The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations show that the method reaches very low temperatures, at which the liquid-gas density ratio is more than ${10}^{14}$, while the thermodynamic consistency is still preserved. Decoupling the mesh space from the momentum space through a proportional coefficient, a smaller mesh step provides denser lattice nodes to exactly describe the transition region and the resulting dimensional transformation has no loss of accuracy. A compact finite-difference method is applied to calculate the discrete derivatives in the mesh space with high-order accuracy. These enhance the computational accuracy of the nonideal force and suppress the spurious currents to a very low level, even if the density ratio is up to tens of thousands. The simulation of drop splashing verifies that the present model is Galilean invariant for the dynamic flow field. An upper limit of the chemical potential is used to reduce the influence of nonphysical factors and improve the stability.

A quantified model-competition (QMC) mechanism for multiscale flows is extracted from the integral (analytical) solution of the Boltzmann-BGK model equation. In the QMC mechanism, the weight of the rarefied model and the weight of the continuum (aerodynamic and hydrodynamic) model are quantified. Then, a simplified unified wave-particle method (SUWP) is constructed based on the QMC mechanism. In the SUWP, the stochastic particle method and the continuum Navier-Stokes method are combined together. Their weights are determined by the QMC mechanism quantitatively in every discrete cell of the computational domain. The validity and accuracy of the present numerical method are examined using a series of test cases including the high nonequilibrium shock wave structure case, the unsteady Sod shock-tube case with a wide range of Kn number, the hypersonic flow around the circular cylinder from the free-molecular regime to the near continuum regime, and the viscous boundary layer case. In the construction process of the present method, an antidissipation effect in the continuum mechanism is also discussed.

Disordered systems are ubiquitous in physical, biological, and material sciences. Examples include liquid and glassy states of condensed matter, colloids, granular materials, porous media, composites, alloys, packings of cells in avian retina, and tumor spheroids, to name but a few. A comprehensive understanding of such disordered systems requires, as the first step, systematic quantification, modeling, and representation of the underlying complex configurations and microstructure, which is generally very challenging to achieve. Recently, we introduced a set of hierarchical statistical microstructural descriptors, i.e., the “$n$-point polytope functions” $P_{\mathrm{n}}$, which are derived from the standard $n$-point correlation functions $S_{\mathrm{n}}$, and successively included higher-order $n$-point statistics of the morphological features of interest in a concise, explainable, and expressive manner. Here we investigate the information content of the $P_{\mathrm{n}}$ functions via optimization-based realization rendering. This is achieved by successively incorporating higher-order $P_{\mathrm{n}}$ functions up to $n=8$ and quantitatively assessing the accuracy of the reconstructed systems via unconstrained statistical morphological descriptors (e.g., the lineal-path function). We examine a wide spectrum of representative random systems with distinct geometrical and topological features. We find that, generally, successively incorporating higher-order $P_{\mathrm{n}}$ functions and, thus, the higher-order morphological information encoded in these descriptors leads to superior accuracy of the reconstructions. However, incorporating more $P_{\mathrm{n}}$ functions into the reconstruction also significantly increases the complexity and roughness of the associated energy landscape for the underlying stochastic optimization, making it difficult to convergence numerically.

A thring is a recent addition to the zoo of spiral wave phenomena found in excitable media and consists of a scroll ring that is threaded by a pair of counter-rotating scroll waves. This arrangement behaves as a particle that swims through the medium. Here, we present results on the dynamics, interaction, and collective behavior of several thrings via numerical simulation of the reaction-diffusion equations that model thrings created in chemical experiments. We reveal an attraction between two thrings that leads to a stable bound pair that thwarts their individual locomotion. Furthermore, such a pair emits waves at a higher frequency than a single thring, which protects the pair from the advances of any other thring and rules out the formation of a triplet bound state. As a result, the long-term evolution of a colony of thrings ultimately yields an unusual frozen nonequilibrium state consisting of a collection of pairs accompanied by isolated thrings that are inhibited from further motion by the waves emanating from the pairs.

Many living systems use assemblies of soft and slender structures whose deflections allow them to mechanically probe their immediate environment. In this work, we study the collective response of artificial soft hair assemblies to a shear flow by imaging their deflections. At all hair densities, the deflection is found to be proportional to the local shear stress with a proportionality factor that decreases with density. The measured collective stiffening of hairs is modeled both with a microscopic elastohydrodynamic model that takes into account long-range hydrodynamic hair-hair interactions and a phenomenological model that treats the hair assemblies as an effective porous medium. While the microscopic model is in reasonable agreement with the experiments at low hair density, the phenomenological model is found to be predictive across the entire density range.

The extreme slowing down associated with glass formation in experiments and in simulations results in serious difficulties to prepare deeply quenched, well annealed, glassy material. Recently, methods to achieve such deep quenching were proposed, including vapor deposition on the experimental side and “swap Monte Carlo” and oscillatory shearing on the simulation side. The relation between the resulting glasses under different protocols remains unclear. Here we show that oscillatory shear and swap Monte Carlo result in thermodynamically equivalent glasses sharing the same statistical mechanics and similar mechanical responses under external strain.

