Subcritical transition to turbulence, in which the laminar state is linearly stable yet finite-amplitude perturbations develop into turbulence, is ubiquitous but predicting it from the structure of the governing equations remains difficult. We demonstrate such a framework using a shell model of turbulence, in which external forcing breaks the phase symmetry of the governing equations. This symmetry breaking suppresses the linear instability of the laminar state, while the energy cascade and spectrum of the developed turbulent state are preserved. A complementary single-triad model admits an exact elliptic neutral stability curve, revealing that the stabilization depends only on the breaking strength and not on the nonlinear coupling coefficients. Since the phase symmetry of the shell model corresponds to Galilean invariance in the Navier-Stokes equations, this mechanism may offer a new perspective on subcritical transition in fluid systems.

We study the ferromagnetic Ising model on a two-dimensional transition lattice that continuously interpolates between the Lieb and kagome lattices via a geometric deformation parameterized by the angle $\theta$. The exchange couplings follow a distance-dependent decay controlled by an exponent $n$, enabling us to disentangle the interplay between geometry and interaction range. Using extensive Monte Carlo simulations and Binder cumulant analysis, we map the phase diagram $T_c\left(\theta \right)$ and show that the critical temperature increases monotonically as the lattice acquires higher effective connectivity. In the large-$n$ limit, the system approaches a nearest-neighbor regime in which the Monte Carlo critical temperatures converge to the known exact values of the Lieb and kagome limits. Finite-size scaling and data collapse confirm that the entire interpolation belongs to the two-dimensional Ising universality class. Beyond demonstrating the robustness of the critical behavior across the Lieb-kagome transition, the present framework suggests natural extensions. The continuous geometric interpolation between the nonfrustrated Lieb lattice and the frustrated kagome lattice offers a suitable platform to explore antiferromagnetic interactions, where the interplay between frustration and long-range couplings may induce nontrivial ordering.

Thermoacoustic instabilities pose a critical challenge in the design and operation of many combustion systems. We report a low-dimensional statistics approach for inferring the parameters of the stochastic Van der Pol oscillator from trajectory observations. From the exponential family structure of the stationary amplitude distribution, we identify sufficient statistics that capture essential parametric information. To break the parameter degeneracy inherent to stationary distribution methods, we incorporate the amplitude autocorrelation time, which provides independent information about noise intensity through relaxation dynamics. The inverse mapping from sufficient statistics to parameters can be effectively approximated by quadratic polynomial regression, achieving comparable accuracy to neural networks while requiring orders of magnitude fewer parameters and providing interpretable closed-form expressions. Comparison with previous parameter identification approaches reveals complementary strengths. In the critical regime near the Hopf bifurcation, our method enables regime classification with reasonable accuracy. Under measurement noise, a periodogram-based moment correction yields graceful degradation across all three parameter estimates, with residual high-noise error dominated by autocorrelation-time bias rather than moment bias. The methodology provides interpretable symbolic expressions suitable for thermoacoustic stability monitoring, and can be extended to other stochastic oscillator systems.

Temporal-network models have provided key insights into how time-varying connectivity shapes dynamical processes such as spreading. Among them, the activity-driven model is a widely used, analytically tractable benchmark. Yet many temporal networks, such as those of physical proximity, are also embedded in space, and spatial constraints are known to affect dynamics unfolding on the networks strongly. Despite this, there is a lack of similar simple and solvable models for spatiotemporal contact structures. Here we introduce a spatial activity-driven model in which short-range contacts are more frequent. This model is analytically tractable and captures the joint effects of space and time. We show analytically and numerically that the model reproduces several characteristic features of social and contact networks, including strong and weak ties, clustering, and triangles having weights above the median. These traits can be attributed to space acting as a form of memory. Simulations of spreading dynamics on top of the model networks further illustrate the role of space, highlighting how localization slows down spreading. Furthermore, the framework is well suited for modeling social distancing in a principled way as an intervention measure aimed at reducing long-range links. We find that, unlike for nonspatial networks, even a small spatially targeted reduction in the total number of contacts can be very effective. More broadly, by offering a tractable framework, the model enables systematic exploration of dynamical processes on spatiotemporal networks.

