We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation matrices in multivariate financial data by considering an informational cascade modeled as a hierarchical structure akin to the Kolmogorov statistical theory of turbulence. Our approach extends the Marchenko-Pastur distribution to account for distinct characteristic scales, capturing a larger fraction of data variance, and challenging the traditional view of noise-dressed financial markets. We conjecture that the effectiveness of our method stems from the increased complexity in financial markets, reflected by new characteristic scales and the growth of computational trading. These findings not only support the turbulent market hypothesis as a source of noise but also provide a practical framework for noise reduction in empirical correlation matrices, enhancing the inference of true market correlations between assets.

It has been shown that poly(3-hexylthiophene) ($\mathrm{P}3\mathrm{HT}$) dissolved in chloroform ($\mathrm{CHC}{\mathrm{l}}_3$) undergoes efficient aggregation with permanent polaron formation when submitted to phototreatment mediated by visible pulsed radiation. Although the need for pulsed radiation has been addressed, the role of $\mathrm{CHC}{\mathrm{l}}_3$ in the aggregation process and permanent polaron formation has been elusive. Here we show that $\mathrm{CHC}{\mathrm{l}}_3$ is a major player in photoaggregated products because it undergoes dissociation into hydrogen chloride ($\mathrm{HCl}$) when submitted to high-energy radiation. $\mathrm{HCl}$ is a strong acid and binds to the $\mathrm{P}3\mathrm{HT}$ thiophene ring, establishing a required $p$-doped structure rich in counter ions that stabilize the polarons. UV-Vis absorption, photoluminescence, and Raman modes provide spectroscopic fingerprints, indicating that the planarization of polymeric chains occurs and that such planarization is maintained by the permanent polarons formed throughout the structure when they are present. We also show that methanol $\left(\mathrm{MeOH}\right)$ in an acidic environment works as a facilitator that enhances the efficiency of the polymeric doping process, polaron formation, and controllability of the aggregates' character.

We reformulate the Leslie effects that describe the dynamic cross-couplings in chiral liquid crystals driven by the transport of heat, electric charge, and mass. The Ericksen-Leslie model is extended in the linear response framework by representing nematic order with the $Q$ tensor. Subsequently, the thermodynamic uncertainty relation is applied to identify the upper bounds of the Leslie cross-coupling coefficients. We reveal that the cross-coupling coefficients are dependent on the scalar order parameter and vanish in the isotropic phase. In addition, the chirality of the phase allows torque induced by a transport current parallel to the director. The mutual signs of the Leslie thermohydrodynamic and thermomechanical coefficients are likely to be opposite in calamitic liquid crystals, as suggested by recent experimental observations. Our model is applicable to the thermal, chemical, and electrical Leslie effects. The present arguments suggest that a common underlying principle may govern both the Leslie effects and the thermal Edelstein effect in chiral solid crystals attributed to chiral phonons.

Predicting electrical double-layer (EDL) capacitance from continuum theories without fitting parameters has remained a long-standing challenge due to an incomplete understanding of interfacial electrostatics. In this work, we construct a classical framework that achieves favorable agreement with experiments without fitting for three distinct electrolytes over a range of concentrations. Our model reveals near-electrode ion-specific hydration to be the most important physical mechanism in determining EDL capacitance, followed by the field-dependent dielectric response of water and ion-specific dielectric decrement. It also uncovers the modest role of excluded-volume electrostatics in determining EDL capacitance, although this factor significantly affects the EDL structure. Our classical first-principles framework demystifies electrochemical phenomena, enables predictive modeling of EDLs, and could be incorporated into implicit solvation models in quantum-mechanical calculations.

As engineering advances toward the nanoscale, understanding design principles for molecular motors becomes increasingly valuable. Many molecular motors consist of coupled components transducing one free-energy source into another. Here, we study the performance of coupled rotary molecular motors with different rotational symmetries under constant and scaling driving forces. Under constant driving and strong coupling, symmetry match between the motors decreases the output power. In contrast, under a scaling driving force, the output power is not sensitive to symmetries. However, driving the upstream motor too strongly reduces the downstream motor's output power, leading to a perhaps counterintuitive phenomenon we term disruption, in which the two motors become disconnected. Across both driving schemes, output power peaks at intermediate coupling, confirming the value of flexible coupling. Beyond providing insights into biological motors, these findings could inform the future design of synthetic nanomotors and structure-based drugs.

We study many-body correlation functions within various Fundamental Measure Theory (FMT) formulations and compare their predictions to Monte Carlo simulations of hard-sphere fluids. FMT accurately captures the qualitative behavior of three- and four-body structures, particularly at low and intermediate wave vectors. At higher wave vectors, the predictions of FMT vary in quantitative accuracy. We show that the dominant contributions to the four-point structure factor arise from direct triplet correlations, allowing the evaluation of four-point correlations to be greatly simplified. In glass-forming liquids at high volume fractions, FMT correctly reproduces deviations from the convolution approximation, highlighting FMT's ability to capture growing structural multipoint correlations upon supercooling.

