We systematically investigate the existence, stability, and dynamics of optical solitons in the framework of the one-dimensional nonlinear Schrödinger equation with the Riesz-fractional diffraction operator, cubic self-focusing, and linear loss, balanced by a linear parametric drive. The model, which can be realized in a laser cavity, produces standing and moving solitons, the latter ones existing below a critical velocity. One of the soliton species is stable in a wide range of parameters, while others are unstable. The fractional diffraction significantly alters the existence conditions and stability thresholds of the solitons. Collisions between moving solitons are considered too. The results essentially expand the variety of nonlinear modes in media with fractional diffraction.

We study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, we explore how the survival probability depends on the position and size of the hole, as well as on the billiard shape parameter. We find that the survival probability exhibits a two-stage decay pattern: an initial exponential regime followed by a long-time power-law tail, a signature of the stickiness effect. Our results show that the short-time exponential decay rate follows a power-law dependence on the hole size, with different scaling exponents for holes placed in chaotic regions versus mixed phase-space regions. For holes located in mixed phase-space regions, the decay exponent of the long-time power-law tail remains approximately constant, while the amplitude follows a power-law scaling with hole size. We also examine the dependence of short-time exponential decay rate on the billiard shape parameter and observe scaling behavior for small values of this parameter, which breaks down as the parameter increases.

From the perspective of physical properties, the cell membrane is an exotic two-dimensional material that has a dual nature: it exhibits characteristics of fluids, i.e., lipid molecules show lateral diffusion, while also demonstrating properties of solids, evidenced by a nonzero shear modulus. We construct a model for such a semisolid membrane. Our model is a fluctuating randomly triangulated mesh with two different kinds of nodes. The solid nodes never change their neighbors, while the fluid nodes do. As the area fraction occupied by the solid nodes ($\mathrm{\Phi }$) is increased the motion of fluid nodes transitions from diffusion to localization via subdiffusion. Next, the solid nodes are pinned to mimic the pinning of the plasma membrane to the cytoskeleton. For the pinned membrane, there exists a range of $\mathrm{\Phi }$ over which the model has both a nonzero shear modulus and a nonzero lateral diffusivity. The bending modulus, measured through the spectrum of height fluctuations, remains unchanged.

Magnetars are young, isolated neutron stars that possess an exceptionally strong magnetic field, with surface dipolar strengths on the order of ${10}^{15}\mathrm{G}$. One of the plausible scenarios for generating such a strong field is an exponential amplification by a turbulent convective dynamo during the protoneutron star phase. However, the short expected duration of the convection ($\sim 10\mathrm{s}$) imposes a stringent constraint on the dynamo growth rate. We perform an extensive set of 82 three-dimensional convective dynamo simulations in the anelastic approximation and investigate the kinematic phase to quantify the dynamo growth rate $\gamma$. We find that $\gamma$ increases with both the magnetic Prandtl number $\text{Pm}$ and the Rayleigh number $\text{Ra}$, with the most unstable mode becoming highly nonaxisymmetric and multipolar. We further observe a gradual transition from large-scale to small-scale dynamo as the magnetic Reynolds number $\text{Rm}$ increases, resulting in a magnetic field that is predominantly concentrated at small scales. The trend remains unchanged when the outer magnetic boundary condition is varied. Since resolving the increasingly small scales becomes numerically impractical, we employ the theoretical small-scale Kazantsev dynamo model to explore the large $\text{Pm}$ regime characteristic of protoneutron stars. The model qualitatively captures the growth rate behavior observed in simulations and, upon extrapolation to the large $\text{Pm}$ limit, indicates that $\gamma$ is only weakly dependent on the resistivity in a PNS. Under conditions relevant to the PNS, this model predicts a magnetic energy growth rate of the order of $\sim 1{\mathrm{ms}}^{-1}$.

