Multiscale periodic metamaterials have been designed for numerous applications, such as impact absorption, acoustic cloaking, photonic band gaps, and mechanical logic gates. This prior work has focused on optimizing mesoscale structure for desired bulk isotropic properties. In contrast, we seek to develop materials with highly anisotropic elastic properties. To quantify elastic anisotropy, we introduce two rotationally invariant, normalized quantities that characterize the anisotropic response to shear and compression, respectively, $A_G$ and $A_C$. $A_G \left(A_C\right)$ is the normalized variance of the shear (uniaxial compressive) modulus obtained by changing the coordinate axes. We find that typical crystalline solids possess average elastic anisotropy ${\overline{A}}_G\approx 0.15$ and ${\overline{A}}_C\approx 0.09$. Compared to atomic crystals, jammed granular materials can attain elastic anisotropies that are several orders of magnitude larger. Since grain rearrangements reduce anisotropy in granular materials, to preserve strong elastic anisotropy, we design tessellated granular materials that consist of multiple connected grain-filled voxels, which limit rearrangements and enable highly anisotropic elastic properties. Bulk granular packings with $N$ grains prepared at pressure $p$ have maximal anisotropy for $p{N}^2\sim 1$ and become isotropic in the large-$p{N}^2$ limit. We show that homogeneously tessellated granular systems can inherit the elastic response of the constituent voxel configurations with elastic anisotropy up to 100 times that of crystalline compounds over a range of $p{N}^2$. We show further methods to enhance the elastic anisotropy of tessellations by designing heterogeneously patterned voxel configurations and tessellations that allow large boundary deformations.

Period doubling is a robust feature of systems subjected to time-dependent parameter modulation, which manifests among a variety of fields including physics, chemistry, and biology. When the parameter is modulated in space, an analogous behavior can occur, characterized by the emergence of patterns with a wavelength twice that of the underlying modulation. Here, we consider the case of a system depending both on time and space. Using a simple mechanical model, here a vibrating strip, we show that such a modulation yields a dynamics richer than in the classical (i.e., purely temporal or spatial) case. In particular, instead of standard period doubling, we report a dual subharmonic response exhibiting occurrences of tristability. These features are captured within a unified framework, which further reveals that the frequency content of the response can be tuned via the ratio of the system size to the modulation length scale, a control parameter that can be adjusted through the strip's material properties, length, or tension.

When the time-reversal and parity symmetries in a fluid are broken, transverse transport coefficients can arise in response to perturbations, an example being odd viscosity. We refer to these systems as odd fluids. While much progress has been made in the continuum theory of odd-viscous fluids, and noncollisional models for odd viscous fluids have been proposed, a classical microscopic description in which the transverse responses originate from collisions is lacking. In this paper, we show that a dilute granular gas of rough and inelastic particles driven by a constant torque is a minimal microscopic model of an odd fluid. By applying the methods of Boltzmann kinetic theory, we obtain a hydrodynamic description of the microscopic model. Then, using the method of adiabatic elimination, we numerically compute all the response coefficients of the model, explicitly showing that the model has many odd response terms. Our theory predicts that certain odd response coefficients can change sign even when the direction of the external torque is fixed. While we choose a particular case, the procedure we present can be applied to any collisional model. We also present a semiquantitative method to determine the hydrodynamic variables of the theory by observing the eigenvalue spectrum of the linear collision operator. In the end, we repeat the analysis to study a system with rotational drag. We observe that including rotational drag can affect the choice of hydrodynamic variables and numerical values of response coefficients.

