Urban systems often exhibit scale-invariant properties, with power-law distributions observed in various spatial and temporal patterns of human behavior. A prominent example is the distribution of commercial activities and other points of interest (POIs) across cities. However, the mechanisms by which such heavy-tailed behaviors emerge from local urban dynamics remain poorly understood. In this work we demonstrate that global inhomogeneity in the spatial distribution of POIs can arise from the aggregation of locally homogeneous processes. Using Foursquare data from the city of Bologna, we show that POI distributions exhibit clear power-law scaling when analyzed at city scale. We develop a theoretical framework in which this behavior naturally emerges from spatial clusters defined by shared intensity levels across disjoint areas, rather than spatial contiguity. By analytically and empirically linking these local processes to the observed global distribution, we provide a generative explanation for the emergence of scale-free patterns in urban commercial structure. To further relax the assumptions underlying the purely spatial model, and to account for the empirical observation that areas with similar activity intensity can be spatially disjoint, we introduce a hybrid hierarchical approach that combines spatial clustering with statistical heterogeneity across regions of comparable density, modeled via Poisson mixtures. This enables us to capture real-world deviations from local regularity while preserving interpretability. Our findings highlight a key insight: complex global phenomena in cities can arise from the spatial superposition of simple, locally uniform dynamics. This connection between microlevel homogeneity and macroscale complexity offers tools for interpreting, modeling, and classifying urban space.
We study the 6 model and derive two broad classes of lattice discretizations that admit static, translationally invariant kinks; that is, stationary kink profiles that can be centered at an arbitrary position relative to the lattice. These discretizations are constructed using a one-dimensional map, n+1 = F( n), which provides a direct and systematic algorithm for generating such models. Numerical computations for two representative cases show that the discrete kinks do not possess internal modes, consistent with the continuum theory, although an additional high-frequency mode may appear above the upper edge of the phonon band. We also show that generic discretizations of the 6 model do not support static kink solutions. Instead, the resulting dynamics produce autotraveling and self-accelerating kinks that propagate at the maximal group velocity while continuously emitting radiation.
Nonequilibrium steady states are investigated in a two-dimensional billiard table, called the Lorentz circuit, consisting of two circular urns connected by two rectangular strips: an active channel, where a feedback mechanism operates, and a passive finite-size Lorentz channel, which is a finite network of Sinai billiards, i.e., a specific environment populated with an array of circular scatterers of fixed radius. We show that, in the finite-horizon regime, a variation of any of the four geometrical parameters of the Lorentz channel can trigger a phase transition in the circuit. Our analytic derivations identify the critical parameters governing these transitions and predict whether they are continuous or discontinuous. We find that both transition orders are realized upon changing just one of the geometrical parameters. Our analysis further highlights the validity of Fick's law in the Lorentz channel, which in our model mirrors the validity of Ohm's law in electrical circuits. All analytic results are corroborated by an extensive set of numerical simulations of the particle dynamics.
We investigate the critical phenomena of the asymmetric quantum Rabi model (AQRM), where parity symmetry is broken by an external bias. Through both analytical and numerical calculations, we identify second-order and first-order phase transitions, with the latter absent in the standard quantum Rabi model. We derive an analytical two-variable scaling function that describes the finite-frequency scaling behavior of the AQRM, and numerical results confirm this framework. The introduction of bias leads to additional critical exponents, including a bias-related critical exponent ν_{h} and susceptibility exponent γ. Moreover, we demonstrate that critical scaling persists even below the conventional critical coupling, indicating the emergence of field-induced quantum criticality. These findings establish a robust theoretical framework for understanding universal quantum criticality in light-matter systems.
