The distributions of trade values and relationships among countries and product categories reflect how countries select their trade partners and design export portfolios. Here we consider the exporter-importer network and the exporter-product network with links weighted by the logarithm of the corresponding export values each year from 1962 to 2018, and study how the weights of the outgoing links from each country are distributed. Such local logarithmic export distributions by destinations and products are found to follow approximately the Gaussian distribution across exporters and time, implying random assignment of export values on a logarithmic scale. However, a nonzero skewness is identified, changing from positive to negative as exporters have more partner importers and more product categories in their portfolios. Seeking the origin, we analyze how local exports depend on the out-degree of the exporter and the in-degrees of destinations or products and formulate their quantitative and measurable relation incorporating randomness, which uncovers the fundamental nature of the export strategies of individual countries.

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming speeds. On the other hand, high fractions of long cells form a bottleneck for efficient swarming. Our results suggest a physical advantage for the spontaneous heterogeneity of bacterial swarm populations.

Asymmetry is omnipresent in human society and nature and the reasons causing asymmetry are multiple. To think about the impact of asymmetries on the cooperation systems, we focus on a typical model of great asymmetric traits—the boxed pigs game—and extended the one-to-one interaction to the interaction in population. We consider the asymmetry of payoff and the spatial structure of the two populations in space. Our results have shown that the almost equal abundance and strength of two populations kills cooperative behavior. The single increase of either strength-asymmetry or abundance-asymmetry promotes cooperation. But high levels of both asymmetries would inhibit cooperative behavior, making the powerful mechanism of cooperation broken.

A colloidal particle is often termed “Janus” when some portion of its surface is coated by a second material which has distinct properties from the native particle. The anisotropy of Janus particles enables unique behavior at interfaces. However, rigorous methodologies to predict Janus particle dynamics at interfaces are required to implement these particles in complex fluid applications. Previous work studying Janus particle dynamics does not consider van der Waals interactions and realistic, nonuniform coating morphology. Here we develop semianalytic equations to accurately calculate the potential landscape, including van der Waals interactions, of a Janus particle with nonuniform coating thickness above a solid boundary. The effects of both nonuniform coating thickness and van der Waals interactions significantly influence the potential landscape of the particle, particularly in high ionic strength solutions, where the particle samples positions very close to the solid boundary. The equations developed herein facilitate more simple, accurate, and less computationally expensive characterization of conservative interactions experienced by a confined Janus particle than previous methods.

In this paper, we develop a theory to calculate the structural relaxation time ${\tau }_{\alpha }$ of fragile supercooled liquids. Using the information of the configurational entropy and structure, we calculate the number of dynamically free, metastable, and stable neighbors around a central particle. In supercooled liquids, the cooperatively reorganizing clusters (CRCs) in which the stable neighbors form “stable” nonchemical bonds with the central particle emerge. For an event of relaxation to take place, these bonds have to reorganize irreversibly; the energy involved in the processes is the effective activation energy of relaxation. The theory brings forth a temperature $T_a$ and a temperature-dependent parameter $\psi \left(T\right)$ which characterize slowing down of dynamics on cooling. It is shown that the value of $\psi \left(T\right)$ is equal to 1 for $T>T_a,$ indicating that the underlying microscopic mechanism of relaxation is dominated by the entropy-driven processes, while for $T<T_a,$ $\psi \left(T\right)$ decreases on cooling, indicating the emergence of the energy-driven processes. This crossover of $\psi \left(T\right)$ from high to low temperatures explains the crossover seen in ${\tau }_{\alpha }$. The dynamics of systems that may have similar static structure but very different dynamics can be understood in terms of $\psi \left(T\right)$. We present results for the Kob-Anderson model for three densities and show that the calculated values of ${\tau }_{\alpha }$ are in excellent agreement with simulation values for all densities. We also show that when $\psi \left(T\right),$ ${\tau }_{\alpha },$ and other quantities are plotted as a function of $T/T_a$ $(\mathrm{or} T_a/T)$, the data collapse on master curves.