We study relations between three inequality indices, namely the Gini ($g$), Pietra ($p$) and Kolkata ($k$) introduced in 1912, 1915, and 2014 respectively, and all are derived from the Lorenz function $L\left(x\right)$ introduced in 1905. The Kolkata index [which corresponds to a fixed point of the complementary Lorenz function $L_c\left(x\right)\equiv 1-L\left(x\right)$] gives the fraction $k$ of wealth possessed by the richest $1-k$ fraction of people ($k$ = 0.8 corresponds to Pareto's 80-20 law from 1896). We show rigorously that while the Pietra index value $p$ should be greater than or equal to $2k-1$, the Robin Hood index should strictly be equal to the excess wealth fraction $2k-1$ possessed by the richest $1-k$ fraction of people. Our numerical data analysis for U.S. IRS income data (1983–2022), Bollywood (India) movie income data (1999–2024), and the citation inequalities across the publications by forty Nobel laureates (2020–2025) in economics, physics, chemistry, and medicine clearly show that $p/(2k-1)$ is always greater than unity but the deviation is never more than 5%. Assuming some simple analytic form for the Lorenz function, we also derived the relations $k=(1/2)+(3/8)g$ for small $g$ values and $p/g=3/4$. However, by considering the Lorenz function appropriate for the generalized Pareto power law distribution, we obtain an extended range ($1_{+}<p/g\le e/2$) that captures most of the empirical data.

Capillarity-dominated two-phase displacement in porous media can continue beyond the initial invasion-percolation (IP) breakthrough when surfactants progressively modify interfacial properties and reopen pathways previously sealed by capillary barriers. We study this post-breakthrough secondary invasion, in which adsorption-driven reductions in interfacial tension and wettability shifts lower the capillary-pressure entry thresholds of yet-uninvaded throats, enabling further displacement under a fixed inlet pressure. To capture this mechanism, we develop a time-dependent pore-network framework that couples quasistatic IP to a reduced-order transport-adsorption module: local fluxes follow Poiseuille flow on the invaded cluster, interfacial adsorption is described by a Langmuir isotherm, and wettability evolution is represented via a phenomenological relation. Network heterogeneity is prescribed by Gaussian throat-size distributions, with the variance controlling structural disorder. The resulting invasion trajectories are sigmoidal and well described by Gaussian cumulative statistics, indicating that surfactant mass-transfer kinetics and network variance primarily rescale invasion timescales while preserving the overall functional form. Overall, the framework links interfacial conditioning to time-varying capillary-pressure thresholds and clarifies how surfactant-mediated processes govern secondary, post-breakthrough dynamics in heterogeneous porous systems.

An important process for antimatter experiments is the cooling of particles in a Penning-Malmberg trap to experimentally useful temperatures. A non-neutral plasma of one species (e.g., antiprotons) can be collisionally cooled on another colder species (e.g., electrons). Modeling temperature relaxation in these devices is challenging from a plasma physics perspective because the particles are strongly magnetized (the gyrofrequency exceeds the plasma frequency). Recently, a theoretical model based on the generalized collision operator was proposed to describe the temperature evolution in these conditions, predicting a multistep relaxation process where temperatures parallel to the magnetic field relax much faster than perpendicular to it [L. Jose et al., Phys. Rev. E 111, 035201 (2025)]. Here, this model is tested using molecular dynamics simulations. Two analysis methods are applied: one based on an imposed temperature difference, and the other based on a Green-Kubo relation. The results of the simulations support the predictions of this new model. This work extends previous molecular dynamics simulation studies of temperature anisotropy relaxation in one-component non-neutral plasmas to two-component systems.

We investigate structure-dynamics relations in binary mixtures of highly charged colloidal suspensions employing multi-component mode-coupling theory (MCT) based on partial static structure factors from thermodynamically consistent integral equations with Rogers-Young (RY) closure. In mixtures of identically charged particles with different sizes and thus short-time mobilities, MCT predicts long time dynamical coupling effects between different species in qualitative accordance to Brownian dynamics (BD) simulations. Within a rescaled MCT scheme based on structure factors of systems with reduced number of effective charges, quantitative agreement of long-time self-diffusion coefficients from MCT and BD is achieved. At intermediate scales of time, however, even in the results within the rescaled MCT scheme, small deviations between rescaled MCT and BD results are observed.

Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the theoretical limits of equilibrium self-assembly systems for solving computing problems, focusing on the directed Hamiltonian path problem (HPP) as a benchmark for NP-complete problems. The HPP is encoded via particles with directional lock-key patches, where self-assembled chains form candidate solution paths. We determine constraints on the required energy gap between on-target and off-target binding for an acyclic HPP to be encoded and solved. We simultaneously examine whether components with the required energy gap can be designed. Combining these results yields a phase diagram identifying regions where HPP problems are both solvable and designable. These results establish fundamental upper bounds on equilibrium molecular computation and highlight the necessity of nonequilibrium approaches for scalable molecular computing architectures.

Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are simultaneously reset, recent work has shown that resetting only a subset of degrees of freedom (subsystem resetting) can qualitatively alter collective behavior in interacting many-body systems. In this work, we develop a general theoretical framework for analyzing subsystem resetting in Kuramoto-type coupled-oscillator systems. Building on a continued-fraction approach, we derive self-consistent equations for the stationary-state order parameter of the nonreset subsystem, applicable to both noisy and noiseless dynamics and to models with arbitrary interaction harmonics. Using this framework, we systematically investigate how the stationary state and phase transitions depend on the resetting rate, the size of the reset subsystem, and the reset configuration. We show that subsystem resetting can shift or even suppress synchronization transitions, and can give rise to nontrivial features such as reentrant behavior and restructuring of phase boundaries. In specific cases, including the noiseless Kuramoto model with a Lorentzian frequency distribution, our results recover known analytical predictions and extend them to more general settings. These results establish subsystem resetting as a versatile control protocol for engineering collective dynamics in nonequilibrium interacting systems.

Explosive synchronization (ES) is characterized by irreversible transitions to collective coherence in coupled oscillator networks. A recent study [Phys. Rev. Res. 4, 033009 (2022)] has predicted a richer phenomenon, double explosive synchronization (DES), in which a multilayer system exhibits two consecutive discontinuous transitions. Experimental evidence of DES, however, has remained lacking. Here we report the experimental observation of DES using multilayer networks of Wien-bridge oscillators. By coupling a strongly synchronized low-frequency driving layer to a weakly synchronized high-frequency controlled layer and gradually varying the interlayer coupling, we observe two distinct hysteretic transitions accompanied by bistability. Complementary LTspice circuit simulations reproduce the experimental behavior. These results establish DES as a robust and physically realizable phenomenon in multilayer oscillator networks.

Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscape topographies, giving rise to error thresholds and lethal mutagenesis. Motivated by experimental evidence that polymerase-targeting antivirals limit replication, we analyze replicating systems with explicit time lags in replication-enzyme availability by means of delay differential equations. Our approach is not equivalent to a simple renormalization of the rate of replication, since explicit delays introduce memory and temporal nonlocality into the dynamics. We identify a lag-induced critical transition driven by the loss of temporal coordination between genome expression and replication. At fixed mutation and replication rates ensuring persistence, populations cross an extinction threshold solely due to replication delays. In our delay-extended quasispecies model, the timing of replicase availability emerges as an independent dynamical control parameter, defining a route to extinction that is fundamentally distinct from transitions driven by mutation rates or replicative fitness. These results further suggest that perturbing the temporal coordination of viral replication may provide an alternative antiviral strategy for driving viral populations toward collapse. More generally, we propose that the extinction mechanism described here constitutes a form of lag-time-induced tipping, which we denote as $\tau$-tipping.

