We consider instability and localized patterns arising from the long-wave–short-wave resonance in the nonintegrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and the instability with a bubblelike spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.

Model-free reconstruction of bifurcation diagrams of Chua's circuits using the technique of parameter-aware reservoir computing is investigated. We demonstrate that (1) reservoir computer can be utilized as a noise filter to restore the system dynamics from noisy signals; (2) for a single Chua circuit, a machine trained by the noisy time series measured at several sampling states is capable of reconstructing the whole bifurcation diagram of the circuit with a high precision; and (3) for two coupled chaotic Chua circuits with mismatched parameters, the machine trained by the noisy time series measured at several coupling strengths is able to anticipate the variation of the synchronization degree of the coupled circuits with respect to the coupling strength over a wide range. Our studies verify the capability of the technique of parameter-aware reservoir computing in learning the dynamics of chaotic circuits from noisy signals, signifying the potential application of this technique in reconstructing the bifurcation diagram of real-world chaotic systems.

In many applications in biology, engineering, and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical divergences quantify the difference between two distributions. However, their estimation is very difficult and empirical methods often fail, especially when the samples are small. We develop a Bayesian estimator of the Kullback-Leibler divergence between two probability distributions that makes use of a mixture of Dirichlet priors on the distributions being compared. We study the properties of the estimator on two examples: probabilities drawn from Dirichlet distributions and random strings of letters drawn from Markov chains. We extend the approach to the squared Hellinger divergence. Both estimators outperform other estimation techniques, with better results for data with a large number of categories and for higher values of divergences.

Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static triadic closure (STC) model for clustered networks, whereby starting from an arbitrary fixed backbone network, each triad is closed independently with a given probability. Assuming a locally treelike backbone we derive exact expressions for the expected number of various small, loopy motifs (triangles, 4-loops, diamonds, and 4-cliques) as a function of moments of the backbone degree distribution. In this way we determine how transitivity and its suitably defined generalizations for higher-order motifs depend on the heterogeneity of the original network, revealing the existence of transitions due to the interplay between topologically inequivalent triads in the network. Furthermore, under reasonable assumptions for the moments of the backbone network, we establish approximate relationships between motif densities, which we test in a large dataset of real-world networks. We find a good agreement, indicating that STC is a realistic mechanism for the generation of clustered networks, while remaining simple enough to be amenable to analytical treatment.

We study the effects of inertia in dense suspensions of polar swimmers. The hydrodynamic velocity field and the polar order parameter field describe the dynamics of the suspension. We show that a dimensionless parameter $R$ (ratio of the swimmer self-advection speed to the active stress invasion speed [Phys. Rev. X 11, 031063 (2021)]) controls the stability of an ordered swimmer suspension. For $R$ smaller than a threshold $R_1$, perturbations grow at a rate proportional to their wave number $q$. Beyond $R_1$ we show that the growth rate is $\mathcal{O}\left(q^2\right)$ until a second threshold $R=R_2$ is reached. The suspension is stable for $R>R_2$. We perform direct numerical simulations to characterize the steady-state properties and observe defect turbulence for $R<R_2$. An investigation of the spatial organization of defects unravels a hidden transition: for small $R\approx 0$ defects are uniformly distributed and cluster as $R\to R_1$. Beyond $R_1$, clustering saturates and defects are arranged in nearly stringlike structures.

