Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding pulses is regarded as their prototypical signature. Here we show that colliding excitable pulses may exhibit solitonlike crossover and pulse nucleation if the system obeys a mass conservation constraint. In contrast to previous observations in systems without mass conservation, these alternative collision scenarios are robustly observed over a wide range of parameters. We demonstrate our findings using a model of intracellular actin waves since, on time scales of wave propagations over the cell scale, cells obey conservation of actin monomers. The results provide a key concept to understand the ubiquitous occurrence of actin waves in cells, suggesting why they are so common, and why their dynamics is robust and long-lived.

Nonperiodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present paper develops a time-domain model to capture the nonlinear dynamic response of a heterogeneous medium containing a dilute concentration of subwavelength nonlinear inclusions embedded in a lossy, nearly incompressible medium. Each length scale is modeled via a modified Rayleigh-Plesset equation, which differs from the standard form used in bubble dynamics by accounting for inertial and viscoelastic effects of the oscillating spherical element and includes constitutive equations formulated with incremental deformations. The two length scales are coupled through the constitutive relations and viscoelastic loss for the effective medium, both dependent on the inclusion and matrix properties. The model is then applied to an example nonlinear inclusion with incremental negative linear stiffness stemming from microscale elastic instabilities embedded in a lossy, nearly incompressible host medium. The macroscopic damping performance is shown to be tunable via an externally applied hydrostatic pressure with the example system displaying over two orders of magnitude change in energy dissipation due to changes in prestrain. The numerical results for radial oscillations versus time, frequency spectra, and energy dissipation obtained from the coupled dynamic model captures the expected response for quasistatic and dynamic regimes for an example buckling inclusion for both constrained and unconstrained negative stiffness inclusions.

Foreign power interference in domestic elections is an existential threat to societies. Manifested through myriad methods from war to words, such interference is a timely example of strategic interaction between economic and political agents. We model this interaction between rational game players as a continuous-time differential game, constructing an analytical model of this competition with a variety of payoff structures. All-or-nothing attitudes by only one player regarding the outcome of the game lead to an arms race in which both countries spend increasing amounts on interference and counterinterference operations. We then confront our model with data pertaining to the Russian interference in the 2016 United States presidential election contest. We introduce and estimate a Bayesian structural time-series model of election polls and social media posts by Russian Twitter troll accounts. Our analytical model, while purposefully abstract and simple, adequately captures many temporal characteristics of the election and social media activity. We close with a discussion of our model's shortcomings and suggestions for future research.

Optimal strategies for epidemic containment are focused on dismantling the contact network through effective immunization with minimal costs. However, network fragmentation is seldom accessible in practice and may present extreme side effects. In this work, we investigate the epidemic containment immunizing population fractions far below the percolation threshold. We report that moderate and weakly supervised immunizations can lead to finite epidemic thresholds of the susceptible-infected-susceptible model on scale-free networks by changing the nature of the transition from a specific motif to a collectively driven process. Both pruning of efficient spreaders and increasing of their mutual separation are necessary for a collective activation. Fractions of immunized vertices needed to eradicate the epidemics which are much smaller than the percolation thresholds were observed for a broad spectrum of real networks considering targeted or acquaintance immunization strategies. Our work contributes for the construction of optimal containment, preserving network functionality through nonmassive and viable immunization strategies.

We propose a stochastic model to study phonetic changes as an evolutionary process driven by social interactions between two groups of individuals with different phonological systems. Particularly, we focus on the changes in the place of articulation, inspired by the drift $/\mathrm{\Phi }/\to /\mathrm{h}/$ observed in some words of Latin root in the Castilian language. In the model, each agent is characterized by a variable of three states, representing the place of articulation used during speech production. In this frame, we propose stochastic rules of interactions among agents which lead to phonetic imitation and consequently to changes in the articulation place. Based on this, we mathematically formalize the model as a problem of population dynamics, derive the equations of evolution in the mean-field approximation, and study the emergence of three nontrivial global states, which can be linked to the pattern of phonetic changes observed in the language of Castile and in other Romance languages.

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes–based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.

We investigate numerically and analytically size-polydisperse granular mixtures immersed into a molecular gas. We show that the equipartition of granular temperatures of particles of different sizes is established; however, the granular temperatures significantly differ from the temperature of the molecular gas. This result is surprising since, generally, the energy equipartition is strongly violated in driven granular mixtures. Qualitatively, the obtained results do not depend on the collision model, being valid for a constant restitution coefficient $\varepsilon$, as well as for the $\varepsilon$ for viscoelastic particles. Our findings may be important for astrophysical applications, such as protoplanetary disks, interstellar dust clouds, and comets.

