In an iterated two-person game, for instance prisoner's dilemma or the snowdrift game, there exist strategies that force the payoffs of the opponents to be equal. These equalizer strategies form a subset of the more general zero-determinant strategies that unilaterally set the payoff of an opponent. A challenge in the attempts to understand the role of these strategies in the evolution of animal behavior is the lack of iterations in the fights for mating opportunities or territory control. We show that an arbitrary two-parameter strategy may possess a corresponding equalizer strategy which produces the same result: statistics of the fight outcomes in the contests with competitors are the same for each of these two strategies. Therefore, analyzing only the equalizer strategy space may be sufficient to predict animal behavior if nature, indeed, reduces (marginalizes) complex strategies to equalizer strategy space. The work's main finding is that there is a unique equalizer strategy that predicts fight outcomes without symmetric cooperation responses. The lack of symmetric cooperation responses is a common trait in conflict escalation contests that generally require a clear winner. In addition, this unique strategy does not assess information of the opponent's state. The method bypasses the standard analysis of evolutionary stability. The results fit well the observations of combat between male bowl and doily spiders and support an empirical assumption of the war of attrition model that the species use only information regarding their own state during conflict escalation.

We study precessing turbulence, which appears in several geophysical and astrophysical systems, by direct numerical simulations of homogeneous turbulence where precessional instability is triggered due to the imposed background flow. We show that the time development of kinetic energy $\mathcal{K}$ occurs in two main phases associated with different flow topologies: (i) an exponential growth characterizing three-dimensional turbulence dynamics and (ii) nonlinear saturation during which $\mathcal{K}$ remains almost time independent, the flow becoming quasi-two-dimensional. The latter stage, wherein the development of $\mathcal{K}$ remains insensitive to the initial state, shares an important common feature with other quasi-two-dimensional rotating flows such as rotating Rayleigh-Bénard convection, or the large atmospheric scales: in the plane $k_{\parallel }=0$, i.e., the plane associated to an infinite wavelength in the direction parallel to the principal rotation axis, the kinetic energy spectrum scales as $k_{\perp }^{-3}$. We show that this power law is observed for wave numbers ranging between the Zeman “precessional” and “rotational” scales, $k_S^{-1}$ and $k_{\mathrm{\Omega }}^{-1}$, respectively, at which the associated background shear or inertial timescales are equal to the eddy turnover time. In addition, an inverse cascade develops for $(k_{\perp },k)<k_S$, and the spherically averaged kinetic energy spectrum exhibits a $k^{-2}$ inertial scaling for $k_S<k<k_{\mathrm{\Omega }}$.

To study the activated dynamics of mean-field glasses, which takes place on times of order $exp\left(N\right)$, where $N$ is the system size, we introduce a new model, the correlated random energy model (CREM), that allows for a smooth interpolation between the REM and the $p$-spin models. We study numerically and analytically the CREM in the intermediate regime between REM and $p$-spin. We fully characterize its energy landscape, which is like a golf course but, at variance with the REM, has metabasins (or holes) containing several configurations. We find that an effective description for the dynamics, in terms of traps, emerges, provided that one identifies metabasins in the CREM with configurations in the trap model.

With the advances in artificial particle synthesis, it is possible to create particles with unique shapes. Particle shape becomes a feasible parameter for tuning the percolation behavior. How to accurately predict the percolation threshold by particle characteristics for arbitrary particles has aroused great interest. Towards this end, a versatile family of cuboidlike particles and a numerical contact detection algorithm for these particles are presented here. Then, combining with percolation theory, the continuum percolation of randomly distributed overlapping cuboidlike particles is studied. The global percolation threshold ${\varphi }_c$ of overlapping particles with broad ranges of the shape parameter $m$ in $[1.0,+\infty )$ and aspect ratio $a/b$ in [0.1, 10.0] is computed via a finite-size scaling technique. Using the generalized excluded-volume approximation, an analytical formula is proposed to quantify the dependence of ${\varphi }_c$ on the parameters $m$ and $a/b$, and its reliability is verified. The results reveal that the percolation threshold ${\varphi }_c$ of overlapping cuboidlike particles is heavily dependent on the shapes of particles, and much more sensitive to $a/b$ than $m$. As the cuboidlike particles become spherical (i.e., $m=1.0$ and $a/b=1.0$), the maximum threshold ${\varphi }_{c,max}$ can be obtained.

