Reaction-diffusion processes play an important role in a variety of physical, chemical, and biological systems. Conventionally, the kinetics of these processes are described by the law of mass action. However, there are various cases where these equations are insufficient. A fundamental challenge lies in accurately accounting for the microscopic correlations that inevitably arise in bimolecular reactions. While approaches to describe microscopic correlations in many specific cases exist, no general theory for multistage reactions has been established. In this article, we apply the quantum field theory approach to derive kinetic equations for general multistage reactive systems termed complete modified encounter theory (CMET). CMET can be formulated as a set of coupled partial differential equations that can be easily integrated numerically, thereby serving as a versatile tool for investigating reaction-diffusion processes. Across multiple case studies, we demonstrated that CMET reproduces the kinetics predicted by many other theories within their respective scopes of applicability.

We study the effects of spatially inhomogeneous diffusion on the nonequilibrium phase transition in the unidimensional contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism at higher dimensions and for other absorbing state transitions and nonequilibrium phase transitions in general.

Feedback between game strategies and environmental states is common in human–natural systems. Existing studies have reported several interesting dynamical behaviors by studying the impact of environmental state on strategy selection. In this paper we construct a characterization of environmental states, assuming that environmental states are determined by local and global environmental states. Based on this we construct a spatial multiagent coevolutionary model to describe the strategy evolution of populations and analyze the model's dynamics by means of Monte Carlo simulations and mean-field approximation. We find that spatial structure can enhance the system stability, preventing the emergence of complex dynamical behaviors such as chaos. Furthermore, we incorporate a diffusion mechanism into the model. Results show that resource diffusion accelerates strategy switching by weakening differences in local environmental states. Numerical results further indicate that spatial structure significantly affects the system stability: the system self-organizes into stable spatial structures analogous to Turing patterns, thus enhancing the system stability. This study investigates the mechanisms by which environmental states and spatial structures influence system stability, offering new insights into understanding the coevolutionary dynamics in real-world systems.

Complex networked systems are prevalent in biology, engineering, and the social sciences, yet their high-dimensional, nonlinear dynamics pose major challenges for analysis and prediction. A mathematically rigorous route to simplification is to represent system behavior on a low-dimensional, smooth invariant manifold known as a spectral submanifold (SSM). Here we present a comprehensive SSM reduction framework and its globalized extension (gSSM) for dimensionality reduction in large-scale nonlinear networks. Our approach yields accurate global and node-level predictions across synthetic and real networks, including highly heterogeneous topologies and systems with higher-order interactions. Crucially, SSM is a robust tipping-point predictor: even at low truncation order [e.g., $O\left(2\right)$] it reliably identifies the onset of sustained activity, while higher orders and gSSM capture postonset amplitudes and saturation. Consistently, the reduction collapses the full network dynamics to a one-dimensional system, offering clarity and efficiency. Across all the realizations, SSM and gSSM consistently outperform classical spectral and mean-field methods in modeling critical transitions at both microscopic and macroscopic scales, establishing SSM-based reduction as a robust, interpretable tool for nonlinear networked systems with broad applicability to epidemiology, ecology, and engineered networks.

Robustness of simplicial complexes under triangle deletion is often characterized by the instantaneous smallest positive eigenvalue of the Hodge 1-Laplacian. We show that this observable can change spectral index when the kernel grows, and therefore it need not follow the same nonharmonic edge-space eigenmode along the deletion process. To remove this ambiguity, we define fixed-index spectral robustness by monitoring the eigenvalue whose index is selected by the first nonzero eigenvalue of the intact complex. The corresponding triangle sensitivity follows from first-order perturbation theory and identifies simplices that produce the steepest initial decrease of this monitored eigenvalue. Across synthetic and empirical clique complexes, a small fraction of triangles can drive the monitored eigenvalue to zero while the 1-skeleton and graph-level robustness measures remain unchanged. These results show that higher-order robustness is a genuinely simplicial spectral property that cannot be inferred from graph-level connectivity alone.