The dissipation-coherence bound is a conjectured trade-off between entropy production and the quality of stochastic oscillations. We show that this bound can be derived by combining the higher-order “thermodynamic uncertainty relation” with a simple condition on phase-current fluctuations. In one-dimensional cyclic systems, our proposed condition is shown to be equivalent to the dissipation-coherence bound itself. Our approach yields an elementary proof in the weak-noise Gaussian regime and extends naturally to some non-Gaussian systems, as we illustrate with a run-and-tumble particle. Finally, we contrast current-based and spectral formulations of the dissipation-coherence bound.

We experimentally investigate the dynamics of synthetic active particles composed of gravitationally bouncing, superwalking droplets confined within an annular fluid bath. Driven by a topologically pumping dual-frequency waveform, the droplets exhibit alternating active (walking) and dormant (bouncing) phases, producing intermittent azimuthal motion. Tracking individual droplets reveals pseudolaminar chaotic dynamics in the time series of the particle's angular position, characterized by laminar plateaus that are interrupted by short, irregular bursts of activity. Increasing the driving amplitude induces a qualitative change in the active particle's intermittent dynamics, arising from a symmetry-breaking transition in its Faraday-wave field environment: continuous $\mathrm{SO}\left(2\right)$-symmetric “channeling” waves give way to discrete “trapping” patterns. These findings demonstrate how environmental symmetry and spatiotemporal structure modulate motility and intermittency in synthetic active matter.

Statistical mechanics reveals that the properties of a macroscopic physical system emerge as an average over an ensemble of statistically independent microscopic subsystems, each occupying a specific microstate. In the study of quantum systems, these microstates can be chosen to correspond to the pure state wave functions of individual quantum systems. However, the physical principles that govern the distribution of a pure state wave function ensemble, even under conditions of thermal equilibrium, are not well established. For instance, the canonical Boltzmann distribution cannot be applied to wave functions because they lack a definite energy. In this paper we present a maximum entropy principle for the quantum wave function ensemble at thermal equilibrium, the so-called Scrooge ensemble. We highlight that a constraint on the energy expectation value, or even the shape of the associated eigenstate distribution, fails to yield a valid equilibrium state. We find that in addition to these constraints, one must also constrain the measurement entropy to be equal to the Rényi divergence of the ensemble with respect to the Gibbs state, indicating that the Rényi divergence may have uninvestigated physical importance to thermal equilibrium in quantum systems.

A large family of multispin interacting one-dimensional quantum spin models with $Z\left(N\right)$ symmetry and a free-particle eigenspectra are known in the literature. They are free-fermionic ($N=2$) and free-parafermionic ($N\ge 2$) quantum chains. The essential ingredient that implies the free-particle spectra is the fact that these Hamiltonians are expressed in terms of generators of a $Z\left(N\right)$ exchange algebra. In all these known quantum chains, the number of spins in all the multispin interactions (range of interactions) is the same and, therefore, the models have a homogeneous interacting range. In this paper, we extend the $Z\left(N\right)$ exchange algebra by introducing different models with a free-particle spectra, where the interaction ranges of the multispin interactions are no longer uniform and depend on the lattice sites (nonhomogeneous interacting range). We obtain the general conditions that the site-dependent ranges of the multispin interactions have to satisfy to ensure a free-particle spectra. Several simple examples are introduced. We study in detail the critical properties in the case where the range of interactions of the even (odd) sites is constant. The dynamical critical exponent is evaluated in several cases.

We study a conservative stochastic lattice gas (Kawasaki dynamics) coupled in the bulk to a heat bath, which leads to standard phase separation at low uniform temperatures. Instead, a macroscopic temperature gradient drives the system into a nonequilibrium steady state. In this state, the usual long-range order is replaced by robust convection patterns, featuring regularly spaced stripe structures. We show that these nonequilibrium states differ markedly from equilibrium configurations with the same local temperature profiles. Finally, we develop a macroscopic description that captures these behaviors and provides a unified framework for understanding the observed patterns.