Almost four decades ago, Gacs, Kurdyumov, and Levin introduced three different cellular automata to investigate whether one-dimensional nonequilibrium interacting particle systems are capable of displaying phase transitions, and, as a byproduct, they introduced the density classification problem (the ability to classify arrays of symbols according to their initial density) in the cellular automata literature. Their model II became a well-known model in theoretical computer science and statistical mechanics. The other two models, however, did not receive much attention. Here we characterize the density classification performance of Gacs, Kurdyumov, and Levin's model IV, a four-state cellular automaton with three absorbing states—only two of which are attractive—by numerical simulations. We show that model IV compares well with its sibling model II in the density classification task: the additional states slow down the convergence to the majority state but confer a slight advantage in classification performance. We also show that, unexpectedly, initial states diluted in one of the nonclassifiable states are more easily classified. The performance of model IV under the influence of noise was also investigated, and we found signs of an ergodic-nonergodic phase transition at some small finite positive level of noise, although the evidence is not entirely conclusive. We set an upper bound on the critical point for the transition, if any.

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the “Zipfian ensemble” in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sublinear, and saturating) that we characterize quantitatively.

Nonresonant spectral hole burning has proven to be a versatile method to characterize the dynamics of complex fluids, including polymers. Early work focused on dielectric susceptibility measurements in glass forming liquids, while recent work from our lab used mechanical viscoelastic measurements to investigate polymer melts and solutions. While the observed results were similar, the interpretations were different, with the former being interpreted by attributing the “holes” in the response as being due to dynamic heterogeneity in the system that is related to the glass or other transition, while the latter was interpreted in a way that suggested that the observed holes depend on the type of dynamics (Rouse, terminal, etc.) rather than an identifiable spatial heterogeneity. In this work, we have expanded mechanical spectral hole burning (MSHB) into the stress-controlled domain and carried out experiments in the rubbery regime of a polystyrene solution, similar to one which was tested previously with strain-controlled MSHB. The effects of pump stress amplitude, pump frequency, and waiting time were investigated. The mechanical holes in both directions (vertical and horizontal) were successfully burned, unlike the strain-controlled MSHB experiments on the same polystyrene solution, in which vertical holes were at best incomplete. The hole intensity exhibits a linear relationship with the amount of energy dissipated in the system during the large mechanical pump modification. The results suggest that the stress-controlled MSHB can be combined with strain-controlled MSHB to build a more complete framework to investigate the dynamics of polymeric materials and is consistent with the dynamic heterogeneity being related to the type of dynamics rather than to localized heating effects.

We investigate the performance of a three-spin quantum absorption refrigerator using a refined open quantum system model valid across all interspin coupling strengths. It describes the transition between previous approximate models for the weak and the ultrastrong coupling limit, and it predicts optimal refrigeration for moderately strong coupling, where both approximations are inaccurate. Two effects impede a more effective cooling: the coupling between the spins no longer reduces to a simple resonant energy exchange (the rotating wave approximation fails), and the interactions with the thermal baths become sensitive to the level splitting, thus opening additional heat channels between the reservoirs. We identify the modified conditions of refrigeration as a function of the interspin coupling strength, and we show that, contrary to intuition, a high-temperature work reservoir thwarts refrigeration in the strong coupling regime.

We investigate quantum corrections to the classical work characteristic function (CF) as a semiclassical approximation to the full quantum work CF. In addition to explicitly establishing the quantum-classical correspondence of the Feynman-Kac formula, we find that these quantum corrections must be in even powers of $\hslash$. Exact formulas of the lowest corrections (${\hslash }^2$) are proposed, and their physical origins are clarified. We calculate the work CFs for a forced harmonic oscillator and a forced quartic oscillator respectively to illustrate our results.

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system sufficiently well to exhibit chaos synchronization. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronize with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronize with the reservoir computer. We illustrate this behavior on the Mackey-Glass and Lorenz systems. We then show that trained reservoir computers can be used to crack chaos based cryptography and illustrate this on a chaos cryptosystem based on the Mackey-Glass system. We conclude by discussing why reservoir computers are so good at emulating chaotic systems.