Ultracold neutral plasma (UNP) experiments allow for careful control of plasma properties across Coulomb coupling regimes. Here, we examine how UNPs can be used to study heterogeneous, nonequilibrium phenomena, including nonlinear waves, transport, hydrodynamics, kinetics, stopping power, and instabilities. Through a series of molecular dynamics simulations, we have explored UNPs formed with spatially modulated ionizing radiation. We have developed a computational model for such sculpted UNPs that includes an ionic screened Coulomb interaction with a spatiotemporal screening length, and Langevin-based spatial ion-electron and ion-neutral collisions. We have also developed a hydrodynamics model and have extracted its field quantities (density, flow velocity, and temperature) from the molecular dynamics simulation data, allowing us to investigate kinetics by examining moment ratios and phase-space dynamics; we find that it is possible to create UNPs that vary from nearly perfect fluids (Euler limit) to highly kinetic plasmas. We have examined plasmas in three geometries: a solid rod, a hollow rod, and a gapped slab; we have studied basic properties of these plasmas, including the spatial Coulomb coupling parameter. By varying the initial conditions, we find that we can design experimental plasmas that would allow the exploration of a wide range of phenomena, including shock and blast waves, stopping power, two-stream instabilities, and much more. Using an evaporative cooling geometry, our results suggest that much larger Coulomb couplings can be achieved, possibly in excess of 10.

Carbon shell areal density measurements from many types of inertial confinement fusion implosions at the National Ignition Facility (NIF) demonstrate that the final state of the outside portion of the shell is set primarily by capsule coast time, the coasting period between main laser shut off and peak fusion output. However, the fuel areal density does not correlate with the increasing carbon compression. While two-dimensional (2D) radiation-hydrodynamic simulations successfully capture the carbon compression, energy must be added to the simulated fuel-ice layer to reproduce fuel areal density measurements. The data presented demonstrates that the degradation mechanisms that reduce the compressibility of the fuel do not reduce the compressibility of the ablator.

We obtain explicit expressions for the annealed complexities associated, respectively, with the total number of (i) stationary points and (ii) local minima of the energy landscape for an elastic manifold with internal dimension $d<4$ embedded in a random medium of dimension $N\gg 1$ and confined by a parabolic potential with the curvature parameter $\mu$. These complexities are found to both vanish at the critical value ${\mu }_c$ identified as the Larkin mass. For $\mu <{\mu }_c$ the system is in complex phase corresponding to the replica symmetry breaking in its $T=0$ thermodynamics. The complexities vanish, respectively, quadratically (stationary points) and cubically (minima) at ${\mu }_c^{-}$. For $d\ge 1$ they admit a finite “massless” limit $\mu =0$ which is used to provide an upper bound for the depinning threshold under an applied force.

Cell-cell communication is often achieved by secreted signaling molecules that bind membrane-bound receptors. A common class of such receptors are G-protein coupled receptors, where extracellular binding induces changes on the membrane affinity near the receptor for certain cytosolic proteins, effectively altering their chemical potential. We analyze the minimum-dissipation schedules for dynamically changing chemical potential to induce steady-state changes in protein copy-number distributions, and illustrate with analytic solutions for linear chemical reaction networks. Protocols that change chemical potential on biologically relevant timescales are experimentally accessible using optogenetic manipulations, and our framework provides nontrivial predictions about functional dynamical cell-cell interactions.

We theoretically design a kind of diffusion bistability (and even multistability) in the macroscopic scale, which has a similar phenomenon but different underlying mechanism from its microscopic counterpart [Phys. Rev. Lett. 101, 267203 (2008)]; the latter has been extensively investigated in literature, e.g., for building nanometer-scale memory components. By introducing second- and third-order nonlinear terms (that opposite in sign) into diffusion coefficient matrices, a bistable energy or mass diffusion occurs with two different steady states identified as “0” and “1.” In particular, we study heat conduction in a two-terminal three-body system and show that this bistable system exhibits a macroscale thermal memory effect with tailored nonlinear thermal conductivities. The theoretical analysis is confirmed by finite-element simulations. Also, we suggest experiments with metamaterials based on shape memory alloys. This theoretical framework blazes a trail on constructing intrinsic bistability or multistability in diffusive systems for macroscopic energy or mass management.

