the regularity properties of the velocity field and the estimate of its Hölder exponent $h$. A first method is to detect potential singularities via extrema of an “inertial” dissipation $D*={lim}_{\ell \to 0}{D}_{\ell }^I$ that is independent of viscosity [Duchon and Robert, Nonlinearity 13, 249 (2000)]. Another possibility is to use the concept of multifractal analysis that provides fractal dimensions of the subspace of exponents $h$. However, the multifractal analysis is a global statistical method that only provides global information about local Hölder exponents, via their probability of occurrence. In order to explore the local regularity properties of a velocity field, we have developed a local statistical analysis that estimates locally the Hölder continuity. We have compared outcomes of our analysis with results using the inertial energy dissipation $D_{\ell }^I$. We observe that the dissipation term indeed gets bigger for velocity fields that are less regular according to our estimates. The exact spatial distribution of the local Hölder exponents however shows nontrivial behavior and does not exactly match the distribution of the inertial dissipation.

Transport properties of high-energy-density plasmas are influenced by the ion collision rate. Traditionally, this rate involves the Coulomb logarithm, $ln\mathrm{\Lambda }$. Typical values of $ln\mathrm{\Lambda }$ are $\approx 10–20$ in kinetic theories where transport properties are dominated by weak-scattering events caused by long-range forces. The validity of these theories breaks down for strongly coupled plasmas, when $ln\mathrm{\Lambda }$ is of order one. We present measurements and simulations of collision data in strongly coupled plasmas when $ln\mathrm{\Lambda }$ is small. Experiments are carried out in the first dual-species ultracold neutral plasma (UNP), using ${\mathrm{Ca}}^{+}$ and ${\mathrm{Yb}}^{+}$ ions. We find strong collisional coupling between the different ion species in the bulk of the plasma. We simulate the plasma using a two-species fluid code that includes Coulomb logarithms derived from either a screened Coulomb potential or a the potential of mean force. We find generally good agreement between the experimental measurements and the simulations. With some improvements, the mixed ${\mathrm{Ca}}^{+}$ and ${\mathrm{Yb}}^{+}$ dual-species UNP will be a promising platform for testing theoretical expressions for $ln\mathrm{\Lambda }$ and collision cross-sections from kinetic theories through measurements of energy relaxation, stopping power, two-stream instabilities, and the evolution of sculpted distribution functions in an idealized environment in which the initial temperatures, densities, and charge states are accurately known.

The fidelity susceptibility measures the sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here, we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system sizes. The results are verified by a comparison with numerical data.

Renewable generators perturb the electric power grid with heavily non-Gaussian and time correlated fluctuations. While changes in generated power on timescales of minutes and hours are compensated by frequency control measures, we report subsecond distribution grid frequency measurements with local non-Gaussian fluctuations which depend on the magnitude of wind power generation in the grid. Motivated by such experimental findings, we simulate the subsecond grid frequency dynamics by perturbing the power grid, as modeled by a network of phase coupled nonlinear oscillators, with synthetically generated wind power feed-in time series. We derive a linear response theory and obtain analytical results for the variance of frequency increment distributions. We find that the variance of short-term fluctuations decays, for large inertia, exponentially with distance to the feed-in node, in agreement with numerical results both for a linear chain of nodes and the German transmission grid topology. In sharp contrast, the kurtosis of frequency increments is numerically found to decay only slowly, not exponentially, in both systems, indicating that the non-Gaussian shape of frequency fluctuations persists over long ranges.

Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity, various material parameters, and the preparation protocol. In spite of numerous studies of granular flows a predictive theory of the amount of dilation is still lacking. Here, we offer a scaling theory that is focused on such a prediction as a function of shear rate and the dissipative parameters of the granular assembly. The resulting scaling laws are universal with respect to changing the interparticle force laws.

We consider the stochastic dynamics of a system linearly coupled to a hierarchical thermal bath with two well-separated inherent timescales: one slow, and one fast. The slow part of the bath is modeled as a set of harmonic oscillators and taken into account explicitly, while the effects of the fast part of the bath are simulated by dissipative and stochastic Langevin forces, uncorrelated in space and time, acting on oscillators of the slow part of the bath. We demonstrate for this model the robust emergence of a fractional Langevin equation with a power-law decaying memory kernel. The conditions of such an emergence and the specific value of the fractional exponent depend only on the asymptotic low-frequency spectral properties of the slow part of the bath.

We present an analytical derivation of the transport coefficients of a relativistic gas in $(2+1)$ dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the $(3+1)$-dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.