We develop a stochastic simplex framework for width partitioning in braided river cross sections, modeling normalized channel widths as random compositional vectors. Two complementary models are introduced: the symmetric Dirichlet distribution, which models width allocation as exchangeable stochastic fluctuations around a uniform baseline with no preferred channel, and the isotropic logistic-normal distribution, which accommodates systematic width concentration through a single scale parameter. Both models carry independent physical content: the Dirichlet characterizes morphodynamic states in which all channels are statistically equivalent, while the logistic-normal identifies and quantifies organized concentration regimes. We derive exact closed-form expressions for the expected concentration index and width concentration fraction under both models, establish a parameter-free structural breakdown criterion, and analyze the temporal evolution of model parameters across 11 annual surveys of the Brahmaputra-Jamuna River (Bangladesh) spanning 1976–2007. The analysis reveals a decadal-scale morphodynamic transition: for 1976–1985, width is distributed among channels in a statistically uniform fashion consistent with the Dirichlet model. From 1995 onwards, a progressive increase in the logistic-normal scale parameter ${\sigma }^{*}$, optimized independently for each survey year and fitted by a logistic regression ($R^2=0.997$), indicates systematic growth of channel width concentration. A parameter-free structural breakdown criterion certifies the failure of the Dirichlet model between 1995 and 1999, where the logistic-normal model recovers goodness-of-fit values above 0.95. Both ${\sigma }^{*}$ and the Dirichlet parameter $c^{*}$ retain memory of the concentration phase above pretransition levels throughout the observational window.

Navigation during colony relocation by the tandem-running ants, Diacamma indicum, is a tour de force of biological traffic coordination, as this directly impact the survival and fitness of the whole colony. Even on one-lane paths, the ants tactfully manage a bidirectional flow: An informed individual (termed leader) guides one nest mate (termed follower) to a new optimal nest, and then returns to recruit additional followers (one follower at a time). We propose that encounters between the ants moving in opposite directions can be modeled within the framework of game theory, leading to an understanding of the mechanism behind observed behaviors. Our experiments reveal that, upon encountering a tandem pair (a leader and its follower) on a narrow path, the returning leader reverses her direction and proceeds toward the new nest again. This observed behavior is consistent with game-theoretic predictions, provided the assumption of perfect rationality is relaxed in favor of bounded rationality—specifically, procedural rationality, i.e., an agent explores all her actions independently before adopting a particular action. In other words, the experimental outcomes are consistent with sampling equilibrium—the game theoretic equilibrium realized when procedural rational players are pitted against one another—but not with Nash equilibrium. Our work, which strives to bring the essence of behavioral game theory into the world of ants, demonstrates sampling equilibrium in a scenario without human players, extending the concept beyond its traditional application to human decision-making.

For gas mixtures flowing through conical capillaries with small feature sizes, intermolecular collisions compete with ballistic transport. This leads to discrepancies between real flow rates and predicted results by conventional hydraulic methods. A model is established to calculate the flow rates of rarefied gas flowing through long conical capillaries at arbitrary pressure and concentration drop. The applicability of the model extends from binary gas mixtures to reduced single-species gases. The research results show that the diode effect exists for either binary gas mixtures or single-species gases. The maximum and minimum of the diode effect is obtained in the intermediate flow regime, where the intermolecular collisions and the ballistic transport contribute comparably. The diode-effect curve associated with the heavy species exhibits the same nonmonotonic dependence on the mean rarefaction parameter as observed in the single-species gas case. Interestingly, the diode effect for the light species is exactly the opposite, presenting a trend of first decreasing and then increasing. This abnormal diode effect can be heuristically interpreted, within the framework of the present long-capillary approximation, as resulting from the combined influences of local gas-surface interactions, cross collisions between binary species molecules, and gas separation.