Twist-bend (${\mathrm{N}}_{\mathrm{tb}}$) and ferroelectric (${\mathrm{N}}_{\mathrm{F}}$) nematic liquid crystals exhibit several novel effects and new physical properties. Here, we report experimental studies on the phase diagram and some physical properties of binary mixtures of CB9CB and RM734 mesogens. Both N-${\mathrm{N}}_{\mathrm{tb}}$ and N-${\mathrm{N}}_{\mathrm{F}}$ phase transition temperatures and the corresponding enthalpies decrease significantly and, eventually, these transitions disappear at some intermediate compositions, stabilizing wide nematic phase (N). Temperature-dependent birefringence several degrees above the N-${\mathrm{N}}_{\mathrm{tb}}$ phase transition shows strong director tilt fluctuations. The critical range of the fluctuations increases with the nematic range and the critical exponent is consistent with the mean field. The spontaneous polarization of RM734 decreases drastically with the addition of CB9CB mesogen. The temperature dependence of the splay elastic constant of the mixtures' high-temperature nematic (N) phase strikingly differs from that of the pristine CB9CB and RM734 mesogens. The study shows that a small inclusion of either compound has a substantial effect on the phase diagram and physical properties.

To better understand the three-dimensional topology of the interaction between the shock train and the background wave, the steady and dynamic characteristics of a shock train were investigated using wind-tunnel experiments and numerical simulation. A 14° wedge placed at the bottom and sidewalls was used to generate background waves traveling in different directions. Mounting the wedge on the bottom wall at an incoming Mach number of 1.85 leads to the formation of two symmetric and two asymmetric λ-shaped shock train leading shocks (STLSs), while an incoming Mach number of 2.70 results in one symmetric and two asymmetric X-shaped STLSs. The shock train, which runs perpendicular to the background wave, is always symmetrical at an incoming Mach number of 1.85 when the wedge is mounted on the lateral wall. A flow phenomenon in which the STLS transforms from asymmetric to symmetric after undergoing rapid movement is observed at an incoming Mach number of 2.70. The mean and root-mean-square (rms) pressure profiles confirm the morphological transformation of the STLS. The dynamic properties of the shock train are analyzed by combining the STLS trajectory with the transient wall pressure. Power spectral-density analysis reveals that the frequency of pressure oscillations is independent of whether the shock train is in the same flow cross section as the background wave and depends only on the incoming Mach number and the backpressure. The three-dimensional steady-state numerical simulation reveals the mutual interference structure of the background wave and shock train.

It was observed experimentally that after crossing a waveguide filled with a neutral gas a short powerful microwave pulse leaves a periodic glow of plasma along the waveguide, persisting for several tens of nanoseconds. A theoretical model is presented which in combination with numerical simulations proposes a possible explanation for this phenomenon.

The possibility of existence of weak ferromagnetism in antiferromagnetic systems on the body-centered octahedral lattice is investigated in the framework of the corresponding spin-$1/2J_1\text{−}{J}_2$ model in the recursive-lattice approach. The exact solution of the model is found and its phase diagram is determined. The magnetic and thermodynamic properties of all phases are studied, the nature of all phase transitions is established, and an equation that determines the positions of all second-order phase transitions of the model is found. The magnetic and entropy properties of all ground states of the model are also determined. It is shown that the weak ferromagnetism predicted earlier in the pure spin-$1/2$ antiferromagnetic system on the octahedral lattice remains present even in the case of the model on the body-centered octahedral lattice with antiferromagnetic as well as ferromagnetic interactions between the central site of each elementary octahedron and each of its vertices. However, the presence of the interacting central site suppresses the weak ferromagnetism at very low temperatures, where the standard antiferromagnetic phase emerges. At the same time, the temperature region with the antiferromagnetic phase increases with simultaneous decreasing of the region, where the weak ferromagnetism can be observed, when the strength of the interaction between the central site of each elementary octahedron and each of its vertices increases. Moreover, the phenomenon of weak ferromagnetism disappears completely when this interaction becomes sufficiently stronger than the nearest-neighbor antiferromagnetic interaction between spin variables placed in vertices of each elementary octahedron of the lattice. Moreover, the possibility of the existence of the classical spin-liquid behavior in such magnetic systems is also discussed.