A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and nonequilibrium stationary states. An equilibrium system is here defined as a system whose stationary distribution equals the Boltzmann distribution, the relation of this definition to the conditions of detailed balance and vanishing probability current is discussed both for underdamped as well as for overdamped systems. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy ${\mathcal{S}}_{\mathrm{free}}\left(t\right)$, is constructed. For the stationary distribution ${\mathcal{S}}_{\mathrm{free}}\left(t\right)$ becomes maximal and its time derivative, the free entropy production ${\dot{\mathcal{S}}}_{\mathrm{free}}\left(t\right)$, is minimal and vanishes. Thus, ${\mathcal{S}}_{\mathrm{free}}\left(t\right)$ characterizes equilibrium as well as nonequilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e., if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature and thus corresponds to the Massieu function which was previously introduced in an alternative formulation of statistical mechanics. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the nonequilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. This does not constitute a violation of the second law of thermodynamics, but rather demonstrates that a particle in such a nonequilibrium system is not characterized by an effective temperature which equals the temperature of the heat bath it is coupled to. Active particle models can be described in the same general framework, which thereby allows us to characterize their entropy production not only in the stationary state but also in the approach to the stationary nonequilibrium state. Finally, the connection to nonequilibrium thermodynamics formulations that include the reservoir entropy production is discussed.

Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semiclassical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited $s$-state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the $d$-state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of $\sim 1/r^{d+\sigma }$ (denoted as LTDP), where $r$ is the separation, $d$ is the spatial dimension, and $\sigma$ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension $d_c=\min (3,1.5\sigma )$. We numerically obtain a set of critical exponents in the LTDP class and determine the interval of $\sigma$ for the LTDP class. Finally, we construct a diagram of universality classes in the space ($d,\sigma$).

Previous work has introduced scale-split energy density ${\psi }_{l,L}(\mathbf{x},t)=\frac{1}{2}{\mathbf{B}}_l·{\mathbf{B}}_L$ for vector field $\mathbf{B}(\mathbf{x},t)$ coarse grained at scales $l$ and $L$, in order to quantify the field stochasticity or spatial complexity. In this formalism, the ${\mathcal{L}}_p$ norms $S_p\left(t\right)=\frac{1}{2}\left|\right|1-{\widehat{\mathbf{B}}}_l·{\widehat{\mathbf{B}}}_L{\left|\right|}_p, p\mathrm{th}$-order stochasticity level, and $E_p\left(t\right)=\frac{1}{2}\left|\right|B_l{B}_L{\left|\right|}_p, p\mathrm{th}$ order mean cross energy density, are used to analyze the evolution of the stochastic field $\mathbf{B}(\mathbf{x},t)$. Application to turbulent magnetic fields leads to the prediction that turbulence in general tends to tangle an initially smooth magnetic field increasing the magnetic stochasticity level, ${\partial }_t{S}_p>0$. An increasing magnetic stochasticity in turn leads to disalignments of the coarse-grained fields ${\mathbf{B}}_d$ at smaller scales, $d\ll L$, thus they average to weaker fields ${\mathbf{B}}_L$ at larger scales upon coarse graining, i.e., ${\partial }_t{E}_p<0$. Magnetic field resists the tangling effect of the turbulence by means of magnetic tension force. This can lead at some point to a sudden slippage between the field and fluid, decreasing the stochasticity ${\partial }_t{S}_p<0$ and increasing the energy ${\partial }_t{E}_p>0$ by aligning small-scale fields ${\mathbf{B}}_d$. Thus the maxima (minima) of magnetic stochasticity are expected to approximately coincide with the minima (maxima) of cross energy density, occurrence of which corresponds to slippage of the magnetic field through the fluid. In this formalism, magnetic reconnection and field-fluid slippage both correspond to $T_p={\partial }_t{S}_p=0\text{and}{\partial }_t{T}_2<0$. Previous work has also linked field-fluid slippage to magnetic reconnection invoking totally different approaches. In this paper, (a) we test these theoretical predictions numerically using a homogeneous, incompressible magnetohydrodynamic (MHD) simulation. Apart from expected small-scale deviations, possibly due to, e.g., intermittency and strong field annihilation, the theoretically predicted global relationship between stochasticity and cross energy is observed in different subvolumes of the simulation box. This indicate ubiquitous local field-fluid slippage and reconnection events in MHD turbulence. In addition, (b) we show that the conditions $T_p={\partial }_t{S}_p=0\text{and}{\partial }_t{T}_p<0$ lead to sudden increases in kinetic stochasticity level, i.e., ${\tau }_p={\partial }_t{s}_p\left(t\right)>0$ with $s_p\left(t\right)=\frac{1}{2}\left|\right|1-{\widehat{\mathbf{u}}}_l.{\widehat{\mathbf{u}}}_L{\left|\right|}_p$, which may correspond to fluid jets spontaneously driven by sudden field-fluid slippage-magnetic reconnection. Otherwise, they may correspond only to field-fluid slippage without energy dissipation. This picture, therefore, suggests defining reconnection as field-fluid slippage (changes in $S_p$) accompanied with magnetic energy dissipation (changes in $E_p$). All in all, these provide a statistical approach to the reconnection in terms of the time evolution of magnetic and kinetic stochasticities, $S_p$ and $s_p$, their time derivatives, $T_p={\partial }_t{S}_p, {\tau }_p={\partial }_t{s}_p$, and corresponding cross energies, $E_p, e_p\left(t\right)=\frac{1}{2}\left|\right|u_l{u}_L{\left|\right|}_p$. Furthermore, (c) we introduce the scale-split magnetic helicity based on which we discuss the energy or stochasticity relaxation of turbulent magnetic fields—a generalized Taylor relaxation. Finally, (d) we construct and numerically test a toy model, which resembles a classical version of quantum mean field Ising model for magnetized fluids, in order to illustrate how turbulent energy can affect magnetic stochasticity in the weak field regime.