The self-organization of microbial ecosystems involves a large variety of mechanisms, ranging from biochemical signaling to population dynamics. Among these, the role of motility regulation has been little studied, despite the importance of active migration processes. Here we show how weak, random motility regulation suffices to induce complex forms of organization in bacterial mixtures comprising a large number of coexisting strains. First, we simulate microscopic models of run-and-tumble bacteria whose self-propulsion speeds are weakly regulated by the local density of each strain, mimicking the impact of weak, random metabolic interactions. Our simulations reveal that, as the heterogeneity of the interaction network increases, the system undergoes a phase transition leading to the emergence of distinct, spatially segregated communities. To account for these results and assess their robustness, we use random-matrix theory to analyze the hydrodynamic description of the bacterial mixture, obtaining a quantitative agreement with our microscopic simulations. Our results hold for a variety of motility-regulation mechanisms and highlight the need to characterize the role of motility regulation in experimentally relevant situations.

Biological membranes are dynamic surfaces whose shape and function are critically influenced by protein inclusions (PIs). While membrane deformations induced by PIs have been extensively studied in the small-deformation regime, a variety of processes involve strong membrane deformations. We investigate the interaction between lipid membranes and PIs in the large-deformation (LD) regime, with the finite-element method. We develop an approximate analytical solution that captures key features of the LD regime. We show that the force exerted by the membrane on a PI displays nonmonotonic behavior with respect to the PI vertical displacement. The qualitative features of this force appear to be independent of the protein geometry. For two interacting PIs, the membrane-mediated potential exhibits sub-power-law decay with interprotein distance, reflecting the complex nature of the elastic medium. The interaction potential shows that conical PIs with identical and opposite orientations repel and attract, respectively, confirming the analogy between PI orientation and electric charge, in the LD regime. In the presence of membrane flows, we identify a characteristic velocity that separates two regimes in which bending rigidity and viscous effects dominate, respectively, implying the onset of flow-induced deformations above such velocity threshold. Overall, our results provide quantitative predictions for membrane-protein systems in biologically relevant scenarios involving LDs, with implications for protein sorting, clustering, and membrane trafficking.

The behavior of protein condensates driven by weak multivalent interactions has been extensively studied in bulk systems, yet their interfacial behavior remains far less explored. Using coarse-grained simulations, we investigated protein clusters adsorbed onto interfaces grafted with short peptides through weak multivalent interactions. We found that interface-mediated coarsening and fusion significantly enhance the coacervation of clusters into condensates. Moreover, the mobility of the grafted peptides plays a key role in determining condensate behavior: On interfaces with immobile peptides, increasing surface coverage drives a transition from dewetting to partial wetting, whereas on interfaces with mobile peptides, partial wetting is more likely to occur. Importantly, the weak protein-interface interactions do not impair the dynamic molecular exchange between the condensates and the surrounding solution. Our study provides valuable insights into how protein condensates behave at biological interfaces.

Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially resolved measurement, the steady state can feature collective behavior similar to what is typically observed at phase transitions. Here we investigate such conditional reset protocol in a system of noninteracting spins, where the reset state is chosen as a magnetization eigenstate, that is selected (conditioned) on the outcome of a previous magnetization measurement. The stationary states that emerge from this protocol are characterized by the density of spins in a given magnetization eigenstate, which is the analog of the order parameter. The resulting stationary phase diagram features multiple nonanalytic points. They are of first-order type for half-integer spin, while multicritical behavior, signalled by both first and second-order discontinuities, is found for integer spin. We also show that the associated dynamics is nonergodic, i.e., which stationary state the system ultimately assumes is determined by the initial state. Interestingly, the mechanism underlying these phenomena does not rely on interactions, but the emergent nonlinear behavior is solely a consequence of correlations induced by the measurement.

