A rigorous formalism is presented for the time-averaged acoustic radiation force on a spherical particle near an infinite planar boundary subjected to a plane wave. The background medium is assumed to be a weakly thermoviscous fluid, with the viscous and thermal boundary layers much smaller than either the acoustic wavelength or the particle radius. The total acoustic field, composed of the incident, scattered, and reflected fields, is derived using the finite series expansion theory and the image method. Based on the approximate solution to the governing equations of acoustic pressure, velocity, and temperature, we analyze the vorticity mode, the acoustic mode, and the thermal mode in the surrounding fluid, further yielding the boundary conditions at the surface of rigid or nonrigid particles from continuity of velocity. Subsequently, the radiation force function in terms of scattering coefficients is obtained neglecting the contributions of the acoustic streaming effect, followed by a variety of numerical examples. A significant deviation of the force function curves from the ideal-fluid results occurs especially at low reflection coefficients and high incident frequencies. In the Rayleigh frequency range, the first three terms are sufficiently accurate to describe the radiation force, with the critical value of dimensionless frequency decreasing along with the boundary layers. Potential applications include the development of acoustic tweezers involving precise manipulation of microparticles in a bounded and nonideal fluid.

In this work, an improved Allen-Cahn-based phase-field lattice Boltzmann model is presented which is applicable to heat transfer in two-phase flow involving evaporation. The vapor concentration at the liquid-vapor interface serves as the driving force for vaporization. In our improved model, four distribution functions are used to describe the velocity field, the phase field, the temperature field, and the vapor concentration field where the vapor concentration and temperature fields are coupled by the Clausius-Clapeyron correlation. We evaluate several numerical tests to verify the accuracy of the presented model, including the one-dimensional (1D) Stefan flow and the two-dimensional or three-dimensional (2D or 3D) droplet evaporation problem. The results obtained demonstrate good agreement with theoretical expectations. We also compare two evaporation driving modes: the temperature gradient and vapor concentration gradient. Additionally, we investigate the impacts of the volume expansion rate term $F_{\beta }$ and the volume-specific heat gradient term $T_{\alpha }$ on the model. In the case of 1D Stefan flow, the result without $T_{\alpha }$ exhibits the largest deviation of 52.1% at $Y_{v,I}=0.8$, while the result without $F_{\beta }$ shows a deviation of only 12.2%.

Langevin dynamical simulations are performed to investigate the depinning dynamics of a two-dimensional (2D) solid dusty plasma, which is modulated by one-dimensional (1D) nonlinear deformed periodic substrates, and also driven by the combination of the DC and AC forces. As the DC driving force increases gradually, pronounced subharmonic and harmonic Shapiro steps are discovered under the combined modulation of the deformed substrate and the external AC drive. These observed subharmonic and harmonic Shapiro steps are attributed to the dynamic mode locking. The data analysis results indicate that the nonlinear deformed substrate strongly influences these subharmonic Shapiro steps, which can be accurately diagnosed using the fraction of sixfold coordinated particles. Furthermore, the diagnostic of the kinetic temperature clearly indicates the difference between harmonic and subharmonic Shapiro steps, i.e., the particle motion is slightly less synchronized at subharmonic Shapiro steps, caused by the unstable locations of the deformed substrate.

Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of the Ising model, tremendous effort has been devoted to developing solvers for Ising-type problems over the past decades. Recent advances in controlling and manipulating both quantum and classical systems have enabled novel computing paradigms such as quantum simulators and coherent Ising machines to tackle hard optimization problems. Here, we examine and benchmark several physics-inspired optimization algorithms, including coherent Ising machines, gain-dissipative algorithms, simulated bifurcation machines, and Hopfield neural networks, which we collectively refer to as stochastic driven nonlinear dynamical systems. Most importantly, we benchmark these algorithms against random Ising problems with planted solutions and compare them to simulated annealing as a baseline leveraging the same software stack for all solvers. We further study how different numerical integration techniques and graph connectivity affect performance. This work provides an overview of a diverse set of new optimization paradigms.

Lattice-gas algorithms (LGA) are a class of algorithms including, in chronological order, binary lattice-gas cellular automata, integer lattice-gas algorithms (ILGA), and lattice Boltzmann method (LBM). They are largely used for simulating nonlinear systems. Starting from one-dimensional ILGA, we design an algorithm where we carry out a fraction of the possible collisions. These fractions are then adapted to reproduce LBM equilibrium distributions, resulting in an adaptive lattice-gas algorithm that achieves the same simulation results of LBM. Considering this, we develop a quantum algorithm that involves a linear collision operator capable of simulating the same phenomena, while still using a measurement and reinitialization procedure. Multi-time-step implementation is possible in some specific cases, briefly discussed.

