A percolation model inspired by crossword puzzle games is introduced. A game proceeds by solving words, which are segments of sites in a two-dimensional lattice. As a test case, the iid variant allows for independently occupying sites with letters, only the percolation criterion depends on the existence of solved words. For the game variant, inspired by real crossword puzzles, it becomes more likely to solve crossing words which share sites with the already solved words. In this way avalanches of solved words may occur. Both model variants exhibit a percolation transition as a function of the a priori site or word solving probability, respectively. The iid variant is in the universality class of standard two-dimensional percolation. The game variant exhibits a nonuniversal critical exponent $\nu$ of the correlation length. The actual value of $\nu$ depends on the function which controls how much solved words accelerate the solution of crossing words.

Near a tipping point, a critical transition occurs when small changes in input conditions lead to abrupt, often irreversible shifts in a dynamical system's state. This phenomenon is observed in various biological and physical systems, including the collapse of species in ecosystems. Several statistical indicators, known as early warning signals (EWSs), have been developed to anticipate such collapses, garnering significant attention for their broad applicability. This paper investigates the stochastic versions of a bistable algae-zooplankton food-chain model under demographic and environmental noise. Our findings show that an increase in the predatory fish population, which consumes zooplankton, triggers a collapse in zooplankton abundance through a saddle-node bifurcation. Basin stability measure reveals that the resilience of the underexploited steady state significantly diminishes as the system approaches the collapse point. We evaluate the efficacy of various generic EWSs in predicting sudden collapses under both types of noise through statistical analysis. The robustness of AR(1) and variance are assessed through a comprehensive sensitivity analysis of processing parameters. We also calculate conditional heteroskedasticity, which minimizes false positive signals in the time series. Our results indicate that the prediction accuracy of variance and conditional heteroskedasticity remains independent of the noise type. However, AR(1) and skewness perform better in the presence of environmental noise.

A modeling framework for the complete evaporation of particle-laden droplets, including touchdown events where the air-liquid interface approaches the substrate, is presented. The inclusion of particle jamming into the model, creating a transition from free advection to an immobile porous plug, is essential to making realistic predictions for the deposit's dimensions. By removing the need to track jammed particle fronts explicitly, as often considered, we are able to run simulations until solute has jammed everywhere in the drop. This allows for valid comparisons with experimental findings on the dried deposit's topography. Our model can also be easily applied to general contact line geometries, allowing us to explore the influence of contact line curvature on the local deposit profile.

Using extensive simulations, we study the dynamic critical phenomena of the ${\mathbb{Z}}_q$ model in an oscillating field. We find Berezinskii-Kosterlitz-Thouless transitions for $q=6$ in two dimensions and a first-order transition for $q=3$ in three dimensions, hence the equilibrium-nonequilibrium correspondence is conditionally validated. Surprisingly, the correspondence is apparently violated at $q=5$, 6, and 7 in three dimensions, for which the equilibrium and nonequilibrium scenarios feature a single transition and two transitions, respectively. In the nonequilibrium case, the discrete $q$-fold order is washed away by the first dynamic transition at the period $P_{\mathrm{z}}$ of the oscillating field, where an O(2) symmetry-breaking Nambu-Goldstone phase starts to emerge, persisting up to a higher period $P_{\mathrm{o}}$. The dynamic transition at $P_{\mathrm{o}}$ falls into the $\mathrm{O}\left(2\right)$ critical universality class. We relate the highly nontrivial dynamic behaviors to the two-length criticality arising from dangerously irrelevant fields and find that the dynamics decode the extremely subtle equilibrium criticality. Our findings significantly expand the current understanding of emergent phenomena and offer a promising methodology for elucidating critical phenomena that are notoriously challenging.

Large-mass condensates, which coexist with a power-law-decaying distribution in the one-dimensional Takayasu model of mass aggregation with input, were recently found in numerical simulations. Here, we establish the occurrence of condensates by analyzing exact recursions for finite systems and further show that they have a strong effect on the properties of the system. In the steady state of a large but finite system, there is a single condensate, whose random movement through the system leads to a reorganization of the mass profile on a macroscopic scale. A scaling analysis of the mean mass and standard deviation at different distances from the condensate leads to the surprising conclusion that the mass distribution on a macroscopic number of sites around the condensate follows a power-law decay with an exponent 5/3, while farther-away sites show the customary Takayasu exponent 4/3, with a crossover in between. Finally, the exit of condensates from a system with open boundaries has a strong effect on the temporal fluctuations of the total mass in the steady state. Their departure is followed by a buildup of mass and subsequent departures, leading to strong intermittency, established through a divergence of the flatness as the scaled time approaches zero.

