Prevailing view asserts that the disproportionately greater productivities of larger cities, or superlinear urban scaling, are the result of human interactions channeled by urban networks. But this view was established by considering the spatial organization of urban infrastructure and social networks—the urban “arteries” effects—but neglecting the functional organization of urban production and consumption entities—the urban “organs” effects. Here, adopting a metabolic view and using water consumption as a proxy for metabolism, we empirically quantify the scaling of entity number, size, and metabolic rate for the functionally specific urban residential, commercial, public or institutional, and industrial sectors. Sectoral urban metabolic scaling is highlighted by a disproportionate coordination between residential and enterprise metabolic rates, attributable to the functional mechanisms of mutualism, specialization, and entity size effect. The resultant whole-city metabolic scaling exhibits a constant superlinear exponent for water-abundant regions in numerical agreement with superlinear urban productivity, with varying exponent deviations for water-deficient regions explainable as adaptations to climate-driven resource constraints. These results present a functional organizational, non-social-network explanation of superlinear urban scaling.

The COVID-19 pandemic has evolved over time through multiple spatial and temporal dynamics. The varying extent of interactions among different geographical areas can result in a complex pattern of spreading so that influences between these areas can be hard to discern. Here, we use cross-correlation analysis to detect synchronous evolution and potential interinfluences in the time evolution of new COVID-19 cases at the county level in the United States. Our analysis identified two main time periods with distinguishable features in the behavior of correlations. In the first phase, there were few strong correlations that only emerged between urban areas. In the second phase of the epidemic, strong correlations became widespread and there was a clear directionality of influence from urban-to-rural areas. In general, the effect of distance between two counties was much weaker than that of the counties’ population. Such analysis can provide possible clues on the evolution of the disease and may identify parts of the country where intervention may be more efficient in limiting the disease spread.

Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest-neighbor interactions, connected in a loop and with rotational symmetry, so each oscillator resembles every other oscillator in the chain. Numerical integrations of the discrete phase oscillator systems and a continuum approximation show that directional models (those that do not obey reversal symmetry), can exhibit instability to short wavelength perturbations but only in regions where the slope in phase has a particular sign. This causes short wavelength perturbations to develop that can vary the winding number that describes the sum of phase differences across the loop and the resulting metachronal wave speed. Numerical integrations of stochastic directional phase oscillator models show that even a weak level of noise can seed instabilities that resolve into metachronal wave states.

Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle ${\theta }_Y$. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with $0<{\theta }_Y<\pi /2$, complete wetting is possible below a critical applied tension due to the deformation of the sheet in contrast with rigid substrates requiring ${\theta }_Y=0$. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid, and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and “vesicle” solution are found. For moderately small bending stiffnesses, partial wetting can coexist with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, ${\lambda }_{\text{BC}}$, and find that the shape of the drop is determined by the ratio $A/{\lambda }_{\text{BC}}^2$, where $A$ is the area of the drop.

We study two-dimensional incompressible inertial flows through porous media. At core (small) scale, we prove that the constitutive, nonlinear model can be rewritten into a linear one by means of a new parameter $K^{★}$ which encompasses all the inertial effects. In natural (large-scale) formations, $K^{★}$ is erratically changing, and we analytically compute its counterpart, which is coined generalized effective conductivity, by the self-consistent approach (SCA). In spite of its approximate nature, the SCA leads to simple results that are in good agreement with Monte Carlo simulations.

An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a good agreement with existing analytical expressions in the metallic regime and with heuristic relations widely used in studies of the PBRM model in the presence of orthogonal and unitary symmetries. Moreover, our results confirm that the multifractal behavior of disordered systems at criticality can be probed by measuring scattering and transport properties, which is of paramount importance from the experimental point of view. Thus, a full picture of the scattering and transport properties of the PBRM model at criticality corresponding to the three classical Wigner-Dyson ensembles is provided.

Recently, a maximal-valence model has been proposed to model a liquid-liquid phase transition induced by polymerization in sulfur. In this paper we present a simple generic model to describe liquid polyamorphism in single-component fluids using a maximum-valence approach for any arbitrary coordination number. The model contains three types of interactions: (i) atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) additional repulsive forces between atoms with maximal valence and atoms with any valence. This additional repulsion generates liquid-liquid phase separation and the region of the negative heat expansion coefficient (density anomaly) on a $P-T$ phase diagram. We show the existence of liquid-liquid phase transitions for dimerization, polymerization, gelation, and network formation for corresponding coordination numbers $z=1,2,...,6$ and discuss the limits of this generic model for producing fluid polyamorphism.

In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work we show that lean blowout (LBO) in a turbulent thermoacoustic system is accompanied by a power law leading to finite-time singularity. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of the dominant mode of low-frequency oscillations $\left(A_f\right)$ existing in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that $A_f$ shows a faster-than-exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of $A_f$ based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowouts can be predicted even several seconds earlier. The predicted time of LBO is in good agreement with the actual time of occurrence of LBO obtained from the experiment.

