The eigenstate thermalization hypothesis (ETH) and the theory of linear response (LRT) are celebrated cornerstones of our understanding of the physics of many-body quantum systems out of equilibrium. While the ETH provides a generic mechanism of thermalization for states arbitrarily far from equilibrium, LRT extends the successful concepts of statistical mechanics to situations close to equilibrium. In our work, we connect these cornerstones to shed light on the route to equilibrium for a class of properly prepared states. We unveil that, if the off-diagonal part of the ETH applies, then the relaxation process can become independent of whether or not a state is close to equilibrium. Moreover, in this case, the dynamics is generated by a single correlation function, i.e., the relaxation function in the context of LRT. Our analytical arguments are illustrated by numerical results for idealized models of random-matrix type and more realistic models of interacting spins on a lattice. Remarkably, our arguments also apply to integrable quantum systems where the diagonal part of the ETH may break down.

Social networks are the prime channel for the spreading of computer viruses. Yet the study of their propagation neglects the temporal nature of social interactions and the heterogeneity of users' susceptibility. Here, we introduce a theoretical framework that captures both properties. We study two realistic types of viruses propagating on temporal networks featuring $Q$ categories of susceptibility and derive analytically the invasion threshold. We found that the temporal coupling of categories might increase the fragility of the system to cyber threats. Our results show that networks' dynamics and their interplay with users' features are crucial for the spreading of computer viruses.

We derive, with the projection operator technique, the equations of motion for the time-dependent average of the discrete mass and momentum densities of a fluid confined by planar walls under the assumption that the flow field is translationally invariant along the directions tangent to the walls. Shear flow and sound propagation perpendicular to the walls can be described with the discrete hydrodynamic equations. The interaction with the walls is not given through boundary conditions but rather in terms of impenetrability and friction forces appearing in the discrete hydrodynamic equations. Microscopic expressions for the transport coefficients entering the discrete equations are provided. We further show that the obtained discrete equations can be interpreted as a Petrov-Galerkin finite-element discretization of the continuum equations presented by Camargo et al. [J. Chem. Phys. 148, 064107 (2018)] when restricted to planar geometries and flows.

We present doubly periodic solutions of the infinitely extended nonlinear Schrödinger equation with an arbitrary number of higher-order terms and corresponding free real parameters. Solutions have one additional free variable parameter that allows one to vary periods along the two axes. The presence of infinitely many free parameters provides many possibilities in applying the solutions to nonlinear wave evolution. Being general, this solution admits several particular cases which are also given in this article.

We investigate a six-species class of May-Leonard models leading to the formation of two types of competing spatial domains, each one inhabited by three species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting population dynamics using stochastic numerical simulations in two-dimensional space. We find that as three-species domains shrink, there is an increasing probability of extinction of two of the species inhabiting the domain, with the consequent creation of one-species domains. We determine the critical initial radius beyond which these one-species spatial domains are expected to expand. We further show that a transient scaling regime, with a slower average growth rate of the characteristic length scale $L$ of the spatial domains with time $t$, takes place before the transition to a standard $L\propto t^{1/2}$ scaling law, resulting in an extended period of coexistence.

Controlling and suppressing bacterial accumulation at solid surfaces is essential for preventing biofilm formation and biofouling. Whereas various chemical surface treatments are known to reduce cell accumulation and attachment, the role of complex surface geometries remains less well understood. Here, we report experiments and simulations that explore the effects of locally varying boundary curvature on the scattering and accumulation dynamics of swimming Escherichia coli bacteria in quasi-two-dimensional microfluidic channels. Our experimental and numerical results show that a concave periodic boundary geometry can decrease the average cell concentration at the boundary by more than 50% relative to a flat surface.

Differential excitatory and inhibitory interactions, specifically lateral inhibition, between the constituent elements of complex systems underlie a wide range of spatiotemporal patterns in nature. Here, we show that when systems of relaxation oscillators, whose dynamics involve widely separate timescales, are coupled primarily through diffusion of the inactivation component, they exhibit strikingly similar patterns regardless of specific details of the model kinetics and spatial topology. This universality stems from the fact that all observed patterns can be viewed as either specific manifestations of, or arising through interactions between, two fundamental classes of collective dynamics, viz., a state comprising clusters of synchronized oscillators, and a time-invariant spatially inhomogeneous state resulting from oscillator death. Our work provides an unifying framework for understanding the emergent global behavior of various chemical, biological, and ecological systems spanning several time and length scales.