Diffuse interface methods for multiphase flow simulations often exhibit nonphysical droplet or bubble shrinkage, particularly when based on the Cahn-Hilliard equation. This well-known artifact introduces a critical radius below which droplets vanish, thereby limiting the fidelity of simulations involving small-scale structures. In this study we examine a conservative Allen-Cahn model and demonstrate, through both analytical and numerical investigations, that it inherently avoids this shrinkage behavior. We show that the conservative Allen-Cahn model enforces an exact local balance of interfacial terms, enabling the stable preservation of droplets with radii larger than the interface thickness, regardless of the initial droplet size or domain geometry. Our analysis also provides a different theoretical treatment of the shrinkage phenomenon in the Cahn-Hilliard equation, distinguishing itself from earlier works by providing a rigorous explanation of why conservative Allen-Cahn models avoid this problem. The analysis reveals that conservative Allen-Cahn formulations achieve exact cancellation of curvature-driven terms through a local geometric force balance, while Cahn-Hilliard models exhibit systematic shrinkage due to unbalanced curvature effects that create driving forces for mass transport. Theoretical and numerical findings show that there is a shrinkage relation between interface radius r_{I} and time t in the form of r_{I}^{3}(t)∼-t, which leads to a power law t_{f}∝r_{0}^{3} for the disappearance time t_{f} versus initial radius r_{0}. Numerical experiments across a wide range of droplet sizes corroborate the theoretical predictions. These results position the conservative Allen-Cahn model as a robust and accurate phase-field approach, particularly well suited for applications demanding the resolution of fine features or long-time integration, such as multiphase transport in porous media.
We explore the synchronization dynamics of Kuramoto oscillators in three 2-simplicial ring networks-node-coupled, edge-coupled, and ring-star-covering both identical and nonidentical systems. Notably, the 2-simplicial ring networks support much richer antiphase fully synchronized states than those in traditional simplicial complex models, with cluster sizes following a universal, finite-size-effect-free Gaussian distribution. Regarding in-phase fully synchronized states, we verify via the cellular dynamics method that they are linearly stable yet practically unreachable from random initial conditions due to their extremely small attraction basins. Under frequency heterogeneity, partial synchronization emerges, where oscillator frequencies cluster into two distinct groups. Among these networks, the ring-star 2-simplicial ring network exhibits the narrowest range of coupling strengths supporting partial synchronization states, while displaying the most significant disparity in cluster sizes. This research highlights the pivotal role of simplicial coupling and ring topology in regulating synchronization, offering new insights into higher-order complex networks.
We investigate the dynamics of an inertial active Ornstein-Uhlenbeck particle suspended in a non-Markovian environment. The particle is additionally subjected to external forces, such as harmonic confinement and a magnetic field. Motivated by the importance of understanding the non-Markovian behavior of complex environments, we examine the impact of a viscoelastic medium by employing the Jeffreys fluid framework for modeling the particle motion, which effectively captures both viscous and elastic contributions of the environment. Within this model, we explicitly derive the corresponding Fokker-Planck equation for each case. Building on this, we extend the analysis to the general non-Markovian framework and derive the corresponding generalized Fokker-Planck equation for a free active particle. Furthermore, we obtain the probability distribution function valid for an arbitrary memory kernel under various conditions, including both free and confined motion with and without a magnetic field. This formulation provides a solid basis for analyzing the dynamics of an active particle in a non-Markovian environment, such as mucus and polymer solutions, and further allows the study of relaxation in confined geometries and responses to external fields.
Turing patterns are a well-studied model of reaction-diffusion equations for developmental patterning. Their applicability has often been limited by the difficulty in identifying candidate molecules that satisfy the requisite criteria for patterning. Here, we build on recent work on geometric models to describe Turing patterning as a potential flow. We show how the universal dynamics of Turing patterning is described by a landscape, largely independent of the underlying reaction-diffusion equations. We apply our framework to three-component systems and demonstrate that we can accurately capture the dynamics of any given component. We extend our framework to larger networks and to models of Turing patterns coupled with external morphogens that provide positional information. We provide a quantitative description of the dynamics of chosen markers and apply it to the dynamics of SOX9 expression during digit patterning.
We consider a cigar-shaped Bose-Einstein condensate (BEC) of two-level atoms subjected to laser-induced Rabi coupling. By expanding the geometric vector potential to second order in the density-dependent fields and developing a quasi-one-dimensional (1D) reduction of the full three-dimensional problem via wave-function factorization, we derive an extended chiral Gross-Pitaevskii (GP) equation. We also derive traveling-wave solutions of the extended chiral GP equation using a projection (orthogonality) method, obtaining both bright and dark chiral solitons whose amplitudes and widths depend explicitly on the propagation direction. The chiral character of these solutions is confirmed through analytical analysis and numerical simulations. A BEC confined in a ring-shaped trap is also analyzed, leading to chiral soliton ring geometries. We show that a subtle interplay among density-dependent gauge potentials, confinement-induced interaction corrections, and higher-order current nonlinearities can give rise to alternative topological states, including chiral solitons and chiral ring solitons, in quasi-1D ultracold Bose gases. These results illustrate how higher-order corrections enrich BEC dynamics and provide means to control spatiotemporal structures in density-dependent condensates.