Irreversible multilayer adsorption of semirigid $k$-mers on one-dimensional lattices of size $L$ is studied by numerical simulations complemented by exhaustive enumeration of configurations for small lattices. The deposition process is modeled by using a random sequential adsorption algorithm, generalized to the case of multilayer adsorption. The paper concentrates on measuring the jamming coverage for different values of $k$-mer size and number of layers $n$. The bilayer problem ($n\le 2$) is exhaustively analyzed, and the resulting tendencies are validated by the exact enumeration techniques. Then, the study is extended to an increasing number of layers, which is one of the noteworthy parts of this work. The obtained results allow the following: (i) to characterize the structure of the adsorbed phase for the multilayer problem. As $n$ increases, the $(1+1)$-dimensional adsorbed phase tends to be a “partial wall” consisting of “towers” (or columns) of width $k$, separated by valleys of empty sites. The length of these valleys diminishes with increasing $k$; (ii) to establish that this is an in-registry adsorption process, where each incoming $k$-mer is likely to be adsorbed exactly onto an already adsorbed one. With respect to percolation, our calculations show that the percolation probability vanishes as $L$ increases, being zero in the limit $L\to \infty$. Finally, the value of the jamming critical exponent ${\nu }_j$ is reported here for multilayer adsorption: ${\nu }_j$ remains close to 2 regardless of the considered values of $k$ and $n$. This finding is discussed in terms of the lattice dimensionality.

Calculating how long a coupled multispecies reactive-diffusive transport process in a heterogeneous medium takes to effectively reach steady state is important in many applications. In this paper, we show how the time required for such processes to transition to within a small specified tolerance of steady state can be calculated accurately without having to solve the governing time-dependent model equations. Our approach is valid for general first-order reaction networks and an arbitrary number of species. Three numerical examples are presented to confirm the analysis and investigate the efficacy of the approach. A key finding is that for sequential reactions our approach works better provided the two smallest reaction rates are well separated.

We study the time dependence of the local persistence probability during a nonstationary time evolution in the disordered contact process in $d=1$, 2, and 3 dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply at the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dependent local persistence is shown to be characterized by a universal limit distribution of effective persistence exponents. Using a phenomenological approach of rare-region effects in the active phase, we obtain a nonuniversal algebraic decay of the average persistence for $d=1$ and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay remains valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.

Brownian motion is a Gaussian process describing normal diffusion with a variance increasing linearly with time. Recently, intracellular single-molecule tracking experiments have recorded exponentially decaying propagators, a phenomenon called Laplace diffusion. Inspired by these developments we study a many-body approach, called the Hitchhiker model, providing a microscopic description of the widely observed behavior. Our model explains how Laplace diffusion is controlled by size fluctuations of single molecules, independently of the diffusion law which they follow. By means of numerical simulations Laplace diffusion is recovered and we show how single-molecule tracking and data analysis, in a many-body system, is highly nontrivial as tracking of a single particle or many in parallel yields vastly different estimates for the diffusivity. We quantify the differences between these two commonly used approaches, showing how the single-molecule estimate of diffusivity is larger if compared to the full tagging method.

Random $K$-satisfiability ($K$-SAT) is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms. The statistical properties of the random $K$-SAT solution space have been extensively investigated, but most earlier efforts focused on solutions that are typical. Here we consider maximally flexible solutions which satisfy all the constraints only using the minimum number of variables. Such atypical solutions have high internal entropy because they contain a maximum number of null variables which are completely free to choose their states. Each maximally flexible solution indicates a dense region of the solution space. We estimate the maximum fraction of null variables by the replica-symmetric cavity method, and implement message-passing algorithms to construct maximally flexible solutions for single $K$-SAT instances.

Today's society faces widening disagreement and conflicts among constituents with incompatible views. Escalated views and opinions are seen not only in radical ideology or extremism but also in many other scenes of our everyday life. Here we show that widening disagreement among groups may be linked to the advancement of information communication technology by analyzing a mathematical model of population dynamics in a continuous opinion space. We adopted the interaction kernel approach to model enhancement of people's information-gathering ability and introduced a generalized nonlocal gradient as individuals' perception kernel. We found that the characteristic distance between population peaks becomes greater as the wider range of opinions becomes available to individuals or the more attention is attracted to opinions distant from theirs. These findings may provide a possible explanation for why disagreement is growing in today's increasingly interconnected society, without attributing its cause only to specific individuals or events.