Classical plasma are typically of low density and/or high temperature. Two of its basic properties are Landau damping and two-stream instabilities. When increasing the plasma density, quantum effects appear and beam-plasma interactions show behavior different from the classical cases. We revisit Landau damping and two-stream instabilities under conditions when quantum hydrodynamic and quantum kinetic theory can be applied, the latter accounting for wave-particle interactions. We find that the instability growth rate behaves as pure two-stream instability without Landau damping when the countering stream velocity exceeds a certain threshold, which differs from the classical case.

Grand-potential based multiphase-field model is extended to include surface diffusion. Diffusion is elevated in the interface through a scalar degenerate term. In contrast to the classical Cahn-Hilliard-based formulations, the present model circumvents the related difficulties in restricting diffusion solely to the interface by combining two second-order equations, an Allen-Cahn-type equation for the phase field supplemented with an obstacle-type potential and a conservative diffusion equation for the chemical potential or composition evolution. The sharp interface limiting behavior of the model is deduced by means of asymptotic analysis. A combination of surface diffusion and finite attachment kinetics is retrieved as the governing law. Infinite attachment kinetics can be achieved through a minor modification of the model, and with a slight change in the interpretation, the same model handles the cases of pure substances and alloys. Relations between model parameters and physical properties are obtained which allow one to quantitatively interpret simulation results. An extensive study of thermal grooving is conducted to validate the model based on existing theories. The results show good agreement with the theoretical sharp-interface solutions. The obviation of fourth-order derivatives and the usage of the obstacle potential make the model computationally cost-effective.

We numerically investigated the transport of a passive colloidal particle in a one-dimensional periodic array of planar counter-rotating convection rolls at high Péclet numbers. We show that advection-enhanced diffusion is drastically suppressed by an external transverse bias but strongly reinforced by a longitudinal drive of appropriate intensity. Both effects are magnified by imposing free-slip flows at the array's edges. The dependence of the diffusion constant on an external forcing is interpreted as a measure of the fluid-mechanical robustness of the flow boundary layer mechanism governing diffusion in convection rolls.

The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.

We develop a theory for the susceptible-infected-susceptible (SIS) epidemic model on networks that incorporate both network structure and dynamic correlations. This theory can account for the multistage onset of the epidemic phase in scale-free networks. This phenomenon is characterized by multiple peaks in the susceptibility as a function of the infection rate. It can be explained by that, even under the global epidemic threshold, a hub can sustain the epidemics for an extended period. Moreover, our approach improves theoretical calculations of prevalence close to the threshold in heterogeneous networks and also can predict the average risk of infection for neighbors of nodes with different degree and state on uncorrelated static networks.

Population extinction is a serious issue both from the theoretical and practical points of view. We explore here how environmental noise influences persistence and extinction of interacting species in presence of a pathogen even when the populations remain stable in its deterministic counterpart. Multiplicative white noise is introduced in a deterministic predator-prey-parasite system by randomly perturbing three biologically important parameters. It is revealed that the extinction criterion of species may be satisfied in multiple ways, indicating various routes to extinction, and disease eradication may be possible with the right environmental noise. Predator population cannot survive, even when its focal prey strongly persists if its growth rate is lower than some critical value, measured by half of the corresponding noise intensity. It is shown that the average extinction time of population decreases with increasing noise intensity and the probability distribution of the extinction time follows the log-normal density curve. A case study on red grouse (prey) and fox (predator) interaction in presence of the parasites trichostrongylus tenuis of grouse is presented to demonstrate that the model well fits the field data.

