In data mining, density-based clustering, which entails classifying datapoints according to their distributions in some space, is an essential method to extract information from large datasets. With the advent of software-based radio, ionospheric radars are capable of producing unprecedentedly large datasets of plasma turbulence backscatter observations, and new automatic techniques are needed to sift through them. We present an algorithm to automatically identify and track clusters of radar echoes through time, using dbscan, a celebrated density-based clustering method for noisy point clouds. We demonstrate our algorithm's efficiency by tracking turbulent structures in the E-region ionosphere, the so-called radar aurora. Through conjugate auroral imagery, as well as in situ satellite observations, we demonstrate that the observed turbulent structures generally track the motion of auroras. What is more, the radar aurora bulk motions exhibit key qualities of auroral electric field enhancements that have previously been observed with various instruments. We present preliminary statistical results using our method, and briefly discuss the method's limitations and potential future adaptations.

Recent empirical studies have found different thermodynamic phases for collective motion in animals. However, such a thermodynamic description of human movement remains unclear. Existing studies of traffic and pedestrian flows have primarily focused on relatively high-speed mobility data, revealing only a fluidlike phase. This focus is partly because the parameter space of low-speed movement, which is governed predominantly by pairwise social interaction, remains largely uncharted. Here, we used ultrawideband radio frequency identification (UWB-RFID) technology to collect high-resolution spatiotemporal data on movements in four different classroom and playground settings. We observed two unique social phases in children's movements: a gaslike phase of free movement and a liquid-vapor coexistence phase characterized by the formation of small social groups. We also developed a simple statistical physics model that can reproduce different empirically observed phases. The proposed UWB-RFID technology can also be used to study the dynamics of active matter systems, including animal behavior, coordinating robotic swarms, and monitoring human interactions within complex systems, potentially benefiting future research in social physics.

Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by means of coupling the protein dynamics on the cell membrane to dynamics in the cytosol. Recent studies demonstrated that modeling the cytosolic dynamics in terms of an averaged protein pool disregards possibly crucial aspects of the pattern formation, most importantly concentration gradients normal to the membrane. At the same time, the coupling of two domains (surface and volume) with different dimensions renders many standard tools for the numerical analysis of self-organizing systems inefficient. Here, we present a generic framework for projecting the cytosolic dynamics onto the lower-dimensional surface that respects the influence of cytosolic concentration gradients in static and evolving geometries. This method uses a priori physical information about the system to approximate the cytosolic dynamics by a small number of dominant characteristic concentration profiles (basis), akin to basis transformations of finite element methods. As a proof of concept, we apply our framework to a toy model for volume-dependent interrupted coarsening, evaluate the accuracy of the results for various basis choices, and discuss the optimal basis choice for biologically relevant systems. Our analysis presents an efficient yet accurate method for analyzing pattern formation with surface-volume coupling in evolving geometries.

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speed up the approach to the Boltzmann steady state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the nonuniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales $\mathcal{O}(NlogN)$ with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in $2d$ ($N={10}^9$) and $3d$ ($N>{10}^7$) and demonstrate the flexibility of the approach by generating structures with designed spectral features at scale. By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level and show that stealthy hyperuniform structures generically display transmission gaps, providing a concrete example of fine-tuning of a physical property. We also show that large $3d$ power-law hyperuniformity in particle packings leads to single-scattering properties nearly identical to those of simple hard spheres. Finally, we demonstrate generalizations of the approach to impose features in either continuous or discrete real space, using constraints in either continuous or discrete reciprocal space. In particular, enforcing large spectral power at peaks with the right symmetry leads to the nondeterministic generation of quasicrystalline structures in $2d$ and $3d$. This technique should become an essential tool to embed, and understand the role of, long-range correlations in disordered metamaterials.

Recently, Dijkman et al. [arXiv:2403.15007] proposed training classical neural density functionals via bulk pair-correlation matching. We show their method to be an efficient regularizer for neural functionals based on local learning of inhomogeneous one-body direct correlations [Sammüller et al., Proc. Natl. Acad. Sci. USA 120, e2312484120 (2023)]. While Dijkman et al. demonstrated pair-correlation matching of a global neural free-energy functional, we argue in favor of local one-body learning for flexible neural modeling of the full Mermin-Evans density-functional map. Using spatial localization gives access to accurate neural free-energy functionals, including convolutional neural networks, that transcend the training box.

The renormalization group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric space, is one of the foundational approaches. However, the current methods assume that the geometric coupling is strong, neglecting weak coupling in many real networks. This paper extends renormalization to weak geometric coupling, showing that geometric information is essential to preserve self-similarity. Our results underline the importance of geometric effects on network topology even when the coupling to the underlying space is weak.

Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.

