Time delays play a significant role in dynamical systems, as they affect their transient behavior and the dimensionality of their attractors. The number, values, and spacing of these time delays influences the eigenvalues of a nonlinear delay-differential system at its fixed point. Here we explore a multidelay system as the core computational element of a reservoir computer making predictions on its input in the usual regime close to fixed point instability. Variations in the number and separation of time delays are first examined to determine the effect of such parameters of the delay distribution on the effectiveness of time-delay reservoirs for nonlinear time series prediction. We demonstrate computationally that an optoelectronic device with multiple different delays can improve the mapping of scalar input into higher-dimensional dynamics, and thus its memory and prediction capabilities for input time series generated by low- and high-dimensional dynamical systems. In particular, this enhances the suitability of such reservoir computers for predicting input data with temporal correlations. Additionally, we highlight the pronounced harmful resonance condition for reservoir computing when using an electro-optic oscillator model with multiple delays. We illustrate that the resonance point may shift depending on the task at hand, such as cross prediction or multistep ahead prediction, in both single delay and multiple delay cases.

We show in experiments that a long, underdense, relativistic proton bunch propagating in plasma undergoes the oblique instability, which we observe as filamentation. We determine a threshold value for the ratio between the bunch transverse size and plasma skin depth for the instability to occur. At the threshold, the outcome of the experiment alternates between filamentation and self-modulation instability (evidenced by longitudinal modulation into microbunches). Time-resolved images of the bunch density distribution reveal that filamentation grows to an observable level late along the bunch, confirming the spatiotemporal nature of the instability. We provide a rough estimate of the amplitude of the magnetic field generated in the plasma by the instability and show that the associated magnetic energy increases with plasma density.

A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.

Scar theory is one of the fundamental pillars in the field of quantum chaos, and scarred functions are a superb tool to carry out studies in it. Several methods, usually semiclassical, have been described to cope with these two phenomena. In this paper, we present an alternative method, based on the novel machine learning algorithm known as reservoir computing, to calculate such scarred wave functions together with the associated eigenstates of the system. The resulting methodology achieves outstanding accuracy while reducing execution times by a factor of ten. As an illustration of the effectiveness of this method, we apply it to the widespread chaotic two-dimensional coupled quartic oscillator.

We demonstrate that nanofluidic diodes in multipore membranes show a memristive behavior that can be controlled not only by the amplitude and frequency of the external signal but also by series and parallel arrangements of the membranes. Each memristor consists of a polymeric membrane with conical nanopores that allow current rectification due to the electrical interaction between the ionic solution and the pore surface charges. This surface charge-regulated ionic transport shows a rich nonlinear physics, including memory and inductive effects, which are characterized here by the current-voltage curves and electrical impedance spectroscopy. Also, neuromorphiclike potentiation of the membrane conductance following voltage pulses (spikes) is observed. The multipore membrane with nanofluidic diodes shows physical concepts that should have application for information processing and signal conversion in iontronics hybrid devices.

Tropical rainforests exhibit a rich repertoire of spatial patterns emerging from the intricate relationship between the microscopic interaction between species. In particular, the distribution of vegetation clusters can shed much light on the underlying process that regulates the ecosystem. Analyzing the distribution of vegetation clusters at different resolution scales, we show the first robust evidence of scale-invariant clusters of vegetation, suggesting the coexistence of multiple intertwined scales in the collective dynamics of tropical rainforests. We use field data and computational simulations to confirm our hypothesis, proposing a predictor that could be particularly interesting to monitor the ecological resilience of the world's “green lungs.”

Odd viscoelastic materials are constrained by fewer symmetries than their even counterparts. The breaking of these symmetries allows these materials to exhibit different features, which have attracted considerable attention in recent years. Immersing a bead in such complex fluids allows for probing their physical properties, highlighting signatures of their oddity and exploring the consequences of these broken symmetries. We present the conditions under which the activity of an odd viscoelastic fluid can give rise to linear instabilities in the motion of the probe particle, and we unveil how the features of the probe particle dynamics depend on the oddity and activity of the viscoelastic medium in which it is immersed.

In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large collections of diverse individuals. Many sociophysics models reproduce the emergence of collective human behavior with interacting agents, which respond to their environment according to simple rules, modulated by random fluctuations. A paragon of this class is the Ising model which, when interactions are strong, predicts that order can emerge from a chaotic initial state. In contrast with many elections, however, this model favors a strong majority. Here we introduce a new element to this classical theory, which accounts for the influence of opinion polls on the electorate. This brings about a new phase in which two groups divide the opinion equally. These political camps are spatially segregated, and the sharp boundary that separates them makes the system size dependent, even in the limit of a large electorate. Election data show that, since the early 1990s, countries with more than about a million voters often found themselves in this state, whereas elections in smaller countries yielded more consensual results. We suggest that this transition hinges on the electorate's awareness of the general opinion.