Phase balanced states are a highly underexplored class of solutions of the Kuramoto model and other coupled oscillator models on networks. So far, coupled oscillator research focused on phase synchronized solutions. Yet, global constraints on oscillators may forbid synchronized state, rendering phase balanced states as the relevant stable state. If, for example, oscillators are driving the contractions of a fluid filled volume, conservation of fluid volume constrains oscillators to balanced states as characterized by a vanishing Kuramoto order parameter. It has previously been shown that stable, balanced patterns in the Kuramoto model exist on circulant graphs. However, which noncirculant graphs first of all allow for balanced states and what characterizes the balanced states is unknown. Here, we derive rules of how to build noncirculant, planar graphs allowing for balanced states from the simple cycle graph by adding loops or edges to it. We thereby identify different classes of small planar networks allowing for balanced states. Investigating the balanced states' characteristics, we find that the variance in basin stability scales linearly with the size of the graph for these networks. We introduce the balancing ratio as an order parameter based on the basin stability approach to classify balanced states on networks and evaluate it analytically for a subset of the network classes. Our results offer an analytical description of noncirculant graphs supporting stable, balanced states and may thereby help to understand the topological requirements on oscillator networks under global constraints.

The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance, however, often these are not metrics (rendering standard data-mining techniques infeasible) or are computationally infeasible for large graphs. In this work we define a new pseudometric based on the spectrum of the nonbacktracking graph operator and show that it cannot only be used to compare graphs generated through different mechanisms but can reliably compare graphs of varying size. We observe that the family of Watts-Strogatz graphs lie on a manifold in the nonbacktracking spectral embedding and show how this metric can be used in a standard classification problem of empirical graphs.

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a winner-takes-all mechanism. For sufficiently large transmission delay we observe the emergence of collective oscillations in the system beyond a critical coupling value. Heterogeneity promotes neural inactivation and asynchronous dynamics and its effect can be counteracted by considering longer time delays. In sparse networks, inhibition has the counterintuitive effect of promoting neural reactivation of silent neurons for sufficiently large coupling. In this regime, current fluctuations are on one side responsible for neural firing of subthreshold neurons and on the other side for their desynchronization. Therefore, collective oscillations are present only in a limited range of coupling values, which remains finite in the thermodynamic limit. Out of this range the dynamics is asynchronous and for very large inhibition neurons display a bursting behavior alternating periods of silence with periods where they fire freely in absence of any inhibition.

Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a nonequilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much larger than the equilibrium one for small enough wave number. In the case of diffusion in binary mixtures such fluctuations are time-symmetric, notwithstanding the fact that they are generated by a nonequilibrium condition. In this paper, we investigate diffusion of two solutes in a ternary liquid mixture by means of fluctuating hydrodynamics theory. We show that the time-cross-correlation function of the concentrations is not time-symmetric, hence showing that time symmetry is violated for such nonequilibrium fluctuations. We discuss the feasibility of experiments aimed at the detection of the asymmetry of the cross-correlation function of nonequilibrium concentration fluctuations in ternary mixtures, as envisaged in the Giant Fluctuations (NEUF-DIX) microgravity project of the European Space Agency.

A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K ($70{}^{\circ }\mathrm{C}$), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Since the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.

Stable dissipative solitons are perfect carries of optical information due to remarkable stability of their waveforms that allows the signal transmission with extremely dense soliton packing without losing the encoded information. Apart from unaffected passing of solitons through a communication network, controllable transformations of soliton waveforms are needed to perform all-optical information processing. In this paper we employ the basic model of dissipative optical solitons in the form of the complex Ginzburg-Landau equation with a potential term to study the interactions between two stationary dissipative solitons under the control influences and use those interactions to implement various logic gates. In particular, we demonstrate not, and, nand, or, nor, xor, and xnor gates, where the plain (fundamental soliton) and composite pulses are used to represent the low and high logic levels.

Cluster synchronization is a phenomenon in which oscillators in a given network are partitioned into synchronous clusters. As recently shown, diverse cluster synchronization patterns can be found using network symmetry when the oscillators are identical. For such symmetry-induced cluster synchronization patterns, subsets called intertwined clusters can exist, in which every cluster in the same subset should synchronize or desynchronize concurrently. In this paper, to reflect the existence of noise in real systems, we consider networks composed of nearly identical oscillators. We show that every cluster in the same intertwined cluster set is nearly synchronized concurrently when the nearly synchronous state of the set is stable. We also consider an extreme case where only one cluster of an intertwined cluster set is composed of nearly identical oscillators while every other cluster in the set is composed of identical oscillators. In this case, deviation from the synchronous state of every cluster in the same set increases linearly with the magnitude of parameter mismatch within the cluster of nearly identical oscillators. We confirm these results by numerical simulation.

