Highly stretchable elastomers show a well-known discontinuous fracture transition, involving crack propagation speed becoming double-valued within a certain window of network stretching. This transition can occur either in continuous stretching or after a sizable step stretch. Crack propagation speed increases sharply with rising temperature, suggesting that dissociation of backbone bonds of network strands is the origin of fracture. Consequently, the nature of transition appears to be related to how the network evolves to redistribute strand tension, getting more strands to participate in the fast crack growth on the upper branch of the transition. Beyond the upper bound of the transition window, sufficiently high stretching leads to only the fast crack growth because load-bearing network strands cannot survive due to the higher bond tension on longer timescales. Conversely, below a minimal degree of stretching, the transition also disappears, and the fracture proceeds with slow crack growth, where very few network strands are ready to undergo chain scission necessary for fracture.

We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme-value statistics of unconfined stochastic processes. This mapping holds regardless of the statistics of the noise driving the dynamics. We first apply this result within Brownian motion theory, deriving the noncrossing probability of a Brownian path with a specific family of curves, from which several well-known results in the field can be recovered in a unified way. We then extend the analysis to non-Markovian processes, using the mapping to a steady-state to compute the long-time noncrossing probability of a pair of run-and-tumble and Brownian particles.

We report experimental observations demonstrating that, in anisotropic media, fatigue cracks under cyclic loading follow strikingly different paths than quasistatic cracks under monotonic loading. We find a qualitatively similar behavior in a computational model, which suggests that this path difference is a general phenomenon. In both experiments and computations, quasistatic cracks follow paths governed by the anisotropy of the fracture energy, as theoretically expected. In contrast, fatigue cracks follow paths predominantly dictated by the symmetry of the loading with the microstructure playing a negligible or subdominant role. Those results pave the way for future studies aimed at elucidating the failure mechanisms underlying this surprising behavior.

In traditional indirect-drive double-shell inertial confinement fusion, high-energy x-ray preheat has always been identified as a major source of degrading implosion performance. However, a significant increase of the neutron yield is observed in ignition-like double-shell implosion experiments performed at Shenguang laser facility by intentionally utilizing high-energy x-ray preheat, mostly from the $M$-band. Permission of more $M$-band x-ray absorption inside the inner shell can both significantly mitigate the mix between the fuel and shell with a more stable Awtood number at the fuel-shell interface during the shell deceleration and slightly improve the symmetry of the imploding shell with a high entropy state of the shell, and the contribution outweighs the potential detriment to destabilizing the inner shell from the $M$-band preheat, which is consistent with radiation-hydrodynamics simulations and theoretical analysis. This novel understanding of the favorable impact of high-energy x-ray preheat on double-shell implosion could facilitate to achieve volumetric ignition and burn with high-Z shells.

We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes—directed bond percolation and branching and annihilating random walks with an even number of offspring. We find that the uncentered PCA of data sets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation, we are furthermore able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of data sets.

Ant colony optimization leverages the parameter $\alpha$ to modulate the decision function's sensitivity to pheromone levels, balancing the exploration of diverse solutions with the exploitation of promising areas. Identifying the optimal value for $\alpha$ and establishing an effective annealing schedule remain significant challenges, particularly in complex optimization scenarios. This study investigates the $\alpha$-annealing process of the linear ant system within the infinite-range Ising model to address these challenges. Here, “linear” refers to the decision function employed by the ants. By systematically increasing $\alpha$, we explore its impact on enhancing the search for the ground state. We derive the Fokker-Planck equation for the pheromone ratios and obtain the joint probability density function (PDF) in stationary states. As $\alpha$ increases, the joint PDF transitions from a monomodal to a multimodal state. In the homogeneous fully connected Ising model, $\alpha$-annealing facilitates the transition from a trivial solution at $\alpha =0$ to the ground state. The parameter $\alpha$ in the annealing process plays a role analogous to the transverse field in quantum annealing. Our findings demonstrate the potential of $\alpha$-annealing in navigating complex optimization problems, suggesting its broader application beyond the infinite-range Ising model.

Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiring the Hessian information, the SPM evolves a single pair of spring-coupled particles on an energy surface. By designing complementary drifting and climbing dynamics based on gradient decomposition, the spring pair converges onto the minimum energy path (MEP) and spontaneously aligns its orientation with the MEP tangent, providing a reliable ascent direction for efficient convergence to saddle points. The SPM fundamentally differs from traditional surface walking methods that rely on the eigenvectors of the Hessian, which may deviate from the MEP tangent and potentially lead to convergence failure or undesired saddle points. The efficiency of the SPM for finding saddle points is verified by ample examples, including Lennard-Jones clusters, Morse clusters, water clusters, and the Landau energy functional involving quasicrystal phase transitions.