In this work, we present a general second-order phase-field model for the transport of insoluble surfactant in incompressible two-phase flows. In this model, a second-order local Allen-Cahn equation is applied for interface capturing, a general form of the simple scalar transport equation [S. S. Jain, J. Comput. Phys. 515, 113277 (2024)] is adopted for interface-confined surfactant, and the consistent and conservative Navier-Stokes equations with the surface tension and Marangoni force are used for fluid flows. To solve this model, we further developed a mesoscopic lattice Boltzmann (LB) method, in which the LB model for a surfactant transport equation is proposed under the general LB framework for the convection-diffusion type equation and it can correctly recover the governing equation for surfactant transport. The accuracy of the present LB method is tested by several benchmark problems and the numerical results show that it has a good performance for the transport of the insoluble surfactant in two-phase flows.

The bulk behavior of granular materials is tied to its mesoscale and particle-scale features: Strength properties arise from the buildup of various anisotropic structures at the particle-scale induced by grain connectivity, force transmission, and frictional mobilization. More fundamentally, these anisotropic structures work collectively to define features like the bulk friction coefficient and the stress tensor at the macroscale and can be explained by the stress-force-fabric (SFF) relationship stemming from the microscale arrangement of the forces and fabric. Although the SFF relation has been extensively verified by discrete numerical simulations, a laboratory realization has remained elusive due to the challenge of measuring both normal and frictional contact forces. In this study, we analyze experiments performed on a photoelastic granular system under four different loading conditions: uniaxial compression, isotropic compression, pure shear, and annular shear. During these experiments, we record particle locations, contacts between particles, and normal and frictional forces to measure the particle-scale response to progressing strain. We experimentally assess the SFF relation across multiple loading conditions in a two-dimensional photoelastic granular system. We track microscale measures like the packing fraction, average coordination number, and average normal force, along with angular distributions of the interparticle contacts and the interparticle forces. We then track the anisotropy in the angular distributions of contacts and forces and connect these particle-scale anisotropies to bulk behavior using the SFF relation. The SFF relation provides compact expressions for both the stress tensor and the bulk friction coefficient in terms of fabric and force anisotropies. Our results demonstrate that these expressions accurately capture the bulk stress and friction across different loading histories, validating the predictive power of the SFF framework. Additionally, we test the assumption that contact and force anisotropies contribute equally to load transmission in our granular packings and show that this assumption is sufficient at large strain values and can be applied to areas like rock mechanics, soft colloids, or cellular tissue where force information is inaccessible.

In recent years the swap Monte Carlo algorithm has led to remarkable progress in equilibrating supercooled model liquids at low temperatures. Applications have so far been limited to systems composed of spherical particles, however, whereas most real-world supercooled liquids are molecular. We introduce here a simple size-polydisperse molecular model that allows for efficient thermal equilibration in silico with the swap Monte Carlo method, resulting in an estimated speedup of ${10}^3\text{–}{10}^6$ at moderate polydispersity (5%–10%). The model exhibits little difference between size-resolved orientational time-autocorrelation functions.

We present the critical behavior of a model for a magnetic polymer under an external magnetic field on the three-dimensional Sierpińsky gasket. Our findings reveal that, at zero magnetic field, the polymer-collapse transition occurs first, followed by a magnetic transition as the temperature is lowered. The first is signaled by a nonzero polymer density with zero magnetization while the second by a spontaneous magnetization. In the presence of a magnetic field the polymer collapses into a magnetized state and there is only one transition. We have mapped the exact phase diagram, identifying the various phases and phase transitions. The model predicts the existence of a reentrance of paramagnetic collapse phase observed even in the absence of a magnetic field. In a limit where only even numbers of spins of each type on an elementary tetrahedron is permitted, we see a stabilization of a paramagnetic-collapsed polymer state against the addition of moderate ferromagnetic field.

Fish shoals exemplify systems composed of interacting and self-propelled particles that exhibit the complex collective dynamics seen in active matter. The group average polarization measures the ability to synchronize collective motion. Here, we analyze the experimental time series of increments in the average polarization of zebrafish shoals confined in a shallow circular test tank. Based on a multiscale approach of turbulence hierarchy and assuming that the local variance of the polarization increments at a given timescale has a gamma conditional distribution, we reveal that a cascade of background events occurs at well-separated timescales in small groups. Up to $\mathcal{N}=5$ cascade levels are identified. The number of distinct timescales decreases with the size of the system. The polarization fluctuations in large groups are shown to be well described by a single-scale background. The crossover from multiple- to single-scale turbulence hierarchy aligns with previous findings indicating a crossover from a strongly correlated non-Rayleigh regime with an anomalous finite-size scaling of polarization to a Rayleigh-like regime.