As an efficient type of recurrent neural network, reservoir computing has been widely applied in time series prediction. However, there remains a scarcity of methods specifically addressing the application of reservoir computing to network dynamics prediction. This paper proposes a coupled reservoir computing method, which integrates network structure into the output layer of reservoir computing, demonstrating significant application potential. On the one hand, it accurately predicts dynamical behaviors by leveraging known network structures, providing a powerful tool for analyzing network dynamics. On the other hand, even with unknown network structures, the method can leverage Granger causality test to effectively predict network topology, overcoming ordinary RC limitations. The results of numerical experiments clearly demonstrate that our method not only offers significant advantages in network dynamics prediction but also enables highly accurate reconstruction of the network structure.

Laser-generated, transient toroidal helium plasma at atmospheric pressure is studied experimentally. Tomographically reconstructed cross-sectional images reveal the gas flow responsible for the formation of the toroidal structure. A splitting of the toroidal plasma during the final phase of its evolution is observed. The plasma dynamics is induced by a two-lobed plasma kernel resulting from a single, focused laser pulse. This kernel generates two shocks that join to form an enhanced third shock, a so-called Mach reflection, in the plane perpendicular to the optical axis. This shock pattern determines the gas flow, which deforms the plasma into a disk, then transforms it into a nonrotating toroid, and finally splits it into two parallel rings. Schlieren imaging, a novel laser scanning-probe imaging technique, thermodynamic modeling, and a deliberately broken flow symmetry confirm this formation mechanism. This study is of interest for the generation of compact toroidal plasma structures in free space, with potential applications in chemical reactors, laser ignition of internal combustion engines, plasma medicine, and linked magnetic field line plasma confinement.

Active colloidal assembly has advanced the construction of patchy architectures and stimuli-responsive microsystems—yet structural diversity remains intrinsically limited by field-aligned polarization—that predominantly yield colloidal chains or aligned clusters. Here, we exploit curved liquid interfaces as geometric guidance to overcome orientation constraints via gravity–electric field interplay. The tilted interface amplified subcritical gradient electric forces $(\sim {10}^{-4} \mathrm{nN})$ against gravitational sedimentation and Brownian noise, enabling even low-density colloidal systems (2.5 wt %) to exhibit a buckling effect that generates counterintuitive assemblies. These processes are mechanistically distinct from well-known evaporation-induced buckling. Crucially, dielectrophoretic self-regulation under electric field confers frequency (10 kHz–1 MHz) and strength-independent buckling behaviors, enabling robust programmable architectures during colloidal spatial repositioning. These findings elucidate a principle where competing nonuniform and uniform fields enable expanding accessible configurations in orientation-agnostic assembly. This framework is generalizable to multimodal physical fields (magnetic, optical, and acoustic), providing promise for reconfigurable optical devices and the programmable patchy capsules.

The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling strength and the coupling range, and show both analytically and numerically the critical transitions in the phase diagram, which include bifurcations of simple spatiotemporal patterns and changes in basin sizes of coherent states with different wave numbers. We highlight that this diagram is fundamentally different from those found in other coupled systems such as in coupled logistic maps or Lorenz systems. Finally, we show an interesting domain-wall phenomenon in the coupled chaotic rotors, where a super-long transient interface state (partially regular and partially chaotic) is observed and can persist exponentially long as the coupling range increases up to a critical threshold.

We introduce a methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasistable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. Our approach then focuses on examining the chaotic itinerancy dynamics through the characterization of residence times within these states and chaotic transitions between them with the help of some statistical tests. We demonstrate the effectiveness of these methods on the system of globally coupled logistic maps (GCMs), a well-known model exhibiting chaotic itinerancy. In particular, we conduct comprehensive computations for a large number of parameters in the GCM system and algorithmically identify itinerant dynamics observed previously by Kaneko in numerical simulations as coherent and intermittent phases.

We study the two-dimensional extension of the energy or charge transfer problem in the long-wave limit along a mechanical lattice of oscillators for the interplay between linear longitudinal and periodic on-site interactions in the Holstein approach [S. Reza-Mejía and L. A. Cisneros-Ake, Wave Motion 130, 103382 (2024)]. It is found that the coupling between the linear Schrödinger and sine-Gordon equations, governing the modeling, holds coupled localized and traveling solutions radially symmetric in shape, contrary to the well-known decoupled case where solutions collapse in finite time. We then use the variational description of the problem to find the parameters regime where localization and further propagation take place. For the steady-state scenario, we find a decreasing and oscillatory branch of solutions for the wave function's power, as depending on the frequency of the phase, and then obtain an extension of the Vakhitov-Kolokolov stability criterion that predicts the bifurcation points. We validate these findings by solving the reduced coupled system in the stationary state by means of the Newton method and the Townes soliton condition in the polar coordinates. Finally, we extend our variational approach to the moving case to find the appropriate model and wave parameters where radial motion and the existence of a critical ratio for the strength between longitudinal and on-site interactions take place. These findings are numerically confirmed by solving the full coupled system with the help of the pseudospectral method.