We report the observation of longitudinal filamentation of an electron-positron pair plasma in a beam-driven QED cascade. The filaments are created in the “pair-reflection” regime, where the generated pairs are partially stopped and reflected in the strong laser field. The density filaments form near the center of the laser pulse and have diameters similar to the laser wavelength. They develop and saturate within a few laser cycles and do not induce sizable magnetostatic fields. We rule out the onset of two-stream instability or Weibel instability and attribute the origin of pair filamentation to laser ponderomotive forces. The small plasma filaments induce strong scattering of laser energy to large angles, serving as a signature of collective QED plasma dynamics.

Nodes in networks that exhibit high connectivity, also called “hubs,” play a critical role in determining the structural and functional properties of networked systems. However, there is no clear definition of what constitutes a hub node in a network, and the classification of network hubs in existing work has either been purely qualitative or relies on ad hoc criteria for thresholding continuous data that do not generalize well to networks with certain degree sequences. Here we develop a set of efficient nonparametric methods that classify hub nodes in directed networks using the Minimum Description Length principle, effectively providing a clear and principled definition for network hubs. We adapt our methods to both unweighted and weighted networks, and we demonstrate them in a range of example applications using real and synthetic network data.

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at leading order. We report hydrodynamic experiments in which we investigate the interaction between two beams or jets of soliton gases having nearly identical amplitudes but opposite velocities of the same magnitude. The space-time evolution of the two interacting soliton gas jets is recorded in a 140-m-long water tank where the dynamics is described at leading order by the focusing one-dimensional nonlinear Schrödinger equation. Varying the relative initial velocity of the two species of soliton gas, we change their interaction strength and we measure the macroscopic soliton gas density and velocity changes due to the interaction. Our experimental results are found to be in good quantitative agreement with predictions of the spectral kinetic theory of soliton gas despite the presence of perturbative higher-order effects that break the integrability of the wave dynamics.

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e., the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average shape is described in terms of its Fourier components, highlighting a crossover between a diamond and a circular geometry as the noise level is increased. Generally, these isochrones can be understood as fluctuating interfaces with an inhomogeneous local width which reveals the underlying lattice structure. We show that once these inhomogeneities have been taken into account, the fluctuations fall into the Kardar-Parisi-Zhang universality class with very good accuracy, where they reproduce the Family-Vicsek Ansatz with the expected exponents and the Tracy-Widom histogram for the local radial fluctuations.

We study an exclusion process on a ring comprising a free defect particle in a bath of normal particles. The model is one of the few integrable cases in which the bath particles are partially asymmetric. The presence of the free defect creates localized or shock phases according to parameter values. We use a functional approach to Bethe equations resulting from a nested Bethe ansatz to calculate exactly the mean currents and diffusion constants. The results agree very well with Monte Carlo simulations and reveal the main modes of fluctuation in the different phases of the steady state.

Online social networks have become primary means of communication. As they often exhibit undesirable effects such as hostility, polarization, or echo chambers, it is crucial to develop analytical tools that help us better understand them. In this paper we are interested in the evolution of discord in social networks. Formally, we introduce a method to calculate the probability of discord between any two agents in the multistate voter model with and without zealots. Our work applies to any directed, weighted graph with any finite number of possible opinions, allows for various update rates across agents, and does not imply any approximation. Under certain topological conditions, the opinions are independent and the joint distribution can be decoupled. Otherwise, the evolution of discord probabilities is described by a linear system of ordinary differential equations. We prove the existence of a unique equilibrium solution, which can be computed via an iterative algorithm. The classical definition of active links density is generalized to take into account long-range, weighted interactions. We illustrate our findings on real-life and synthetic networks. In particular, we investigate the impact of clustering on discord and uncover a rich landscape of varied behaviors in polarized networks. This sheds lights on the evolution of discord between, and within, antagonistic communities.

The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological relevance of the parameters is not always clear. However, for stationary inputs, such functions can be obtained without the adjustment of free parameters by using mean-field methods. In this work, we expand current Fokker-Planck approaches to account for the concurrent influence of colored and multiplicative noise terms on generic conductance-based integrate-and-fire neurons. We reduce the resulting stochastic system through the application of the diffusion approximation to a one-dimensional Langevin equation. An effective Fokker-Planck is then constructed using Fox Theory, which is solved numerically using a newly developed double integration procedure to obtain the transfer function and the membrane potential distribution. The solution is capable of reproducing the transfer function and the stationary voltage distribution of simulated neurons across a wide range of parameters. The method can also be easily extended to account for different sources of noise with various multiplicative terms, and it can be used in other types of problems in principle.