The dynamics of chaos in quantum systems has attracted much interest in connection with the fundamental aspects of quantum mechanics. We study the chaotic dynamics of both the excitonic mode and the cavity mode in a microcavity containing a quantum well driven by an external field. We investigate how the chaotic dynamics is influenced by the frequencies of the exciton and the cavity, the coupling constant between the exciton and cavity, the Coulomb interaction between excitons, and the response of the exciton to the cavity and the external field. We show that chaos can be generated synchronously in both the cavity and the excitonic mode by choosing appropriate parameters. Moreover, this kind of chaos can be controlled by the coupling constant, the strength of the interaction between excitons, the external field, the response of the excitons to the cavity, and the detuning between the cavity field and the excitonic field. The present study may have applications in chaos-based neural networks and extreme event statistics.

We consider large networks of globally coupled spiking neurons and derive an exact low-dimensional description of their collective dynamics in the thermodynamic limit. Individual neurons are described by the Ermentrout-Kopell canonical model that can be excitable or tonically spiking and interact with other neurons via pulses. Utilizing the equivalence of the quadratic integrate-and-fire and the theta-neuron formulations, we first derive the dynamical equations in terms of the Kuramoto-Daido order parameters (Fourier modes of the phase distribution) and relate them to two biophysically relevant macroscopic observables, the firing rate and the mean voltage. For neurons driven by Cauchy white noise or for Cauchy-Lorentz distributed input currents, we adapt the results by Cestnik and Pikovsky [Chaos 32, 113126 (2022)] and show that for arbitrary initial conditions the collective dynamics reduces to six dimensions. We also prove that in this case the dynamics asymptotically converges to a two-dimensional invariant manifold first discovered by Ott and Antonsen. For identical, noise-free neurons, the dynamics reduces to three dimensions, becoming equivalent to the Watanabe-Strogatz description. We illustrate the exact six-dimensional dynamics outside the invariant manifold by calculating nontrivial basins of different asymptotic regimes in a bistable situation.

Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce complex hypergraphs (chygraphs), bringing together concepts from hypergraphs, multilayer networks, simplicial complexes, and hyperstructures. To illustrate the applicability of this combinatorial structure I calculate the component sizes statistics and identify the transition to a giant component. To this end I introduce a vectorization technique that tackles the multilevel nature of chygraphs. I conclude that chygraphs are a unifying representation of complex systems allowing for analytical insight.

The local navigation of pedestrians is assumed to involve no anticipation beyond the most imminent collisions, in most models. These typically fail to reproduce some key features experimentally evidenced in dense crowds crossed by an intruder, namely, transverse displacements toward regions of higher density due to the anticipation of the intruder's crossing. We introduce a minimal model based on mean-field games, emulating agents planning out a global strategy that minimizes their overall discomfort. By solving the problem in the permanent regime thanks to an elegant analogy with the nonlinear Schrödinger's equation, we are able to identify the two main variables governing the model's behavior and to exhaustively investigate its phase diagram. We find that, compared to some prominent microscopic approaches, the model is remarkably successful in replicating the experimental observations associated with the intruder experiment. In addition, the model can capture other daily-life situations such as partial metro boarding.

We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the ground-state wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically exact full configuration-interaction values.

For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat.

We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $\mu$, diffusing in one dimension. The particle starts its motion from $x>0$ and it is subject to stochastic resetting with constant rate $r$. We first unveil the relation between the probability of reaching the target and the mean first-passage time of the corresponding problem in absence of mortality, which allows us to deduce under which conditions the former can be increased by adjusting the restart rate. We then consider the first-passage time conditioned on the event that the particle reaches the target before dying, and provide exact expressions for the mean and the variance as functions of $r$, corroborated by numerical simulations. By studying the impact of resetting for different mortality regimes, we also show that, if the average lifetime ${\tau }_{\mu }=1/\mu$ is long enough with respect to the diffusive time scale ${\tau }_D=x^2/\left(4D\right)$, there exist both a resetting rate $r_{\mu }^{*}$ that maximizes the probability and a rate $r_m$ that minimizes the mean first-passage time. However, the two never coincide for positive $\mu$, making the optimization problem highly nontrivial.

We investigate, by simulations and analytic theory, the sensitivity of nonequilibrium relaxation to interaction potential and dimensionality by using Boltzmann's $H$ function $H\left(t\right)$. We evaluate $H\left(t\right)$ for three different intermolecular potentials in all three dimensions and find that the well-known $H$ theorem is valid and that the $H$ function exhibits rather strong sensitivity to all these factors. The relaxation of $H\left(t\right)$ is long in one dimension, but short in three dimensions, longer for the Lennard-Jones potential than for the hard spheres. The origin of the ultraslow approach to the equilibrium of $H\left(t\right)$ in one-dimensional systems is discussed. Importantly, we obtain a closed-form analytic expression for $H\left(t\right)$ using the solution of the Fokker-Planck equation for velocity space probability distribution and compare its predictions with the simulation results. Interestingly, $H\left(t\right)$ is found to exhibit a linear response when vastly different initial nonequilibrium conditions are employed. The microscopic origin of this linear response is discussed. The oft-quoted relation of $H$ function with Clausius's entropy theorem is discussed.

Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity not only depends on the Hamiltonian but also on the chosen operator, in this work we study the level of generality of this hypothesis by studying how the saturation value varies in the integrability to chaos transition when different operators are expanded. To do this, we work with an Ising chain with a longitudinal-transverse magnetic field and compare the saturation of the Krylov complexity with the standard spectral measure of quantum chaos. Our numerical results show that the usefulness of this quantity as a predictor of the chaoticity is strongly dependent on the chosen operator.