Wildland fire operates across multiple spatial and temporal scales, linking local combustion chemistry and turbulent heat transport to continental patterns of burned area. A quantitative bridge between microscale ignition physics and macroscale propagation has remained elusive because operational simulators treat ignition empirically, while statistical lattice models simplify combustion to binary states. This study derives ignition probabilities from an energy-balance law, embeds them in a branching-process formulation allied to percolation theory, and connects the discrete description to a reaction-diffusion continuum via a real-space-renormalization invariant. The resulting framework yields closed-form fuel-load thresholds, explains scale-free burned-area distributions, and clarifies why modest meteorological changes can precipitate abrupt transitions from smouldering to landscape-spanning fire.

Phase diagram of the two-temperature Ashkin-Teller model with Kawasaki dynamics has been investigated. The system is placed in contact with two heat baths at different temperatures, each of which controls the dynamics of nearest-neighbor exchange in the two perpendicular directions. It was observed that the second order phase transition lines (which separate the paramagnetic, ferromagnetic, and dimer phases) in the equilibrium model (equal temperatures) bifurcate into transition surfaces at nonequilibrium. The equilibrium four-state Potts point where all three orders meet extends into a line in the nonequilibrium case, along which these phases again meet.

In this work, we develop, in the Gurevich-Pitaevskii framework, an analytic theory for the evolution of localized pulses in the defocusing modified Korteweg–de Vries equation theory for situations when a dispersive shock does not eventually transform into a sequence of well-separated solitons. We found solutions to the Whitham modulation equations for the corresponding “quasisimple” dispersive shock waves and illustrated this solution with concrete examples of an initial pulse. Comparison of the analytical solution with direct numerical simulations showed that the modulation theory provides a very accurate description of the wave pattern even at one wavelength scale.

Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [T. Dobrowolski et al., Phys. Rev. E 111, 024203 (2025)], we propose an analogous effective description of ${\varphi }^4$ kinks. Three different reduced models based on the kink position, width and internal mode amplitude are introduced and compared systematically with the numerical solution of the equation with space- and time-dependent perturbations. In all cases considered, the model based on the kink position and width agrees the best with the full numerical solution. As long as the external driving frequency of the perturbation remains moderate, it captures with remarkable accuracy the intricate dynamical processes taking place in the system.

We study a one-dimensional swarmalator model with inertia. Previous studies have focused almost exclusively on the overdamped limit. We find inertia introduces an unsteady collective state in which the rainbow order parameters undergo multiharmonic oscillations. This “thrashing” phase wave bifurcates from the model's static phase wave state through a subcritical Hopf bifurcation that coincides with a saddle node of limit cycles. The wave itself exists in clockwise and counterclockwise symmetric pairs. For small populations we observe attractor switching between these chiral states, while for larger systems the dynamics settle onto a single branch.

We present a numerical study of several inequality measures across two kinetic wealth-exchange models with extreme inequality features (namely the Banerjee model, and the Chakraborti or yard-sale model) and two earthquake simulating models (namely the Chakrabarti-Stinchcombe two-fractal overlap model and the nonlinear dynamical Burridge-Knopoff model). For each model we compute numerically the Lorenz function for the respective models' wealth, overlap magnitude or avalanche distributions. We then estimate the variations of Gini ($g$), Pietra ($p$), and Kolkata ($k$) indices in these models with systematic variations of saving propensity (for the two wealth-exchange models), with systematic variations of generation or block numbers (for the two earthquake simulating models). We find that for appropriate values of the respective model parameters, the inequality indices $g$ and $k$ in corresponding the distributions (of “wealth” or “avalanche”) show quantitatively similar behavior, namely $g=k\simeq 0.86$, which was identified earlier to correspond to the precursor point of criticality in self-organized critical models ($k=0.80$ corresponds to that for Pareto's 80-20 law). The values of $p/(2k-1)$ in all these (wealth exchange and earthquake) models remain a little above unity, as was predicted theoretically. These observations for the inequality indices $g, k$, and $p$ across the socioeconomic and geophysical models indicate the presence of unifying subtle features in the statistics of such disparate dynamical systems.