Causal emergence (CE) based on effective information (EI) demonstrates that macrostates can exhibit stronger causal effects than microstates in dynamics. However, the identification of CE and the maximization of EI both rely on coarse-graining strategies, which is a key challenge. A recently proposed CE framework based on approximate dynamical reversibility, utilizing singular-value decomposition (SVD), is independent of coarse-graining. Still, it is limited to transition probability matrices in discrete states. To address this, this article proposes a CE quantification framework for Gaussian iterative systems, based on approximate dynamical reversibility derived from the SVD of inverse covariance matrices in forward and backward dynamics. The positive correlation between SVD-based and EI-based CE, along with the equivalence condition, is given analytically. After that, we provide precise coarse-graining strategies directly from singular-value spectra and orthogonal matrices. This new framework can be applied to any dynamical system with continuous states and Gaussian noise, such as autoregressive growth models, Markov-Gaussian systems, and even SIR modeling using neural networks. Numerical simulations on typical cases validate our theory and offer a new approach to studying the CE phenomenon, emphasizing noise and covariance over dynamical functions in both known models and machine learning.

This study explores the application of elongated particle interaction models, traditionally used in liquid crystal phase research, in the context of early bacterial biofilm development. Through computer simulations using an agent-based model, we have investigated the possibilities and limitations of modeling biofilm formation and growth using different models for interaction between bacteria, such as the Hertz model, soft repulsive spherocylindrical model, and attractive Kihara model. Our approach focuses on understanding how mechanical forces due to the interaction between cells, in addition to growth and diffusive parameters, influence the formation of complex bacterial communities. By comparing such force models, we evaluate their impact on the structural properties of bacterial microcolonies. The results indicate that, although the specific force model has some effect on biofilm properties, the intensity of the interaction between bacteria is the most important determinant. This study highlights the importance of properly selecting interaction strength in simulations to obtain realistic representations of biofilm growth and suggests which adapted models of rod-shaped bacterial systems may offer a valid approach to study the dynamics of complex biofilms.

Debris flows often exhibit coherent wave structures—shocklike roll waves on steeper slopes and weaker, more sinusoidal dispersive pulses on gentler slopes. Coarse-rich heads raise basal resistance, whereas fines-rich tails lower it; in gentle reaches, small-amplitude pulses can locally transport momentum across low-resistance segments. We focus on this gentle-slope, long-wave, low-amplitude regime, where the base-flow Froude number is order unity. In this limit, we obtain a Korteweg–de Vries (KdV) reduction from depth-averaged balances with frictional (Coulomb) and viscous-plastic basal options, using a curvature-type internal normal-stress closure in the long-wave small-$k$ regime. Multiple-scale analysis yields effective nonlinear and dispersive coefficients. We also introduce a practical nonlinearity diagnostic that can be computed from observed crest speeds and flow thicknesses. When laboratory-frame crest celerity is available, we estimate an effective quadratic coefficient from the KdV speed-amplitude relation and report its ratio to the shallow-water reference. When only a depth-averaged first-surge speed and thickness are available, we use the same construction to form a velocity-based proxy and note its bias near zero. A Froude-slope diagram organizes published cases into a steep-slope roll-wave domain and a gentle-slope corridor where KdV pulses are admissible. Numerical solutions of the full depth-averaged model produce cnoidal and solitary waves that agree with the reduced KdV predictions within this corridor. We regard dispersive pulses as a regime-specific complement to roll-wave dynamics, offering a condition-dependent contribution to mobility on gentle reaches rather than a universal explanation for long runout.

