The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the solid-fluid interaction scheme yields very large spurious currents in the simulations involving curved boundaries, while the virtual-density scheme produces an unphysical thick mass-transfer layer near the solid boundary although it gives much smaller spurious currents. We also extend the geometric-formulation scheme in the phase-field method to the pseudopotential LB model. Nevertheless, in comparison with the solid-fluid interaction scheme and the virtual-density scheme, the geometric-formulation scheme is relatively difficult to implement for curved boundaries and cannot be directly applied to three-dimensional space. By analyzing the features of these three schemes, we propose an improved virtual-density scheme to implement contact angles in the pseudopotential LB simulations with curved boundaries, which does not suffer from a thick mass-transfer layer near the solid boundary and retains the advantages of the original virtual-density scheme, i.e., simplicity, easiness for implementation, and low spurious currents.

Pore size distribution (PSD), which is defined as the percentage of the pores of each size to the total volume of the pores, is a key parameter to characterize the microstructure of porous media. Based on the pore geometry definition of three-dimensional (3D) maximal ball and two-dimensional (2D) maximal disk in discrete space, an improved algorithm is proposed to obtain PSD from pore space images of porous media. To validate the accuracy of our algorithm, a synthetic porous medium with a known PSD is generated by computer simulation. In addition, other 2D and 3D images of various types of samples, including sandstones, carbonates, and man-made materials, were also used to obtain PSD. The PSDs were compared quantitatively with that obtained by using the existing state of the art algorithm. The results show that our algorithm is more accurate in characterizing the pore structure and more consistent with the direct visual identification. In addition, the efficiency of our algorithm was also evaluated by calculating the PSD of large-scale 3D images, the results of which indicate that all calculations can be completed in a relatively short time.

In this paper, we generalize the principle of a generated first-order acoustic vortex (AV) with the acoustic resonances (AR) of a metasurface, from which we have also proposed a method for generating the higher-order AVs by arranging the sequences of the AR metasurface properly. The usable frequency range of the designed AR metasurface has been investigated and is discussed in detail, which is about $4470–4600\text{Hz}$ and covers the range $0.977–1.006f$ ($f=4573.31\mathrm{Hz}$ is the preset working frequency) approximately. Meanwhile, the designed AR metasurface can produce a frequency-adjustable AV field efficiently by adjusting the structure size and parameters of the planar AR layer. By discretizing the continuous phase distribution, the multiplexed AV beam with multiple orbital angular momentum states can also be generated effectively by arranging AR metasurface properly. The generated single and multiplexed AV beams can also be detected with the aid of the acoustic reverse phase plates accordingly.

We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviation function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property does not hold for an arbitrary contact dynamics, but is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factorization property. However, the nonequilibrium chemical potentials of the systems in contact keep track of the contact dynamics, and thus do not obey an equation of state. These nonequilibrium chemical potentials can be related either to the equilibrium chemical potential, or to the nonequilibrium chemical potential of the isolated systems. Results are applied both to an exactly solvable driven lattice gas model and to the Katz-Lebowitz-Spohn model using a numerical procedure to evaluate the chemical potential. The breaking of the additivity property is also illustrated on the exactly solvable model.

We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures ${\beta }_h$ and ${\beta }_c(>{\beta }_h)$ with $(k_B\equiv 1)\beta =1/T$. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as ${\eta }_{mp}={\left({\eta }_C^{\mathrm{gen}}\right)}^2/[{\eta }_C^{\mathrm{gen}}-(1-{\eta }_C^{\mathrm{gen}})ln(1-{\eta }_C^{\mathrm{gen}})]$, where the generalized Carnot efficiency ${\eta }_C^{\mathrm{gen}}$ in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter $\gamma$: ${\eta }_C^{\mathrm{gen}}=1-{\beta }_h/[{\beta }_{c}cosh\left(2\gamma \right)]$. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.