We revisit the problem of describing creep in heterogeneous materials by an effective temperature by considering more realistic (and complex) non-mean-field elastic redistribution kernels. We show first, from theoretical considerations, that, if elastic stress redistribution and memory effects are neglected, the average creep failure time follows an Arrhenius expression with an effective temperature explicitly increasing with the quenched heterogeneity. Using a thermally activated progressive damage model of compressive failure, we show that this holds true when taking into account elastic interactions and memory effects, however, with an effective temperature $T_{\mathrm{eff}}$ depending as well on the nature of the (nondemocratic) elastic interaction kernel. We observe that the variability of creep lifetimes, for given external conditions of load and temperature, is roughly proportional to the mean lifetime and therefore depends as well on $T$, on quenched heterogeneity, and the elastic kernel. Finally, we discuss the implications of this effective temperature effect on the interpretation of macroscopic creep tests to estimate an activation volume at the microscale.

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By making the cluster components mechanically stable against their natural tendency to flip and coalesce, we can monitor the torque experienced by individual magnets through the macroscopic tilt angles they acquire when exposed to noncollinear external fields. A mathematical model that reproduces the empirical observations is introduced, enabling us to go beyond the experimental cases considered. The model confirms the existence of alternative orderings as the number of objects increases. Furthermore, a simpler and more mathematically transparent version of our model enables us to establish the conditions under which the cluster structure is stable and when it will collapse. We argue that our simple experimental setup combined with the accompanying models may be useful to describe general features seen in systems composed of mutually repulsive particles in the presence of modulating confining fields.

Nonreciprocal systems exhibit diverse dynamical phases whose character depends on the type and degree of nonreciprocity. In this study, we theoretically investigate dynamical structures in a mixture of nonreciprocally aligning polar active particles with repulsion, focusing on the performance on (and connection between) different levels of description. Linear stability analyses of the associated continuum model predict a profound influence of nonreciprocity, leading to phase separation, (anti-)flocking, and asymmetric clustering behavior. On the microscopic level, particle simulations confirm the emergence of these dynamical phases and allow for a more in-depth investigation of (microscopic) properties, including orientational correlations and susceptibilities. The drastic impact of orientational couplings alone on the density dynamics is demonstrated in particle simulations without repulsion, where nonreciprocal alignment leads to the asymmetric formation of single-species polarized clumps. Overall, our findings demonstrate that certain dynamical properties, like a chase-and-run behavior in the asymmetrical clustering phase, are overlooked in mean-field continuum theory, making microscopic simulations an indispensable tool for studying the effects of nonreciprocal alignment couplings.

In this work, we present an analytical study of a linear kinetic energy harvester driven by Gaussian noise through a nonequilibrium potential (NEP) approach. Taking advantage of the NEP, we conduct a statistical and thermodynamic analysis that reveals the stationary probability distribution function and its moments, offering insight into the harvester's stochastic behavior. Additionally, we make use of the energy landscape approach to visualize the implications of connecting a high load resistor, highlighting its impact on performance. Our findings also include generalized formulations of the Clausius inequality and Jarzynski equation, which we verify numerically.