Changing environmental conditions can significantly affect the dynamics of disease spread. These changes may arise naturally or result from human interventions; in the latter case, lockdown measures that lead to abrupt but temporary reductions in transmission rates are used to combat disease spread. Yet, the impact of these measures on rare events in heterogeneous populations remains understudied. Here, we analyze the susceptible-infected-susceptible (SIS) model in a stochastic setting where disease extinction—a sudden clearance of the infection—–occurs via a rare, large fluctuation. We use a semiclassical approximation and numerical simulations on heterogeneous assortative networks, with degree-degree correlations between neighboring nodes, to show how the extinction risk of the disease depends on the lockdown's duration and magnitude, and on the network topology.

Degree centrality is one of the most fundamental measures of local importance in directed networks. Its fractional version is defined via the fractional directed Laplacian with parameter $\gamma$, a well-known nonlocal operator. When $\gamma =1$, the fractional centrality reduces to the out-degree centrality. In contrast to undirected networks, where the measure remains predominantly local as $\gamma$ varies, we demonstrate that its intriguing behavior in directed networks reflects global effects beyond purely local contributions. We show that, in the limit $\gamma \to 0^{+}$, the fractional centrality is characterized by rooted spanning trees, thereby quantifying how frequently each node acts as a broadcaster rather than a sink and reflecting its role in global information dissemination across the network. Through experiments on both real-world and random directed networks, we demonstrate the transition of the fractional centrality from a local measure to a global one as $\gamma$ decreases from 1 to 0. These results establish the fractional centrality as a unifying framework integrating local and global influences in directed networks.

Cellular Potts model (CPM) simulations display significant variation in dynamics, structural ordering, and observed phase transitions. Such differences may emerge, at least in part, because CPM simulations are not implemented in a uniform manner, specifically in terms of the definitions of cell perimeters and cell contact lengths. These definitions can have a significant effect on cell shape, dynamics, and data reproducibility. Here we explore different implementations of edge length computation and its effects on phase transitions as a function of cellular adhesion energy in confluent monolayers. While we find that edge length definition has only a modest effect on the transition point from fluidlike to solidlike behavior, it strongly impacts the structural order and dynamics of the monolayer across regimes. Lattice-based artifacts from cell-lattice alignment and overcounting of the cell contact length limit cooperative motion and structural order and cause early dynamical arrest. Using an updated, self-consistent implementation that corrects contact length in a manner that mirrors continuum models of cell migration, we find that monolayers undergo a transition from a fluid through a transient hexatic phase into an ordered solidlike phase that retains significant cooperative motion. This cooperative, fluctuation-driven solidlike phase is unique to this updated CPM implementation. Cell shapes in such monolayers are well-behaved and adhere to the expected shape thresholds used as structural indicators in other multicellular systems, making their application and comparison to experimental systems more readily interpretable.

Hydrodynamic instabilities seeded by isolated internal defects remain a critical performance-limiting factor in inertial confinement fusion experiments. Here we extend the concept of dynamic stabilization via temporally modulated laser pulses from the main drive [K. G. Zhao et al., Phys. Rev. E 109, 025213 (2024)] to the prepulse stage, which stabilizes the hydrodynamic evolution of perturbations seeded by micrometer-scale (low-density) internal defects. Analysis of the unperturbed ablative flow generated by the modulated laser prepulse indicates that the periodic oscillatory configuration has the potential to stabilize the instability growth from such defects. A single defect under the modulated laser prepulse is compared with that in the unmodulated case. The results show that the modulated laser prepulse reduces the bubble penetration depth and vorticity generation. This stabilization arises from a phase difference between the density and pressure gradients, which induces a reversal of the baroclinic term in the vorticity transport equation. Moreover, the results show that the stabilization effect of the modulated laser prepulse is more significant for shallower defects and diminishes progressively with increasing defect depth.

