A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the species' coexistence. One key prediction is that biodiversity is jeopardized and eventually lost when mobility exceeds a certain value—a conclusion at odds with empirical observations of highly mobile species coexisting in nature. To address this discrepancy, we introduce a joint reinforcement learning framework to study a spatial RPS model, where individuals' mobility for each species is not fixed but is guided by a common experience pool in the form of a $Q$-table, and its members jointly revise it via a $Q$-learning algorithm. Our results show that all three species can coexist stably, with extinction probabilities remaining low across a broad range of baseline migration rates. Mechanistic analysis reveals that individuals develop two behavioral tendencies: survival priority (escaping from predators) and predation priority (remaining near prey). While species coexistence emerges from the balance of the two tendencies, their imbalance jeopardizes biodiversity. Notably, there is a symmetry breaking of action preference in a particular state that is responsible for the divergent species densities. Furthermore, when $Q$-learning species interact with fixed-mobility counterparts, those with adaptive mobility exhibit a significant evolutionary advantage. Our study suggests that joint reinforcement learning offers a promising perspective for uncovering the mechanisms of biodiversity and designing conservation strategies.

The synchronization of oscillations in spatially extended ecological systems is a pervasive phenomenon. Here, we investigate the spatial synchronization of stochastic predator-prey oscillations in a multi-patch landscape. We model the system using the Rosenzweig-MacArthur model with demographic stochasticity. We demonstrate that the collective phase dynamics of the coupled ecological oscillators can be analytically mapped onto a framework inspired by the XY model of statistical mechanics. In this analogy, migration between patches acts as the coupling strength, while intrinsic demographic noise functions as an effective temperature that promotes disorder. This framework allows us to characterize the emergence of spatial synchrony as a noise-induced phase transition. We analytically and numerically identify the critical migration threshold required for global synchronization and show how the interplay between noise and coupling shapes the system's coherence. Our findings provide a robust statistical mechanics foundation for understanding large-scale ecological synchrony and offer new insights into the resilience of metapopulations.

We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing preferences onto analogous quantities in statistical physics, we define an effective free energy which is minimized in the grand canonical ensemble. Using a mean field approximation, we observe phase transitions in the model from disordered events in time to orderings that closely reproduce those seen in music. We then compare the range of rhythmic characteristics predicted by the model to a data set drawn from compositions by Johann Sebastian Bach, finding generally good quantitative agreement. The results provide a lens through which to study musical rhythm and a method for generatively producing rhythms.

While single-molecule (SM) experiments using fluorescent probes have provided critical insight for molecular and polymeric glass formers, the microscopic mechanism of probe transport remains largely unexplored in such systems at the molecular length scale. Here, we report SM translational dynamics of molecular probes in high molecular weight polystyrene at three temperatures near the glass transition temperature ($T_{\mathrm{g}}$). The probes exhibit quasistationary position fluctuations, non-Gaussian displacement distributions, subdiffusive transport with anticorrelated displacements, and a characteristic translational relaxation time. The observations are quantitatively described using a microscopic framework based on the generalized Langevin equation and supported by numerical modeling for heterogeneous transport. The probe dynamics reveal a progressive softening of effective viscoelastic confinement with increasing temperature and direct microscopic evidence of dynamic heterogeneity and suggest a pathway to more fully understand glassy dynamics in glass formers near $T_{\mathrm{g}}$.

Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in nematically ordered systems self-propel. While some previous theoretical descriptions relied on assuming that the defect shape remains unperturbed by activity, we show that this assumption can lead to inconsistent predictions. We compute the shape of $-1/2$ defects and show that the one of $+1/2$ is intimately related to their self-propulsion speed. Our analytical predictions are corroborated via numerical simulations of a generic active nematic theory.

Is it possible to develop a “physics of language” which can explain the spatial, temporal, and social patterns we see and which can predict future change like we forecast the weather? Such a theory is likely to involve ideas from statistical physics. A substantial literature already applies these ideas to language. However, we lack a model which can match the spatial-temporal detail of historical changes at the level of individual linguistic features and which offers a principled mechanism to predict the future. Here we present a statistical field theory for the evolution of linguistic variables which takes steps to fill this gap. Linguistic variant frequencies are represented as a stochastic state field with spatial interaction and social conformity, coupled to a latent bias field with Onsager–Machlup action that reduces overfitting to data. We derive parameter inference procedures and demonstrate them using examples of large-scale dialect survey data from the 20th-century United States. The bias field has a characteristic half-life, which determines the horizon over which linguistic change can be predicted. Inferred model parameters provide evidence for surface-tension-driven coarsening of dialect regions, with population-density gradients exerting systematic forces on interfaces.

In this work, we propose a theory for the kinetics of emulsions in which a continuous supply of matter feeds droplet growth. We consider cases where growth is either limited by bulk diffusion or the transport through the droplets' interfaces. Our theory extends the Lifshitz-Slyozov-Wagner (LSW) theory by two types of matter supply, where either the supersaturation is maintained or the supply rate is constant. In emulsions with maintained supersaturation, we find a decoupling of droplets at all times, with the droplet size distribution narrowing in the diffusion-limited regime and a drifting distribution of a fixed shape in the interface-resistance-limited case. In emulsions with a constant matter supply, there is a transition between narrowing and broadening in the diffusion-limited regime, and the distribution is nonuniversal. For the interface-resistance-limited regime, there is no transition to narrowing, and we find a universal law governing coarsening kinetics that is valid for any constant matter supply. The average radius evolves according to a power law that is independent of the matter supply, and we find a closed-form expression for the droplet size distribution function. Our theory is relevant to biological systems, such as biomolecular condensates in living cells, since droplet material is not conserved and the growth of small droplets is proposed to be interface-resistance-limited.

Eukaryotic cells generally sense chemical gradients using the binding of chemical ligands to membrane receptors. To perform chemotaxis effectively in different environments, cells need to adapt to different concentrations. We present a model of gradient sensing where the affinity of receptor-ligand binding is increased when a protein binds to the receptor's cytosolic side. This interior protein (allosteric factor) alters the sensitivity of the cell, allowing the cell to adapt to different ligand concentrations. We propose a reaction scheme where the cell alters the allosteric factor's availability to adapt the average fraction of bound receptors to $1/2$. We calculate bounds on the chemotactic accuracy of the cell and find that the cell can reach near-optimal chemotaxis over a broad range of concentrations. We find that the accuracy of chemotaxis depends strongly on the diffusion of the allosteric compound relative to other reaction rates. From this, we also find a tradeoff between adaptation time and gradient sensing accuracy.

Processing of sensory signals by the brain is subject to physical limitations, both external (statistical quality of sensory input) and internal (physiological limitations on neural signals). Efficient use of limited resources requires that the brain match its processing strategies to the statistical structure of input signals. We test this idea in the context of motion estimation in the fly visual system, where the optics of the compound eye and signals and noise in the retina are well understood and we can record from output neurons that encode velocity estimates. Still missing is a full characterization of the statistical relation between visual signals and motions relevant for flies in a natural context. Therefore, we develop a specialized camera mimicking fly eye optics, with inertial motion sensors providing ground truth about motions. We describe the design, construction, and performance characteristics of this FlEye camera. From camera data sampled in nature we construct optimal local motion estimators. These estimators show characteristic biases that are also observed in flies and other biological systems. Physical limitations of the camera data and computational estimator are negligible compared to biological systems. That we nevertheless observe similar biases suggests that biological performance is effectively limited by external statistics, not physiology.

The electron cyclotron resonance ion plasma accelerator (ECRIPAC) is an original accelerator concept proposed in the 1990s for the generation of highly energetic pulsed ion beams, suitable for a wide array of applications. The initial studies on the subject were characterized by an important calculation mistake, leading to incomplete and erroneous literature on the topic. Nevertheless, the simple and well-mastered techniques involved in the system (radio frequency and magnetic field), together with the device compactness, are strong motivations for further studies on the ECRIPAC. This Letter proposes a comprehensive introduction to ECRIPAC physics, including a summary of its corrected theory. The designs of several compact demonstrator devices, able to accelerate different ion species to energies up to 100 MeV, are presented. Particular focus is devoted to a ${\mathrm{He}}^{2+}$ accelerator, capable of generating 9.5-MeV/nucleon ions inside a 1.8-m-long accelerating cavity. This device has been simulated using a Monte Carlo (MC) code, developed to model the electron dynamics inside this system. The MC results show excellent agreement with the updated theory, which validates the new theoretical framework of the ECRIPAC. Finally, some estimations for the beam parameters of the ion bunch extracted from the accelerator are provided.

We investigate a two-dimensional dynamical absorbing state model of monodisperse disks, in which rich phase behavior arises from interactions consisting solely of repulsive displacements between overlapping particles. The phase diagram reveals several unconventional features, including a disordered and static absorbing configuration, where no particles overlap, separated by a second-order phase transition to a continuously evolving active hexagonal crystal with collective ring diffusion, which in turn undergoes a first-order phase transition to an active isotropic liquid. The only driving parameter is $\epsilon$, the maximum size of the random repulsive kicks. Small $\epsilon$ facilitates self-organization into an ordered state, but large $\epsilon$ prevents this organization from occurring. This is very different from typical order-disorder transitions, where there are two competing influences, energy and entropy, that drive the transition.

Collective motion in biological swarms emerges from local interactions among individuals with limited sensing and cognition, offering valuable insights for decentralized engineered systems. This study presents a systematic framework for extracting interaction graphs from multiagent trajectory data. Three graph identification methods, sparse regression, Granger causality, and cross-correlation, together with geometric anisotropy analysis, are applied to experimental recordings of honey bees during scattered and focused return-to-hive behaviors, aggregations of midges, and flocking passerine jackdaws. Connectivity analysis reveals task-dependent interaction structures: scattered honey bees exhibit causal interactions with up to ten neighbors, whereas focused bees interact with only two to three agents, with midges showing slightly lower connectivity. Cross-correlation analysis indicated honey bees exhibit distance-sensitivity in close proximity, while flocking birds exhibit a distance-dependent correlation decline. These results highlight diverse coordination mechanisms relevant to bio-inspired networked systems.

We investigate the dynamics of elastic capsules suspended in two-dimensional active nematic fluids using lattice Boltzmann simulations. The capsules, modeled as flexible membranes enclosing active internal regions, exhibit a rich variety of behaviors shaped by their geometry and the interplay between internal and external activity. Circular capsules with active interiors undergo persistent rotation driven by internally confined $+1/2$ topological defects. Axisymmetric capsules, such as boomerangs, develop directed motion along their axis of symmetry due to unbalanced active forces generated by defect distributions near their boundaries. We further show that capsule flexibility suppresses motility and rotation, as active stresses are dissipated into shape deformations. These findings reveal how shape, deformability, and defect dynamics cooperate to produce emergent motility in soft active matter, with potential applications in the design of microswimmers and drug delivery vehicles.

In the usual segregation scenario for stable inclined chute flows of bidisperse mixtures of fine and coarse spherical particles, coarse particles rise toward the free surface, forming a coarse-rich region atop the flowing pile. Beyond a threshold coarse-to-fine diameter ratio of approximately 4, conversely, the weight of the coarse particles exceeds the segregation driving forces, causing individual coarse particles to sink within the pile and producing a reversed segregation state. However, an understanding of the collective evolution of the pile structure is still lacking when the particle diameter ratio exceeds 4 and the coarse-particle mass fraction is appreciable. To explore this broadly bidisperse limit, we perform discrete element method simulations considering mean particle diameter ratios of up to 8 and coarse-particle mass fractions spanning 0.1 to 0.9. The steady-state flow profiles reveal several intriguing behaviors that depend on the diameter ratio and mass fraction. These include a previously identified transition from usual to reverse segregation and a newfound tendency to self-organize into alternating coarse- and fine-rich particle layers stacked along the shear gradient direction, with layer thickness dictated by the coarse-particle diameter. A fuller understanding of segregation at this scale could pave the way for enhanced mixing or demixing techniques at the commercial scale.

Platinum-coated polystyrene Janus particles exhibit a combination of stochastic and deterministic motion in hydrogen peroxide solutions, making them promising candidates for applications in microscale cargo transport, drug delivery, and environmental remediation. The dynamics of Janus particles very near a boundary are dictated by conservative and nonconservative interactions that depend on particle, substrate, and solution properties. This study investigated the influence of orientational quenching by measuring the effect of changes in cap thickness and hydrogen peroxide concentration on particle velocity and maximum displacement. Janus particles with cap thicknesses of 3 nm, 7 nm, 10 nm, 20 nm, and 35 nm were analyzed in 1 wt./vol.% and 3 wt./vol.% hydrogen peroxide solutions near the bottom and top boundaries of the fluid cell. Results indicated that particles with lower cap thicknesses exhibit higher velocities, with faster particles in 3 wt./vol.% peroxide as compared to 1 wt./vol.% peroxide. Furthermore, results suggest a combined influence of activity and gravitational effects influenced whether particles moved along the top boundary, i.e., ceiling or bottom boundary, i.e., flooring. Particles with heavier caps in lower peroxide concentration solution showed a lower probability to experience ceiling as compared to particles with lighter caps in higher peroxide concentration. We also find a global reduction in velocity for when a single surface of the two is plasma cleaned surface. These findings highlight the important interplay between cap properties, surface treatment, and propulsion force in determining the dynamics of Janus particles.

