The nonlinear excitation of zonal flows (ZFs) generated by the ion-temperature-gradient turbulence in a tokamak plasma is investigated by using the global gyrokinetic code nlt. It is found that ZFs are initially driven by the nonlinear self-interaction of the eigenmode. In the nonlinear saturation, the modulational instability becomes important, and its contribution to ZFs can finally be comparable to that of the self-interaction mechanism. More importantly, both types of nonlinear wave-wave interactions can be well described by the turbulent energy flux model.

Probabilistic cellular automata provide a simple framework for exploring classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state along a fictitious discrete time dimension via the sequential application of quantum gates. The resulting $(1+1)$-dimensional space-time structure makes these automata special cases of recurrent quantum neural networks which can implement broad classes of classical nonequilibrium processes. Here, we present a general prescription by which these models can be extended into genuinely quantum nonequilibrium models via the systematic inclusion of asynchronism. This is illustrated for the classical contact process, where the resulting model is closely linked to the quantum contact process (QCP), developed in the framework of open quantum systems. Studying the mean-field behavior of the model, we find evidence of an “asynchronism transition,” i.e., a sudden qualitative change in the phase transition behavior once a certain degree of asynchronicity is surpassed, a phenomenon we link to observations in the QCP.

While there are many physical processes showing subdiffusion and some useful particle models for understanding the underlying mechanisms have been established, a systematic study of subdiffusive energy transport is still lacking. Here we present convincing evidence that, in the range of system size investigated, the energy subdiffusion can take place in a Hamiltonian lattice system with both harmonic nearest-neighbor and anharmonic long-range interactions. In particular, we show that the interaction range dependence of antipersistent energy-current correlations are relevant to this special type of energy subdiffusion. The underlying mechanisms are related to the various scattering processes of phonons and discrete breathers. Our results shed light on understanding the extremely slow energy transport.

Heat and noise control is essential for the continued development of quantum technologies. For this purpose, a particularly powerful tool is the heat rectifier, which allows for heat transport in one configuration of two baths but not the reverse. Here we propose a class of rectifiers that exploits the unidirectionality of a low temperature bath to force the system into a dark state, thus blocking heat transport in one configuration of the two baths. However, if the two baths are switched around, a heat current is observed. An implementation using a qutrit coupled to two harmonic oscillators is proposed and rectification values beyond ${10}^3$ are achieved for realistic parameter values. Furthermore, we show that the heat current can be amplified by an order of magnitude through external driving without diminishing the diode functionality. The heat rectification effect is seen for a large range of parameters and it is robust towards both decay and dephasing.

Using combinatorial optimization techniques we study the critical properties of the two- and three-dimensional Ising models with uniformly distributed random antiferromagnetic couplings $(1\le J_i\le 2)$ in the presence of a homogeneous longitudinal field, $h$, at zero temperature. In finite systems of linear size, $L$, we measure the average correlation function, $C_L(\ell ,h)$, when the sites are either on the same sublattice, or they belong to different sublattices. The phase transition, which is of first order in the pure system, turns to mixed order in two dimensions with critical exponents $1/\nu \approx 0.5$ and $\eta \approx 0.7$. In three dimensions we obtain $1/\nu \approx 0.7$, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.

Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic Hamiltonians studied in this context so far is the presence of random terms that act as a source of disorder. Here we introduce tight-binding billiards in two dimensions, which are described by noninteracting spinless fermions on a disorder-free square lattice subject to curved open (hard-wall) boundaries. We show that many properties of tight-binding billiards match those of quantum-chaotic quadratic Hamiltonians: The average entanglement entropy of many-body eigenstates approaches the random matrix theory predictions and one-body observables in single-particle eigenstates obey the single-particle eigenstate thermalization hypothesis. On the other hand, a degenerate subset of single-particle eigenstates at zero energy (i.e., the zero modes) can be described as chiral particles whose wave functions are confined to one of the sublattices.

