Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the associated mean fixation times can be more intricate, especially when selection is strong. The intuition is that fixation of a beneficial mutant happens fast in a dominance game, that fixation takes very long in a coexistence game, and that strong selection eliminates demographic noise. Here we show that these intuitions can be misleading in structured populations. We analyze mean fixation times on the cycle graph under strong frequency-dependent selection for two different microscopic evolutionary update rules (death-birth and birth-death). We establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size. Depending on the underlying game, we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring (death-birth update). In contrast, if selection for an offspring occurs before random removal (birth-death update), then strong selection can remove demographic noise almost entirely.

To date investigations of the dynamics of driven colloidal systems have focused on hydrodynamic interactions and often employ optical (laser) tweezers for manipulation. However, the optical fields that provide confinement and drive also result in electrodynamic interactions that are generally neglected. We address this issue with a detailed study of interparticle dynamics in an optical ring vortex trap using 150-nm diameter Ag nanoparticles. We term the resultant electrodynamically interacting nanoparticles a driven optical matter system. We also show that a superior trap is created by using a Au nanoplate mirror in a retroreflection geometry, which increases the electric field intensity, the optical drive force, and spatial confinement. Using nanoparticles versus micron sized colloids significantly reduces the surface hydrodynamic friction allowing us to access small values of optical topological charge and drive force. We quantify a further 50% reduction of hydrodynamic friction when the nanoparticles are driven over the Au nanoplate mirrors versus over a mildly electrostatically repulsive glass surface. Further, we demonstrate through experiments and electrodynamics–Langevin dynamics simulations that the optical drive force and the interparticle interactions are not constant around the ring for linearly polarized light, resulting in a strong position-dependent variation in the nanoparticle velocity. The nonuniformity in the optical drive force is also manifest as an increase in fluctuations of interparticle separation, or effective temperature, as the optical driving force is increased. Finally, we resolve an open issue in the literature on periodic modulation of interparticle separation with comparative measurements of driven 300-nm-diameter polystyrene beads that also clearly reveal the significance of electrodynamic forces and interactions in optically driven colloidal systems. Therefore, the modulations in the optical forces and electrodynamic interactions that we demonstrate should not be neglected for dielectric particles and might give rise to some structural and dynamic features that have previously been attributed exclusively to hydrodynamic interactions.

We study, using Langevin dynamics simulations, the change in composition of a binary colloidal mixture confined in a finite-length channel, induced by an external field. The field-induced transition from a near-bulk composition to an inverted population is studied as a function of time, for different field strengths and system parameters. For state points corresponding to reversible field cycles, the cyclic filling and emptying of the channel by the minority species are compared. Extrapolation of the physical relaxation times to the colloidal regime is performed through a series of simulations at increasing value of the damping parameter. For state points at which the mixture is unstable at zero field, reproducible irreversible cycles are illustrated. For reversible field cycles, the scaling with the particles size of the characteristic cycling time is discussed.

A Langmuir monolayer can be considered as a two-dimensional (2D) sheet at higher surface pressure which structurally deform with mechanical compression depending upon the elastic nature of the monolayer. The deformed structures formed after a certain elastic limit are called collapsed structures. To explore monolayer collapses at lower surface pressure and to see the effect of ions on such monolayer collapses, out-of-plane structures and in-plane morphologies of stearic acid Langmuir monolayers have been studied both at lower (≈6.8) and higher (≈9.5) subphase $p\mathrm{H}$ in the presence of $\mathrm{M}{\mathrm{g}}^{2+},\mathrm{C}{\mathrm{a}}^{2+},\mathrm{Z}{\mathrm{n}}^{2+},\mathrm{C}{\mathrm{d}}^{2+}$, and $\mathrm{B}{\mathrm{a}}^{2+}$ ions. At lower subphase $p\mathrm{H}$ and in the presence of all cations, the stearic acid monolayer remains as a monolayer before collapse, which generally takes place at higher surface pressure $\left({\pi }_{\mathrm{c}}>50\mathrm{mN}/\mathrm{m}\right)$. However, at higher subphase $p\mathrm{H}$, structural changes of stearic acid monolayers occur at relatively lower surface pressure depending upon the specific dissolved ions. Among the same group elements of $\mathrm{M}{\mathrm{g}}^{2+},\mathrm{C}{\mathrm{a}}^{2+}$, and $\mathrm{B}{\mathrm{a}}^{2+}$, only for $\mathrm{B}{\mathrm{a}}^{2+}$ ions does monolayer to multilayer transition take place from a much lower surface pressure of the monolayer, remaining, however, as a monolayer for $\mathrm{M}{\mathrm{g}}^{2+}$ and $\mathrm{C}{\mathrm{a}}^{2+}$ ions. For another same group elements of $\mathrm{Z}{\mathrm{n}}^{2+}$ and $\mathrm{C}{\mathrm{d}}^{2+}$ ions, a less covered bilayer structure forms on top of the monolayer structure at lower surface pressure, which is evidenced from both x-ray reflectometry and atomic force microscopy. Fourier transform infrared spectroscopy confirms the presence of two coexisting conformations formed by the two different metal-headgroup coordinations and the monolayer to trilayer or multilayer transformation takes place when the coverage ratio of the two molecular conformations changes from the critical value $\left(p_{\mathrm{c}}\right)$ of $\approx 0.66$. Such ion-specific monolayer collapses are correlated with the 2D lattice percolation model.

Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an ${8192}^3$ periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.

We show the existence of chimeralike states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimeralike states occurs only for a small range of frequency difference between the two populations, and these states disappear for an increase of mismatch between the frequencies. Here the chimeralike states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. We also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions. Perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states. An imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population I and synchronized oscillations in population II. Also the existence of chimera state is independent of the increase of frequency mismatch between the populations. We also find the coexistence of different dynamical states with respect to different initial conditions, which causes multistability in the globally coupled system. In the case of nonlocal coupling, the system does not show multistability except in the cluster state region.

We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting generalized Langevin equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, which we take from numerical evaluation of a marginally stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye $\sim {\omega }_p^2$ law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at $T\lesssim T_g$. Good agreement is found for both the reactive (real) part of the response and for the $\alpha$-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches. On the low-frequency side of the $\alpha$ peak, the fitting supports the presence of $\sim {\omega }_p^4$ modes at vanishing eigenfrequency as recently shown [E. Lerner, G. During, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)]. $\alpha$-wing asymmetry and stretched-exponential behavior are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.

We study a network of $N$ identical leaky integrate-and-fire model neurons coupled by $\alpha$-function pulses, weighted by a coupling parameter $K$. Studies of the dynamics of this system have mostly focused on the stability of the fully synchronized and the fully asynchronous splay states, which naturally depends on the sign of $K$, i.e., excitation vs inhibition. We find that there is also a rich set of attractors consisting of clusters of fully synchronized oscillators, such as fixed $(N-1,1)$ states, which have synchronized clusters of sizes $N-1$ and 1, as well as splay states of clusters with equal sizes greater than 1. Additionally, we find limit cycles that clarify the stability of previously observed quasiperiodic behavior. Our framework exploits the neutrality of the dynamics for $K=0$ which allows us to implement a dimensional reduction strategy that simplifies the dynamics to a continuous flow on a codimension 3 subspace with the sign of $K$ determining the flow direction. This reduction framework naturally incorporates a hierarchy of partially synchronized subspaces in which the new attracting states lie. Using high-precision numerical simulations, we describe completely the sequence of bifurcations and the stability of all fixed points and limit cycles for $N=2\text{–}4$. The set of possible attracting states can be used to distinguish different classes of neuron models. For instance from our previous work [Chaos 24, 013114 (2014)] we know that of the types of partially synchronized states discussed here, only the $(N-1,1)$ states can be stable in systems of identical coupled sinusoidal (i.e., Kuramoto type) oscillators, such as $\theta$-neuron models. Upon introducing a small variation in individual neuron parameters, the attracting fixed points we discuss here generalize to equivalent fixed points in which neurons need not fire coincidently.

Many evolutionary game models for network reciprocity are based on an imitation dynamics, yet how semirational imitators prevail has seldom been explained. Here we use a model to investigate the coevolutionary dynamics of cooperation and partnership adjustment in a polygenic population of semirational imitators and rational payoff maximizers. A rational individual chooses a strategy best responding to its neighbors when updating strategy and switches to a new partner who can bring it the maximal payoff from all candidates when adjusting the partnership. In contrast, a semirational individual imitates its neighbor's strategy directly and adjusts its partnership based upon a simple reputation rule. Individual-based simulations show that cooperation cannot evolve in a population of all best responders even if they can switch their partners to somebody who can reward them best in game playing. However, when imitators exist, a stable community that consists of cooperative imitators emerges. Further, we show that a birth-death selection mechanism can eliminate all best responders, cultivating a social regime of all cooperative imitators. Compared with parallel simulations that assume fixed networks, cooperative imitators are evolutionarily favored, provided they are able to adjust their partners.