In the context of complex networks, designing a null model that preserves certain properties of the original network is a fundamental problem. While for binary bipartite networks, the problem has been solved by the curveball algorithm, which preserves the degree of each node exactly, for weighted bipartite networks, finding a null model that strictly preserves some features of the original network is still an open challenge. In this work, we present a microcanonical algorithm that preserves exactly the degree and the strength of each node in a weighted bipartite network. The algorithm is based on an edge-swap procedure that combines three different moves: weight shuffling, simple edge swap, and bridge edge swap. The algorithm has been built to guarantee that the underlying transition matrix of the Monte Carlo Markov chain (MCMC) is symmetric, which is a crucial property to obtain an unbiased sample of random graphs. We validate our algorithm empirically, showing through a χ-square test that for small graphs, the algorithm produces an unbiased sample of graphs. Finally, we also provide a heuristic method to estimate the mixing time of the MCMC.

We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the relationship between the Pearson assortativity coefficient $r$ and the percolation threshold $p_c$ is not always monotonic. More specifically, in certain regions of the parameter space of our model, moderately disassortative networks can be more fragile than either strongly disassortative or uncorrelated networks. We observe this nonmonotonic behavior for trimodal networks as well as for networks with Poisson and power-law degree distributions. We then extend our analysis to hypergraphs with correlations between node hyperdegree and hyperedge cardinality. For this case, we find that positively correlated hypergraphs tend to be more fragile than negatively correlated ones. Additionally, as in the dyadic case, the relationship between $r$ and $p_c$ is nonmonotonic, and the most fragile configuration does not correspond to the most assortative hypergraph.

The equilibrium partitioning of linear polymer chains into flexible polymer networks is governed by intricate entropic constraints arising from the configurational degrees of freedom of both chains and networks; however, a quantitative understanding remains elusive. Using model hydrogels with precisely defined network structures, we experimentally demonstrate a universal law governing the partitioning of linear polymers into flexible polymer networks. We establish a label-free contactless method to measure the partition ratio, based on the increase in the osmotic pressure induced by the partitioning of the external polymer chains. Moreover, we reveal a universal law in which the partition ratio is determined solely by $R_g/l_{\mathrm{cycle}}$, where $R_g$ is the gyration radius of the polymer chain and $l_{\mathrm{cycle}}\equiv {\xi }^{-1/3}$ is the characteristic mesh size of the network, defined by the cycle rank $\xi$, i.e., the number density of elastically effective cycles.

Simple shear flow can induce flow-aligned chain formation of particles suspended in viscoelastic fluids. Although this phenomenon has been reported for decades, direct in situ measurements of the alignment dynamics and particle trajectories during chain formation remain limited. Here, we develop an in situ observation platform based on a parallel-plate geometry with a fixed top plate and a rotating bottom plate, separated by a gap comparable to the particle diameter, enabling simultaneous observation of particle alignment under radially varying shear rates. The narrow gap strongly confines particle motion, thereby enhancing hydrodynamic interactions and collision events between particles. Using a viscoelastic fluid embedding zircon particles as the sample, we find that alignment occurs once the local particle Weissenberg number exceeds unity $({\mathrm{Wi}}_{\mathrm{p}}\ge 1)$, defined using an effective shear rate based on the wall velocity and the available gap width. Particle tracking further reveals an intermittent back-and-forth motion along the flow direction, observed in a reference frame corotating at half the angular velocity of the bottom plate, where the fluid velocity vanishes at the channel midplane. This motion arises from switching between two stable particle heights and is hereafter referred to as “shuttling,” which we define explicitly to avoid ambiguity. Using the image brightness in a dyed fluid as a proxy for out-of-plane position, we demonstrate that this shuttling motion originates from vertical displacement of the particles. We further construct a minimal agent-based model in which the particle height follows a Ginzburg-Landau-type double-well potential, and show that collision-driven accumulation emerges in simulations. In the strongly confined geometry, alignment occurs via an effective attraction induced by collisions, which is qualitatively reminiscent of clustering phenomena in active matter.

In liquid mixtures, changes in structural decay have been observed in particle simulations and experiments, and are an important element of their analysis. The work presents a comprehensive description of the long-range behavior of structural pair correlation functions of binary hard-sphere (BHS) mixtures. It is revealed that in BHS mixtures there exists a well-defined framework throughout the entire phase diagram of the particle sizes and fluid densities. The framework is based on special points representing the asymptotic oscillatory decay of the correlation functions as a superposition of three different wavelengths, whose arrangement shows surprising regularity and is described by power functions. The disclosed framework sets a limit on the particle size ratio for the presence of these special points and related structural crossover effects in the phase diagram. Similar frameworks are expected to occur in different binary mixtures. They can help resolve structural correlation functions at intermediate particle separations in different regions of the phase diagrams of asymmetric mixtures.