While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to the stability of the grid, are traditionally studied numerically with the conventional viewpoint of two regimes of extended (inter-area) or localized (intra-area) modes. In this article we introduce an analogy based on stochastic quantum models and demonstrate its applicability to power systems. We show from simple models that at low frequency the mean free path induced by disorder is inversely cubic in the frequency. This stems from the Courant-Fisher-Weyl theorem [Teschl, Mathematical methods in quantum mechanics (American Mathematical Soc., 2014), Vol. 157], a characterization of the eigenvectors of the Laplacian of the network, which provides an intuitive understanding of how eigenvectors organize themselves into nodal domains resistant to disorder at low frequency. As a consequence, a power oscillation, induced by some local disruption of the grid, can propagate in a ballistic, diffusive, or localized regime. In contrast with the conventional viewpoint, the existence of these three regimes is confirmed in a realistic model of the European power grid.

Jammed (mechanically rigid) polydisperse circular-disk packings in two dimensions (2D) are popular models for structural glass formers. Maximally random jammed (MRJ) states, which are the most disordered packings subject to strict jamming, have been shown to be hyperuniform. The characterization of the hyperuniformity of MRJ circular-disk packings has covered only a very small part of the possible parameter space for the disk-size distributions. Hyperuniform heterogeneous media are those that anomalously suppress large-scale volume-fraction fluctuations compared to those in typical disordered systems, i.e., their spectral densities ${\tilde{\chi }}_{{}_V}\left(\mathbf{k}\right)$ tend to zero as the wavenumber $k\equiv \left|\mathbf{k}\right|$ tends to zero and are often described by the power-law ${\tilde{\chi }}_{{}_V}\left(\mathbf{k}\right)\sim k^{\alpha }$ as $k\to 0$ where $\alpha$ is the so-called hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with a size ratio $\beta =D_L/D_S$, where $D_L$ and $D_S$ are the large and small disk diameters, respectively, and the molar ratio of the two disk sizes is 1:1. In particular, by characterizing the rattler fraction ${\varphi }_R$, the fraction of configurations in an ensemble with fixed $\beta$ that are isostatic, and the $n$-fold orientational order metrics ${\psi }_n$ of ensembles of packings with a wide range of size ratios $\beta$, we show that size ratios $1.2\lesssim \beta \lesssim 2.0$ produce maximally random jammed (MRJ)-like states, which we show are the most disordered strictly jammed packings according to several criteria. Using the large-$R$ scaling of the volume fraction variance ${\sigma }_{{}_V}^2\left(R\right)$ associated with a spherical sampling window of radius $R$, we extract the hyperuniformity scaling exponent $\alpha$ from these packings, and find the function $\alpha \left(\beta \right)$ is maximized at $\beta =1.4$ (with $\alpha =0.450\pm 0.002$) within the range $1.2\le \beta \le 2.0$. Just outside of this range of $\beta$ values, $\alpha \left(\beta \right)$ begins to decrease more quickly, and far outside of this range the packings are nonhyperuniform, i.e., $\alpha =0$. Moreover, we compute the spectral density ${\tilde{\chi }}_{{}_V}\left(\mathbf{k}\right)$ and use it to characterize the structure of the binary circular-disk packings across length scales and then use it to determine the time-dependent diffusion spreadability of these MRJ-like packings. The results from this work can be used to inform the experimental design of disordered hyperuniform thin-film materials with tunable degrees of orientational and translational disorder.

A theoretical model of stimulated Brillouin scattering (SBS) developed by a broadband laser in inhomogeneous plasmas is proposed and further investigated through a series of numerical simulations using the low-coherence laser model of the Kunwu facility. Polychromatic beamlets are coupled to develop a scattering mode, when all the poles of the beamlets are on the integration path of SBS dispersion relations. The coupled beamlets can be regarded as a monochromatic beam with the same incident energy, owing to their nearly identical amplification coefficients. Therefore, a broadband laser behaves as several decoupled beams with a frequency difference around the coupling threshold of the beamlets. In the direct-drive scheme, the overall saturation level of scattering light can be reduced by the broadband laser, if the bandwidth is larger than $c_s/c\sim {10}^{-3}$, where $c_s$ and $c$ are the velocities of ion acoustic wave and light, respectively. Two-dimensional simulations demonstrate the robust mitigation of SBS by the low-coherence laser with a moderate bandwidth $\sim 0.6\%$, even in the ignition regime. The laser plasma parameters have a minor impact on the mitigation of SBS with broadband lasers. The speckle structures vary rapidly over time at the focal plane due to the introduction of the broadband, which results in the further reduction of SBS and filamentation compared with the monochromatic laser.