We adapt statistical models of the physics of complex fluids to study the rheology of granular liquids. This allows us to provide laws of granular rheology based on first principles, which compare well with previously established phenomenological laws. In particular, the very successful law of $\mu \left(\mathcal{I}\right)$ rheology can be understood within our model as the lowest order nontrivial Padé approximant of the macroscopic laws of rheology if one takes into account processes taking place at three distinct types of time scales: Collisions occurring at microscopic scales, collective motions like cage effect taking place at intermediate, mesoscopic scales, and finally advection that takes place at the macroscopic time scale. Our model's ability to describe granular physics outside of the Bagnold scaling regime allows for a natural extension to the rheology of granular suspensions.

We present a dynamical model of crystal growth, in which it is possible to reliably achieve asymmetric products, beginning from symmetric initial conditions and growing within an isotropic environment. The asymmetric growth is the result of a positive feedback mechanism that amplifies the effect of thermal fluctuations in the coverage of surfactants on the growing crystalline facets. Within our simple model, we are able to understand the kinetic and thermodynamic factors involved in both the onset of symmetry breaking and the persistence of anisotropic growth. We demonstrate that the mechanism is general by studying models with increasing complexity. We argue that this mechanism of symmetry breaking underpins observations of colloidal, seed-mediated syntheses of single crystalline metal nanorods capped with strongly interacting surfactants. The parameters within our model are related to experimental observables such as the concentration, hydrophobicity, and binding strength of the surfactants, which suggests a potential route to optimize the yield of asymmetric products in colloidal nanoparticle syntheses.

We investigate the impact of network heterogeneity on synergistic contagion dynamics. By extending a synergistic contagion model to diverse heterogeneous network topologies, we uncover the emergence of novel dynamical regimes characterized by multiple stable states, separated by a rich set of bifurcations reaching up to codimension 4. Additionally, we demonstrate how synergy fundamentally reshapes the influence of nodes based on their degree. Unlike in nonsynergistic epidemics, low-degree nodes can play a pivotal role in enabling network invasion at the onset of spread, while high-degree nodes can trigger explosive contagion. These findings challenge conventional control strategies, highlighting the need for new approaches to enhance or suppress synergistic contagion.

Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: The most probable trajectory between two states minimizes an action functional and corresponds to an optimal control strategy. In Langevin dynamics, the noise term itself serves as the control. For general Markov jump processes, such as chemical reaction networks or electronic circuits, we use the Doi-Peliti formalism to identify the “response” (or “momentum”) field $\pi$ as the control variable. This resolves a long-standing interpretational problem in the field-theoretic description of stochastic systems: Although $\pi$ evolves backward in time, it has a clear physical role as the control that steers the system along rare trajectories. This implies that nature is constantly sampling control strategies. We illustrate the mapping on multistable chemical reaction networks, systems with unstable fixed points, and specifically on stochastic resonance and Brownian ratchets. The noise-control mapping justifies agential descriptions of these phenomena and builds intuition for otherwise puzzling phenomena of stochastic systems: why probabilities are generically nonsmooth functions of state out of thermal equilibrium; why biological mechanisms can work better in the presence of noise; and how agential behavior emerges naturally without recourse to mysticism.

We investigate the effects of microalloying via random pinning on the yielding transition under oscillatory shear through extensive computer simulations. Random pinning refers to freezing the relaxation degrees of freedom for a fraction of randomly selected particles, which is often termed as hard pinning. Experimentally, pinning effects can be realized by introducing particles with much larger masses and diameters than the particles in the host medium, which is termed soft pinning. Many multicomponent glasses, especially metallic glasses, are good examples of such systems in which the mass and sizes of constituent molecules can vary considerably. Large molecules in these systems can act like soft pinning particles with respect to other particles due to a large timescale separation in their relaxation process. Using the Kob-Andersen model as our glass former, we create a randomly pinned system by pinning a fraction of the particles permanently, as well as by increasing their masses, thereby creating soft pinning sites. Increasing the fraction of hard or soft pinned particles transforms the system from a fragile to a strong glass former, enabling a systematic investigation of how fragility influences the yielding transition. Our findings reveal significant differences in the yielding behavior between strong and fragile glasses. These findings, along with earlier studies where fragility was tuned by varying the packing fraction in soft-sphere systems, demonstrate a universal relationship between fragility and yielding. Moreover, by varying the spatial dimensions, we demonstrate that the relationship is independent of both the dimensionality and the underlying origin of fragility in these model systems.