A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation permits the consideration of arbitrary polymer chain behaviors when interactions among chains may be neglected. This careful treatment highlights the naturally occurring correspondence between single-chain mechanical behavior and the equilibrium distribution of chains in the network, as well as the correspondences between different single-chain thermodynamic ensembles. We demonstrate these important distinctions with the extensible freely jointed chain model. This statistical mechanical theory is then extended to the continuum scale, where we utilize traditional macroscopic constitutive theory to ultimately retrieve the Cauchy stress in terms of the deformation and polymer network statistics. Once again using the extensible freely jointed chain model, we illustrate the importance of the naturally occurring statistical correspondences through their effects on the stress-stretch response of the network. We additionally show that these differences vanish when the number of links in the chain becomes sufficiently large enough, and discuss why certain methods perform better than others before this limit is reached.

Flocks of birds, schools of fish, and insect swarms are examples of the coordinated motion of a group that arises spontaneously from the action of many individuals. Here, we study flocking behavior from the viewpoint of multiagent reinforcement learning. In this setting, a learning agent tries to keep contact with the group using as sensory input the velocity of its neighbors. This goal is pursued by each learning individual by exerting a limited control on its own direction of motion. By means of standard reinforcement learning algorithms we show that (i) a learning agent exposed to a group of teachers, i.e., hard-wired flocking agents, learns to follow them, and (ii) in the absence of teachers, a group of independently learning agents evolves towards a state where each agent knows how to flock. In both scenarios, the emergent policy (or navigation strategy) corresponds to the polar velocity alignment mechanism of the well-known Vicsek model. These results (a) show that such a velocity alignment may have naturally evolved as an adaptive behavior that aims at minimizing the rate of neighbor loss, and (b) prove that this alignment does not only favor (local) polar order, but it corresponds to the best policy or strategy to keep group cohesion when the sensory input is limited to the velocity of neighboring agents. In short, to stay together, steer together.

Individual fire ants are inherently active as they are living organisms that convert stored chemical energy into motion. However, each individual ant is not equally disposed to motion at any given time. In an active aggregation, most of the constituent ants are active, and vice versa for an inactive aggregation. Here we look at the role activity plays on the nonlinear mechanical behavior of the aggregation through large amplitude oscillatory shear measurements. We find that the level of viscous nonlinearity can be decreased by increasing the activity or by increasing the volume fraction. In contrast, the level of elastic nonlinearity is not affected by either activity or volume fraction. We interpret this in terms of a transient network with equal rates of linking and unlinking but with varying number of linking and unlinking events.

Understanding of multiphase flow in porous media is important for a wide range of applications such as soil science, environmental remediation, energy resources, and $\mathrm{C}{\mathrm{O}}_2$ sequestration. This phenomenon depends on the complex interplay between the fluid and solid forces such as gravitational, capillary, and viscous forces, as well as wettability of the solid phase. Such interactions along with the geometry of the medium give rise to a variety of complex flow regimes. Although much research has been done in the area of wettability, its mechanical effect is not well understood, and it continues to challenge our understanding of the phenomena on macroscopic and microscopic scales. In this paper, therefore, the effect of wettability on the deformation of porous media and fluid-fluid patterns is studied through a series of three-dimensional (3D) simulations. To this end, the discrete element method (DEM) and volume of fluid (VOF) are coupled to accurately model free-surface flow interaction in a cylindrical pack of spheres. The fluid-particle interactions are modeled by exchanging information between DEM and VOF, while the effect of wettability is considered to study how it controls fluid displacement. The results indicate that the drag force and deformation in the pack vary with the change in wettability and capillary number. To demonstrate the effect of both wettability and capillary number, a series of numerical experiments were conducted with two capillary numbers and three wettability conditions. Our results show that the drag force was greatest for near extreme wettability conditions, which resulted in a larger deformation.

Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic framework to characterize and optimize the performances of such cycles. Based on a minimal model, we put forward a protocol which extracts work by controlling only the properties of the confining walls at boundaries, and we rationalize the transitions between optimal cycles. We show that the corresponding power and efficiency are generally proportional, so that they reach their maximum values at the same cycle time in contrast with thermal cycles, and we provide a generic relation constraining the fluctuations of the power.

We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems.

We study bond percolation on the simple cubic lattice with various combinations of first, second, third, and fourth nearest neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the bond thresholds. Correlations between percolation thresholds and lattice properties are discussed, and our results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number $z$ quite accurately according to a power-law $p_c\sim z^{-a}$ with exponent $a=1.111$. However, for large $z$, the threshold must approach the Bethe lattice result $p_c=1/(z-1)$. Fitting our data and data for additional nearest neighbors, we find $p_c(z-1)=1+1.224z^{-1/2}$.

The behavior of a stochastic perfect integrate-and-fire (PIF) model of neurons is considered. The effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing Lévy-type subordinator. Using a first-passage-time formulation, we find exact expressions for the output interspike interval (ISI) statistics. Particularly, it is shown that at some parameter regimes the ISI density exhibits a multimodal structure. Moreover, it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current $\mu$, i.e., the ISI's regularity is maximized at an intermediate value of $\mu$. The features of spike statistics, analytically revealed in our study, are compared with previously obtained results for a perfect integrate-and-fire neuron model driven by dichotomous noise (without subordination).