Fibrin polymerization is responsible for the formation of blood clots and is used in many biomedical applications. Considering polymerization as a dynamic phase transition, we constructed a scaling theory of fibrin networks formation. We show that in the transient state, protofibrils and branched clusters are self-assembled as a result of diffusion-controlled reactions with free fibrin monomers. The rate of reactions increases with initial concentrations of fibrinogen and thrombin. Protofibrils and clusters aggregate laterally, forming fibers, the elongation of which leads to their crosslinking to form a fibrin network. We calculated the network structure for different ratios of lag time and fibrinogen activation time. At a low ratio of fibrinogen and thrombin concentrations, sparse networks of thick and long fibers are formed, whereas at a high ratio, dense networks of thin and short fibers. The predicted concentration dependences of network parameters are in agreement with experimental data.

We analyze the thermodynamics and criticality properties of four families of $\mathrm{su}\left(m\right|n)$ supersymmetric spin chains of Haldane-Shastry (HS) type, related to both the $A_{N-1}$ and the $B{C}_N$ classical root systems. Using a known formula expressing the thermodynamic free energy per spin of these models in terms of the Perron (largest in modulus) eigenvalue of a suitable inhomogeneous transfer matrix, we prove a general result relating the $\mathrm{su}\left(kp\right|kq)$ free energy with arbitrary $k=1,2,\cdots$, to the $\mathrm{su}\left(p\right|q)$ free energy. In this way we are able to evaluate the thermodynamic free energy per spin of several infinite families of supersymmetric HS-type chains, and study their thermodynamics. In particular, we show that in all cases the specific heat at constant volume features a single marked Schottky peak, which in some cases can be heuristically explained by approximating the model with a suitable multilevel system with equally spaced energies. We also study the critical behavior of the models under consideration, showing that the low-temperature behavior of their thermodynamic free energy per spin is the same as that of a $(1+1)$-dimensional conformal field theory with central charge $c=m+n/2-1$. However, using a motif-based description of the spectrum we prove that only the three families of $\mathrm{su}\left(1\right|n)$ chains of type $A_{N-1}$ and the $\mathrm{su}\left(m\right|n)$ HS chain of $B{C}_N$ type with $m=1,2,3$ (when the sign ${\varepsilon }_B$ in the Hamiltonian takes the value $-1$ in the latter case) are truly critical.

The growing self-avoiding walk has been extensively studied, particularly in relation to whether it shares universality classes with equally weighted self-avoiding walks. This study expands the understanding of growing self-interacting self-avoiding walks and presents perspective on how lattice geometry and interaction strength interplay. We compare these walks on square and honeycomb lattices, and enhance the analysis of their decision points to deepen insights into the trapping effect in these models. The main numerical results uncover a minimum in the mean trapping length as the interaction strength varies for the honeycomb lattice, similar to what is known for the square lattice, and saturation effects in mean trapping lengths, as well as insights originating from the trap size.

The Barkley model has been widely used to simulate diverse reaction-diffusion systems exhibiting various self-organization processes, including creation of spiral waves. Depending on the given parameters, this model is capable of simulating monostable, bistable, or oscillatory dynamics that are often observed in nature. This study is concentrated on the general features of spiral wave dynamics in the extended parameter range of the Barkley model, including both monostable and bistable dynamics. The numerical data obtained and the results of analytical studies illustrate the existence and the interplay between spiral wave dynamics in these two different but closely related regimes. In particular, the symmetry between the spiral waves in monostable and bistable regions is demonstrated, analytical expressions for the boundaries of these regions are found, the existence of the hysteresis phenomenon in the dynamics of spiral waves is discovered, and an additional region of existence of spiral waves is found in the region of a low excitability.