We show that the bias of the approximate maximum-likelihood estimation (MLE) objective of a persistent chain energy-based model (EBM) is precisely equal to the thermodynamic excess work of an overdamped Langevin dynamical system. We then answer the question of whether such a model can be trained with minimal excess work, that is, energy dissipation, in a finite amount of time. We find that a Gaussian energy function with constant variance can be trained with minimal excess work by controlling only the learning rate. This proves that it is possible to train a persistent chain EBM in a finite amount of time with minimal dissipation and also provides a lower bound on the energy required for the computation. We refer to such a learning process that minimizes the excess work as minimal-dissipation learning. We then provide a generalization of the optimal learning rate schedule to general potentials and find that it induces a natural gradient flow on the MLE objective, a well-known second-order optimization method.

Sodium acetate trihydrate (SAT) is a promising phase change material for thermal energy storage through phase transition, yet its microscopic mechanisms of phase transition, especially melting and intrinsic supercooling, remain unclear. In this study, all-atom molecular-dynamics simulations were performed to elucidate the melting pathway, supercooling mechanism, and facet-dependent stability of SAT. The analysis of melting dynamics reveals a three-stage transition comprising interfacial relaxation, melting-front propagation, and liquid stabilization. Melting is driven by the breakdown of long-range ionic order and the reorganization of water molecules into a bulk hydrogen-bonded network, where ${\mathrm{H}}_2\mathrm{O}\text{−}{\mathrm{H}}_2\mathrm{O}$ interactions transform from repulsive to attractive. Under isothermal conditions, liquid SAT remains metastable down to 220 K without crystallization during 1000 ns. The energetic decomposition reveals a dual stabilization mechanism: (i) electrostatic trapping arising from strengthened $\mathrm{N}{\mathrm{a}}^{+}\text{−}\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}$ pairing and enhanced short-range charge correlations, and (ii) ion-water cooperative stabilization that locks hydration shells and slows the reorientation of water molecules. These effects produce a polarized yet dynamically constrained liquid network, in which the number of hydrogen bonds increases while their collective electrostatic coherence weakens. Comparative simulations of the (402), (–402), and (062) crystal planes further reveal distinct interfacial energetics and hydrogen-bond organizations, with the (402) facet exhibiting the strongest interfacial stability and the (062) facet showing diffuse hydration and weak lattice cohesion.

A second-order modified mean-field theory has been developed to predict the static magnetization and initial magnetic susceptibility of textured ensembles of immobilized interacting superparamagnetic nanoparticles with uniaxial anisotropy. The theory takes into account the orientational texture of the easy magnetization axes and interparticle dipole-dipole interactions, including three-particle correlations. Simple analytical expressions are proposed for calculating the magnetization and initial magnetic susceptibility of ensembles of interacting immobilized particles with random, parallel, and perpendicular texturing of the easy magnetization axes with respect to the applied magnetic field. It is shown that texture manipulation allows the collective magnetic response to be controlled: parallel orientation of the axes leads to a rapid increase in susceptibility, whereas perpendicular orientation leads to its suppression. The results of the theory demonstrate quantitative agreement with the data of computer modeling performed using the Monte Carlo method, significantly exceeding the accuracy of known theories. The theory developed in this work is a tool for predicting and purposeful designing the magnetic properties of modern magnetically active materials.

The self-removal of sessile droplets under low-pressure conditions is critical for extreme-environment surface engineering. Combining high-speed photography with quantitative analysis, we reveal the unique dynamics of ethylene glycol-water solution droplets on irregular micro-nanostructured superhydrophobic surfaces. The experimental results demonstrate asymmetric depinning driven by evaporation-induced local overpressure gradients, generating a recoil momentum toward the pinned side that propels the droplet to move along the surface at a steady acceleration. This acceleration follows a quadratic scaling law with the evaporation flux. When the local overpressure exceeds the triple-phase line pinning forces, the droplets transition to the levitation phase. However, the unevenness of the surface micro-nanostructures leads to the instability of levitation, causing the droplet to rapidly recontact the surface and enter the secondary steady acceleration phase. Subsequently, the droplet maintains a dual-phase periodic transition mode of acceleration–levitation until it disappears from the field of view. In this study, we elucidate the synergy between recoil momentum and dynamic overpressure, advancing the fundamental understanding of low-pressure complex droplet dynamics and enabling surface morphology design strategies for droplet control in extreme environments.

