The pseudopotential model in lattice Boltzmann method is widely used to simulate two-phase flows. Thermodynamic consistency is an important issue in the pseudopotential model. To achieve thermodynamic consistency, various force schemes have been proposed for the pseudopotential model. However, their performance under transient and moving conditions remains insufficiently validated. We evaluate existing force schemes and find that most of them suffer from interfacial velocity slip. A Chapman-Enskog analysis reveals that these schemes introduce error terms in the macroscopic equations, leading to the interfacial velocity slip. While other schemes avoid this slip, they fail to achieve thermodynamic consistency. To address this issue, we propose a novel pseudopotential model achieving thermodynamic consistency while preventing interfacial velocity slip. Our model introduces a new pseudopotential force by adding a term $2\gamma {\nabla }^2\psi \mathbf{\nabla }\psi +O\left({\nabla }^5\right)$ to the original force. Here, $\psi$ represents the pseudopotential and the coefficient $\gamma$ is used to tune the coexistence densities. The applicability of our model under moving conditions is validated through simulations of two-phase Couette flow and two-phase Poiseuille flow. Numerical results confirm that our model achieves second-order accuracy. The transient results of our model are compared with those of volume of fluid method, validating the applicability of our model under transient conditions. Finally, droplet splashing and liquid film evaporation under shear flow are also simulated to demonstrate our model's capability for simulating two-dimensional flow and interphase mass transfer.

A physics-based analytical model describing the phase transition from crystalline to conformationally disordered (condis) crystalline phase is developed. In the model, the free energy is written as a function of temperature and the lattice parameter (mean distance between neighboring chains). It consists of two contributions: elastic and conformational. The elastic contribution describes the interaction between neighboring chains, while the conformational part takes into account the conformation of one chain inside the potential tube, formed by the neighboring chains. To verify this approach, polyethylene—the simplest polymer possessing the condis phase—was chosen as a modeling object. Previous experiments and molecular dynamics simulations show that the typical conformation of a polymer chain in a crystalline phase consists mainly of trans dihedrals and a small fraction of gauche dihedrals, which can be considered as defects of the crystalline lattice. These defects displace the chain inside the tube thus increasing the potential energy. The energy required to form such a defect decreases rapidly with increasing distance between neighboring chains. This leads to a first-order phase transition at a certain temperature to the condis phase, in which distance between neighboring chains is large and a fraction of gauche dihedrals is high. This physical picture of the phase transition is described by the proposed analytical model, the parameters of which were calibrated against the results of molecular dynamics simulations for atmospheric pressure. The model predictions for the pressure of 500 and 1000 atm are in perfect agreement with the results of molecular dynamics simulations.

Controlled self-assembly using external rotating electric or magnetic fields is an emerging area in soft matter, with applications in creating functional materials, three-dimensional bioprinting, and tissue engineering. Experimental studies in this field are typically conducted on substrates with pinning zones, which affect diffusion and, consequently, self-assembly processes, though the detailed impact of pinning on diffusion has not been systematically studied before. In the present work, we systematically calculate diffusion in a system relevant to a monolayer of colloidal particles with tunable interactions induced by external electric or magnetic fields, placed on a substrate with pinning zones. Using molecular dynamics simulations, we explore the diffusion of particles over a wide range of parameters for attractive and repulsive interaction regimes induced by different field configurations. We derive simple fits that accurately capture the effect of pinning on diffusion across a broad portion of the phase diagram. We believe this fit will be useful for analyzing and designing experiments with two-dimensional soft matter systems with tunable interactions and for various potential applications.

Natural flocks need to cope with various forms of heterogeneities, for instance, their composition, motility, interaction, or environmental factors. Here, we study the effects of such heterogeneities on the flocking dynamics of the reciprocal two-species Vicsek model [Phys. Rev. E 107, 024607 (2023)], which comprises two groups of self-propelled agents with antialigning interspecies interactions and exhibits either parallel or antiparallel flocking states. The parallel and antiparallel flocking states vanish upon reducing the size of one group, and the system transitions to a single-species flock of the majority species. At sufficiently low noise (or high density), the minority species can exhibit collective behavior, antialigning with the liquid state of the majority species. Unequal self-propulsion speeds of the two species strongly encourage antiparallel flocking over parallel flocking. However, when activity landscapes with region-dependent motilities are introduced, parallel flocking is retained if the faster region is given more space, highlighting the role of environmental constraints. Under noise heterogeneity, the colder species (subjected to lower noise) attain higher band velocity compared to the hotter one, temporarily disrupting any parallel flocking, which is subsequently restored. These findings collectively reveal how different forms of heterogeneity, both intrinsic and environmental, can qualitatively reshape flocking behavior in this class of reciprocal two-species models.