Nonreciprocal interactions are widespread in neural circuits, arising both within local excitatory-inhibitory (E/I) dynamics and through directed coupling between distinct populations. Here we investigate how these two levels of asymmetry combine in a modified Wilson-Cowan model of locally non-normal E/I populations connected by directed excitatory projections. We analyze minimal three-node motifs interpolating between a cyclic feedback architecture and a purely feedforward chain. We find that cyclic coupling is largely reducible to an effective shift of the local excitatory coupling, preserving the activation scaling of an isolated E/I module. Feedforward coupling, by contrast, introduces a structural source of non-normality: It produces stage-dependent activation scaling and enhances transient reactivity even at fixed local non-normality. With intrinsic finite-size noise, both motifs exhibit fluctuation-driven switching between inactive and active states but organize activity differently: Feedback promotes coherent, correlated activation, whereas feedforward coupling generates sequential, steplike propagation. These results show how local and structural nonreciprocity play distinct roles in shaping transient amplification and noise-driven dynamics in coupled neural populations, thereby contributing to the growing understanding of the dynamical effects of non-normality across complex systems.

We study the coplanar ground-state manifold of the kagome Heisenberg antiferromagnet using a phase-space network representation, in which nodes correspond to coplanar ground states and edges represent transitions generated by weathervane loop rotations. In the coplanar manifold, each configuration can be mapped to a three-coloring problem on the dual honeycomb lattice, where a weathervane mode corresponds to a closed loop of two alternating colors. By comparing networks that include all weathervane loops with networks restricted to elementary six-spin loops, we examine how energetic constraints shape phase-space structure. We find that connectivity distributions are sharply peaked in large systems, while restrictions to short loops reduce typical connectivity. Spectral properties further distinguish the two cases, with short-loop networks exhibiting Gaussian spectra and full networks displaying non-Gaussian features associated with correlated loop updates. Finally, a box-counting analysis reveals distinct finite-size geometric trends: short-loop networks show algebraic, fractal-like behavior, whereas full networks are more compact in graph distance due to longer-loop shortcuts. These results show that the hierarchy of weathervane loop rotations provides a direct link between microscopic constraints and emergent phase-space geometry in a frustrated magnet.

It has been observed in numerous experiments, simulations, and various theoretical studies that the spreading of particles can be modeled by the continuous-time random walk. We consider two widely used cases, namely Gaussian and discrete displacements, to compute the position distribution and demonstrate the emergence of exponential decay in the far tails when a bias is introduced. We further analyze the temporal rate function and the positional rate function to examine the convergence of the theoretical predictions. For Gaussian displacements, we also discuss the relationship between the position distributions with and without bias in different asymptotic limits.

Edge states are expected to allow for robust, nearly lossless transport along surfaces and interfaces in the presence of disorder. Here we show that this expectation can break down when localized random surface perturbation enables coupling between surface waves and bulk modes, even when it is a weak perturbation. We study the transmission of edge states in a conservative, prototypical spring-mass lattice half plane whose boundary is perturbed by finitely many random variations of surface masses or surface springs. We analyze how an incident surface wave is reflected, transmitted, and partially radiated into the bulk. Using a modal expansion on the orthonormal eigenfunctions of the unperturbed system and a multiscale analysis of the resulting random scattering problem, we apply diffusion approximation theory to characterize the statistics of reflectivity, transmissivity, and radiative loss. This approach yields explicit expressions for the moments of these quantities in the regime of weak disorder and large propagation distances. We identify structural and frequency regimes in which radiative losses into the bulk become substantial, reaching $20\text{−}80\%$ of the incident energy flux carried by the edge state in the high-frequency range. Our results demonstrate that ballistic edge transport is not guaranteed by the mere existence of an edge mode but depends sensitively on disorder characteristics and unperturbed surface structure. These findings suggest alternative possibilities for engineering surface properties to control wave transport, with implications for phononic, photonic, and electronic systems, including graphene-based structures and nanoscale materials.

We study a Brownian particle in a harmonic trap whose stiffness switches between two values with arbitrary waiting-time statistics, leading to semi-Markovian dynamics. To restore Markovianity, we formulate the problem in an enlarged age-structured state space. Using this framework, we obtain steady-state integral equations for the stationary distributions and exact expressions for stationary moments, injected power, and potential energy. In the second part of the paper, we focus on the stochastic-resetting limit, corresponding to a particle alternately released and trapped. By representing the stationary spatial distribution as a superposition of Gaussian states for different effective stiffness (or variance), the problem can be reformulated in variance space, leading to a simplified description amenable to direct analytical treatment.