We investigate the collective behavior of a system of social agents subject to the competition between two mass media influences considered as external fields. We study under what conditions either of two mass media with different intensities can impose its message to the majority. In addition to a collective state dominated by the stronger mass media and a disordered phase, we characterize two nontrivial effects as the parameters of the system are varied: (i) the appearance of a majority sharing the state of the weaker mass media, and (ii) the emergence of an alternative ordering in a state different from those of either media. We explore the dependence of both phenomena on the topology of the network of interactions. We show that the presence of long-range interactions rather than random connections is essential for the occurrence of both effects. The model can be extended to include multiple mass media and we illustrate it by considering three mass media fields acting on the system. Nontrivial collective behaviors persist for some ranges of parameters: the weakest mass media can convince the majority, and the system can spontaneously order against all applied fields.

While many materials exhibit a complex, hysteretic response to external driving, there has been a surge of interest in how the complex dynamics of internal materials states can be understood and designed to process and store information. We consider a system of connected rubber balloons that can be described by a Preisach model of noninteracting hysterons under pressure control but for which the hysterons become coupled under volume control. We study this system by exploring the possible transition graphs, as well as by introducing a configuration space approach which tracks the volumes of each balloon. Changes in the transition graphs turn out to be related to changes in the topology of the configuration space of the balloons, providing a particularly geometric view of how transition graphs can be designed, as well as additional information on the existence of hidden metastable states. This class of systems is more general than just balloons.

The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints each material component imposes on a set of underlying degrees of freedom, the theorem relates the emergence of rigidity to constraint counting arguments. However, the Maxwell-Calladine paradigm is significantly limited—its exclusive reliance on the geometric relationships between constraints and degrees of freedom completely neglects the actual energetic costs of deforming individual components. To address this limitation, we derive a generalization of the Maxwell-Calladine index theorem based on susceptibilities that naturally incorporate local energetic properties such as stiffness and prestress. Using this extended framework, we investigate how local energetics modify the classical constraint counting picture to capture the relationship between deformations and external forces. We then combine this formalism with group representation theory to design mechanical metamaterials where differences in symmetry between local energy costs and structural geometry are exploited to control responses to external forces.

We investigate the statistics of the local time $\mathcal{T}={\int }_0^T\delta (x\left(t\right))dt$ that a run and tumble particle (RTP) $x\left(t\right)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the number of times the RTP crosses the origin, we find that the local time distribution $P\left(\mathcal{T}\right)$ satisfies the large deviation principle $P\left(\mathcal{T}\right)\sim e^{-TI(\mathcal{T}/T)}$ in the large observation time limit $T\to \infty$. Remarkably, we find that in the presence of drift the rate function $I\left(\rho \right)$ is nonanalytic: we interpret its singularity as a dynamical phase transition of first order. We then extend these results by studying the statistics of the amount of time $\mathcal{R}$ that the RTP spends inside a finite interval (i.e., the occupation time), with qualitatively similar results. In particular, this yields the long-time decay rate of the probability $P(\mathcal{R}=T)$ that the particle does not exit the interval up to time $T$. We find that the conditional end-point distribution exhibits an interesting change of behavior from unimodal to bimodal as a function of the size of the interval. To study the occupation time statistics, we extend the Donsker-Varadhan large-deviation formalism to the case of RTPs, for general dynamical observables and possibly in the presence of an external potential.

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so on. Topological signals can undergo collective phenomena such as synchronization, however, only some higher-order network topologies can sustain global synchronization of topological signals. Here we consider global topological synchronization of topological signals on weighted simplicial complexes. We demonstrate that topological signals can globally synchronize on weighted simplicial complexes, even if they are odd-dimensional, e.g., edge signals, thus overcoming a limitation of the unweighted case. These results thus demonstrate that weighted simplicial complexes are more advantageous for observing these collective phenomena than their unweighted counterpart. In particular, we present two weighted simplicial complexes: the weighted triangulated torus and the weighted waffle. We completely characterize their higher-order spectral properties and demonstrate that, under suitable conditions on their weights, they can sustain global synchronization of edge signals. Our results are interpreted geometrically by showing, among the other results, that in some cases edge weights can be associated with the lengths of the sides of curved simplices.

Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual oscillators are well understood, those of systems of coupled oscillators remain challenging to characterize. Here we determine the parametric resonance conditions for time-modulated mechanical systems by exploiting the internal symmetries arising from the real-valued and symplectic nature of classical mechanics. We also determine how these conditions are further constrained when the system exhibits external symmetries. In particular, we analyze systems with space-time symmetry where the system remains invariant after a combination of discrete translation in both space and time. For such systems, we identify a combined space-time translation operator that provides more information about the dynamics of the system than the Floquet operator does and use it to derive conditions for one-way amplification of traveling waves. Our exact theoretical framework based on symmetries enables the design of exotic responses such as nonreciprocal transport and one-way amplification in dynamic mechanical metamaterials and is generalizable to all physical systems that obey space-time symmetry.