We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Grønbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the phase space. Another is the recent discovery that also kinetics can be accurately sampled for the GJF method. Through a complete investigation of all possible finite-difference approximations to the velocity, we arrive at two main conclusions: (1) It is not possible to define a so-called on-site velocity such that kinetic temperature will be correct and independent of the time step, and (2) there exists a set of infinitely many possibilities for defining a two-point (leap-frog) velocity that measures kinetic energy correctly for linear systems in addition to the correct configurational statistics obtained from the GJF algorithm. We give explicit expressions for the possible definitions, and we incorporate these into convenient and practical algorithmic forms of the normal Verlet-type algorithms along with a set of suggested criteria for selecting a useful definition of velocity.

The origin of amplitude synchronization (AS), or amplitude envelope synchronization, as a peculiar form of strong correlation between amplitudes of oscillators is studied by using a model of coupled Landau-Stuart periodic oscillators. We find that the AS extensively occurs within the traditional phase drift region, and the amplitude correlation does not change with variation of the coupling strength but is dampened with increase of the frequency mismatch. The AS appears only at weak couplings and before the occurrence of phase synchronization (PS), and the oscillator amplitude is modulated by its phase. This study could build a solid foundation for AS, which has not drawn much attention in the nonlinear dynamics field before, providing a clear physical picture for synchronization including not only PS, but also AS, and arousing general interest in many interdisciplinary fields, such as neuronal systems, laser dynamics, nanomechanical resonators, and power systems, etc., where phase and amplitude are always mutually influenced and both are important.

The Ott-Antonsen ansatz is a powerful tool to extract the behaviors of coupled phase oscillators, but it imposes a strong restriction on the initial condition. Herein, an extension of the Ott-Antonsen ansatz is proposed to relax the restriction, enabling the systematic approximation of the behavior of a globally coupled phase oscillator system with an arbitrary initial condition. The proposed method is validated on the Kuramoto-Sakaguchi model of identical phase oscillators. The method yields cluster and chimera-like solutions that are not obtained by the conventional ansatz.

We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac $\delta$ is rotating at constant speed. The spectrum of stationary solutions in the $\delta$ comoving frame is analyzed in terms of the nonlinear coupling, $\delta$ velocity, and $\delta$ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating $\delta$. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.

In the past 20 years network science has proven its strength in modeling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Nevertheless, in many relevant cases, interactions are not pairwise but involve larger sets of nodes at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. Here we propose and study a class of random walks defined on such higher-order structures and grounded on a microscopic physical model where multibody proximity is associated with highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterization of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalized random-walk Laplace operator that reduces to the standard random-walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have full control of the high-order structures and on real-world networks where higher-order interactions are at play. As the first application of the method, we compare the behavior of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As the second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unraveling the effect of higher-order interactions on diffusive processes in higher-order networks, shedding light on mechanisms at the heart of biased information spreading in complex networked systems.