Investigation of the emergence of entanglement in a classical two-particle Brownian system through nonequilibrium driving is carried out. The Brownian particles are in contact with independent thermal bath, where one particle is driven by a time-dependent potential and the other remains in a static harmonic trap. The particles are harmonically coupled, enabling thermal correlation and information exchange. Using stochastic simulations, we compute an entanglement witness based on osmotic velocities and position correlations. We show that stronger driving enhances entanglement generation, with protocol-specific features. Thermodynamic quantities such as entropy production and the Jarzynski equality are also examined, revealing a close link between nonequilibrium control and classical entanglement in mesoscopic systems.

Unknown node attributes in complex networks may introduce community structures that are important to distinguish from those driven by known attributes. We propose a block-corrected modularity that discounts given block structures present in the network to reveal communities masked by them. We show analytically how the proposed modularity finds the community structure driven by an unknown attribute in a simple network model. Further, we observe that the block-corrected modularity finds the underlying community structure on a number of simple synthetic network models while methods using different null models fail. We develop an efficient spectral method as well as two Louvain-inspired fine-tuning algorithms to maximize the proposed modularity and demonstrate their performance on several synthetic network models. Finally, we assess our methodology on various real-world citation networks built using the OpenAlex data by correcting for the temporal citation patterns.

We investigate the full temporal evolution of epidemic outbreaks in complex networks, focusing on the susceptible-infected (SI) model of disease transmission. Combining theoretical analysis with large-scale numerical simulations, we uncover two universal patterns of epidemic growth, determined by the structure of the underlying network. In small-world networks, the prevalence follows a Gompertz-like curve, while in fractal networks it evolves according to Avrami-type dynamics, typical of spatially constrained systems. These regimes define distinct universality classes that remain robust across arbitrary transmission rates. Notably, our approach provides explicit analytical formulas for the global epidemic prevalence and class-specific scaling relations capturing its dependence on the transmission rate. We show that the commonly assumed early exponential growth occurs only in small-world networks, where it corresponds to the short-time approximation of the Gompertz function. In contrast, this exponential phase is entirely absent in fractal networks, where spreading is markedly slower and governed by different mechanisms. Our approach clarifies the structural origins of these contrasting behaviors and offers a unified framework for understanding epidemic dynamics across diverse network topologies.

Cohesive granular materials, such as wet sand, retain their shape before yielding under stress, exhibiting a solid-like behavior. As the loading increases, the material typically flows. However, cohesive materials can also develop cracks, similar to those observed in brittle materials. This study investigates the formation of cracks during the indentation of a granular pile. A solid cylindrical indenter is pushed quasistatically into the wet granular medium, causing radial cracks to appear. These cracks resemble mode I cracks observed in brittle elastic solid materials. We characterize the crack pattern through direct observation and three-dimensional X-ray microtomography. Notably, we establish a correlation between the dilation of the material during shearing and the appearance of cracks.

The polymer network liquid crystal (PNLC), in which a polymer network is formed within a nematic liquid crystal, can be regarded as a porous medium. In this study, we discover electroconvection in the PNLC and examine its nonlinear, nonequilibrium physical properties. As the monomer weight fraction increases, distortions in the convective pattern emerge and the temporal fluctuations slow. The polymer network hinders the reorientation of the liquid crystal molecules, thereby suppressing the motion of the convection pattern. Furthermore, measurements of the electric Nusselt number, which characterizes the electrical transport phenomena, reveal that, as the monomer weight fraction increased, the threshold voltage for the onset of convection increased and the efficiency of charge transport decreased. This study quantitatively evaluated the nonlinear, nonequilibrium phenomena of the PNLC as flow phenomena in porous media.