Despite past investigations of the buckling instability, the kinetics of the buckling process is not well understood. We develop a generic framework for determining the buckling kinetics of membranes under compressive stress $\left({\sigma }_{\mathrm{b}}\right)$ via molecular dynamics simulations. The buckling time $\left(t_{\mathrm{b}}\right)$ is modeled by an extended Boltzmann-Arrhenius-Zhurkov equation accounting for temperature $\left(T\right)$ and scale-dependent bending rigidity. We discern three regimes: (I) $t_{\mathrm{b}}$ decreases with $T$; (II) $t_{\mathrm{b}}$ increases with $T$; (III) $t_{\mathrm{b}}$ is $T$ independent. Regime II coheres with the predictions of the theory of fluctuating sheets (TFS). Regime I is seen at small scales due to fluctuations about equilibrium and is not predicted by the TFS.

An indirect-drive inertial fusion experiment on the National Ignition Facility was driven using 2.05 MJ of laser light at a wavelength of 351 nm and produced $3.1\pm 0.16$ MJ of total fusion yield, producing a target gain $G=1.5\pm 0.1$ exceeding unity for the first time in a laboratory experiment [Phys. Rev. E 109, 025204 (2024)]. Herein we describe the experimental evidence for the increased drive on the capsule using additional laser energy and control over known degradation mechanisms, which are critical to achieving high performance. Improved fuel compression relative to previous megajoule-yield experiments is observed. Novel signatures of the ignition and burn propagation to high yield can now be studied in the laboratory for the first time.

In this work we present the design of the first controlled fusion laboratory experiment to reach target gain $G>1$ N221204 (5 December 2022) [Phys. Rev. Lett. 132, 065102 (2024)], performed at the National Ignition Facility, where the fusion energy produced (3.15 MJ) exceeded the amount of laser energy required to drive the target (2.05 MJ). Following the demonstration of ignition according to the Lawson criterion N210808, experiments were impacted by nonideal experimental fielding conditions, such as increased (known) target defects that seeded hydrodynamic instabilities or unintentional low-mode asymmetries from nonuniformities in the target or laser delivery, which led to reduced fusion yields less than 1 MJ. This Letter details design changes, including using an extended higher-energy laser pulse to drive a thicker high-density carbon (also known as diamond) capsule, that led to increased fusion energy output compared to N210808 as well as improved robustness for achieving high fusion energies (greater than 1 MJ) in the presence of significant low-mode asymmetries. For this design, the burnup fraction of the deuterium and tritium (DT) fuel was increased (approximately $4\%$ fuel burnup and a target gain of approximately 1.5 compared to approximately $2\%$ fuel burnup and target gain approximately 0.7 for N210808) as a result of increased total (DT plus capsule) areal density at maximum compression compared to N210808. Radiation-hydrodynamic simulations of this design predicted achieving target gain greater than 1 and also the magnitude of increase in fusion energy produced compared to N210808. The plasma conditions and hotspot power balance (fusion power produced vs input power and power losses) using these simulations are presented. Since the drafting of this manuscript, the results of this paper have been replicated and exceeded (N230729) in this design, together with a higher-quality diamond capsule, setting a new record of approximately $3.88\mathrm{MJ}$ of fusion energy and fusion energy target gain of approximately 1.9.

Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when ${\eta }_{0}k$, the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same ${\eta }_{0}k$ but different length scales, characterized by the wavelength $\lambda$ varying by a factor of 4.9 from 65 to 130 to $320\mu \mathrm{m}$. Three such targets with different fixed ${\eta }_0{k}^{\prime }\mathrm{s}$ were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as $\lambda$ decreased. The different ${\eta }_{0}k$ targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for $320-65\mu \mathrm{m}$ wavelength perturbations, the effective strain rates increased from $8.7\times {10}^6$ to $3.3\times {10}^7{\mathrm{s}}^{-1}$, a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates.

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. We present a detailed study of these periodic solutions and their bifurcations. Starting from an integrodifferential model, we show how to reduce the system to a set of finite-dimensional maps. We then demonstrate that the parameter regions of existence of periodic solutions can be understood in terms of discontinuity-induced bifurcations and their stability is determined by smooth bifurcations. Using this technique, we are able to show that slowly oscillating solutions are always stable if they exist. We also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions.