We explore the potential of data assimilation (DA) within the multiscale framework of a shell model of turbulence, with a focus on the ensemble Kalman filter (EnKF). The central objective is to understand how measuring mesoscales (i.e., inertial-range scales) enhances the prediction of both large-scale and small-scale intermittent variables, by systematically varying observation frequency and the set of measured scales. We demonstrate that measurements conducted at frequencies that exceed those of the observed scales enable full synchronization of larger scales, provided that at least two adjacent mesoscales are measured. In addition, we benchmark the EnKF against two other DA methods, namely, nudging and ensemble four‐dimensional variational method. EnKF is clearly superior to the former and comparable with the latter but achieving the result with a lower computational complexity. Moreover, our results underscore the need for a tailored, scale-aware inflation technique to stabilize the assimilation process, preventing filter divergence and ensuring robust convergence.

In this work, molecular-dynamics simulations were performed on the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([BMIM][TFSI]) to investigate the influence of external electric fields on the ion-transport properties. In the low-field regime (0–0.2 V/nm), the two-state model effectively analyzes the deviation from the Nernst-Einstein relation by quantifying the contribution of bound ions to self-diffusion and estimating the range of the free-ion fraction. In the high-field regime (0.2–1.8 V/nm), both mobility and diffusivity exhibit nonlinear growth, accompanied by ionic dipole alignment and field-induced local redistribution of counterions, as revealed by normal and angular-dependent radial-distribution functions (RDFs and ARDFs). We observed saturation of both dipole alignment and radial-distribution functions in the highest fields, which contrasts with the continued increase in mobility and diffusivity. In further analysis of ionic dynamics, we found that the mean residence time of bound ions decreases exponentially with the field strength. This suggests that accelerated ion dynamics might be the key factor driving the continued enhancement of diffusivity and mobility.

The generalized Lotka-Volterra (GLV) equations with quenched random interactions have been extensively used to investigate the stability and dynamics of complex ecosystems. However, the standard linear interaction model suffers from pathological unbounded growth, especially under strong cooperation or heterogeneity. This work addresses that limitation by introducing a Monod-type saturating nonlinear response into the GLV framework. Using Dynamical Mean-Field Theory, we derive analytical expressions for the species abundance distribution in the Unique Fixed Point phase and show the suppression of unbounded dynamics. Numerical simulations reveal a rich dynamical structure in the Multiple Attractor phase, including a transition between high-dimensional chaotic and low-volatility regimes, governed by interaction symmetry. These findings offer a more ecologically realistic foundation for disordered ecosystem models and highlight the role of nonlinearity and symmetry in shaping the diversity and resilience of large ecological communities.

Impacted with sufficiently large stress, a dense, initially liquidlike suspension can be forced into a solidlike state through a process known as shear jamming. While the onset of shear jamming has been investigated extensively, much less is known about the resulting solidlike state in the high-stress limit and, in particular, about its failure mode. We report on experiments that produce such high-stress failure by impacting dense suspensions with a cylindrical rod moving at controlled speed. Using suspensions of cornstarch particles we vary the impact speed over several orders of magnitude and change the fluid viscosity as well as the surface tension in order to identify the conditions for failure. The results are compared with similarly dense suspensions of potato starch or polydisperse silica particles. In all cases where the shear-jammed suspension fails by fracturing, similar to brittle solids, we observe two types of cracks: a primary circular crack around the impacting rod followed by secondary radial cracks. Mapping out the onset of radial fracturing for different particle volume fractions $\varphi$ and impact speeds, we identify the requirements for failure via crack formation to occur with at least 50% likelihood and record the corresponding normal stress ${\sigma }_{\text{N}}$ on the impactor. We find that this likelihood is not particularly sensitive to changes in particle diameter, but increases when the solvent's viscosity or its surface tension are reduced. In the state diagram for dense suspensions we use these data to delineate the upper limit of shear-jammed rigidity and the crossover into a fracture regime at large $\varphi$ and large ${\sigma }_{\text{N}}$, several orders of magnitude above the stress required for the onset of shear jamming. We find that the onset of fracturing in many cases is correlated with signatures of internal ductile deformation of the shear-jammed material underneath the impactor, observable in ${\sigma }_{\text{N}}$ as a function of axial strain. However, for smaller suspension volumes and larger impact speeds, we find strain hardening up to the point of fracturing. This more brittle behavior results in a modulus that, just before crack formation, is roughly an order of magnitude larger than what we observe in shear-jammed suspensions undergoing internal ductile deformation.

We demonstrate the existence of a frequency band exhibiting acoustic transparency in two- and three-dimensional dense granular suspensions, enabling the transmission of a low-frequency ballistic wave excited by a high-frequency broadband ultrasound pulse. This phenomenon is attributed to spatial correlations in the structural disorder of the medium. To support this interpretation, we use an existing model that incorporates such correlations via the structure factor. Its predictions are shown to agree well with those of the generalized coherent potential approximation (GCPA) model, which is known to apply at high volume fractions, including the close packing limit, but does not explicitly account for disorder correlation. Within the transparency band, attenuation is found to be dominated by absorption rather than scattering. Measurements of the frequency dependence of the absorption coefficient reveal significant deviations from conventional models, challenging the current understanding of acoustic absorption in dense granular media.

We study the necessary condition to detect, by means of spectral modularity optimization, the ground-truth partition in networks generated according to the weighted planted-partition model with two equally sized communities. We analytically derive a general expression for the maximum level of mixing tolerated by the algorithm to retrieve community structure, showing that the value of this detectability threshold depends on the first two moments of the distributions of node degree and edge weight. We focus on the standard case of Poisson-distributed node degrees and compare the detectability thresholds of five edge-weight distributions: Dirac, Poisson, exponential, geometric, and signed Bernoulli. We show that Dirac distributed weights yield the smallest detectability threshold, while exponentially distributed weights increase the threshold by a factor of $\sqrt{2}$, with other distributions exhibiting distinct behaviors that depend, either or both, on the average values of the degree and weight distributions. Our results indicate that larger variability in edge weights can make communities less detectable. In cases where edge weights carry no information about community structure, incorporating edge weights in community detection is detrimental.

Compressed ultrafast photography (CUP) is applied to laser breakdown in argon and xenon under pressures up to 40 bars to obtain two-dimensional images of the plasma dynamics of single events with a spatial resolution of $250\times 100$ pixels and an equivalent frame rate of 500 GHz. Light emission as a function of position and time is measured through red, green, blue, and broadband filters. The spatially encoded and temporally sheared image normally used in CUP is now enhanced by the introduction of a constraint given by a spatially integrated and temporally sheared unencoded signal. The data yield insights into the temperature, opacity, the plasma formation process, and heat flow within the plasma and to the surrounding ambient gas. Contours of constant emission indicate that plasmas formed from sufficiently dense gas contract rather than expand despite having a temperature of a few eV. Plasmas formed from relatively low pressure gases such as 7-bar argon can radiate with emissivity near unity. Modeling transport and opacity as arising from inverse Bremsstrahlung requires a degree of ionization that strongly exceeds expectations based on Saha's equation even as customarily modified to include density and screening. According to this model, both electrons and ions are strongly coupled with a plasma coefficient $\gtrsim 1$. During the first few nanoseconds after formation, Stefan-Boltzmann radiation and thermal conduction to ambient gas are too weak to explain the observed cooling rates, suggesting that transport within the plasma dominates its evolution. Yet, thermal conduction within the plasma itself is also small as indicated by the persistence of thermal inhomogeneities for far longer timescales. The fact that plasma is isolated from the surroundings makes it an excellent system for the study of the equation of state and hydrodynamics of such dense plasmas via the systems and techniques described.

Roughness in a potential landscape is canonically understood as a kinetic impediment that invariably suppresses the diffusion of thermally driven particles, particularly in the absence of an external bias. Here we reveal a contrasting principle for systems driven by nonequilibrium fluctuations. Focusing on a paradigmatic model of such fluctuations, such as Poisson shot noise, we demonstrate that for driven particles, roughness on an asymmetric potential can act as an effective means to accelerate diffusion. In a specific regime, the effective diffusion coefficient exhibits a pronounced enhancement, culminating in a peak value that unambiguously surpasses the benchmark value set by free-particle diffusion. This phenomenon originates from a microscopic mechanism we term unidirectional slide inhibition: A synergy between the potential's global asymmetry and its local roughness selectively arrests the particle's backward slide on the gentler slope. This selective arrest acts as a ratchet, enhancing the efficiency of forward barrier crossings. This process simultaneously boosts net transport and magnifies displacement variance by promoting successful, long-range forward jumps over backward slides. Our findings establish a new principle for nonequilibrium control, demonstrating that potential roughness can be harnessed to dramatically enhance diffusion, opening avenues for novel particle separation technologies and offering a new framework for understanding transport in biological and soft-matter systems where such rugged energy landscapes are ubiquitous.

Cell migration is a dynamic process that is of critical importance to various aspects of living organisms, including organogenesis, wound healing, and immune responses. Several external factors are known to influence and direct active cell movement, such as chemokine gradients and the composition and mechanical properties of the extracellular matrix (ECM). While progress has been made in elucidating some of the biochemical pathways that control cell migration, little is known about the impact of the porous structure of the ECM on active cell motion. Here, by combining computational modeling and theory, we reveal how porous environments, as represented by the ECM, determine cell migration dynamics. Simulating cell movement in a 3D cellular Potts model accounting for amoeboid-like cell shape dynamics, we show that cell migration within disordered porous environments is characterized by distinct transient motility regimes that deviate from persistent motion and are best described by the ‘hopping’ of cells between ‘traps.’ Using theory, we can show how these motility regimes and large-scale transport properties are linked to geometrical properties of the microstructure. Importantly, our analyses reveal that spatial heterogeneities in the porosity lead to nonhomogeneous cell distributions and effectively guide cell movement toward regions of low porosity, an effect which we term as porotaxis. Overall, our work reveals the porosity of the ECM as an important control parameter that shapes cell migration and cellular distribution, and provides a conceptual framework to relate experimentally observed cell motility modes to tissue structures and vice versa. This connection between geometry and cell motility could enhance our understanding of how structural elements shape cell migration and tissue organization in various conditions, such as chronic inflammation, immunity, and cancer.

We study the scaling behaviors of the active model $\mathrm{B}+$ using the functional renormalization group (FRG) approach based on the nonequilibrium effective action formulated via the Martin-Siggia-Rose path-integral formalism. We derive the $\beta$ functions for all couplings of the system in generic $d$ dimensions, revealing regulator independence in various contributions to the renormalization group (RG) flow at specific values for $d$. After identifying specific regions of the parameter space that define submodels closed under RG transformations, we determine all fixed points of potential physical relevance. We confirm the existence of a bicritical fixed point, which was conjectured within the perturbative momentum-shell RG method for being responsible for the transition from bulk phase separation to microphase separation in active systems. We argue that, within the FRG approach, global flows significantly differ from those obtained in its perturbative counterpart.

Electric fields can modify protein-protein interactions and thereby influence phase behavior. In lysozyme–sodium thiocyanate solutions, we recently observed shifts in both the crystallization boundary and the liquid-liquid phase separation line under a weak applied field, along with a range of distinct crystal morphologies. Here, we explore how forming protein crystals respond to variations in field frequency and amplitude, focusing on the morphologies of complex, multiarm structures. At constant protein and salt concentrations, the applied field governs both the number and the angular distribution of crystal arms. These features are analyzed through Fourier analysis of microscopy images, revealing cooperative angular ordering among the arms. Based on these observations, we classify three principal multiarm protein crystal (pX) morphologies: flowerlike pX (dominant at high field strengths), triconic pX (appearing nonmonotonically at lower fields), and conic pX (widely observed under low-field conditions). Near the crystallization boundary, field-driven metastable structures such as tubules, clusters, nematic domains, and fibers also occur in response to the field. These findings demonstrate that electric fields effectively steer protein crystallization pathways and provide insight into the mechanisms of various multiarm crystallization.

Triadic interactions are special types of higher-order interactions that occur when regulator nodes modulate the interactions between other two or more nodes. In the presence of triadic interactions, a percolation process occurring on a single-layer network becomes a full fledged dynamical system, characterized by period doubling and a route to chaos. Here we generalize the model to multilayer networks and name it as the multilayer triadic percolation (MTP) model. We find a much richer dynamical behavior of the MTP model than its single-layer counterpart. MTP displays a Neimark-Sacker bifurcation, leading to oscillations of arbitrarily large period or pseudoperiodic oscillations. Moreover, MTP admits period-two oscillations without negative regulatory interactions, whereas single-layer systems only display discontinuous hybrid transitions. This comprehensive model offers new insights on the importance of regulatory interactions in real-world systems such as brain networks, climate, and ecological systems.

The onset of Bose-Einstein condensation in systems with various densities of states is examined, with particular attention to the role of the behavior of their energy spectrum at low and high energies. Specifically, the results of Chaterjee and Diaconis [J. Phys. A: Math. Theor. 47, 085201 (2014)], which rely exclusively on the high-energy behavior, are compared and reconciled with those of the standard physics approach, where the existence of condensation is determined by the low-energy behavior.

In this work, we focus on the influence of an interface on liquid rise through an immersed granular bed. Based on laboratory experiments, we consider the migration of water injected at constant flow rate at the bottom center of a Hele-Shaw cell filled with two layers of grains immersed in water. The bottom layer is made of coarse grains, large enough to ensure liquid percolation without grain motion. The top layer consists of a bidisperse medium of fine grains and dusts about four times smaller in diameter, which can penetrate the interface between coarse and fine grains. When the liquid invades the cell, above a critical flow rate, the dusts are washed out of the coarse grains, a process called elutriation. The flow pattern self-organizes, generating fluidization chimneys at the interface between coarse and fine grains with regular spatial distribution. A model based on pressure-drop estimations predicts the pattern wavelength, which depends on the dust size and the number of coarse grains in the cell gap.

Stochastic processes on graphs are a powerful tool for modeling complex dynamical systems such as epidemics. A recent line of work focused on the inference problem where one aims to estimate the state of every node at every time, starting from partial observation of a subset of nodes at a subset of times. In these works, the initial state of the process was assumed to be random independent and identically distributed over nodes. Such an assumption may not be realistic in practice, where one may have access to a set of covariate variables for every node that influences the initial state of the system. In this work, we will assume that the initial state of a node is an unknown function of such covariate variables. Given that functions can be represented by neural networks, we will study a model where the initial state is given by a simple neural network—notably the single-layer perceptron acting on the known nodewise covariate variables. Within a Bayesian framework, we study how such neural-network prior information enhances the recovery of initial states and spreading trajectories. We derive a hybrid belief propagation and approximate message passing (BP-AMP) algorithm that handles both the spreading dynamics and the information included in the node covariates, and we assess its performance against the estimators that use only the spreading information or use only the information from the covariate variables. We show that in some regimes, the model can exhibit first-order phase transitions when using a Rademacher distribution for the neural-network weights. These transitions create a statistical-to-computational gap where even the BP-AMP algorithm, despite the theoretical possibility of perfect recovery, fails to achieve it.

We present an experimental investigation of the pressure dynamics during the flow of self-propelled particles through narrow passages. When the ensemble is flowing, pressure fluctuates around a constant value that does not depend on the crowd size, suggesting that the orifice locally determines the dynamics in this scenario. On the contrary, when the system clogs, pressures are higher for larger crowd sizes, highlighting the importance of the whole collectivity in the process. Then, by correlating the pressure evolution with the exit time of the self-propelled particles, we discover that when a clog is resolved, pressure suddenly drops as a consequence of system reorganization. After this dramatic event, there is a sustained pressure growth over time that shows a square-root dependence, compatible with the structural aging that has been proposed to be behind the broad tail distributions of clogging times.

How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the random hierarchy model (RHM)—an ensemble of probabilistic context-free grammars designed to capture the hierarchical structure of natural language while remaining analytically tractable. Previously, we developed a theory of representation learning based on data correlations that explains how deep learning models capture the hierarchical structure of the data sequentially, one layer at a time. Here, we extend our theoretical framework to account for architectural differences. In particular, we predict and empirically validate that convolutional networks, whose structure aligns with that of the generative process through locality and weight sharing, enjoy a faster scaling of performance compared to transformer models, which rely on global self-attention mechanisms. This finding clarifies the architectural biases underlying neural scaling laws and highlights how representation learning is shaped by the interaction between model architecture and the statistical properties of data.

Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustration drives structured arrays of topological defects. In the dilute limit, these systems have been shown to form a novel state of self-limiting assembly, in which the equilibrium size of multiparticle domains are finite and well defined. In this article we employ Monte Carlo simulations of a recently developed 2D lattice model of geometrically frustrated assembly [Hackney et al., Phys. Rev. X 13, 041010 (2023)] to study the phase transitions between the self-limiting and defect bulk phase driven by two distinct mechanisms: (1) increasing concentration and (2) decreasing temperature or frustration. The first transition is mediated by a concentration-driven percolation transition of self-limiting, wormlike domains into an intermediate heterogeneous network mesophase, which gradually fills in at high concentration to form a quasiuniform defect bulk state. We find that the percolation threshold is weakly dependent on frustration and shifts to higher concentration as frustration is increased, but depends strongly on the ratio of cohesion to elastic stiffness in the model. The second transition takes place between self-limiting assembly at high-temperature or frustration and phase separation into a condensed bulk state at low temperature or frustration. We consider the competing influences that translational and conformational entropy have on the critical temperature or frustration and show that the self-limiting phase is stabilized at higher frustrations and temperatures than previously expected. Taken together, this understanding of the transition pathways from self-limiting to bulk defect phases of frustrated assembly allows us to map the phase behavior of this 2D minimal model over the full range of concentration.

Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or filaments. Yet most existing models for spatial network formation focus on node-based growth, leaving a significant gap in our understanding of systems built from spatially extended components. Here we introduce a minimal model for spatial networks, rooted in the iterative growth and intersection of lines, a mechanism inspired by diverse systems including transportation networks, fungal hyphae, and vascular structures. Unlike classical approaches, our model constructs networks by sequentially adding lines across a domain populated with randomly distributed points. Each line grows greedily to maximize local coverage, while subject to angular continuity and the requirement to intersect existing structures. This emphasis on extended, interacting elements governed by local optimization and geometric constraints leads to the spontaneous emergence of a core-and-branches architecture. The resulting networks display a range of nontrivial scaling behaviors: the number of intersections grows subquadratically; Flory exponents and fractal dimensions emerge consistent with empirical observations; and spatial scaling exponents depend on the heterogeneity of the underlying point distribution, aligning with measurements from subway systems. Our model thus captures the key organizational features observed across diverse real-world networks, establishing a universal paradigm that goes beyond node-based approaches and demonstrates how the growth of spatially extended elements can shape the large-scale architecture of complex systems.

A century after Ising introduced the Ising measure to study equilibrium systems, its relevance has expanded well beyond equilibrium contexts, notably appearing in nonequilibrium frameworks such as the Katz-Lebowitz-Spohn (KLS) model. In this work, we investigate a class of generalized asymmetric simple exclusion processes (ASEPs) for which the Ising measure serves as the stationary state. We show that the average stationary current in these models can display current reversal and other unconventional behaviors, offering insights into transport phenomena in nonequilibrium systems. Moreover, although long-range interaction rates often give rise to long-range interactions in the potential function, our model provides a counterexample: Even with long-range interactions in the dynamics, the resulting potential remains short ranged. Finally, our framework encompasses several well-known models as special cases, including ASEPs, the KLS model, the facilitated exclusion process, the cooperative exclusion process, and the assisted exchange model.