We investigate three kinds of heat produced in a system and a bath strongly coupled via an interaction Hamiltonian. By studying the energy flows between the system, the bath, and their interaction, we provide rigorous definitions of two types of heat, $Q_{\mathrm{S}}$ and $Q_{\mathrm{B}}$, from the energy loss of the system and the energy gain of the bath, respectively. This is in contrast to the equivalence of $Q_{\mathrm{S}}$ and $Q_{\mathrm{B}}$, which is commonly assumed to hold in the weak-coupling regime. The bath we consider is equipped with a thermostat which enables it to reach an equilibrium. We identify another kind of heat $Q_{\mathrm{SB}}$ from the energy dissipation of the bath into the superbath that provides the thermostat. We derive the fluctuation theorems (FTs) for the system variables and various heats, which are discussed in comparison with the FT for the total entropy production. We take an example of a sliding harmonic potential of a single Brownian particle in a fluid and calculate the three heats in a simplified model. These heats are found to equal, on average, in the steady state of energy, but show different fluctuations at all times.

The presence of spatial inhomogeneity in a nonlinear medium restricts the formation of solitary waves (SW) on a discrete set of positions, whereas a nonlocal nonlinearity tends to smooth the medium response by averaging over neighboring points. The interplay of these antagonistic effects is studied in terms of SW formation and propagation. Formation dynamics is analyzed under a phase-space approach and analytical conditions for the existence of either discrete families of bright SW or continuous families of kink SW are obtained in terms of Melinikov's method. Propagation dynamics are studied numerically and cases of stable and oscillatory propagation as well as dynamical transformation between different types of SW are shown. The existence of different types and families of SW in the same configuration, under appropriate relations between their spatial width and power with the inhomogeneity and the nonlocality parameters, suggests an advanced functionality of such structures that is quite promising for applications.

We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation toward its “frozen” state with quasistationary spiral structures. We study the transition kinetics from either the defect turbulence regime or random initial configurations to the frozen state with a well-defined low density of quasistationary topological defects. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts. We study two distinct situations, namely when the system is quenched either far from the transition limit or near it. In the former deeply quenched case, the average nucleation time for different system sizes is measured over many independent realizations. We employ an extrapolation method as well as a phenomenological formula to account for and eliminate finite-size effects. The nonzero (dimensionless) barrier for the nucleation of single spiral droplets in the extrapolated infinite system size limit suggests that the transition to the frozen state is discontinuous. We also investigate the nucleation of spirals for systems that are quenched close to but beyond the crossover limit and of target waves which emerge if a specific spatial inhomogeneity is introduced. In either of these cases, we observe long, “fat” tails in the distribution of nucleation times, which also supports a discontinuous transition scenario.

The effect of group structure on cooperative behavior is not well understood. In this paper, we study the dynamics of a public goods game involving $n$-agent interactions. In the proposed setup, the population is organized into groups. We associate the individual fitness to group performance, while the evolutionary dynamics takes place globally. We derive analytical expressions and show that the model exhibits several fixed points, including the symmetric homogeneous states of total cooperation and total defection, which are unstable and stable, respectively. Interestingly, even if both individual and group levels are organized as well-mixed populations, the dynamics displays intermediate values of cooperation under the replicator dynamics. Namely, as soon as one of the groups, at least, is fully cooperative, intermediary fixed points appear for the rest of the groups. In addition to the analytical approach, we have performed numerical simulations that reproduce the internal fixed points obtained theoretically, showing coexisting intermediate levels of cooperation. Potential implications of these results in terms of group selection and the role of social norms are also discussed.

We investigate vapor homogeneous nucleation in a superheated Lennard-Jones liquid with computer simulations. Special simulation techniques are required to address this study since the nucleation of a critical vapor bubble—one that has an equal chance to grow or shrink—in a moderately superheated liquid is a rare event. We use the Seeding method, which combines Classical Nucleation Theory with computer simulations of a liquid containing a vapor bubble to provide bubble nucleation rates in a wide temperature range. Seeding has been successfully applied to investigate the nucleation of crystals in supercooled fluids, and here we apply it to the liquid-to-vapor transition. We find that the Seeding method provides nucleation rates that are consistent with independent calculations not based on the assumptions of Classical Nucleation Theory. Different criteria to determine the radius of the critical bubble give different rate values. The accuracy of each criterion depends of the degree of superheating. Moreover, seeding simulations show that the surface tension depends on pressure for a given temperature. Therefore, using Classical Nucleation Theory with the coexistence surface tension does not provide good estimates of the nucleation rate.