The kinetic equation for anisotropic motion-by-curvature is ill posed when the surface energy is strongly anisotropic. In this case, corners or edges are present on the Wulff shape, which span a range of missing orientations. In the sharp-interface problem the surface energy is augmented with a curvature-dependent term that rounds the corners and regularizes the dynamic equations. This introduces a new length scale in the problem, the corner size. In phase-field theory, a diffuse description of the interface is adopted. In this context, an approximation of the Willmore energy can be added to the phase-field energy so as to regularize the model. In this paper, we discuss the convergence of the Allen-Cahn version of the regularized phase-field model toward the sharp-interface theory for strongly anisotropic motion-by-curvature in three dimensions. Corners at equilibrium are also compared to theory for different corner sizes. Then we investigate the dynamics of the faceting instability, when initially unstable surfaces decompose into stable facets. For crystal surfaces with trigonal symmetry, we find the following scaling law $L\sim t^{1/3}$, for the growth in time $t$ of a characteristic morphological length scale $L$, and coarsening is found to proceed by either edge contraction or cube removal, as in the sharp-interface problem. Finally, we study nucleation of crystal surfaces in a two-phase system, as for a terrace-and-step surface. We find that, as compared with saddle-point nucleation, ridge crossing is dynamically favored. However, the induced nucleation mechanism, when a facet induces at its wake formation of additional facets, is not evidenced with a type-A dynamics.

In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps and Hamiltonians with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This makes possible to determine explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation, as well as an extension of the work by Neishtadt et al. [Regul. Chaotic Dyn. 18, 686 (2013)] on a restricted class of quasi-integrable systems with time-dependent exciters.

In the brain, common inputs play an important role in eliciting synchronous firing in the assembly of neurons. However, common inputs are usually unknown to observers. If an unobserved common input can be reconstructed only from outputs, it would be beneficial to the understanding of communication in the brain. Thus, we have developed a method for reconstructing a common input only from output firing rates of uncoupled neuron models. To this end, we propose a superposed recurrence plot (SRP) comprising points determined by using a union of points at each pixel among multiple recurrence plots. The SRP method can reconstruct a common input when using various types of neurons with different firing rate baselines, even when using uncoupled neuron models that exhibit chaotic responses. The SRP method robustly reconstructs the common input applied to the neuron models when we select adequate time windows to calculate the firing rates in accordance with the width of the fluctuations. These results suggest that certain information is embedded in the firing rate. These findings could be a possible basis for analyzing whole-brain communication utilizing rate coding.

We present a benchmark study of autonomous, chemical agents exhibiting associative learning of an environmental feature. Associative learning systems have been widely studied in cognitive science and artificial intelligence but are most commonly implemented in highly complex or carefully engineered systems, such as animal brains, artificial neural networks, DNA computing systems, and gene regulatory networks, among others. The ability to encode environmental information and use it to make simple predictions is a benchmark of biological resilience and underpins a plethora of adaptive responses in the living hierarchy, spanning prey animal species anticipating the arrival of predators to epigenetic systems in microorganisms learning environmental correlations. Given the ubiquitous and essential presence of learning behaviors in the biosphere, we aimed to explore whether simple, nonliving dissipative structures could also exhibit associative learning. Inspired by previous modeling of associative learning in chemical networks, we simulated simple systems composed of long- and short-term memory chemical species that could encode the presence or absence of temporal correlations between two external species. The ability to learn this association was implemented in Gray-Scott reaction-diffusion spots, emergent chemical patterns that exhibit self-replication and homeostasis. With the novel ability of associative learning, we demonstrate that simple chemical patterns can exhibit a broad repertoire of lifelike behavior, paving the way for in vitro studies of autonomous chemical learning systems, with potential relevance to artificial life, origins of life, and systems chemistry. The experimental realization of these learning behaviors in protocell or coacervate systems could advance a new research direction in astrobiology, since our system significantly reduces the lower bound on the required complexity for autonomous chemical learning.