Vegetation in arid and semi-arid ecosystems often exhibits self-organized spatial patterns as a collective adaptation to water limitation. While reaction-diffusion models have successfully captured such pattern formation, the influence of individual-level traits, particularly root phenotypic plasticity, whereby plants adjust root architecture in response to environmental conditions, remains underexplored. Here, we develop a minimal reaction-diffusion framework that integrates vertical soil stratification with adaptive root conversion to explain the coexistence of multiple spatial scales commonly observed in dry-land vegetation. Building on the single-layer model of Hardenberg et al. [Phys. Rev. Lett. 87, 198101 (2001)0031-900710.1103/PhysRevLett.87.198101], we introduce a second soil layer and a unidirectional biomass conversion from shallow- to deep-rooted phenotype. Analytical and numerical analyses reveal that strong contrasts in diffusion scales, coupled with adaptive conversion, generate two coexisting Turing modes that give rise to robust multiscale vegetation structures. Shallow-rooted biomass with higher diffusivity forms broad vegetation bands, whereas deep-rooted biomass with lower diffusivity clusters at finer scales. The proposed framework provides a mechanistically transparent and ecologically grounded model for multiscale pattern formation, linking adaptive plant traits with the physics of coupled soil-water interactions.
When considering effective interactions in a many-body or thermodynamic system, it is important to recognize that the inherent character of the effective forces between two bodies already incorporates many-body effects that appear unified in a nontrivial way. Working backward to disentangle these effects into the contributions of pairs, triplets, or larger groups is generally complicated and seldom accomplished. However, this could offer essential insights into the structural architecture and self-assembly of complex systems, such as soft materials. In this contribution, we tackle this problem by employing a simulation-based method, here termed contraction of the bare forces (CBF), which, on the one hand, permits a precise evaluation of the effective interactions between colloids [de los Santos-López et al., J. Chem. Phys. 157, 074903 (2022)0021-960610.1063/5.0099919] and, on the other hand, makes it possible to quantify the many-body contributions to these effective interactions. The CBF approach is applied to calculate the depletion forces in asymmetric binary mixtures of hard spheres; the approach is sufficiently sensitive to quantify the effects of higher-order terms on the depletion forces between large particles. To assess the accuracy of our approach, we first explore and confirm the long-established prediction founded on purely geometric considerations, which states that for the particle size ratio, q, smaller than q<q_{3}=0.1547, the depletion interaction between large colloids does not depend on the concentration of large particles, provided that the chemical potential of the smaller particles is kept constant. In contrast, for mixtures with less size asymmetry, such effects become considerably influential. Specifically, we have conducted an in-depth examination of scenarios with size asymmetries values of q=0.45 and 0.60. We directly compare our results for the depletion forces with those obtained from the integral equation framework for effective interactions. Through the use of a naive approximation formulated at the level of the bridge functions, this comparison has further enabled us to identify higher-order contributions to the depletion forces between large colloids, thereby improving and sharpening the underlying theoretical approximations. More importantly, in this work, we explicitly disentangle the many-body components of the depletion forces and assess how significantly they affect the contact attraction strength as a function of both the size ratio and the concentration of the large colloids.
We derive and analyze the amplitude equation for roll patterns in the generalized Active Model B (AMB) with chemical reactions in d=1. We start from the generalized AMB+, which differs from the original AMB+ introduced by Tjhung et al. [Phys. Rev. X 8, 031080 (2018)2160-330810.1103/PhysRevX.8.031080] through the inclusion of an additional quadratic term gϕ^{2} in the equilibrium part of the current. The model incorporates a rotation-free active current with strength λ and a rotational current with strength ξ. In d=1, generalized AMB+ reduces to generalized AMB with an effective rotation-free active current of strength λ_{eff}=λ-ξ/2, while the rotational current is absent. The inclusion of a chemical reaction with rate Γ removes the conservation constraint and introduces a preferred wave number that governs the pattern formation below a critical reaction rate Γ_{c}. We argue for the analytical form of the amplitude equation based on symmetry considerations and explicitly derive it using multiscale analysis. By taking different limits of g, λ, and ξ, we recover amplitude equations for several well-known physical models as special cases and determine the nature of transitions close to the onset of instability. We find that, for g=0, the transition is always supercritical, whereas for g≠0, the transition between the supercritical and subcritical regimes depends sensitively on the model parameters. Furthermore, we derive the condition for the Eckhaus instability from the stability analysis of the amplitude equation as well as from the phase-diffusion equation and find that it is independent of g.