We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period $L$. FPT statistics are crucially affected by the disorder realization. In the large-$L$ limit, we obtain exact formulas for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulas are still useful for nonperiodic heterogeneous environments; i.e., the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.

We investigate the relationship between a diffusive motion of an interface, heat conduction, and the roughening transition in the three-dimensional Ising model. We numerically compute the thermal conductivity and the diffusion constant and find that the diffusion constant shows a crossover in its temperature dependence. The crossover temperature is equal to the roughening transition temperature in equilibrium and deviates from it when heat flows in the system. From these results, we discuss the possibility that heat conduction causes a shift of the roughening transition temperature.

We study the phase diagram of a system of $2\times 2\times 2$ hard cubes on a three-dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size $2\times L\times L$ where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solidlike sublattice-ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size $2\times 2\times L$, where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite-size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the $O\left(3\right)$ universality class perturbed by cubic anisotropy as predicted by the Landau theory.

We view the operator spreading in chaotic evolution as a stochastic process of height growth. The height of an operator represents the size of its support and chaotic evolution increases the height. We consider $N$-spin models with all two-body interactions and embody the height picture in a random model. The exact solution shows that the mean height, being proportional to the squared commutator, grows exponentially within $logN$ scrambling time and saturates in a manner of logistic function. We propose that the temperature dependence of the chaos bound could be due to initial height biased toward high operators, which has a smaller Lyapunov exponent.

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey–like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey–type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.

Many theoretical works have attempted to coarse grain gene expression at the level of transcription and translation via frameworks based on exclusion processes. Usually in these models the three-dimensional conformation of the substrates (DNA and mRNA) is neglected, and particles move on a static unidimensional lattice in contact to an infinite reservoir. In this work we generalize the paradigmatic exclusion process and study the transport of particles along a unidimensional polymerlike flexible lattice immersed in a three-dimensional particle reservoir. We study the recycling of particles in the reservoir, how the transport is influenced by the global conformation of the lattice, and, in turn, how particle density dictates the structure of the polymer.

Determining the microstructure of colloidal suspensions under shear flows has been a challenge for theoretical and computational methods due to the singularly perturbed boundary-layer nature of the problem. Previous approaches have been limited to the case of hard-sphere systems and suffer from various limitations in their applicability. We present an alternative analytic scheme based on intermediate asymptotics which solves the Smoluchowski diffusion-convection equation including both intermolecular and hydrodynamic interactions. The method is able to recover previous results for the hard-sphere fluid and to predict the radial distribution function (rdf) of attractive fluids such as the Lennard-Jones (LJ) fluid. In particular, a new depletion effect is predicted in the rdf of the LJ fluid under shear. This method can be used for the theoretical modeling and understanding of real fluids subjected to flow, with applications ranging from chemical systems to colloids, rheology, plasmas, and atmospherical science.

We report on experiments investigating the dynamics of a slider that is pulled by a spring across a granular medium consisting of a vertical layer of photoelastic disks. The motion proceeds through a sequence of discrete events, analogous to seismic shocks, in which elastic energy stored in the spring is rapidly released. We measure the statistics of several properties of the individual events: the energy loss in the spring, the duration of the movement, and the temporal profile of the slider motion. We also study certain conditional probabilities and the statistics of mainshock-aftershock sequences. At low driving rates, we observe crackling with Omori-Utsu, Båth, and waiting time laws similar to those observed in seismic dynamics. At higher driving rates, where the sequence of events shows strong periodicity, we observe scaling laws and asymmetrical event shapes that are clearly distinguishable from those in the crackling regime.

The two-dimensional lattice Boltzmann method was used to numerically study a sedimentation system with two particles having different densities in a vertical channel for Galileo numbers in the range of $5\le \mathrm{Ga}\le 15$ (resulting in a Reynolds number, based on the settling velocity, approximately ranging between 0.6 and 7). Two types of periodic motion, differing from each other in terms of the size of the limit cycle, the magnitude of the time period, and their changes upon increasing the density difference between particles, are identified depending on whether there is a wake effect. The most prominent features of this system are discontinuous changes in the settling velocity $(6.7\le \mathrm{Ga}<9.7)$ and time period of oscillation $(10.5\le \mathrm{Ga}\le 15)$ at a critical value of the density difference between particles. The first discontinuity results in an abrupt increase in the Reynolds number, associated with a Hopf bifurcation without the presence of vortex shedding. The second discontinuity is accompanied by the disappearance of “abnormal rotation” (referring to the situation in which a particle appears to roll up a wall when settling) of the heavy particle, which directly results from a sharp increase in the amplitude of oscillation induced by the enhanced wake effect at another critical density difference between particles. The wall effects on these discontinuous changes were also examined.