Pattern formation in active biological matter typically arises from the feedback between chemical concentration fields and mechanical stresses. The actomyosin cortex of cells is an archetypal example of an active thin film that displays such patterns. Here, we show how pulsatory patterns emerge in a minimal model of the actomyosin cortex with a single stress-regulating chemical species that exchanges material with the cytoplasm via a linear turnover reaction. Deriving a low-dimensional amplitude-phase model, valid for a one-dimensional periodic domain and a spherical surface, we show that nonlinear waves arise from a secondary parity-breaking bifurcation that originates from the nonreciprocal interaction between spatial modes of the concentration field. Numerical analysis confirms these analytical predictions and also reveals analogous pulsatory patterns on impermeable domains. Our study provides a generic route to the emergence of nonreciprocity-driven pulsatory patterns that can be controlled by both the strength of activity and the turnover rate.

We derive an analytical expression for the propagator and the transition path time distribution of a two-dimensional active Brownian particle crossing a parabolic barrier with absorbing boundary conditions at both sides. By taking those of a passive Brownian particle as basis states and dealing with the activity as a perturbation, our solution is expressed in terms of the perturbed eigenfunctions and eigenvalues of the associated Fokker-Planck equation once the latter is reduced by taking into account only the coordinate along the direction of the barrier and the self-propulsion angle. We show that transition path times are typically shortened by the self-propulsion of the particle. Our solution also allows us to obtain the survival probability and the first-passage times distribution, which display a strong dependence on the particle's activity, while the rotational diffusivity influences them to a minor extent.

Without imposing additional restrictions on the magnitude of induced scattering of waves by ions, the numerical solution of the nonlinear integral equation for the ion-acoustic waves distribution function over the angles of the wave vector is obtained. This solution complements the analytical and numerical solutions obtained earlier in the limits of weak [Zh. Eksp. Teor. Fiz. 82, 1886 (1982); Sov. Phys.-Lebedev Inst. Rep. 10, 55 (1987)] and strong [Sov. J. Plasma Phys. 10, 17 (1984)] influence of induced scattering on the distribution of ion-acoustic waves. It is shown how, as the electric field strength or electron pressure gradient increases, the position of the maximum of the ion-acoustic wave distribution shifts away from the direction of the turbulence symmetry axis. The obtained solution allowed us to quantitatively describe the electron fluxes of charge and energy in a plasma with ion-acoustic turbulence in a wide range of electron drift velocities. The expression for the current density can be used to calculate the magnitude of the current in the plume of the hollow cathode.

An extension of Maxwell's original prescription for an ideal gas is adopted to derive a broad class of kappa-type velocity distributions, encompassing both fat and short-tailed forms. Within this general framework, a physically consistent fat-tailed kappa distribution is identified that accurately fits recent suprathermal data. In particular, a kinetic physical temperature $T$ emerges naturally from the model, eliminating the need to invoke an effective temperature $T_{\kappa \ell }$, as is commonly done in the literature. Finally, it is argued that only a particular value of $\ell$ ensures a satisfactory fit to the data when the physical kinetic temperature is employed.

Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can, in principle, encode arbitrary optimization problems, practical implementations are often hindered by soft constraints that either slow down mixing when too strong or fail to enforce feasibility when too weak. We introduce a two-dimensional extension of the powerful parallel tempering algorithm (PT) that addresses this challenge by adding a second dimension of replicas interpolating the penalty strengths. This scheme ensures constraint satisfaction in the final replicas, analogous to low-energy states at low temperature. The resulting two-dimensional parallel tempering algorithm (2D-PT) improves mixing in heavily constrained replicas and eliminates the need to explicitly tune the penalty strength. In a representative example of graph sparsification with copy constraints, 2D-PT achieves near-ideal mixing, with Kullback-Leibler divergence decaying as $O(1/t)$. When applied to sparsified Wishart instances, 2D-PT yields orders-of-magnitude speedup over conventional PT with the same number of replicas. The method applies broadly to constrained Ising problems and can be deployed on existing Ising machines.

Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture of $M$ molecular species, can be made to coexist in equilibrium. While such “super-Gibbs” phase coexistence is possible in the grand-canonical ensemble by tuning interactions among the $M$ species, there is no straightforward equivalence in the canonical ensemble: Only a subset of the grand-canonical phases will generically be realized. Here, we show that, upon further design of interface tensions, it is possible to stabilize a super-Gibbs number of phases also in the experimentally relevant canonical ensemble, thus effectively restoring equivalence to the grand-canonical one. Using a graph-theoretical approach, we determine a sufficient set of inequalities for the interfacial tensions for which all grand-canonical phases are realized. We illustrate the design method for a two-component mixture with four coexisting phases and point out the route for generalizing this to a higher number of components.

We introduce a minimum Ising model with two different types of ferromagnetically interacting spin variables and the addition of chiral interactions according to the suggestions of the Dzyaloshinskii-Moryia mechanism to account for the onset of helical structures in magnetic systems. The investigation of the phase diagram on a Cayley tree is reduced to the analysis of the attractors of a discrete nonlinear map. This elementary system presents a complex phase behavior, which is reminiscent of the spatially modulated structures in the well-known axial next-nearest-neighbor Ising model of magnetism. We characterize the presence of some ordered as well as a certain number of modulated structures. Also, we sketch a layer-by-layer mean-field calculation for the phase diagram of a similar monoaxial Ising system on a cubic lattice.

We study an open quantum system of two qubits that are coupled by swapping interaction. Using the coupling strength between the qubits as a timescale, the Liouvillian of the system has exceptional points that depend on the disparity between the decay rates of the qubits. We find that the configuration of the initial states plays an important role in deciding the character of the entanglement dynamics at the initial stage of evolution. Depending on whether or not the initial excitations of the qubits can be swapped by the interaction that couples them, a change in the total decay rate can be either consistently unfavorable to entanglement generation, or shift the dynamics from hindering to enhancing entanglement generation, or vice versa, as the system traverses the exceptional points. The shift could also occur in a wide range of mixed states. We clarify the origin of the behavior in this work.

Random exchanges of energy arise naturally in stochastic systems. As a consequence, apparent violations of the second law of thermodynamics can occur at the trajectory level, even though the law holds true on average. Here, we investigate the occurrence of these apparent violations—termed free lunches—in a quantum-classical system comprised of levitated nanoparticles exchanging energy via the Coulomb interaction. We consider different initial states for the quantum system, and how these exert work and fluctuations upon the classical particle affecting the probability of free lunches. With that, we initiate the study of hybrid quantum-classical systems through the lens of stochastic thermodynamics.

We investigate the overdamped directed transport of elastically coupled Brownian particles in asymmetric periodic potentials, driven by nonequilibrium fluctuations modeled as Poisson shot noise (PSN). Our findings reveal distinct modulations in the coupling effect, characterized by alternating regimes of transport enhancement, suppression, and even coupling-induced current reversal. This complex phenomenology arises from nonequilibrium fluctuations, whereas thermal equilibrium fluctuations are unable to induce net transport in the absence of external deterministic drives. Based on the discrete nature of PSN, we propose two underlying mechanisms responsible for these observed modulations: dual-mode motion and passive push-pull dynamics between coupled particles. By analyzing the velocity difference between coupled and single particles, we demonstrate that these modulations in coupling-induced transport are determined by the interplay between nonequilibrium fluctuations and the potential barrier height. Specifically, for low mean strengths of the nonequilibrium fluctuations, a characteristic three-stage pattern of coupling effects (suppression-enhancement-suppression) is observed with increasing potential barrier height. Furthermore, the interplay between the rate and average amplitude of the discrete pulses defining these nonequilibrium fluctuations also profoundly shapes the coupling effect, yielding diverse transport characteristics. Moreover, the potential's asymmetry coefficient, the noise skewness, and the interparticle coupling strength are shown to significantly modulate the coupling-induced transport. Our study establishes a theoretical framework for understanding the intricate collective transport dynamics of coupled particles driven by nonequilibrium fluctuations. These findings provide critical insights for the design and control of directed motion in artificial micro- and nanoscale systems operating under discrete energy pulses in nonequilibrium environments.