Ehrenfests' wind-tree model (EWTM) refers to a two-dimensional system where noninteracting point tracer particles move through a random arrangement of overlapping or nonoverlapping square-shaped scatterers. Here, extensive event-driven molecular dynamics simulations of the EWTM at different reduced scatterer densities $\rho$ are presented. For nonoverlapping scatterers, the asymptotic motion of the tracer particles is diffusive. We compare their diffusion coefficient $D$, as obtained from the simulation, with that predicted by kinetic theory where $D^{-1}$ is expanded up to the second order in the scatterer density. While at low density quantitative agreement between theory and simulation is found, we show that beyond the low-density regime deviations to the theory are associated with the emergence of a maximum in the non-Gaussian parameter at intermediate times. For the case of overlapping scatterers, in agreement with a theoretical prediction, the asymptotic motion of the tracer particles is subdiffusive, i.e., the mean-squared displacement at long times $t$ grows like $t^{1-2\rho /3}$. We propose a model of the van Hove correlation function that describes the density dependence of the tracer particles' asymptotic subdiffusive transport on a quantitative level.

The Curzon-Ahlborn (CA) efficiency, as the efficiency at the maximum power (EMP) of the endoreversible Carnot engine, has significant impact on finite-time thermodynamics. However, the CA engine is based on many assumptions. In the past few decades, although a lot of efforts have been made, a microscopic theory of the CA engine is still lacking. By adopting the method of the stochastic differential equation of energy, we formulate a microscopic theory of the CA engine realized with a highly underdamped Brownian particle in a class of nonharmonic potentials. This theory gives microscopic interpretation of all assumptions made by Curzon and Ahlborn. In other words, we find a microscopic counterpart of the CA engine in stochastic thermodynamics. Also, based on this theory, we derive the explicit expression of the protocol associated with the maximum power for any given efficiency, and we obtain analytical results of the power and the efficiency statistics for the Brownian CA engine. Our research brings new perspectives to experimental studies of finite-time microscopic heat engines featured with fluctuations.

We analyze the dynamical mechanisms underlying the formation of arrhythmogenic early afterdepolarizations (EADs) in two mathematical models of cardiac cellular electrophysiology: the Sato et al. biophysically detailed model of a rabbit ventricular myocyte of dimension 27 and a reduced version of the Luo-Rudy mammalian myocyte model of dimension 3. Based on a comparison of the two models, with detailed bifurcation analysis using spike-counting techniques and continuation methods in the simple model and numerical explorations in the complex model, we locate the point where the first EAD originates in an unstable branch of periodic orbits. These results serve as a basis to propose a conjectured scheme involving a hysteresis mechanism with the creation of alternans and EADs in the unstable branch. This theoretical scheme fits well with electrophysiological experimental data on EAD generation and hysteresis phenomena. Our findings open the door to the development of novel methods for pro-arrhythmia risk prediction related to EAD generation without actual induction of EADs.

The Monte Carlo method is often used to simulate systems which can be modeled by random walks. To calculate observables, in many implementations the “walkers” carry a statistical weight which is generally assumed to be positive. Some random walk simulations, however, may require walkers to have positive or negative weights: it has been shown that the presence of a mixture of positive and negative weights can impede the statistical convergence, and special weight-cancellation techniques must be adopted to overcome these issues. In a recent work we demonstrated the usefulness of one such method, exact regional weight cancellation, to solve eigenvalue problems in nuclear reactor physics in three spatial dimensions. The method previously exhibited had several limitations (including multigroup transport and isotropic scattering) and needed homogeneous cuboid cancellation regions. In this paper we lift the previous limitations, in view of applying exact regional cancellation to more realistic continuous-energy neutron transport problems. This extended regional cancellation framework is used to optimize the efficiency of the weight cancellation. Our findings are illustrated on a benchmark configuration for reactor physics.

In this Letter, we report on an experimental study which analyzes the compressive behavior of two-dimensional bidisperse granular assemblies made of soft (hyperelastic) and hard grains in varying proportions ($\kappa$ is the portion of soft grains). By means of a recently developed uniaxial compression setup [Vu and Barés, Phys. Rev. E 100, 042907 (2019)] and using an advanced digital image correlation method, we follow, beyond the jamming point, the evolution of the main mechanical observables, from the global scale down to the strain field inside each deformable grain. First, we validate experimentally and extend to the uniaxial case a recently proposed micromechanical compaction model linking the evolution of the applied pressure $P$ to the packing fraction $\varphi$ [Cantor et al., Phys. Rev. Lett. 124, 208003 (2020)]. Second, we reveal two different linear regimes depending on whether the system is above or below a crossover strain unraveling a transition from a discrete to a continuous-like system. Third, the evolution of these linear laws is found to vary linearly with $\kappa$. These results provide a comprehensive experimental and theoretical framework that can now be extended to a more general class of polydisperse soft granular systems.

The small-scale statistical properties of velocity circulation in classical homogeneous and isotropic turbulent flows are assessed through a modeling framework that brings together the multiplicative cascade and the structural descriptions of turbulence. We find that vortex structures exhibit short-distance repulsive correlations, which is evidenced when they are “tomographically” investigated, by means of planar cuts of the flow, as two-dimensional vortex gases. This phenomenon is suggested from model improvements which allow us to obtain an accurate multiscale description of the intermittent fluctuations of circulation. Its crucial new ingredient, the conjectured hard disk behavior of the effective planar vortices, is then found to be strongly supported from a study of their spatial distributions in direct numerical simulations of the Navier-Stokes equations.