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, $N_1$ and $N$. We also calculate the gap length, the capture zone and the island distributions. For all the sets of barriers considered, the results given by the proposed analytical model are compared with those from kinetic Monte Carlo simulations. We found that the behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol allows more control and understanding on the island formation mechanism because it intrinsically separates the nucleation and aggregation processes in different time regimes.

Complex phenomena incorporating several physical properties are abundant while they are occasionally revealing the variation of power-law behavior depending on the scale. In the present work, the global scaling behavior of the dynamical impact of a solid sphere onto an elastic surface is described. Its fundamental dimensionless function was successfully obtained by applying dimensional analysis combined with a solution by energy conservation complementally. It demonstrates that its power-law behavior is given by the competition between two power-law relations representing inertial and elastic properties respectively, which is strengthened by the scale size of the sphere. These factors are successfully summarized by the newly defined dimensionless parameters, which give two intermediate asymptotics in a different scale range. These power-law behaviors given by the theoretical model were compared with experimental results, showing good agreement. This study supplies the insights to dimensional analysis and self-similarity in general.

Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry, and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability, and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at $70\mathrm{Hz}$ are in qualitative agreement with the predictions of our modeling.

Recent work on quantum annealing has emphasized the role of collective behavior in solving optimization problems. By enabling transitions of clusters of variables, such solvers are able to navigate their state space and locate solutions more efficiently despite having only local connections between elements. However, collective behavior is not exclusive to quantum annealers, and classical solvers that display collective dynamics should also possess an advantage in navigating a nonconvex landscape. Here we give evidence that a benchmark derived from quantum annealing studies is solvable in polynomial time using digital memcomputing machines, which utilize a collection of dynamical components with memory to represent the structure of the underlying optimization problem. To illustrate the role of memory and clarify the structure of these solvers we propose a simple model of these machines that demonstrates the emergence of long-range order. This model, when applied to finding the ground state of the Ising frustrated-loop benchmarks, undergoes a transient phase of avalanches which can span the entire lattice and demonstrates a connection between long-range behavior and their probability of success. These results establish the advantages of computational approaches based on collective dynamics of continuous dynamical systems.

While it is well known that permeability is a tensorial property, it is usually reported as a scalar property or only diagonal values are reported. However, experimental evaluation of tensorial flow properties is problematic. Pore-scale modeling using three-dimensional (3D) images of porous media with subsequent upscaling to a continuum scale (homogenization) is a valuable alternative. In this study, we explore the influence of different types of boundary conditions on the external walls of the representative modeling domain along the applied pressure gradient on the magnitude and orientation of the computed permeability tensor. To implement periodic flow boundary conditions, we utilized stochastic reconstruction methodology to create statistically similar (to real porous media structures) geometrically periodic 3D structures. Stochastic reconstructions are similar to encapsulation of the porous media into statistically similar geometrically periodic one with the same permeability tensor. Seven main boundary conditions (BC) were implemented: closed walls, periodic flow, slip on the walls, linear pressure, translation, symmetry, and immersion. The different combinations of BCs amounted to a total number of 15 BC variations. All these BCs significantly influenced the resulting tensorial permeabilities, including both magnitude and orientation. Periodic boundary conditions produced the most physical flow patterns, while other classical BCs either suppressed crucial transversal flows or resulted in unphysical currents. Our results are crucial to performing flow properties upscaling and will be relevant to computing not only single-phase but also multiphase flow properties. Moreover, other calculation of physical properties such as some mechanical, transport, or heat conduction properties may benefit from the technique described in this study.