When exposed to an external magnetic field, 2D layers of spherical superparamagnetic colloids form specific structures which depend on the features of the external field. If the magnetic field is constant along time, superparamagnetic colloids self-organize into chains oriented in the direction of the field. If the magnetic field is rotating in the plane of the suspension, below a critical frequency, the superparamagnetic beads still aggregate into chains, but these chains rotate with the magnetic field. When the rotation reaches a certain speed, the colloids aggregate in rotating disklike clusters. In this work, we focused on the early stages of the disklike clusters' aggregation and the dynamics of this process. In particular, we observed experimentally that before clustering into disklike structures, the colloids were aggregating into rotating chains, just as they did in suspensions submitted to a magnetic field rotating at a lower rate. Over time, the chains interact with one another and aggregate into disklike clusters, resulting in a mixture of chains and disks in the sample. Finally, we propose a model to characterize the suspension over time in terms of the proportion of chains and disklike clusters, and report its deduced temporal evolution for different frequencies and volume fractions.

The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to be weakly conducting, so that that the leaky dielectric model applies. The Laplace equation for the electric potential is solved in bipolar coordinate system and the potential is obtained in terms of a series expansion of Legendre polynomials. The force on the particle is calculated using the Maxwell tensor. We find that in the case of normal electric field, which corresponds to a particle near an electrode, the force is always attractive but at a given separation it varies nontrivially with particle-suspending medium conductivity ratio; the force on a particle that is more conducting than the suspending medium is much larger compared to the force on a particle less conducing than the suspending medium. In the case of tangential electric field, which corresponds to a particle near an insulating boundary, the force is always repulsive.

One of the unusual liquid crystalline phases exhibited by some compounds with bent-core (BC) molecules is designated as $\mathrm{Sm}A{P}_R$, in which transverse polarization (P) of smectic layers with upright molecules has a random orientational distribution. Most of such compounds undergo a transition to the $\mathrm{Sm}A{P}_A$ phase with antiferroelectric order of adjacent layers as the temperature is lowered. Second harmonic studies have shown that the medium consists of polarized domains with only a few hundred molecules, the number increasing at lower temperatures. This is in contrast to the random orientations of entire layers predicted by a few phenomenological models which have been proposed for the $\mathrm{Sm}A{P}_R$ phase. In this paper we show that the two-state model, developed earlier by us to describe modulated phases found in compounds with BC molecules, can successfully account for all the experimental results on the $\mathrm{Sm}A{P}_R$ phase. It is proposed that polarized domains which are made of ground state conformers, with a large bend of the aromatic cores, nucleate as circular disks in a first order transition from the isotropic phase. Excited state conformers (with a smaller bend) freely rotate about their long axes and surround the disks. The polarization in the disk has a spontaneous splay distortion which generates a texture with an expelled center of a partial disclination. The interdisk electrostatic energy is lower than the thermal energy and the disks are subject to significant rotational fluctuations, resulting in the uniaxial symmetry of the medium. Calculated equilibrium properties of the medium as functions of temperature and electric field reflect the trends seen in experiments. The model overestimates properties such as the radius of the disks as the transition to a lower temperature uniform phase is approached, and physical arguments are given to show that interlayer interactions ignored in the model become important in that regime, and should be included for an improved description of the medium.

Electron-beam plasma interaction has long been a topic of great interest. Despite the success of the quasilinear and weak turbulence theories, their validities are limited by the requirements of a sufficiently dense mode spectrum and a small wave amplitude. In this paper, we extensively study the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma by performing high-resolution two-dimensional particle-in-cell simulations and using analytical theories. We confirm that, during the initial stage of two-stream instability between the beam and background cold electrons, it is saturated due to the well-known wave-trapping mechanism. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the regimes are analyzed in detail. We identify a new regime in the strong Langmuir turbulence featured by what we call electron modulational instability (EMI) that could create a local Langmuir wave packet growing faster than the ion plasma frequency. Ions do not have time to respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually, the beam-plasma wave interaction stops being resonant due to the strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction occurs in a repetitive (intermittent) process. The beam electrons are strongly scattered by waves, and the Langmuir wave spectrum is significantly broadened, which in turn gives rise to strong heating of bulk electrons. Associated energy transfer from the beam to the background plasma electrons has been studied. A resulting kappa (κ) distribution and a wave-energy spectrum $E^2\left(k\right)\sim k^{-5}$ are observed in the strong turbulent regime.