Fractional calculus has become an essential framework in geophysics, optics, and biological systems to capture long-range correlations and anomalous transport. In this article, we extend the success of fractional calculus in physical models to explore a particle in a periodic potential, where the Schrödinger equation is extended to its fractional form. This framework enables us to study how the Lévy index $q$ governs the formation and inversion of energy bands, offering a pathway to engineer new physical behaviors and device functionalities by tuning $q$ in periodic quantum systems. We solve the fractional Schrödinger equation for periodic rectangular potentials of varying height $V_0$, barrier thickness $L$, and well width $W$ using an imaginary-time evolution algorithm, and supplement the discrete energy dispersion through Gaussian process regression. This analysis reveals a qualitative shift in the system's band structure at $q=2$, separating into distinct regimes of dispersion that define behavior for $q>2$ and $q<2$. For $q>2$, the energy bands undergo an inverting transformation as symmetric minima emerge within the first Brillouin zone and shift from $k=0$ toward $k=\pm \pi /a$ with increasing $q$. These degenerate minima define a Bloch-momentum qubit, suggesting an analog to valley degrees of freedom used in valleytronics. The $q$ at which the inversion completes scales as $q\propto V_0^{-0.28\pm 0.05}, q\propto L^{-0.35\pm 0.08}$, and $q\propto W^{-0.49\pm 0.06}$ when varying potential parameters individually, indicating a tunable transformation sensitivity to potential geometry. In contrast, for $q<2$, the ground band hardens around $k=0$, with a dispersion following the functional form of ${C\left|k\right|}^q+E_0$ near $k=0$. This suggests an effective mass of 0 for $1<q<2$ at the band's lowest energy state. These results demonstrate that the Lévy index serves as a tunable degree of freedom in quantum periodic systems, capable of driving band inversion, modulating the band gap, and reshaping carrier dynamics through effective-mass control.

We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models. For this purpose, we consider two types of quenched disorder, associated with the sites and plaquettes of the cubic lattice. In both cases, for sufficiently weak disorder, the phase diagram remains similar to that of the pure system, showing two different phases (one of them being a topologically ordered phase), separated by two different continuous transition lines. However, the quenched disorder changes the universality classes of the critical behaviors along some of the transition lines. The random-plaquette disorder turns out to be relevant along the topological ${\mathbb{Z}}_2$ gauge transition line, so the critical behaviors belong to the different random-plaquette ${\mathbb{Z}}_2$ gauge ($\mathrm{RP}{\mathbb{Z}}_2\mathrm{G}$) universality class with length-scale exponent $\nu ={\nu }_{\mathrm{rp}}\approx 0.82$; on the other hand, it turns out to be irrelevant along the other ${\mathrm{Ising}}^{\times }$ transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with $\nu ={\nu }_{\mathcal{I}}\approx 0.63$. The random-site disorder leads to a substantially different scenario: it destabilizes the ${\mathrm{Ising}}^{\times }$ critical behaviors of the pure model, changing them into those of the randomly dilute ${\mathrm{Ising}}^{\times }$ (${\mathrm{RDI}}^{\times }$) universality class with $\nu ={\nu }_{\mathrm{RDI}}\approx 0.68$, while the critical behaviors along the other ${\mathbb{Z}}_2$ gauge topological transition line remains stable, with $\nu ={\nu }_{\mathcal{I}}\approx 0.63$.