Cooperation and defection are social traits whose evolutionary origin is still unresolved. Recent behavioral experiments with humans suggested that strategy changes are driven mainly by the individuals' expectations and not by imitation. This work theoretically analyzes and numerically explores an aspiration-driven strategy updating in a well-mixed population playing games. The payoffs of the game matrix and the aspiration are condensed into just two parameters that allow a comprehensive description of the dynamics. We find continuous and abrupt transitions in the cooperation density with excellent agreement between theory and the Gillespie simulations. Under strong selection, the system can display several levels of steady cooperation or get trapped into absorbing states. These states are still relevant for experiments even when irrational choices are made due to their prolonged relaxation times. Finally, we show that for the particular case of the prisoner dilemma, where defection is the dominant strategy under imitation mechanisms, the self-evaluation update instead favors cooperation nonlinearly with the level of aspiration. Thus, our work provides insights into the distinct role between imitation and self-evaluation with no learning dynamics.

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second- and higher-order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the low dissipation limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE, the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.

The spatial public goods game has been used to examine factors that promote cooperation. Owing to the complexity of the dynamics of this game, previous studies on this model neglected analytical approaches and relied entirely on numerical calculations using the Monte Carlo (MC) simulations. In this paper, we present the approximate master equations (AMEs) for this model. We report that the results obtained by the AMEs are mostly qualitatively consistent with those obtained by the MC simulations. Furthermore, we show that it is possible to obtain phase boundaries analytically in certain parameter regions. In the region where the noise in strategy decisions is very large, the phase boundary can be obtained analytically by considering perturbations from the steady state of the voter model. In the noiseless region, discontinuous phase transitions occur because of the characteristics of the function that represents strategy updating. Our approach is useful for clarifying the details of the mechanisms that promote cooperation and can be easily applied to other group interaction models.

We study the transition from cohesive to noncohesive states of cemented granular materials (synthetic rocks) under oedometric loading, combining simultaneous measurements of ultrasound velocity and acoustic emission (AE: microseosmicity). Our samples are agglomerates made of glass beads bonded with a few percent of cement, either ductile or brittle. These cemented granular samples exhibit an inelastic compaction beyond certain axial stresses likely due to the formation of compaction bands, which is accompanied by a significant decrease of compressional wave velocity. Upon subsequent cyclic unloading-reloading with constant consolidation stress, we found the mechanical and acoustic responses like those in noncohesive granular materials, which can be interpreted within the effective medium theory based on the Digby's bonding model. Moreover, this model allows P-wave velocity measured at vanishing pressure to be interpreted as an indicator of the debonding on the scale of grain contact. During the inelastic compaction, stick-slip-like stress drops were observed in brittle cement-bonded granular samples accompanied by the instantaneous decrease of the P-wave velocity and AEs which display an Omori-like law for foreshocks, i.e., precursors. By contrast, mechanical responses of ductile cement-bonded granular samples are smooth (without visible stick-slip-like stress drops) and mostly aseismic. By applying a cyclic loading-unloading with increasing consolidation stress, we observed a Kaiser-like memory effect in the brittle cement-bonded sample in the weakly damaged state which tends to disappear when the bonds are mostly broken in the noncohesive granular state after large-amplitude loading. In this paper, we show that the macroscopic ductile and brittle behavior of cemented granular media is controlled by the local processes on the scale of the bonds between grains.

Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data, that complex systems are composed of multiple units experiencing many-body interactions that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a topology solely involving many-body, nonlocal, and nonregular interactions, hereby named nonlocal $d$-hyperring, $(d+1)$ being the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and we show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are “flattened” to pairwise ones, the chimera behavior is weaker and more elusive.