We investigate the phenomenology of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of a system of coupled nonlinear Schrödinger equations (NLSEs) with a combination of linear and nonlinear double-well potentials (DWPs), including self- and cross-phase-modulation (SPM and XPM) nonlinear terms. The DWP structure is represented by a symmetric pair of delta functions. This setup can be realized in optics and for matter waves in Bose-Einstein condensates. It is commonly known that SSB states are completely stable in the single one-dimensional NLSE with a combination of DWP and attractive SPM nonlinearity. The objective of the present work is to elaborate on the SSB and SASB phenomenology in the two-component system. One factor that affects the phenomenology (actually, the stability of stationary states) in this context is the relative sign of the two components, the states with identical/opposite signs defined as ones with in-phase/out-of-phase components. We demonstrate that the SSB/SASB, with both components originating from spatially symmetric or antisymmetric modes, of the out-of-phase type, in the coupled NLSEs including the SPM and XPM terms with opposite signs, are similar to their counterparts in the single NLSE. On the other hand, the SSB/SASB of in-phase states in the coupled NLSEs, including the SPM and XPM terms with opposite signs, are quite different from the ones in the single NLSE. In particular, we find that the in-phase SSB/SASB states are unstable in a part of the intervals of their propagation constant if the system includes SPM and XPM terms with opposite signs. As another feature that is possible only in the two-component system, we address mixed-parity states, originally built of spatially symmetric and antisymmetric components, and find that such states, featuring SSB or SASB, are stable in a part of their interval of the propagation constant. We clarify that the spatially antisymmetric component is a dominant one in determining the asymmetry of the established state if it is coupled to the symmetric one, in the case of the repulsive SPM. On the other hand, the symmetric component dominates if it is coupled to the antisymmetric one in the case of the attractive SPM.

While linear stochastic differential equations are exactly solvable, the solutions for nonlinear equations are traditionally sought from the corresponding Fokker-Planck description. Based on the separation of deterministic and stochastic time scales in the dynamics, a method for direct calculation of the mean and variance of the distribution for nonlinear stochastic differential equations is proposed using the renormalization group (RG) technique. We have shown how nonlinearity and its interplay with noise brings corrections to the frequency of the dynamical system, as reflected in the RG flow equations for amplitude and phase. Two broad classes of nonlinear systems were explored, one with linear dissipation, nonlinear potential, and internal noise obeying fluctuation-dissipation relation, and the other with nonlinear dissipation and linear potential, allowing a limit cycle solution subjected to external noise. We analyzed the mean-square displacement as a measure of diffusive behavior and determined the stability threshold of the limit cycle against the external noise. Our theory is compared with full numerical simulations.

Diverse implicit structures of fluids have been discovered recently, providing opportunities to study the physics of fluids applying network analysis. Although considerable work has been devoted to identifying the informative network structures of fluids, we are limited to a primary stage of understanding what kinds of information these identified networks can convey about fluids. An essential question is how the mechanical properties of fluids are embodied in the topological properties of networks or vice versa. Here, we tackle this question by revealing a set of fluid-network relations that quantify the interactions between fundamental fluid-flow properties (e.g., kinetic energy and enstrophy decay laws) and defining network characteristics (e.g., spatial self-similarity, scale-invariance, and control scaling). We first analyze spatial self-similarity in its classic and generalized definitions, which reflect, respectively, whether vortical interactions or their spatial imbalance extents are self-similar in fluid flows. The deviation extents of networks from self-similar states exhibit power-law scaling behaviors with respect to fluid-flow properties, suggesting that the diversity among vortices is an indispensable basis of self-similar fluid flows. Then, the same paradigm is adopted to investigate scale-invariance using renormalization groups, which reveals that the breaking extents of scale-invariance in networks, similar to those of spatial self-similarity, follow power-law scaling with respect to fluid-flow properties. Finally, we define a control problem in networks to study the propagation of perturbations through vortical interactions over different ranges. The minimum cost of controlling vortical networks scales exponentially with range diameters (i.e., control distances), whose growth rates experience temporal decays. We show that this temporal decay speed is fully determined by fluid-flow properties in power-law scaling behaviors. In sum, all these discovered fluid-network relations sketch a picture in which we can study the implicit structures of fluids and quantify their interactions with fluid dynamics.