In elections, the vote shares or turnout rates show a strong spatial correlation. The logarithmic decay with distance suggests that a two-dimensional (2D) noisy diffusive equation describes the system. Based on the study of U.S. presidential elections data, it was determined that the fluctuations of vote shares also exhibit a strong and long-range spatial correlation. Previously, it was considered difficult to induce strong and long-range spatial correlation of the vote shares without breaking the empirically observed narrow distribution. We demonstrate that a voter model on networks shows such a behavior. In the model, there are many voters in a node who are affected by the agents in the node and by the agents in the linked nodes. A multivariate Wright-Fisher diffusion equation for the joint probability density of the vote shares is derived. The stationary distribution is a multivariate generalization of the beta distribution. In addition, we also estimate the equilibrium values and the covariance matrix of the vote shares and obtain a correspondence with a multivariate normal distribution. This approach largely simplifies the calibration of the parameters in the modeling of elections.

We present Monte Carlo simulations for the transport cycle of Escherichia coli lactose permease (LacY), using as a starting point the model proposed by Kaback et al. [Nat. Rev. Mol. Cell Biol. 2, 610 (2001)], which is based on functional properties of mutants and x-ray structures. Kaback's model suggests the existence of six states for the whole cycle of lactose-${\mathrm{H}}^{+}$ symport. However, the free-energy differences between these states have not yet been reported in the literature. Here, we analyzed the biochemical structure of each state and determined a range of possible values for each one of the five free-energy variations. Then, using the Metropolis algorithm in a nonhomogeneous random walk model, we tested all the possible combinations with these values to find the free-energy curve that best reproduces the dynamics of LacY. The agreement between our model predictions and the experimental data suggests that our free-energy curve is appropriate for describing the lactose-${\mathrm{H}}^{+}$ symport. We found not only this curve, but also the time of occupancy of the permease at each conformation. In addition, we paved the way in this work to solve an open question related to this transport mechanism, which is the importance of protonation for lactose binding.

In bulk percolation, we exhibit operators that insert $N$ clusters with any given symmetry under the symmetric group ${\mathcal{S}}_N$. At the critical threshold, this leads to predictions that certain combinations of two-point correlation functions depend logarithmically on distance, without the usual power law. The behavior under rotations of certain amplitudes of correlators is also determined exactly. All these results hold in any dimension, $2\le d\le 6$. Moreover, in $d=2$ the critical exponents and universal logarithmic prefactors are obtained exactly. We test these predictions against extensive simulations of critical bond percolation in $d=2$ and 3, for all correlators up to $N=4$ ($d=2$) and $N=3$ ($d=3$), finding excellent agreement. In $d=3$ we further obtain precise numerical estimates for critical exponents and logarithmic prefactors.

We theoretically study the quantum transport of an electron wave packet on the Fermi arcs and in the bulk of a Weyl semimetal slab. The numerical analysis of the dynamical equations obtained from the Heisenberg equation of motion reveals that the electron motion in the Weyl semimetal exhibits interesting unusual effects. In particular, signatures of chaotic behavior in the transport of the electron wave packet are observed that are diagnosed by the relevant out-of-time-order correlation function and are analyzed using Poincaré maps. We attribute the appearance of such chaotic transport of the electron wave packet to the interplay of Zitterbewegung and cyclotron oscillations in the Weyl semimetal slab. The chaotic nature of the electron transport is exhibited both along the Fermi arcs and in the bulk of the slab, depending strongly upon the spin orientation of the electron. In the presence of a magnetic field, both interband and intraband (cyclotron) frequencies contribute to the resulting oscillation frequency of the electron motion.

Examining the controllability of complex networks has received much attention recently. The focus of many studies is commonly trained on whether we can steer a system from an arbitrary initial state to any final state within finite time with admissible external inputs. In order to accomplish the control at the minimum cost, we must study how much control energy is needed to reach the desired state. At a given control distance between the initial and final states, existing results have offered the scaling behavior of lower bounds of the minimum energy in terms of the control time. However, to reach an arbitrary final state at a given control distance, the minimum energy is actually dominated by the upper bound, whose analytic expression still remains elusive. Here we theoretically show the scaling behavior of a precise upper bound of the minimum energy in terms of the time required to achieve control. Apart from validating the analytical results with numerical simulations, our findings are applicable to any number of nodes that receive inputs directly and any types of networks with linear dynamics. Moreover, more precise analytical results for the lower bound of the minimum energy are derived with the proposed method. Our results pave the way for implementing realistic control over various complex networks with the minimum control cost.