In humans and other animals, category learning is associated with a better ability to discriminate between stimuli that are close to the category boundary, compared with stimuli well within a category. This perceptual within-category compression and between-category separation, called categorical perception, was also empirically observed in artificial neural networks trained on classification tasks. In previous modeling works based on empirical neuroscience data, we took an information-theoretic approach that shows that this expansion-compression is a necessary outcome of efficient learning. As a result, the impact of input or neuronal noise is reduced where it is most detrimental, namely, at the boundary between categories. Here we extend our theoretical framework to artificial feedforward networks. The Bayes cost that we consider is an average over the data distribution of the standard cross-entropy loss function. We show that minimizing this cost implies maximizing the mutual information between the set of categories and the neural activities prior to the decision layer. We then consider structured data, formalized by the assumption of an underlying feature space of small dimension. We show that, for wide networks, and more generally in situations of high signal-to-noise ratio, maximizing the mutual information implies (i) finding an appropriate projection space, and (ii) building a neural representation with the appropriate metric. The latter is based on a Fisher information matrix measuring the sensitivity of the neural activity to changes in the projection space. Optimal learning makes this neural Fisher information follow a category-specific Fisher information, measuring the sensitivity of the category membership to changes in the projection space. One consequence is that category learning induces the main neural correlate of categorical perception, an expansion of neural space near decision boundaries. To make this statement more precise, we characterize the properties of the categorical Fisher information. We show that its eigenvectors give the most discriminant directions at each point of the projection space. We find that, unexpectedly, its maxima are in general not exactly at, but near, the class boundaries. Considering toy models and the MNIST handwritten digits dataset, we numerically illustrate how, after learning, the two Fisher information matrices match and essentially align with the boundaries between categories. Finally, we provide a variety of supplemental analyses, in particular, we relate our approach to that of the information bottleneck, and we exhibit a bias-variance decomposition of the Bayes cost, which is of interest on its own.

Characterizing the degeneracy of local stress states is a central challenge in obtaining the complete statistical mechanics of disordered media. Here, we introduce a minimal force-balance model for isolated granular clusters to probe the structure of the stress space through principal stress orientation and stress anisotropy. We further show that when complemented by physically motivated pairwise constraints, the model produces predictions for the stress alignment in packings of repulsive hard spheres. We compare these predictions against simulation data for grains in hopper and simple shear flows, finding qualitative agreement. This demonstrates the promise of modeling bulk athermal disordered systems through the combinatorics of few primitive geometric motifs.

Micropolar fluid theory, an extension of classical Newtonian fluid dynamics, incorporates angular velocities and rotational inertias and has long been a foundational framework for describing granular flows. We propose a macroscopic model of granular matter based on micropolar fluid dynamics, which incorporates internal rotations, couple stresses, and broken parity through odd viscosity. Our framework extends traditional micropolar theory to describe chiral granular flows driven far from equilibrium, where energy is continuously injected and dissipated. In particular, we focus on steady states and explicitly neglect energy conservation, reflecting the dissipative nature of granular systems maintained in nonequilibrium by external forcing. Within this setup, we study the lift force experienced by a test bead embedded in a compressible, parity-breaking granular flow. We analyze how odd viscosity and microrotation modify the transverse forces, using both analytical results in the linearized Stokes regime and nonlinear finite-element simulations. Our results demonstrate that micropolar fluids provide a physically consistent and symmetry-informed continuum description of chiral granular matter, capable of capturing lift forces that emerge uniquely from odd transport effects.

Active cholesterics are chiral in both their structure, which has continuous screw symmetry, and their active stresses, which include contributions from torque dipoles. Both expressions of chirality give rise to curl forces in the hydrodynamics, which we derive from the active Ericksen-Leslie equations using a geometric approach. This clarifies the hydrodynamics of continuous screw symmetry and provides an example of generalized odd elastic forces that originate from an equilibrium free energy. We also discuss the nonlinear structure of the active hydrodynamics in terms of the Eulerian displacement field of the cholesteric pseudolayers. For the active instability, screw symmetry generates a contribution of chiral activity to the linearized pseudolayer hydrodynamics that is absent in materials with chiral activity but achiral structure. When the two forms are sufficiently antagonistic, this term produces a new active instability with a threshold and a characteristic wave vector distinct from those of the active Helfrich-Hurault instability in chiral active smectics. Finally, we comment on the isotropic chiral hydrodynamics of materials with three-dimensional screw symmetry.

The impact of ionic impurities on the fundamental properties of nematic liquid crystals (LC) has long been observed; however, their influence on fundamental material parameters remains quantitatively unclear. Here we develop and validate a predictive theoretical framework that integrates ionic Coulomb self-energy into the Landau-de Gennes formalism, revealing how free ions nonlinearly suppress the dielectric anisotropy. Additionally, we propose a model that clarifies how electrostatic ion drag contributes to an increase in the rotational viscosity of the nematic phase. We experimentally verify both the dielectric anisotropy model and rotational viscosity model using a dual-frequency nematic LC doped with controlled concentrations of monolayer graphene flakes, which effectively modulates the ionic environment. The experimental results exhibit strong agreement with the theoretical predictions across both positive and negative dielectric regimes, as well as for the ion-modulated rotational viscosity of the LC. Dynamic optical switching measurements further corroborate the rotational viscosity results. This work establishes a self-consistent link between microscopic ionic screening and macroscopic rheo-optic behavior in soft anisotropic media, advancing the fundamental understanding of ion-related electrostatics in complex fluids.