We consider the situation of a large-scale stationary flow subjected to small-scale fluctuations. Assuming that the stable and unstable manifolds of the large-scale flow are known, we quantify the mean behavior and stochastic fluctuations of particles close to the unperturbed stable and unstable manifolds and their evolution in time. The mean defines a smooth curve in physical space, while the variance provides a time- and space-dependent quantitative estimate where particles are likely to be found. This allows us to quantify transport properties such as the expected volume of mixing as the result of the stochastic fluctuations of the transport barriers. We corroborate our analytical findings with numerical simulations in both compressible and incompressible flow situations. We moreover demonstrate the intimate connection of our results with finite-time Lyapunov exponent fields, and with spatial mixing regions.

We introduce a technique for evaluating the changing connectivity of a vector field whose integral curves (field lines) form tangled tubular bundles. Applications of such fields include magnetic flux ropes, relativistic plasma jets, stirred two-dimensional fluids, superfluid vortices, and polymer networks. The technique is based on maps of the field line winding—the average entanglement of a given field line with all other field lines. Previously this had been developed for divergence-free vector fields. By extending some previous theoretical results, we show how it can be applied to any vector field that forms a tubular bundle. We demonstrate the efficacy of this technique on data from laboratory plasma experiments with two interacting magnetic flux ropes. Performed in the UCLA Large Plasma Device, the plasma's magnetic field structure is too complex to identify a single dominant current sheet as an expected site of magnetic reconnection. Previously, this complex structure had restricted the ability to analyze the evolving magnetic connectivity, but this is no such restriction to our method. We demonstrate that the plasma establishes a periodically oscillating cycle of magnetic field structure variation which, while triggered by an ideal instability, is dominated by magnetic reconnection. This reconnection leads to periodically varying coherence of a merged central flux rope, a conclusion supported by analysis of the writhing structure of the magnetic field.

Simulations of passive scalar transport on a three-dimensional (3D) multiresolution grid are presented within the framework of single relaxation time lattice Boltzmann method. The combined modeling of the fluid flow and scalar transport is handled by a double distribution function approach in which the velocity in the fluid flow equation is solved first and then copied to the scalar equation to solve the corresponding scalar quantities. A 3D scaling technique, considering both external forces and scalar source terms, and two-dimensional bicubic interpolation scheme are developed for coupling nonequilibrium velocity and scalar distributions on the interfaces of different resolution grids. The proposed algorithm is validated for three benchmark cases, i.e., the forced convection in a 3D channel, natural convection in a cubical cavity, and turbulent channel flow with heat transfer. Good agreements are found between the present predictions and previous data, which confirms the capability of the proposed method for the computation of passive scalar transport in 3D domains.

We demonstrate that the Einstein relation for the diffusion of a particle in the random-energy landscape with the Gaussian density of states is an exclusive one-dimensional property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish a connection between these properties and dimensionality and spatial correlation of the random-energy landscape.

Diverse processes in statistical physics are usually analyzed on the assumption that the drag force acting on a test particle moving in a resisting medium is linear on the velocity of the particle. However, nonlinear drag forces do appear in relevant situations that are currently the focus of experimental and theoretical work. Motivated by these developments, we explore the consequences of nonlinear drag forces for the thermostatistics of systems of interacting particles performing overdamped motion. We derive a family of nonlinear Fokker-Planck equations for these systems, taking into account the effects of nonlinear drag forces. We investigate the main properties of these evolution equations, including an $H$-theorem, and obtain exact solutions of the stretched $q$-exponential form.

One-dimensional anomalous heat propagation is usually characterized by a Lévy walk superdiffusive spreading function with two side peaks located on the fronts due to the finite velocity of acoustic phonons. In the case when the acoustic phonons vanish, e.g., due to the phonon-lattice interactions such that the system's momentum is not conserved, the side peaks will disappear and a normal Gaussian diffusive heat-propagating behavior will be observed. Here we show that there exists another new type of superdiffusive, non-Gaussian heat propagation but without side peaks in a typical nonacoustic, momentum-nonconserving system. It implies that thermal transport in this system disobeys the Fourier law, in clear contrast with the existing theoretical predictions. The underlying mechanism is related to an effect of optical phonon-phonon interactions. These findings may open a new avenue for further exploring thermal transport in low dimensions.