Percolation is known as one of the most robust continuous transitions, because its occupation rule is intrinsically local. As one of the ways to break the robustness, occupation is allowed to more than one species of particles and they occupy cooperatively. This generalized percolation model undergoes a discontinuous transition. Here we investigate an epidemic model with two contagion steps and characterize its phase transition analytically and numerically. We find that even though the order parameter jumps at a transition point $r_c$, then increases continuously, it does not exhibit any critical behavior: the fluctuations of the order parameter do not diverge at $r_c$. However, critical behavior appears in mean outbreak size, which diverges at the transition point in a manner that the ordinary percolation shows. Such a type of phase transition is regarded as a mixed-order phase transition. We also obtain scaling relations of cascade outbreak statistics when the order parameter jumps at $r_c$.

The solution of today's complex problems requires the grouping of task forces whose members are usually connected remotely over long physical distances and different time zones. Hence, understanding the effects of imposed communication patterns (i.e., who can communicate with whom) on group performance is important. Here we use an agent-based model to explore the influence of the betweenness centrality of the nodes on the time the group requires to find the global maxima of NK-fitness landscapes. The agents cooperate by broadcasting messages, informing on their fitness to their neighbors, and use this information to copy the more successful agents in their neighborhood. We find that for easy tasks (smooth landscapes), the topology of the communication network has no effect on the performance of the group, and that the more central nodes are the most likely to find the global maximum first. For difficult tasks (rugged landscapes), however, we find a positive correlation between the variance of the betweenness among the network nodes and the group performance. For these tasks, the performances of individual nodes are strongly influenced by the agents' dispositions to cooperate and by the particular realizations of the rugged landscapes.

In this study, we investigated inelastic non-Newtonian fluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bubbles. The results reveal that for shear-thinning fluids wall slip can be increased significantly, provided that the system is operated in the shear-thinning regime. For a 0.2 wt% xanthan gum solution with a power-law index of $n=0.4$, the numerical results indicate that wall slip can be enhanced 3.2 times when compared to a Newtonian liquid. This enhancement factor was also predicted from a theoretical analysis, which gave an expression for the maximum slip length that can be attained over flat, heterogeneously slippery surfaces. Although this equation was derived for a no-slip/no-shear unit length that is much larger than the typical size of the system, we found that it can also be used to predict the enhancement in the regime where the slip length is proportional to the size of the no-shear region or the bubble width. The results could be coupled to the hydrodynamic development or entrance length of the system, as maximum wall slip is only reached when the fluid flow can fully adapt to the no-slip and no-shear conditions at the wall.

The Stokes drag force and the gravity force are usually sufficient to describe the behavior of sub-Kolmogorov-size (or pointlike) heavy particles in turbulence, in particular when the particle-to-fluid density ratio ${\rho }_p/{\rho }_f\gtrsim {10}^3$ (with ${\rho }_p$ and ${\rho }_f$ the particle and fluid density, respectively). This is, in general, not the case for smaller particle-to-fluid density ratios, in particular not for ${\rho }_p/{\rho }_f\lesssim {10}^2$. In that case the pressure gradient force, added mass effects, and the Basset history force also play important roles. In this study we focus on the understanding of the role of these additional forces, all of hydrodynamic origin, in the settling of particles in turbulence. In order to qualitatively elucidate the complex dynamics of such particles in homogeneous isotropic turbulence, we first focus on the case of settling of such particles in the flow field of a single vortex. After having explored this simplified case we extend our analysis to homogeneous isotropic turbulence. In general, we found that the pressure gradient force leads to a decrease in the settling velocity. This can be qualitatively understood by the fact that this force prevents the particles from sweeping out of vortices, a mechanism known as preferential sweeping which causes enhanced settling. Additionally, we found that the Basset history force can both increase and decrease the enhanced settling, depending on the particle Stokes number. Finally, the role of the nonlinear Stokes drag has been explored, confirming that it affects settling of inertial particles in turbulence, but only in a limited way for the parameter settings used in this investigation.