Cells are constantly exposed to diverse stimuli—chemical, mechanical, or electrical—that guide their movement. In physiological conditions, these signals often overlap, as seen during infections, where neutrophils and dendritic cells navigate through multiple chemotactic fields. How cells integrate and prioritize competing signals remains unclear. For instance, in the presence of opposing chemoattractant gradients, how do cells decide which direction to go? When should local signals dominate distant ones? A key factor in these processes is the precision with which cells sense each gradient, which depends nonmonotonically on concentrations. Here, we study how gradient sensing accuracy shapes cell navigation in the presence of two distinct chemoattractant sources. We model cells as active random walkers that sense local gradients and combine these estimates to reorient their movement. Our results show that cells sensing multiple gradients can display a range of chemotactic behaviors, including anisotropic spatial patterns and varying degrees of confinement, depending on gradient shape and source location. The model also predicts cases where cells exhibit multistep navigation across sources or a hierarchical response toward one source, driven by disparities in their sensitivity to each chemoattractant. These findings highlight the role of gradient sensing in shaping spatial organization and navigation strategies in multifield chemotaxis.

We study the three-point correlation function of the backbone in the two-dimensional $Q$-state Potts model using the Fortuin-Kasteleyn (FK) representation. The backbone is defined as the biconnected skeleton of an FK cluster after removing all dangling ends and bridges. To circumvent the severe critical slowing down in direct Potts simulations for large $Q$, we employ large-scale Monte Carlo simulations of the $\mathrm{O}\left(n\right)$ loop model on the hexagonal lattice, which is regarded to correspond to the Potts model with $Q=n^2$. Using a highly efficient cluster algorithm, we compute the universal three-point amplitude ratios for the backbone ($R_{\text{BB}}$) and FK clusters ($R_{\text{FK}}$). Our computed $R_{\text{FK}}$ exhibits excellent agreement with exact conformal field theory predictions, validating the reliability of our numerical approach. In the critical regime, we find that $R_{\text{BB}}$ is systematically larger than $R_{\text{FK}}$. Conversely, along the tricritical branch, $R_{\text{BB}}$ and $R_{\text{FK}}$ coincide within numerical accuracy, strongly suggesting that $R_{\text{BB}}=R_{\text{FK}}$ holds throughout this regime. This finding mirrors the known equality of the backbone and FK cluster fractal dimensions at tricriticality, jointly indicating that both structures share the same geometric universality.

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility, and freight transportation. However, despite their importance, the distribution of tour length has long been neglected in individual human mobility models. To fill this gap, we analyze Foursquare users' check-in data and find that the distribution of urban tour length follows a truncated power-law distribution. To reproduce the universal scaling law for human mobility in urban areas, we introduce a tour terminate-continue model. Our model reproduces not only the urban tour length distribution, but also Heaps' law, Zipf's law, and the distribution of the radius of gyration, providing an additional perspective for characterizing individual human mobility.

Understanding how multiscale network structure influences circadian rhythms in the suprachiasmatic nucleus (SCN) is essential for uncovering the principles of rhythmic robustness and synchronization. Previous studies using synthetic SCN networks suggested a size-dependent phenomenon, in which rhythmic activity initially strengthens with network size and then saturates, but it remains unclear whether this occurs in real SCN networks. Here, we apply geometric branch growth (GBG) and geometric renormalization (GR) to generate self-similar scaled-up and scaled-down replicas from a single-scale functional mouse SCN network. Unlike synthetic models, these SCN replicas do not exhibit size-dependent rhythms: average period, amplitude, and synchronization remain stable across scales. By increasing the average degree with network size, we reproduce size-dependent rhythms and show that they arise from network connectivity, whereas low-degree networks fragment and fail to sustain oscillations. Disrupting clustering self-similarity slightly reduces synchronization, but circadian rhythms remain robust, indicating that average degree, rather than clustering, is the dominant structural driver. These results highlight the resilience of SCN rhythms to network scaling and provide a framework for linking multiscale network structure to biological timekeeping.

We provide comprehensive details of how a previously overlooked entropic, or low-temperature Casimir contribution, $W_C$, to the total binding potential for three-dimensional short-ranged wetting may be determined from a microscopic Landau-Ginzburg-Wilson Hamiltonian. The entropic contribution comes from the many microscopic configurations corresponding to a given interfacial one, which arise from bulklike fluctuations about the mean-field (MF) constrained profile, and adds to the usual MF contribution $W_{\text{MF}}$. We determine the functional dependence of $W_C$ on the interface (and wall) shape using a boundary integral method which can be cast as a diagrammatic expansion with each diagram corresponding to successively higher-order exponentially decaying contributions. The decay of $W_C$ is qualitatively different for first-order and critical wetting with the change in form occurring at the MF tricritical point. Including the Casimir contribution to the binding potential preserves the global surface phase diagram but changes, radically, predictions for fluctuation effects at first-order and tricritical wetting, even when capillary-wave fluctuations are not considered.