We present a time-dependent pore-network model that couples transient mass transfer in the aqueous phase, capillary pressure heterogeneity, and realistic pore-throat geometries to capture the dynamic evolution of gas clusters during Ostwald ripening in porous media. The model is applied to Bentheimer sandstone to study Ostwald ripening after imbibition to residual gas saturation. Both imbibition (shrinkage) and drainage (growth) events occur as the local capillary pressure in trapped gas clusters approaches equilibrium. The model tracks event statistics, capillary pressure equilibration, cluster volume distributions, and spatial saturation profiles over 48 h. While the volume-weighted average capillary pressure is constant, there is a rapid initial decline in average number-weighted cluster pressure and a shift in cluster size distributions toward fewer, larger ganglia, consistent with pore-scale imaging studies. Pore and throat occupancy analysis reveal persistent gas trapping in larger pore spaces. Since growth is by drainage, the pore-scale configuration of fluid is different from that predicted by an equilibrium percolation-without-trapping model that only allows imbibition events. The model reproduces the displacement and ganglion rearrangement observed during laboratory experiments. Presented as a preliminary framework study assuming constant fluid properties and a nonreactive system, the model could be extended to incorporate detailed thermophysical equations of state to provide a foundational framework for analyzing time-dependent ripening in porous media, establishing the physics necessary to inform future upscaled constitutive relationships for hydrogen, natural gas and carbon dioxide storage in the subsurface.

This paper presents an experimental investigation of magnetic reconnection between two laser-produced expanding plasmas, focusing on the quantitative evaluation of the reconnection rate and energy conversion under varying initial conditions. By changing the separation distance between the drive laser focal spots (1 mm and 2 mm), we systematically controlled the inflow parameters. The reconnection region was probed using a two-directional laser Thomson scattering (LTS) system, which simultaneously measured the local plasma parameters parallel to the outflows and along the current sheet. Based on our established method incorporating macroscopic energy and mass conservation laws to derive the upstream magnetic field directly from LTS spectra, we characterized the temporal evolution of the current sheet and the reconnection rate. The larger spot separation allows the plasma bubbles to expand for a substantially longer time before the formation of a reconnection current sheet, resulting in different upstream conditions. Nevertheless, both configurations yielded comparable upstream magnetic fields and reconnection rates. These results suggest that the reconnection rate is relatively insensitive to the global inflow conditions and is primarily controlled by the local physics of the reconnection layer once a current sheet is formed.

Equations describing evolution of the velocity of a rarefied ion beam in a plasma with ion-acoustic turbulence are derived and solved. An ion beam with velocity $u$ greater than the sound speed $v_s$ decelerates due to Cherenkov radiation of ion-acoustic waves. Conversely, a beam with $u<v_s$ accelerates to a velocity $\sim v_s$ due to Cherenkov interaction with field beats at a difference frequency of ion-acoustic waves. The acceleration of a slow beam is accompanied by anisotropic turbulent heating of beam ions. Characteristic deceleration (or acceleration) distances of beam ions are obtained.

A dusty plasma cloud hosting a counter-rotating vortex lobe pair is driven through controlled neutral-gas pressure ramps spanning nearly an order of magnitude in rate. The transient response is characterized by the longitudinal transport exponents ${\alpha }_{\mathrm{L}}$ and ${\alpha }_{\mathrm{R}}$, extracted from mean-squared displacements evaluated in the cotranslating frame of each lobe, with cluster-bootstrap confidence intervals. At baseline the two lobes are dynamically inequivalent, with a statistically confirmed asymmetry $\mathrm{\Delta }\alpha ={\alpha }_{\mathrm{R}}-{\alpha }_{\mathrm{L}}<0$ in all four experiments. The pressure ramp drives the exponents toward equalization and ultimately inverts the asymmetry. The inversion is completed within the ramp only for the gentlest forcing, and is deferred to the end of the forcing interval, or beyond it, as the ramp rate increases. A force-scale analysis shows that the per-particle neutral drag remains below the static levitation-force scale, but increases systematically with ramp rate and produces millimeter-scale horizontal advection of the cloud. The behavior is organized by a Deborah number $\mathrm{De}=T_{\mathrm{rot}}/{\tau }_{\mathrm{ramp}}$: the normalized inversion time increases with $\text{De}$ across the four experiments and approaches the end of the ramp for the fastest protocols. These results identify the vortex lobe pair as a rate-dependent, kinetically gated structure and connect its dynamics to the broader phenomenology of driven viscoelastic soft matter.