We show that the Heider model with an external field is equivalent, in the limit of structural balance, to the Ising model with nearest-neighbor interactions without an external field. More precisely, we claim that the signs of the Heider relations that maintain structural equilibrium in the system can be represented as nearest-neighbor Ising spin products. We demonstrate this explicitly for a complete graph and provide a general argument for an arbitrary graph. A consequence of the equivalence is that the system of balanced Heider states undergoes a phase transition, inherited from the Ising model, at a critical value of the social field at which the fluctuations of edge magnetization are maximal.

We establish a sharp criterion for the stability of a class of compactly supported, homogeneous, symmetric states, “minimal compact solitons” or MCS states, of the time-dependent discrete nonlinear Schrödinger equation on a multilattice, $\mathbb{L}$ ($\mathbb{L}$-DNLS). MCS states arise for multilattices where a nearest neighbor, a Laplace-type operator on $\mathbb{L}$, has a flat band. Our stability criterion is in terms of the explicit form of the nonlinearity and the projection of a distinguished vector onto the flat band eigenspace. We apply our general results to MCS states of DNLS with a power-law nonlinearity for the diamond, Kagome, and checkerboard lattices. In lattices where MCS states are unstable, we demonstrate how the variation of the nonlinearity exponent enables the stabilization of small amplitude MCS states.

Considering deterministic classical lattice systems with continuous dynamical variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the temporal evolution of any macroscopic observable is approximately the same for the vast majority of the randomly sampled initial states. Our proof relies on general concentration of measure results which provide tight bounds for the deviation from typical behavior in the case of large system sizes. The only requirement on the dynamics is that the influence of a local perturbation in the initial state decays, at any given instance of time, sufficiently fast with distance. Our results are relevant, in particular, to classical Hamiltonian systems on a lattice, but also apply to a large class of dissipative dynamics. We illustrate our general results with two analytical examples, a coupled map lattice and a Hamiltonian system of coupled rotors with long-range interactions.

We study the dynamics of circuits composed of stochastic and bistochastic controlled gates. This type of dynamics arises from quantum circuits with random controlled gates, as well as in stochastic circuits and deterministic classical cellular automata. We prove that stochastic and bistochastic controlled gates lead to two-point spatiotemporal correlation functions that vanish everywhere except when the two operators act on the same site. More generally, for multipoint correlations the two rightmost operators must act on the same site. We argue that autocorrelation, while hard to compute, typically decays exponentially toward a value that is exponentially small in the system size. Our results reveal a broad class of quantum systems that exhibit surprisingly simple correlation structures despite their complex microscopic dynamics.

The universal prevalence of cooperation is puzzling, as defection typically yields higher payoffs than cooperation, motivating searches for hidden pathways to cooperation. Here we study a game-theoretic model on a lattice structured population in which interaction payoffs are scaled by the minimum of participants' accumulated wealth, reflecting real-world heterogeneity and incorporating the influence of past strategic choices. This wealth scaling allows frequent cooperators to surpass defectors in payoffs through their greater wealth even at high cooperation costs where defection would otherwise dominate. At the elevated critical cost-benefit ratio, the wealth gradient at the cooperator-defector boundary in one dimension exhibits a discontinuous transition. We show that slowing and effective stalling of the boundary trigger an explosive buildup of the wealth gradient, driving the dominance of cooperation below the critical ratio. Remarkably, this promotion of cooperation is stronger at higher temperatures, revealing a constructive role of fluctuations.