A Hamiltonian mean field model, where the potential is inspired by dipole-dipole interactions, is proposed to characterize the behavior of systems with long-range interactions. The dynamics of the system remains in quasistationary states before arriving at equilibrium. The equilibrium is analytically derived from the canonical ensemble and coincides with that obtained from molecular dynamics simulations (microcanonical ensemble) at only long time scales. The dynamics of the system is characterized by the behavior of the mean value of the kinetic energy. The significance of the results, compared to others in the recent literature, is that two plateaus sequentially emerge in the evolution of the model under the special considerations of the initial conditions and systems of finite size. The first plateau decays to a different second one before the system reaches equilibrium, but the dynamics of the system is expected to have only one plateau when the thermodynamics limit is reached because the difference between them tends to disappear as $N$ tends to infinity. Hence, the first plateau is a type of quasistationary state the lifetime of which depends on a power law of $N$ and the second seems to be a true quasistationary state as reported in the literature. We characterize the general behavior of the model according to its dynamics and thermodynamics.

Systems of particles with long-range interactions present two important processes: first, the formation of out-of-equilibrium quasistationary states (QSS) and, second, the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much longer time scale. In this paper, we study the collisional relaxation in the Hamiltonian mean-field model using the appropriate kinetic equations for a system of $N$ particles at order $1/N$: the Landau equation when collective effects are neglected and the Lenard-Balescu equation when they are taken into account. We derive explicit expressions for the diffusion coefficients using both equations for any magnetization, and we obtain analytic expressions for highly clustered configurations. An important conclusion is that in this system collective effects are crucial in order to describe the relaxation dynamics. We compare the diffusion calculated with the kinetic equations with simulations set up to simulate the system with or without collective effects, obtaining a very good agreement between theory and simulations.

Communities in directed networks have often been characterized as regions with a high density of links, or as sets of nodes with certain patterns of connection. Our approach for community detection combines the optimization of a quality function and a spectral clustering of a deformation of the combinatorial Laplacian, the so-called magnetic Laplacian. The eigenfunctions of the magnetic Laplacian, which we call magnetic eigenmaps, incorporate structural information. Hence, using the magnetic eigenmaps, dense communities including directed cycles can be revealed as well as “role” communities in networks with a running flow, usually discovered thanks to mixture models. Furthermore, in the spirit of the Markov stability method, an approach for studying communities at different energy levels in the network is put forward, based on a quantum mechanical system at finite temperature.

Normally, the phase diagram is reported as a property of the binary mixture. We show that the phase diagram (that is, the zones of thermodynamic stability of the states of the binary mixture) is also affected by the size of the container. We investigate the thermodynamic stability of the binary mixture in a closed cavity, and identify the zone in parameters where the binary mixture is heterogeneous in equilibrium (the zone of spinodal decomposition), the zone where the mixture is always homogeneous in equilibrium, and the zone where the transition between these two states is possible (the metastable nucleation zone). In addition, we investigate the properties of the smallest single droplet that may be in equilibrium in the closed cavity (for the given average concentration, all smaller droplets would always dissolve). We show that the size of such droplets depends on the cavity's size, as $\sim L^{1/2}$.

Using molecular dynamics simulations, we study the transient response of a binary Lennard-Jones glass subjected to periodic shear deformation. The amorphous solid is modeled as a three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.

We explore the effect of interplay of interfacial noise and curvature-driven dynamics in a binary spin system. An appropriate model is the generalized two-dimensional voter model proposed earlier [M. J. de Oliveira, J. F. F. Mendes, and M. A. Santos, J. Phys. A: Math. Gen. 26, 2317 (1993)], where the flipping probability of a spin depends on the state of its neighbors and is given in terms of two parameters, $x$ and $y$. $x=0.5\text{and}y=1$ correspond to the conventional voter model which is purely interfacial noise driven, while $x=1$ and $y=1$ correspond to the Ising model, where coarsening is fully curvature driven. The coarsening phenomena for $0.5<x<1$ keeping $y=1$ is studied in detail. The dynamical behavior of the relevant quantities show characteristic differences from both $x=0.5$ and 1. The most remarkable result is the existence of two time scales for $x\ge x_c$ where $x_c\approx 0.7$. On the other hand, we have studied the exit probability which shows Ising-like behavior with a universal exponent for any value of $x>0.5$; the effect of $x$ appears in altering the value of the parameter occurring in the scaling function only.