We develop a linear theory for the prediction of excitation wave quenching—the construction of minimal perturbations which return stable excitations to quiescence—for localized pulse solutions in models of excitable media. The theory accounts for an additional equivariance compared to the homogeneous ignition problem, and thus requires a reconsideration of heuristics for choosing optimal reference states from their group representation. We compare predictions made with the linear theory to direct numerical simulations across a family of perturbations and assess their accuracy for several models with distinct stable excitation structures. We find that the theory achieves qualitative predictive power with only the effort of continuing a scalar root, and achieves quantitative predictive power in many circumstances. Finally, we compare the computational cost of our prediction technique to other numerical methods for the determination of transitions in extended excitable systems.

We derive mean-field equations for a large population of globally coupled quadratic integrate-and-fire neurons subject to weak Gaussian noise and heterogeneous time-independent non-Cauchy distributed currents. We employ a circular cumulant approach that has previously been used only in the context of Cauchy heterogeneity, to the best of our knowledge. We extend this approach to rational distribution functions, which, unlike the Cauchy function, can have many poles in the complex plane. Population dynamics are analyzed for two families of rational functions that are approximations of the uniform and normal distributions. It is found that Gaussian noise and all considered types of heterogeneities have qualitatively the same effect on the population dynamics. This differs from the case of Cauchy noise, which has been shown to have the same effect on population dynamics only in the case of Cauchy heterogeneity, while Cauchy noise and non-Cauchy heterogeneity can have qualitatively different effects. The mean-field equations for both families of distribution functions are validated through a comparison of their solutions with the “exact” solutions of the Fokker-Planck equation, as well as with the results of modeling the stochastic microscopic dynamics of finite-size populations.

Multiagent reinforcement learning (MARL) studies crucial principles that are applicable to a variety of fields, including wireless networking and autonomous driving. We propose a photonic-based decision-making algorithm to address one of the most fundamental problems in MARL, called the competitive multiarmed bandit (CMAB) problem. Our numerical simulations demonstrate that chaotic oscillations and cluster synchronization of optically coupled lasers, along with our proposed decentralized coupling adjustment, efficiently balance exploration and exploitation while facilitating cooperative decision making without explicitly sharing information among agents. Our study demonstrates how decentralized reinforcement learning can be achieved by exploiting complex physical processes controlled by simple algorithms.

We consider experimentally and computationally the phenomenon of the reverse Janssen effect, involving the counterintuitive finding that the force on the base of a column containing granular particles may be larger than the weight of the granular material itself. This finding is in contrast to the common Janssen effect, for which the force on the base is smaller than the particle weight, illustrating one of the best-known differences between granular and liquid systems. We find that the reverse Janssen effect is strongly influenced by the pouring protocol: under Earth's gravitational field, we find that the reverse Janssen effect is strongly and consistently influenced by the pouring height, as well as by (to somewhat lesser degree) pouring flux. Pouring grains from the height measured in tens of particle diameters leads to a reverse Janssen effect that is an order of magnitude stronger than the one found for small pouring heights of few particle diameters. This influence of the particles' delivery protocol allows for the development of a better understanding of the general features of the reverse Janssen effect and of the comparison between experiments and simulations reported in this and previous works.

The mean square displacement (MSD) of intruders (tracer particles) immersed in a multicomponent granular mixture made up of smooth inelastic hard spheres in a homogeneous cooling state is explicitly computed. The multicomponent granular mixture consists of $s$ species with different masses, diameters, and coefficients of restitution. In the hydrodynamic regime, the time decay of the granular temperature of the mixture gives rise to a time decay of the intruder's diffusion coefficient $D_0$. The corresponding MSD of the intruder is determined by integrating the corresponding diffusion equation. As expected from previous works on binary mixtures, we find a logarithmic time dependence of the MSD which involves the coefficient $D_0$. To analyze the dependence of the MSD on the parameter space of the system, the diffusion coefficient is explicitly determined by considering the so-called second Sonine approximation (two terms in the Sonine polynomial expansion of the intruder's distribution function). The theoretical results for $D_0$ are compared with those obtained by numerically solving the Boltzmann equation by means of the direct simulation Monte Carlo method. We show that the second Sonine approximation improves the predictions of the first Sonine approximation, especially when the intruders are much lighter than the particles of the granular mixture. In the long-time limit, our results for the MSD agree with those recently obtained by Bodrova [Phys. Rev. E 109, 024903 (2024)] when $D_0$ is determined by considering the first Sonine approximation.