Plants are a paradigm for active shape control in response to stimuli. For instance, it is well known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along the plant's axis, as in a rotating clinostat, leading to intricate shapes. We use a previously derived rod model to study the response of a growing plant and the joint effects of both stimuli at all rotation speeds. In the absence of rotation, we identify a universal planar shape towards which all shoots eventually converge. With rotation, we demonstrate the existence of a stable family of three-dimensional dynamic equilibria where the plant axis is fixed in space. Further, the effect of axial growth is to induce steady behaviors, such as solitary waves. Overall, this study offers insight into the complex out-of-equilibrium dynamics of a plant in three dimensions and further establishes that internal stimuli in active materials are key for robust shape control.

We present a dynamic light scattering setup to probe, with time and space resolution, the microscopic dynamics of soft matter systems confined within millimeter-sized spherical drops. By using an ad hoc optical layout, we tackle the challenges raised by refraction effects due to the unconventional shape of the samples. We first validate the setup by investigating the dynamics of a suspension of Brownian particles. The dynamics measured at different positions in the drop, and hence different scattering angles, are found to be in excellent agreement with those obtained for the same sample in a conventional light scattering setup. We then demonstrate the setup capabilities by investigating a bead made of a polymer hydrogel undergoing swelling. The gel microscopic dynamics exhibit a space dependence that strongly varies with time elapsed since the beginning of swelling. Initially, the dynamics in the periphery of the bead are much faster than in the core, indicative of nonuniform swelling. As the swelling proceeds, the dynamics slow down and become more spatially homogeneous. By comparing the experimental results to numerical and analytical calculations for the dynamics of a homogeneous, purely elastic sphere undergoing swelling, we establish that the mean square displacement of the gel strands deviates from the affine motion inferred from the macroscopic deformation, evolving from fast diffusivelike dynamics at the onset of swelling to slower, yet supradiffusive, rearrangements at later stages.

We introduce a multiscale model for affinity maturation, which aims to capture the intraclonal, interclonal, and epitope-specific organization of the B-cell population in a germinal center. We describe the evolution of the B-cell population via a quasispecies dynamics, with species corresponding to unique B-cell receptors (BCRs), where the desired multiscale structure is reflected on the mutational connectivity of the accessible BCR space, and on the statistical properties of its fitness landscape. Within this mathematical framework, we study the competition among classes of BCRs targeting different antigen epitopes, and we construct an effective immunogenic space where epitope immunodominance relations can be universally characterized. We finally study how varying the relative composition of a mixture of antigens with variable and conserved domains allows for a parametric exploration of this space, and we identify general principles for the rational design of two-antigen cocktails.

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant $C_2\propto \int \int dxdv\langle f^2\rangle$—a quantity that here plays the role of (negative) entropy of the distribution function. We find that $C_2$ is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of $C_2$ in Fourier space, with $k$ and $s$ denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in $k$ space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of $C_2$ to high $s$ (towards the collisional dissipation range) at every $k$, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of $C_2$ is to both high $k$ and high $s$ simultaneously. Integrating over velocity (spatial) wave numbers, the $k$-space ($s$-space) flux of $C_2$ is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the $(k,s)$ plane, with power-law asymptotics at large $k$ and $s$. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

In open water, social fish gather to form schools, in which fish generally align with each other. In this work, we study how this social behavior evolves when perturbed by artificial obstacles. We measure the behavior of a group of zebrafish in the presence of a periodic array of pillars. When the pillar density is low, the fish regroup with a typical interdistance and a well-polarized state with parallel orientations, similarly to their behavior in open-water conditions. Above a critical density of pillars, their social interactions, which are mostly based on vision, are screened and the fish spread randomly through the aquarium, orienting themselves along the free axes of the pillar lattice. The abrupt transition from natural to artificial orientation happens when the pillar interdistance is comparable to the social distance of the fish, i.e., their most probable interdistance. We develop a stochastic model of the relative orientation between fish pairs, taking into account alignment, antialignment, and tumbling, from a distribution biased by the environment. This model provides a good description of the experimental probability distribution of the relative orientation between the fish and captures the behavioral transition. Using the model to fit the experimental data provides qualitative information on the evolution of cognitive parameters, such as the alignment or the tumbling rates, as the pillar density increases. At high pillar density, we find that the artificial environment imposes its geometrical constraints to the fish school, drastically increasing the tumbling rate.

Cilia are hairlike microactuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to a no-slip wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase-oscillator description by reducing the microsphere dynamics to the slow timescale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of flow near the surface of a cell or tissue to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow near the surface stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wavelengths propagating perpendicularly to the power stroke. Performing simulations of phase-oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.