Two-dimensional lattice Boltzmann (LB) models for the Shakhov kinetic equation are developed. In contrast to several previous thermal LB models with variable Prandtl number, the present approach deals with the models on Cartesian lattices. This allows the standard collide-and-stream implementation. The discrete velocity local equilibrium is evaluated as a projection of the Shakhov local equilibrium on the orthonormal basis spanned by the Hermite polynomials. The local equilibrium distribution explicitly depends on the Prandtl number, and the Shakhov LB models can be established on well-known lattices having 25 and 37 velocities. Next, in order to reproduce the rarefied effects better, a semiautomatic approach for construction of high-order lattices which minimizes the difference between the half moments evaluated from the discrete velocity equilibrium and the Maxwell distribution is proposed. This problem is equivalent to solving a system of linear equations with constraint. Two high-order lattices having 37 velocities are deduced. Several test problems are considered: the thermal wave decay and the thermal Couette flow in the hydrodynamic limit for various Prandtl and Mach numbers, rarefied effects in the athermal Couette and Poiseuille flows, and rarefied effects in the Fourier flow. It is demonstrated that the new models show a good accuracy while considering rarefied flows in slip and transition regimes and some particular problems in the ballistic regime (the Knudsen paradox).

The duration of the quasistationary states (QSSs) emerging in the $d$-dimensional classical inertial $\alpha$-Heisenberg model, i.e., $N$ three-dimensional rotators whose interactions decay with distance $r_{ij}$ as $1/r_{ij}^{\alpha }$ ($\alpha \ge 0$), is studied through first-principle molecular dynamics. These QSSs appear for the very-long-range interaction regime ($0\le \alpha /d\le 1$), for an average energy per rotator $U<U_c$ ($U_c=5/6$), and they do not exist for $U>U_c$. They are characterized by a kinetic temperature $T_{\text{QSS}}$, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature $T_{\text{BG}}>T_{\text{QSS}}$. We investigate here the behavior of their duration $t_{\text{QSS}}$ when $U$ approaches $U_c$ from below, for large values of $N$. The QSS gradually disappears as $U\to U_c$, while its duration undergoes a critical phenomenon, namely $t_{\text{QSS}}\propto {(U_c-U)}^{-\xi }$. Universality is found for the critical exponent $\xi =1\text{.}67\pm 0\text{.}02$ throughout the very-long-range interaction regime.

The assay for transposase-accessible chromatin using sequencing (ATAC-seq) can be used to identify open chromatin regions, providing complementary information to RNA-seq which measures gene expression by sequencing. Single-cell multiome methods offer the possibility of measuring both modalities simultaneously in cells, raising the question of how to analyze them jointly, and also the extent to which the information they provide is better than unregistered data, where single-cell ATAC-seq and single-cell RNA-seq are performed on the same sample, but on different cells. We propose and motivate a biophysical model for chromatin dynamics and subsequent transcription that can be used to parametrize multiome data, and use it to assess the benefits of multiome data over unregistered single-cell RNA-seq and single-cell ATAC-seq. We also show that our model provides a biophysically grounded approach to the integration of chromatin accessibility data with other modalitie, and apply the model to single-cell ATAC-seq data.

We investigate the competing effects of the simultaneous presence of chirality and generalized tumbles in the dynamics of an active Brownian particle. Chiral active particles perform circular motions that give rise to slow transport at late times. By interrupting these circular trajectories at the right time by performing a tumble at the correct angle, we show that particles can enhance their diffusion. After deriving exact expressions for the orientational propagator and correlations, we use this to calculate the first two moments of displacement. For the effective diffusion coefficient, we study various optimal tumbling strategies. We show that under optimization of the tumbling rate, the case of symmetrically distributed tumbles always gives rise to enhanced diffusion, with an effective diffusion coefficient taking a universal value. Next, two cases are considered in detail, namely, directional reversal and tumbles at an arbitrary but fixed angle. We discuss how asymmetric tumbles can enhance diffusion beyond that of symmetric tumbles. Finally, we discuss a situation where the reorientations are realized dynamically in finite time.

Statistical mechanical theory based on the concept of mean-force potentials is used to describe anchoring transitions in a liquid-crystal system near a solid surface. This approach took into account not only the two-particle correlations between the nearest and next-nearest neighbors, but also the surface-attractive interactions. Calculations were performed for a cubic close packing with the Gay-Berne intermolecular potential interaction and with a (9-3)-like orientation-dependent molecule-wall interaction. Our calculations have shown that the number of surface layers to be taken into account depends more on the nature of interparticle correlations in the system than on the direct interaction of the wall with the nematic. It has been shown that there are several scenarios for anchoring transitions in such systems in a certain range of temperatures and volumes.