The superlubric-pinned transition in the depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by 2D triangular periodic substrates is investigated using Langevin dynamical simulations. When the lattice structure of the 2D solid dusty plasma perfectly matches the triangular substrate, two distinctive pinned and moving ordered states are observed as the external uniform driving force gradually increases from zero. When there is a mismatch between the lattice structure and the triangular substrate, however, on shallow substrates, it is discovered that all of the particles can slide freely on the substrate even when the applied driving force is tiny. This is a typical example of superlubricity, which is caused by the competition between the substrate-particle and particle-particle interactions. If the substrate depth increases further, as the driving force increases from zero, there are three dynamical states consisting of the pinned state, the disordered plastic flow state, and the moving ordered state. In an underdense system, where there are fewer particles than potential well minima, it is found that the occurrence of the three different dynamical states is controlled by the depth of the substrate, which is quantitatively characterized using the average mobility.

When a plane electromagnetic wave impinges on a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the outgoing waves in one or more radiation channels vanish. Zero reflection, zero transmission, and perfect absorption are important examples of diffraction anomalies, and they are useful for manipulating electromagnetic waves and light. Since diffraction anomalies appear only at specific frequencies and/or wave vectors, and may require the tuning of structural or material parameters, they are relatively difficult to find by standard numerical methods. Iterative methods may be used, but good initial guesses are required. To determine all diffraction anomalies in a given frequency interval, it is necessary to repeatedly solve the diffraction problem for many frequencies. In this paper, an efficient numerical method is developed for computing diffraction anomalies. The method relies on nonlinear eigenvalue formulations for scattering anomalies and solves the nonlinear eigenvalue problems by a contour-integral method. Numerical examples involving periodic arrays of cylinders are presented to illustrate the new method.

Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.

Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer system variability, hampering noise-induced regime shifts. Our analysis also shows that, in the considered cooperativity range, impending regime shifts can be generically detected by statistical early warning signals from distributional data. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality.

Dynamical simulation of the cascade failures on the Europe and United States (U.S.) high-voltage power grids has been done via solving the second-order Kuramoto equation. We show that synchronization transition happens by increasing the global coupling parameter $K$ with metasatble states depending on the initial conditions so that hysteresis loops occur. We provide analytic results for the time dependence of frequency spread in the large-$K$ approximation and by comparing it with numerics of $d=2,3$ lattices, we find agreement in the case of ordered initial conditions. However, different power-law (PL) tails occur, when the fluctuations are strong. After thermalizing the systems we allow a single line cut failure and follow the subsequent overloads with respect to threshold values $T$. The PDFs $p\left(N_f\right)$ of the cascade failures exhibit PL tails near the synchronization transition point $K_c$. Near $K_c$ the exponents of the PLs for the U.S. power grid vary with $T$ as $1.4\le \tau \le 2.1$, in agreement with the empirical blackout statistics, while on the Europe power grid we find somewhat steeper PLs characterized by $1.4\le \tau \le 2.4$. Below $K_c$, we find signatures of $T$-dependent PLs, caused by frustrated synchronization, reminiscent of Griffiths effects. Here we also observe stability growth following the blackout cascades, similar to intentional islanding, but for $K>K_c$ this does not happen. For $T<T_c$, bumps appear in the PDFs with large mean values, known as “dragon king” blackout events. We also analyze the delaying or stabilizing effects of instantaneous feedback or increased dissipation and show how local synchronization behaves on geographic maps.