Scroll waves are the three-dimensional counterparts of spiral waves in excitable media, and their filaments can form closed loops known as vortex rings. In systems with negative filament tension, such vortex rings tend to expand and may develop into Winfree turbulence, which is regarded as one of the key mechanisms underlying fibrillationlike activity in cardiac tissue. Therefore, controlling the formation and evolution of scroll-wave vortex rings is crucial for treatment of fibrillation. Motivated by recent advances in pulsed electric field (PEF) ablation for fibrillation therapy, we numerically investigate how PEF modulates the dynamics of free scroll-wave vortex rings in the three-dimensional Barkley model. By systematically varying pulse amplitude, pulse duration, pulse number, and field orientation, we show that when the PEF is applied opposite to the natural drift direction of the vortex ring, sufficiently strong and long pulses can reverse ring expansion and induce collapse, thereby suppressing the onset of turbulence. We further propose a kinematic model that combines intrinsic filament dynamics with the electric-field-induced drift of two-dimensional spiral waves to explain the observed transition from expansion to contraction. These results clarify how pulsed electric forcing can control scroll-wave filaments in media with negative filament tension and may provide mechanistic insight for electrical control of cardiac reentry.
The Jeans instability is a fundamental mechanism driving the gravitational collapse and subsequent structure formation in diverse self-gravitating astrophysical environments. We present comprehensive numerical fluid simulations of the Jeans instability in a three component dusty plasma system. The high-energetic nonthermal electrons and ions are considered to follow κ distribution in velocity space with inertial dust as cold fluid. A Gaussian-type of initial density perturbation is introduced in the equilibrium density to initiate the simulations. The effects of the self-gravity parameter (α_{G}) and nonthermal spectral index (κ) on the Jeans instability have been investigated by tracking the evolution of plasma parameters in the simulations. In the absence of gravity (α_{G}=0), the system exhibits stable dust acoustic wave propagation with no Jeans instability growth, confirming pressure-dominated dynamics. Whereas, for α_{G}>0, the density increases exponentially at center of plasma system manifesting localized collapse. The nonlinear growth rates estimated from our simulations increase with α_{G} and show good agreement with the linear theory, particularly for lower α_{G} values. Simulations further demonstrate that the nonlinear growth rate is weakly dependent on κ; however, lower κ values significantly decrease the characteristic collapse time (τ_{c}). These findings establish that nonthermal (non-Maxwellian) environments in protoplanetary disks and molecular clouds are more efficient at catalyzing rapid structure formation than previously predicted by traditional thermal (Maxwellian) models.
Fluids composed of polarizable particles exhibit tunable structural and functional properties when subjected to external electric fields, as the particles tend to reorient and align along the field direction. This field-induced anisotropy leads to pronounced changes in macroscopic properties, rendering these systems highly relevant for applications in nanotechnology. Understanding the dynamics of their response to external fields is crucial for designing responsive materials with fast and controllable actuation. In this work, we employ molecular simulation to study the behavior of suspensions of polarizable rodlike particles under the action of a uniform electric field, with particular attention given to the transient dynamics associated with the switching on and off of the field. Induced dipoles are modeled by independently varying charge magnitude and field strength, yielding a variable effective polarizability. The induced dipole moment of each rod is treated as an effective, externally controlled parameter, and collective polarization effects arising from local electric fields generated by neighboring particles are not explicitly included. The system is studied in a dense regime, where interparticle interactions play a significant role and are implicitly controlled via pressure. We investigate how the characteristic response time depends on the competition between thermal motion and electric forces across a range of temperatures and field strengths. Our results reveal a rich dynamical behavior: at low to moderate field intensities, increasing the temperature significantly reduces the response time, as thermal agitation facilitates reorientation. However, beyond a critical field strength, the response time plateaus, becoming effectively temperature-independent. This saturation indicates a regime where the aligning torque from the field dominates over thermal fluctuations, setting a lower bound for how fast the system can respond. More specifically, we show that the alignment dynamics cannot be inferred from single-particle behavior alone, but emerges from a nontrivial interplay of field-induced dipolar torques, thermal fluctuations, and steric interactions at finite density, producing strongly temperature-dependent and nonlinear trends in both the nematic order parameter and response times.