While $1/f$ noise is ubiquitous and has been found in various systems, its physics remains uncertain. From an analytical study of an ordinary diffusion equation, we find an additional example of the $1/f$ noise. The formula for this example, together with existing knowledge about scaling in fluid turbulence, implies a necessary and sufficient condition for the occurrence of any stationary $1/f$ noise. That is, the noise needs to be characterized by two constant frequencies of $f_{\mathrm{low}}\ll f_{\mathrm{high}}$. For a frequency range from $f=f_{\mathrm{low}}$ to $f_{\mathrm{high}}$, it is further needed that, except for the mean amplitude of the noise, there is no other constant parameter. Then, at $f_{\mathrm{low}}\ll f\ll f_{\mathrm{high}}$, the noise scales asymptotically as $1/f$. Being statistical and simple, our condition applies to any system and hence explains the ubiquity of the $1/f$ noise. It is also applicable to some systems with noise of $\alpha \ne 1.0$ for $1/f^{\alpha }$, via intermittency analogous to that of the turbulence.

Digitally connected societies approach a “transparent” regime where all agents can interact without geographic or social barriers—a limit realized by complete graph topologies. We construct a mean-field theory of a $q$-state Potts model with many-body interactions on this geometry, modeling agents from $q$ distinct communities. Analyzing the illustrative case of competing pairwise and three-body couplings, we identify three equilibrium phases in the thermodynamic limit: symmetric (all communities equal), reduced symmetry ($q-1$ communities surviving), and consensus (one dominant group). For two-community systems, we identify a special coupling regime where the influence of interactions cancels out, yielding purely entropy-driven dynamics—a statistical physics representation of atomized societies without structured influence. Monte Carlo simulations confirm these regimes and reveal metastable switching dynamics in finite systems. Furthermore, we establish a correspondence ($q\leftrightarrow N$) between this model and a mean-field $SU\left(N\right)$ quantum spin system with quadratic and cubic interactions. This “social-quantum” correspondence suggests a representation-theoretic description for classifying symmetry-broken macrostates and offers an interpretive link between quantum mean-field phase structure and opinion stratification.

Machine learning has deeply changed some fields recently, like language and vision. In the case of complex systems, spectacular breakthroughs happened too (e.g., for protein folding) and more are expected to come. Our question is: how and to which extent can one regress scale-free processes, i.e., processes displaying power law behavior, like earthquakes or avalanches? The events one is interested in predicting are the large ones, i.e., events that are typically rare in the training set, so we are basically in the extrapolation regime. While some recent works also tackle scale-free systems by proposing generative models closely aligned with the renormalization group framework, here instead we explore the problem of prediction in the extrapolation regime. We consider two paradigmatic problems that are statistically self-similar. The first one is a two-dimensional fractional Gaussian field obeying linear dynamics, self-similar by construction and amenable to exact analysis. The second one is the Abelian sandpile model, exhibiting self-organized criticality. The emerging paradigm of geometric deep learning shows that including known symmetries into the model's architecture is key to success (as translation invariance for images). Here one may hope to extrapolate only by leveraging scale invariance, which is, however, a peculiar symmetry, as it involves possibly nontrivial coarse-graining operations and anomalous scaling. We perform experiments on various existing architectures like U-net, the Riesz network (scale-invariant by construction), or our own proposals: a wavelet-decomposition-based Graph Neural Network (with discrete scale symmetry), a Fourier embedding layer, and a Fourier-Mellin Neural Operator. Based on these experiments and a complete characterization of the linear case, we identify the main issues relative to spectral biases and coarse-grained representations, and discuss how to alleviate them with the relevant inductive biases.