Controlling environmental effects in surface plasticity/fracture of metals is of interest for areas as diverse as manufacturing processes, product performance, and structural safety. The key to controlling these effects is understanding the effect of adsorbates on surface energy $\left(\gamma \right)$ and surface stress $\left(f\right)$. While $\gamma$ has been well studied, the role of surface stress has received much less attention. We characterize surface stress induced in metals by adsorption of organic monolayers. Linear alkanoic acids of varying chain length (3–18) are deposited by molecular self-assembly onto one side of an aluminum cantilever, several centimeters in length. The surface stress is estimated from in situ measurement of the cantilever deflection. We find that the organic adsorbates induce large surface stress of $-4$ to $+30\mathrm{N}/\mathrm{m}$. Furthermore, we show that $f$ may be tuned by varying adsorbate-molecule chain length. The stress data explain beneficial embrittlement of metal surfaces by organic adsorbates in cutting and comminution processes, and point to a critical role, hitherto ignored, for $f$ in environment assisted cracking (EAC) phenomena. Our results suggest opportunities for utilizing controlled environment-assisted fracture as an aid—fracture as a friend—to enhance material removal processes, apart from using surface stress itself as an experimental probe to explore various manifestations of EAC.

In the present work we explore the interaction of a quasi-one-dimensional line kink of the sine-Gordon equation moving in two-dimensional spatial domains. We develop an effective equation describing the kink motion, characterizing its center position dynamics as a function of the transverse variable. The relevant description is valid both in the Hamiltonian realm and in the nonconservative one bearing gain and loss. We subsequently examine a variety of different scenarios, without and with a spatially dependent heterogeneity. The latter is considered both to be one dimensional ($y$ independent) and genuinely two dimensional. The spectral features and the dynamical interaction of the kink with the heterogeneity are considered and comparison with the effective quasi-one-dimensional description (characterizing the kink center as a function of the transverse variable) is also provided. Generally, good agreement is found between the analytical predictions and the computational findings in the different cases considered.

Contact tracing, the practice of isolating individuals who have been in contact with infected individuals, is an effective and practical way of containing disease spread. Here we show that this strategy is particularly effective in the presence of social groups: Once the disease enters a group, contact tracing not only cuts direct infection paths but can also pre-emptively quarantine group members such that it will cut indirect spreading routes. We show these results by using a deliberately stylized model that allows us to isolate the effect of contact tracing within the clique structure of the network where the contagion is spreading. This will enable us to derive mean-field approximations and epidemic thresholds to demonstrate the efficiency of contact tracing in social networks with small groups. This analysis shows that contact tracing in networks with groups is more efficient the larger the groups are. We show how these results can be understood by approximating the combination of disease spreading and contact tracing with a complex contagion process where every failed infection attempt will lead to a lower infection probability in the following attempts. Our results illustrate how contact tracing in real-world settings can be more efficient than predicted by models that treat the system as fully mixed or the network structure as locally treelike.

Free energies (FEs) in molecular sciences can be used to quantify the stability of folded molecules. In this article, we introduce nanopores for measuring FEs. We pull DNA hairpin-forming molecules through a nanopore, measure work, and estimate the FE change in the slow limit, and with the Jarzynski fluctuation theorem (FT) at fast pulling times. We also pull our molecule with optical tweezers, compare it to nanopores, and explore how sampling single molecules from equilibrium or a folded ensemble affects the FE estimate via the FT. The nanopore experiment helps us address and overcome the conceptual problem of equilibrium sampling in single-molecule pulling experiments. Only when molecules are sampled from an equilibrium ensemble do nanopore and tweezer FE estimates mutually agree. We demonstrate that nanopores are very useful tools for comparing FEs of two molecules at finite times and we propose future applications.

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

We discuss conditions for the enhancement of fusion reactivities arising from different choices of energy distribution functions for the reactants. The key element for potential gains in fusion reactivity is identified in the functional dependence of the tunneling coefficient on the energy, ensuring the existence of a finite range of temperatures for which reactivity of fusion processes is boosted with respect to the Maxwellian case. This is shown using a convenient parametrization of the tunneling coefficient dependence on the energy, analytically in the simplified case of a bimodal Maxwell-Boltzmann distribution, and numerically for kappa distributions. We then consider tunneling potentials progressively better approximating fusion processes and evaluate in each case the average reactivity in the case of kappa distributions.