The theory of scaling processes is a toolbox suitable for the research of damage phenomena. In particular, correlation or self-affine analysis allows us to study the influence of microstructure and energy consumption mechanisms on crack nucleation and growth by topographical analysis of fracture surface morphology. It characterizes the topography of fracture surfaces with experimentally accessible parameters and relates it to process dynamics, allowing us to obtain governing equations. However, estimation of these parameters is not trivial at all; their currently available estimates are either contradictive or misguiding due to the inability to quantify the error of measurements or correlative behavior. In this research, we demonstrate that errors in self-affine analysis are easily quantified with relevant parameters such as the number of independent points in a correlated system and the discretization size per correlation length. Specifically, we study the influence of: (i) the finite-size effect; (ii) the profile's discretization; (iii) the effect of lateral correlation length; and (iv) the self-affine exponent on the accuracy of analysis. Finally, we demonstrate the applicability of the obtained methodology on real data of profiles at gigacycle fatigue fracture for measurements of the self-affine exponent and lateral correlation length. We found that the error in the self-affine analysis is often underestimated at least 8 times. We also give recommendations on how to estimate accuracy in self-affine analysis.

We study the nonequilibrium steady state of a two-dimensional Coulomb gas under the action of an anisotropic harmonic trapping potential along with a nonconservative rotational force. In the case without rotation, the equilibrium (zero temperature) steady state has a uniform density supported over a static elliptical droplet. The addition of a rotational force drives the system into a nonequilibrium steady state where the density is still uniform inside an ellipse, but the ellipse gets tilted by a fixed angle compared to the nonrotational case. In addition, a nonzero current is generated inside the droplet which runs concentrically to the droplet boundary. For large rotational force, the droplet develops a purely circular form. Our results are predicted by a simple hydrodynamic calculation, confirmed by numerical simulations, and provide a full understanding of a driven nonequilibrium state in a strongly interacting system.

Stochastic density-functional theory (SDFT) has been widely used to study the out-of-equilibrium properties of electrolyte solutions. Examples include investigations of electrical conductivity—both within and beyond linear response—and modifications of thermal van der Waals interactions in driven electrolytes. Within the approximation scheme derived from linearizing SDFT for fluctuations around mean densities, the steady-state correlation functions between the $N$ ionic species are governed by linear Lyapunov equations of degree $N(N+1)/2$. Consequently, the system's complexity increases significantly when transitioning from binary to ternary electrolytes, and few analytical results exist for the latter. In this paper, we demonstrate how—for the specific case of electrolytes—the Lyapunov equations can be reduced to a system of $N$ linear equations. We apply this reduction to compute the long-range component of the van der Waals interaction between two slabs containing a ternary electrolyte under an applied electric field parallel to the slabs. Unlike the binary electrolyte case, we show that the resulting van der Waals interaction for a ternary electrolyte depends on the ionic species' diffusion coefficients, highlighting its inherently out-of-equilibrium nature.

Reporting is widespread in human society, yet its theoretical mechanisms for cooperation in a monitored society remain unclear. Here, we introduce a reporting mechanism into the public goods game to investigate its impact on the emergence of cooperative behavior in a monitored environment. We analyze well-mixed populations and structured populations. Through theoretical analysis and numerical calculations, we find that when the fine is low, the introduction of the reporting mechanism effectively transforms the public goods game into a coordination game, thereby enhancing the feasibility of cooperation. Moreover, when the fine is high, cooperation emerges as a globally stable evolutionary strategy. Our results further indicate that reporting intensity exerts a nonlinear effect on public cooperation: moderate reporting intensity favors the evolution of cooperation, whereas excessive frequency or generosity in reporting may weaken its efficacy. Additionally, Monte Carlo simulation results on structured populations are consistent with those obtained in well-mixed populations. Notably, we observe a discontinuous phase transition in cooperation levels upon variation of reporting parameters, which can precipitate an outbreak of cooperation. These findings reveal reporting as a double-edged sword, emphasizing the need to balance its reporting parameters for optimal cooperation.

We consider a coupled system mimicking opinion formation under the influence of a group of $q$ neighbors ($q$-lobby) that consists of an Ising part governed by temperature-like parameter $T$ and a voter dynamics parametrized by noise probability $p$ (independence of choice). Using rigorous analytical calculations backed by extensive Monte Carlo simulations, we examine the interplay between these two quantities. Based on the theory of phase transitions, we derive the relation between $T$ and $p$ at the critical line dividing the ordered and disordered phases, which takes a very simple and generic form $T(p-a)=b$ in the high temperature limit. For specific lobby sizes, we show where the temperature and noise are balanced, and we hint that for large $q$, the temperature-like dynamics prevails.