We examine isotropic and anisotropic random walks which begin on the surface of linear ($N$), square ($N\times N$), or cubic ($N\times N\times N$) lattices and end upon encountering the surface again. The mean length of walks is equal to $N$ and the distribution of lengths $n$ generally scales as $n^{-1.5}$ for large $n$. Our results are interesting in the context of an old formula due to Cauchy that the mean length of a chord through a convex body of volume $V$ and surface $S$ is proportional to $V/S$. It has been realized in recent years that Cauchy's formula holds surprisingly even if chords are replaced by irregular insect paths or trajectories of colliding gas molecules. The random walk on a lattice offers a simple and transparent understanding of this result in comparison to other formulations based on Boltzmann's transport equation in continuum.

We study the propagation of coherent waves in a nonlinearly induced random potential and find regimes of self-organized criticality and other regimes where the nonlinear equivalent of Anderson localization prevails. The regime of self-organized criticality leads to power-law decay of transport [Y. Sharabi et al., Phys. Rev. Lett. 121, 233901 (2018)], whereas the second regime exhibits exponential decay.

In this paper, motivated by a general interest in the stochastic thermodynamics of small systems, we derive an exact expression—via path integrals—for the conditional probability density of a two-dimensional harmonically confined Brownian particle acted on by linear mixed flow. This expression is a generalization of the expression derived earlier by Foister and Van De Ven [J. Fluid Mech. 96, 105 (1980)] for the case of the corresponding free Brownian particle, and reduces to it in the appropriate unconfined limit. By considering the long-time limit of our calculated probability density function, we show that the flow-driven Brownian oscillator attains a well-defined steady state. We also show that, during the course of a transition from an initial flow-free thermal equilibrium state to the flow-driven steady state, the integral fluctuation theorem, the Jarzynski equality, and the Bochkov-Kuzovlev relation are all rigorously satisfied. Additionally, for the special cases of pure rotational flow we derive an exact expression for the distribution of the heat dissipated by the particle into the medium, and for the special case of pure elongational flow we derive an exact expression for the distribution of the total entropy change. Finally, by examining the system's stochastic thermodynamics along a reverse trajectory, we also demonstrate that in elongational flow the total entropy change satisfies a detailed fluctuation theorem.

Medical conditions due to acute cell injury, such as stroke and heart attack, are of tremendous impact and have attracted huge amounts of research effort. The biomedical research that seeks cures for these conditions has been dominated by a qualitative, inductive mind-set. Although the inductive approach has not been effective in developing medical treatments, it has amassed enough information to allow construction of quantitative, deductive models of acute cell injury. In this work we develop a modeling approach by extending an autonomous nonlinear dynamic theory of acute cell injury that offered new ways to conceptualize cell injury but possessed limitations that decrease its effectiveness. Here we study the global dynamics of the cell injury theory using a nonautonomous formulation. Different from the standard scenario in nonlinear dynamics that is determined by the steady state and fixed points of the model equations, in this nonautonomous model with a trivial fixed point, the system property is dominated by the transient states and the corresponding dynamic processes. The model gives rise to four qualitative types of dynamical patterns that can be mapped to the behavior of cells after clinical acute injuries. The nonautonomous theory predicts the existence of a latent stress response capacity (LSRC) possessed by injured cells. The LSRC provides a theoretical explanation of how therapies, such as hypothermia, can prevent cell death after lethal injuries. The nonautonomous theory of acute cell injury provides an improved quantitative framework for understanding cell death and recovery and lays a foundation for developing effective therapeutics for acute injury.

Inspired by protein folding, we smooth out the complex cost function landscapes of two processes: the tuning of networks and the jamming of ideal spheres. In both processes, geometrical frustration plays a role—tuning pressure differences between pairs of target nodes far from the source in a flow network impedes tuning of nearby pairs more than the reverse process, while unjamming the system in one region can make it more difficult to unjam elsewhere. By modifying the cost functions to control the order in which functions are tuned or regions unjam, we smooth out local minima while leaving global minima unaffected, increasing the success rate for reaching global minima.