In many systems with chiral symmetry, including dry active matter around circular obstacles, vortices exhibit no intrinsic preference for clockwise or counterclockwise rotation. Here, we investigate the rotation of an active vortex around a circular obstacle in a nonaligning dry active-matter system with M half-circles distributed around the central disk. We define a dimensionless control parameter as the ratio between the mean angular velocity of the controlled vortex (M>0) and the root-mean-square angular velocity of the isolated vortex (M=0), when there is no half-circular obstacle distributed around the circular obstacle. Two rotational regimes emerge from the obstacle geometry: clockwise rotation when the flat sides of the half-circles face the vortex and counterclockwise rotation when the curved sides face the vortex. We further show that this geometric control induces a nonmonotonic dependence of vortex stability (maintenance and rotation direction) on the distance between the half-circles from the circular obstacle, demonstrating how geometric constraints can be exploited to control spontaneous collective motion in nonaligning dry active-matter systems.
We introduce a simple symmetric Hamiltonian map that models the magnetic field lines of a double-null diverted tokamak and compare its behavior with the corresponding symmetric single-null map. The phase-space structure of both models is characterized using the finite-time Lyapunov exponent and the escape time of magnetic field line trajectories. For increasing perturbation strength, the area of the chaotic layer grows in both systems, but their escape fractions exhibit distinct oscillatory behaviors. To understand the origin of these oscillations, we analyze the mean transient measure and trace the invariant manifolds of hyperbolic fixed points. The results reveal that variations in the escape fraction arise from changes in the formation of escape channels and from the presence of stickiness near secondary island chains.
Shannon entropy is not the only entropy that is relevant to machine-learning datasets, nor possibly even the most important one. Traditional entropies such as Shannon entropy capture information represented by elements' frequencies, but not the richer information encoded by their similarities and differences. Capturing the latter requires similarity-sensitive entropy: "sentropy." Sentropy can be measured using either the recently developed Leinster-Cobbold-Reeve framework (LCR) or the newer Vendi score (VS). This raises the practical question of which one to use: LCR or VS. Here we address this question theoretically and numerically, using 53 large and well-known imaging and tabular datasets. We find that LCR and VS values can differ by orders of magnitude and are complementary, except in limiting cases. We show that both LCR and VS results depend on how similarities are scaled and introduce the notion of "half distance" to parametrize this dependence. We prove that VS provides an upper bound on LCR for all non-negative values of the Rényi-Hill order parameter, as well as for negative values in the special case that the similarity matrix is full rank. We conclude that VS is preferable only when a dataset's elements can be usefully interpreted as linear combinations of a more fundamental set of "ur-elements" or when the system that the dataset describes has a quantum mechanical character. In the broader case where one simply wishes to capture the rich information encoded by elements' similarities and differences as well as their frequencies, we propose that LCR should be favored; nevertheless, for certain half distances, the two methods can complement each other.
Walkers (i.e., bouncing droplets coupled to a local Faraday wave) are sent on an orthogonal standing wave. The trajectories of successive walkers form a straight-propagating beam toward the wave that splits into three distinct paths during the interaction with the wave. At the end of the interaction, walkers' trajectories split again and are deviated into three main directions. The walkers' trajectories show sensitivity to parameters and initial conditions but remain predictable in some regions of the parameter space. The dependence of the statistical distribution of deviations on the wave amplitude markedly differs from the prediction of quantum mechanics for a particle interacting with a standing electromagnetic wave.
Molecular communication is a model of information transmission where the signal is transmitted by information-carrying molecules through their physical transport from a transmitter to a receiver through a communication channel. Prior efforts have identified suitable "information molecules" whose efficacy for signal transmission has been studied extensively in diffusive channels (DC). Although easy to implement, DCs are inefficient for distances longer than tens of nanometers. In contrast, molecular motor-driven nonequilibrium or active transport can drastically increase the range of communication and may permit efficient communication up to tens of micrometers. In this paper, we investigate how active transport influences the efficacy of molecular communication, quantified by the mutual information between transmitted and received signals. We consider two specific scenarios: (a) active transport through relays and (b) active transport through a mixture of active and diffusing particles. In each case, we discuss the efficacy of the communication channel and discuss their potential pitfalls.