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

In hot dense plasmas of intermediate or high-$Z$ elements in the state of local thermodynamic equilibrium, the number of electronic configurations contributing to key macroscopic quantities such as the spectral opacity and equation of state can be enormous. In this work we present systematic methods for the analysis of the number of relativistic electronic configurations in a plasma. While the combinatoric number of configurations can be huge even for mid-$Z$ elements, the number of configurations which have non-negligible population is much lower and depends strongly and nontrivially on temperature and density. We discuss two useful methods for the estimation of the number of populated configurations: (i) using an exact calculation of the total combinatoric number of configurations within superconfigurations in a converged super-transition-array (STA) calculation, and (ii) by using an estimate for the multidimensional width of the probability distribution for electronic population over bound shells, which is binomial if electron exchange and correlation effects are neglected. These methods are analyzed, and the mechanism which leads to the huge number of populated configurations is discussed in detail. Comprehensive average-atom finite-temperature density functional theory (DFT) calculations are performed in a wide range of temperature and density for several low-, mid-, and high-$Z$ plasmas. The effects of temperature and density on the number of populated configurations are discussed and explained.

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically nonchaotic systems [E. B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)]. Here, we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore, our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.

We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties of physical, chemical, and biological systems. The discovery of the Jarzynski equality illumines the way to estimate the equilibrium free-energy difference from the work performed in nonequilibrium driving processes. However, the nonlinear (exponential) relation causes the poor convergence of the Jarzynski equality. Here, we propose a concise method to estimate the free-energy difference through a linear nonequilibrium equality which inherently converges faster than nonlinear nonequilibrium equalities. This linear nonequilibrium equality relies on an accelerated isothermal process which is realized by using a unified variational approach, named variational shortcuts to isothermality. We apply our method to an underdamped Brownian particle moving in a double-well potential. The simulations confirm that the method can be used to accurately estimate the free-energy difference with high efficiency. Especially during fast driving processes with high dissipation, the method can improve the accuracy by more than an order of magnitude compared with the estimator based on the nonlinear nonequilibrium equality.

We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to $32768\times 32768$ spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.

The recent interest into the Brownian gyrator has been confined chiefly to the analysis of Brownian dynamics both in theory and experiment despite the applicability of general cases with definite mass. Considering mass explicitly in the solution of the Fokker–Planck equation and Langevin dynamics simulations, we investigate how inertia can change the dynamics and energetics of the Brownian gyrator. In the Langevin model, the inertia reduces the nonequilibrium effects by diminishing the declination of the probability density function and the mean of a specific angular momentum, $j_{\theta }$, as a measure of rotation. Another unique feature of the Langevin description is that rotation is maximized at a particular anisotropy while the stability of the rotation is minimized at a particular anisotropy or mass. Our results suggest that the Langevin dynamics description of the Brownian gyrator is intrinsically different from that with Brownian dynamics. In addition, $j_{\theta }$ is proven to be essential and convenient for estimating stochastic energetics such as heat currents and entropy production even in the underdamped regime.

Partial information decomposition of the multivariate mutual information describes the distinct ways in which a set of source variables contains information about a target variable. The groundbreaking work of Williams and Beer has shown that this decomposition cannot be determined from classic information theory without making additional assumptions, and several candidate measures have been proposed, often drawing on principles from related fields such as decision theory. None of these measures is differentiable with respect to the underlying probability mass function. We here present a measure that satisfies this property, emerges solely from information-theoretic principles, and has the form of a local mutual information. We show how the measure can be understood from the perspective of exclusions of probability mass, a principle that is foundational to the original definition of mutual information by Fano. Since our measure is well defined for individual realizations of random variables it lends itself, for example, to local learning in artificial neural networks. We also show that it has a meaningful Möbius inversion on a redundancy lattice and obeys a target chain rule. We give an operational interpretation of the measure based on the decisions that an agent should take if given only the shared information.

In this work we study the structure-transport property relationships of small ligand intercalated DNA molecules using a multiscale modeling approach where extensive ab initio calculations are performed on numerous MD-simulated configurations of dsDNA and dsDNA intercalated with two different intercalators, ethidium and daunomycin. DNA conductance is found to increase by one order of magnitude upon drug intercalation due to the local unwinding of the DNA base pairs adjacent to the intercalated sites, which leads to modifications of the density of states in the near-Fermi-energy region of the ligand–DNA complex. Our study suggests that the intercalators can be used to enhance or tune the DNA conductance, which opens new possibilities for their potential applications in nanoelectronics.