While divergences in correlation length and time, hallmarks of criticality, have been established for second-order transitions to synchronization in the Kuramoto model, a comprehensive understanding of analogous scalings for abrupt transitions to desynchronization remains elusive. Through simulations and analytical calculations, we investigate this discontinuous transition for the Kuramoto model with higher-order interactions. We report the emergence of critical slowing down, marked by a diverging relaxation time near the threshold. We verify a finite-time, finite-size scaling by applying the homogeneity assumption using system size, coupling strength, and time as relevant parameters. This work extends the theoretical foundations of critical scaling to include abrupt transitions in coupled oscillator systems.

A recent study [P. Rajamanickam, Q. J. Mech. Appl. Math. 78, hbaf007 (2025)] of non-Boussinesq fluids in narrow channels identified a novel shear-induced horizontal buoyancy force that emerges upon depth-averaging the Navier–Stokes equations. This Letter demonstrates that this force is formally equivalent to the divergence of a Korteweg stress tensor. Unlike classical Korteweg stresses, which are typically attributed to molecular-scale cohesive potentials or implemented through assumed constitutive relations, we show that this emergent stress arises purely from self-coupled transport where the internal Ostroumov flow is kinematically coupled to the local density gradient. We derive explicit expressions for the effective stress coefficients, revealing a fundamental dependence on the Prandtl number and Grashof number. This correspondence is contrasted with classical Taylor dispersion, where the absence of self-coupling yields only a uniaxial stress. Although derived within a narrow-channel framework, our results establish a general hydrodynamic template for how quadratic gradient stresses can emerge from subscale, self-coupled flows, such as Marangoni or active-matter flows, offering a continuous transport-driven alternative to molecular mechanisms.

Many active particles are embedded in environments that exhibit viscoelastic properties. An important class of such media lacks a single characteristic relaxation timescale when subjected to a time-dependent stress. Rather, the stress response spans a broad continuum of timescales, a behavior naturally described by a scale-free, fractal-like power-law relaxation modulus. Using a generalization of the fractional Langevin equation, we investigate an active Brownian particle embedded in a power-law viscoelastic environment with translational and rotational dynamics governed by independent fractional orders. We solve the model analytically, develop a numerical scheme to validate the theoretical predictions, and provide tools that can be used in further studies. A rich variety of diffusion regimes emerges, which modify the intermediate-time behavior of the mean squared displacement. Notably, we find that the competition between translational and rotational contributions favors a superdiffusive persistence over the standard ballistic motion, and overstretches its characteristic timescale, fundamentally altering the standard relation between persistence and propulsion in active matter.

A crucial question in transport theory is determining the critical parameter values at which abrupt changes in phase space occur. In nontwist Hamiltonian systems, this transition is associated with the breakup of the shearless curve. Ideally, once this curve is destroyed, chaotic trajectories should cross the barrier freely. A direct way to characterize this process is to compute the number of crossing trajectories to determine the transmission through the phase space. However, in this work, we show that nonzero transmission is not an immediate consequence of the disappearance of the shearless curve. By computing the parameter space for the existence of the shearless curve and evaluating the transmissivity, we identify regions where transport is zero even in the absence of a complete barrier. Consequently, relying solely on zero transmission leads to inaccurate values for the barrier breakup. By analyzing the underlying invariant manifolds, we show how turnstiles and torus free barriers strongly influence the gap between the breakup of the shearless curve and the onset of positive transport. Furthermore, we investigate how these regions depend on the island periodicity and analyze their evolution as a function of the iteration time. Our results reveal distinct power-law exponents for the decay of the size of the region with no barrier and no transport in the parameter space. The different behaviors for odd and even periods reflect differences in the efficiency of turnstile mechanisms and torus free barriers.