We numerically examine a binary system of particles with repulsive interactions, where one species is driven by a rotating drive and the other is subjected either to a constant drive in a fixed direction or to a rotating drive that is out of phase with the first species. As a function of rotation frequency, we find a variety of order-disorder transitions and pattern-forming states, including density-modulated stripes, partially jammed states, phase-separated fluids, and mixed fluids. When one species has a constant drive and the drive on the other species is rotated at low frequencies, the system switches between different pattern-forming phase-separated lanes including density-modulated stripes and partially jammed states, similar to what is observed for oppositely driven colloids. The lanes tend to align with the net direction of rotation, resulting in a series of order-disorder switching transitions. The transport curves show abrupt jumps up or down at the transitions, which also correspond with changes in the topological order. We find similar switching transitions when both species rotate out of phase with each other. For intermediate driving frequencies, the system becomes increasingly fluidlike and the laning behavior is lost. At high frequencies, however, the system can again exhibit patterned flow when the rotation orbits become smaller than the average spacing between particles. The switching is reduced when a finite temperature is included, but even for temperatures at which the uniform equilibrium bulk system is liquid, the partially jammed state can generate local density enhancements that lead to recrystallization. We demonstrate the pattern-switching behavior for systems with different screened repulsive interaction potentials.

In the supercritical fluid (SCF) region, at temperatures and pressures above the critical point, the thermodynamic singularity separating liquids and gases no longer exists. Recent arguments based on thermodynamics and critical scalings have revived the proposal that the SCF constitutes an intermediate state of matter, separated from the liquid and gas by two supercritical boundaries, the $L^{\pm }$ lines. However, until now, the nature of the supercritical state and the physical signatures of these boundaries have remained elusive. Here, we demonstrate that the SCF is characterized by distinct structural, transport, and dynamical behavior. Specifically, the spatial arrangement of particles—captured by the radial distribution function—as well as the diffusion coefficient, shear viscosity, and velocity autocorrelation function in the SCF regime are qualitatively different from those in both the liquid and gas states and exhibit physical signatures upon crossing the $L^{\pm }$ lines. Our theoretical predictions are supported by molecular dynamics simulations of argon and are further supported by existing experimental evidence. These results provide a clear physical foundation for a refined phase diagram of matter in the supercritical region, comprising three distinct states—gas, supercritical fluid, and liquid—separated by two crossover boundaries obeying universal scaling laws.

We develop a systematic extension of mode-coupling theory that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling transition and show that the corresponding asymptotic series dominates the mean-field prediction below an upper critical dimension $d_c=8$. To resum these divergences, we construct a mapping to a stochastic dynamical process in which the order parameter evolves under random spatiotemporal fields. This reformulation provides a controlled, fully dynamical derivation of an effective theory for $\beta$ relaxation that remarkably coincides with stochastic beta relaxation theory [T. Rizzo, Long-wavelength fluctuations lead to a model of the glass crossover, Europhys. Lett. 106, 56003 (2014)]. All coupling constants of the latter theory are expressed microscopically in terms of the liquid static structure factor and are computed for the paradigmatic hard-sphere system in the Percus-Yevick approximation. The analysis demonstrates that critical fluctuations alone restore ergodicity and replace the putative mean-field transition with a smooth crossover. Our results establish a predictive framework for structural relaxation beyond mean-field.