Longitudinal and transverse instabilities of gravity-capillary solitary waves on shallow water are investigated based on the numerical analysis of the fifth-order Kadomtsev-Petviashvili (KP) equation, which describes the wave phenomena on shallow water where the relevant Bond number is less than and close to 1/3. Two-dimensional (2D) depression gravity-capillary solitary waves are stable to longitudinal perturbations. 2D elevation gravity-capillary solitary waves are unstable to longitudinal perturbations and finally evolve into 2D depression gravity-capillary solitary waves. Three-dimensional (3D) finite-amplitude depression gravity-capillary solitary waves are stable to longitudinal perturbations. 3D finite-amplitude elevation gravity-capillary solitary waves are unstable to longitudinal perturbations and finally evolve into an oscillatory state between two different 3D finite-amplitude depression gravity-capillary solitary waves. 3D small-amplitude depression and elevation gravity-capillary solitary waves are unstable to dilation-type longitudinal perturbations and eventually evolve into an oscillatory state between two different 3D finite-amplitude depression gravity-capillary solitary waves. 3D small-amplitude depression and elevation gravity-capillary solitary waves are unstable to contraction-type longitudinal perturbations and eventually become dispersed out toward still water surface. Finally, 2D depression and elevation gravity-capillary solitary waves are unstable to transverse perturbations and eventually evolve into 3D finite-amplitude depression gravity-capillary solitary waves. Therefore, the only stable gravity-capillary solitary waves on shallow water are 3D finite-amplitude depression gravity-capillary solitary waves. In particular, based on the linear stability analysis, a theoretical proof is presented for the long-wave transverse instability of 2D depression and elevation gravity-capillary solitary waves on shallow water.

We investigate the stability boundaries of a quantum cascade laser subject to phase-conjugate optical feedback. From a three-level model, we reduce our set of equations to the usual modified Lang-Kobayashi equations describing a semiconductor laser subject to phase-conjugate feedback. We then determine the Hopf bifurcation conditions, which we explore by using asymptotic methods. In the limit of large delays, we find approximations of the first Hopf bifurcation that is responsible for the destabilization of the system. We obtain an expression that depends only on three parameters: the feedback strength, the line-width enhancement factor, and the pump current. From this expression, we study the stability boundaries of our system. We compare our results with the initial three-level model using a continuation method. We find qualitative and quantitative agreements of the stability boundaries with the two methods. Finally, we compare our findings with the ones obtained for a quantum cascade laser subject to conventional optical feedback.

Most of the existing methods for the robustness and targeted immunization problems can be viewed as greedy strategies, which are quite efficient but readily induce a local optimization. In this paper, starting from a percolation perspective, we develop two strategies, the relationship-related (RR) strategy and the prediction relationship (PR) strategy, to avoid a local optimum only through the investigation of interrelationships among nodes. Meanwhile, RR combines the sum rule and the product rule from explosive percolation, and PR holds the assumption that nodes with high degree are usually more important than those with low degree. In this manner our methods have a better capability to collapse or protect a network. The simulations performed on a number of networks also demonstrate their effectiveness, especially on large real-world networks where RR fragments each of them into the same size of the giant component; however, RR needs only less than $90\%$ of the number of nodes which are necessary for the most excellent existing methods.

The characterization of information processing is an important task in complex systems science. Information dynamics is a quantitative methodology for modeling the intrinsic information processing conducted by a process represented as a time series, but to date has only been formulated in discrete time. Building on previous work which demonstrated how to formulate transfer entropy in continuous time, we give a total account of information processing in this setting, incorporating information storage. We find that a convergent rate of predictive capacity, comprising the transfer entropy and active information storage, does not exist, arising through divergent rates of active information storage. We identify that active information storage can be decomposed into two separate quantities that characterize predictive capacity stored in a process: active memory utilization and instantaneous predictive capacity. The latter involves prediction related to path regularity and so solely inherits the divergent properties of the active information storage, while the former permits definitions of pathwise and rate quantities. We formulate measures of memory utilization for jump and neural spiking processes and illustrate measures of information processing in synthetic neural spiking models and coupled Ornstein-Uhlenbeck models. The application to synthetic neural spiking models demonstrates that active memory utilization for point processes consists of discontinuous jump contributions (at spikes) interrupting a continuously varying contribution (relating to waiting times between spikes), complementing the behavior previously demonstrated for transfer entropy in these processes.