Field control provides a practical route to programmable active matter, yet how weak fields modify nonequilibrium coexistence and interfaces remains unclear. To address this, we study a minimal flocking model of active Potts particles coupled to an external field and show that even weak fields can reconfigure phase behavior and interfacial dynamics. For a homogeneous unidirectional field, the flocking phase is reshaped: the coexistence regime between an apolar gas and a polar liquid is replaced by a phase separation between two field-aligned polar phases: a low-density, weakly polarized background and a high-density, strongly polarized band, both moving along the field. When the system forms a dense longitudinal lane oriented transverse to the field, it executes a slow treadmilling motion against the field, driven by the weakly polarized background. If the system is divided into regions with opposite field directions, particles accumulate at the interface, leading to field-induced interface pinning with flocks performing back-and-forth oscillatory motion. In the presence of quenched random field orientations, this pinning favors a disordered state in which global order diminishes with increasing system size, consistent with Imry-Ma arguments, while the quenched disorder smoothens sharp first-order signatures, in line with the Aizenman-Wehr theorem, with activity modifying the scaling. A coarse-grained hydrodynamic theory supports these observations and is consistent with microscopic simulations.

The celebrated fluctuation dissipation theorem (FDT) does not apply to nonequilibrium systems. In this context, Cugliandolo and Kurchan [Phys. Rev. Lett. 71, 173 (1993)] introduced a generalized FDT which interprets the nonequilibrium evolution as a composition of time sectors corresponding to different effective temperatures. We use this framework to study domain growth in the $d=2$ long-range Ising model with nonconserved kinetics (Glauber spin flip) and conserved kinetics (Kawasaki spin exchange). We study the dynamical scaling and superuniversal scaling of various two-time quantities, e.g., autocorrelation function, response function, effective temperature, etc. In particular, we investigate how the interaction range and conservation laws affect these characteristic features of domain growth.

We consider random sequential adsorption (RSA) of aligned squares and derive the low-coverage expansion of the availability function $\alpha \left(q\right)$, the fraction of positions accessible to an additional square, up to fourth order in the coverage $q$. At low coverage, the reduction of available space can be understood in terms of geometric overlap between exclusion regions created by previously deposited squares. A single square blocks a finite area; pairs of squares may have overlapping exclusion zones, reducing the total blocked area; similarly, three and four squares can share a common overlap region, leading to higher-order corrections. These contributions can be systematically accounted for through an inclusion–exclusion expansion based on the geometry of overlapping exclusion regions, with alternating signs dictated by inclusion–exclusion. The expansion terminates exactly at fourth order, since no more than four deposited squares can simultaneously overlap the exclusion region of a trial insertion. The coefficients are obtained by explicit enumeration of all such geometrically admissible configurations and are further confirmed by numerical simulations on a discrete lattice, showing agreement within statistical uncertainty.

A more feasible and flexible approach is developed for emission of nonlinear Schrödinger solitons from an impurity-induced localized wave in the $\beta \text{−}\mathrm{FPU}$ model. The impurity structure used for inducing the localized wave is proposed to include an additional elasticity impurity $\alpha$, as well as a mass impurity $m$. It is argued that the driving threshold ${\gamma }_{\mathrm{th}}$ for soliton emission can be controlled by regulating $\alpha$ in combination with $m$, and it can reach its minimum ${\gamma }_{\mathrm{th}}^{(}\min )$ by optimizing the relationship between impurity parameters $(\alpha ,m)$. The theoretical results are validated by both numerical simulations and experiments. Further, numerical and experimental investigations show the flexibility and efficiency of the proposed structure in controlling the amplitude of emitted solitons, the rate of emission, and even, the purity of radiated solitonic pulses, either by regulating the impurity parameters or by varying the driving parameters in a broadened range.

Societies are quintessential open systems, shaped by internal dynamics as well as external influences. The question is how these external influences alter the collective behavior and network dynamics. To answer this, we investigate coevolutionary balance dynamics in a system of independent and open networks. Here, the system consists of two interacting networks with directed (asymmetric) coupling: an independent network evolving autonomously and an open (dependent) network whose dynamics are influenced by the former. Using a mean-field framework, we demonstrate a transition temperature: below the transition temperature, the independent network reaches a state of structural balance, while the open network is destabilized by persistent imbalance states and enters a sustained imbalance phase. This coupling also induces a measurable upward shift in the transition temperature. Direct numerical simulations robustly confirm these analytical predictions.