In cytokinesis of animal cells, the cell is symmetrically divided into two. Since the cell's volume is conserved, the projected area has to increase to allow for the change of shape. Here we aim to predict how membrane gain and loss adapt during cytokinesis. We work with a kinetic model in which membrane turnover depends on membrane tension and cell shape. We apply this model to a series of calculated vesicle shapes as a proxy for the shape of dividing cells. We find that the ratio of kinetic turnover parameters changes nonmonotonically with cell shape, determined by the dependence of exocytosis and endocytosis on membrane curvature. Our results imply that controlling membrane turnover will be crucial for the successful division of artificial cells.

The anomalous behavior of a two-dimensional system of Hertzian disks with exponent $\alpha =7/2$ has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Waterlike density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also in the solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above the maximum melting point $T=0.0058$ of the triangular crystal.

In simplified models of glasses we clarify the existence of two different kinds of coexisting activated dynamics, with one of the two dominating over the other. One is the energy barrier hopping that is typically used to understand activation, and the other, which we call entropic activation, is driven by the scarcity of convenient directions in phase space. When entropic activation dominates, the height of the energy barriers is no longer the primary factor governing the system's slowdown. In our analysis, dominance of one mechanism over the other depends on temperature and the shape of the density of states. We also find that at low temperatures a phase transition between the two kinds of activation can occur. Our observations are used to provide a scenario that can harmonize the facilitation and thermodynamic pictures of the slowdown of glasses into a single description.

We consider a problem of finding a target located in a finite $d$-dimensional domain, using $N$ independent random walkers, when partial information about the target location is given as a probability distribution. When $N$ is large, the first-passage time sensitively depends on the initial searcher distribution, which invokes the question of the optimal searcher distribution that minimizes the first-passage time. Here, we analytically derive the equation for the optimal distribution and explore its limiting expressions. If the target volume can be ignored, the optimal distribution is proportional to the target distribution to the power of one third. If we consider a target of a finite volume and the probability of the initial overlapping of searchers with the target cannot be ignored in the large $N$ limit, the optimal distribution has a weak dependence on the target distribution, with its variation being proportional to the logarithm of the target distribution. Using Langevin dynamics simulations, we numerically demonstrate our predictions in one and two dimensions.

Under low-Reynolds-number conditions, dynamics of convection and diffusion are usually considered separately because their dominant spatial and temporal scales are different, but cooperative effects of convection and diffusion can cause diffusion enhancement [Koyano et al., Phys. Rev. E 102, 033109 (2020)]. In this paper, such cooperative effects are investigated in detail. Numerical simulations based on the convection-diffusion equation revealed that anisotropic diffusion and net shift as well as diffusion enhancement occur under a reciprocal flow. Such anomalous diffusion and transport are theoretically derived by the analyses of the Langevin dynamics.

A study of nonstationary processes that are integrals of stationary random sequences of delta pulses is presented. An integrated renewal process can be represented as the sum of a deterministic linear function of time and a Wiener process of the corresponding intensity. This intensity is determined by the mean value and variance of the waiting times of the pulse process and is greater for super-Poisson processes than for sub-Poisson ones. Linear growth over time of all cumulants is proved. An integrated random process with fixed time intervals can be replaced by the sum of a deterministic linear function and a random process with bounded variance. The analytical results are in good agreement with the numerical ones.

We present numerical and experimental results for the generation of aperiodic motion in coupled active rotators. The numerical analysis is presented for two point particles constrained to move on a unit circle under the Yukawa-like interaction. Simulations exhibit that the collision among the rotors results in chaotic motion of the rotating point particles. Furthermore, the numerical model predicts a route to chaotic motion. Subsequently, we explore the effect of separation between the rotors on their chaotic dynamics. The numerically calculated fraction of initial conditions which led to chaotic motion shed light on the observed effects. We reproduce a subset of the numerical observations with two self-propelled ribbons rotating at the air-water interface. A pinned camphor rotor moves at the interface due to the Marangoni forces generated by surface tension imbalance around it. The camphor layer present at the common water surface acts as chemical coupling between two ribbons. The separation distance of ribbons ($L$) determines the nature of coupled dynamics. Below a critical distance ($L_T$), rotors can potentially, by virtue of collisions, exhibit aperiodic oscillations characterized via a mixture of co- and counterrotating oscillations. These aperiodic dynamics qualitatively matched the chaotic motion observed in the numerical model.

The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics extended to one-dimensional Hamiltonian systems, $\mathcal{H}(x,k)$ constrained by the ${\partial }^2\mathcal{H}/\partial x\partial k=0$ condition. Supported by the Heisenberg-Weyl noncommutative algebra, where $[x,k]=i$, the canonical variables $x$ and $k$ are interpreted in terms of the LV variables, $y=e^{-x}$ and $z=e^{-k}$, eventually associated with the number of individuals in a closed competitive dynamics: the so-called prey-predator system. The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales and for quantifying quantum analog effects. Through the results from the associated Wigner currents, (non-)Liouvillian and stationary properties are described for thermodynamic and Gaussian quantum ensembles in order to account for the corrections due to quantum features over the classical phase-space pattern yielded by the Hamiltonian description of the LV dynamics. In particular, for Gaussian statistical ensembles, the Wigner flow framework provides the exact profile for the quantum modifications over the classical LV phase-space trajectories so that Gaussian quantum ensembles can be interpreted as an adequate Hilbert space state configuration for comparing quantum and classical regimes. The generality of the framework developed here extends the boundaries of the understanding of quantumlike effects on competitive microscopical biosystems.

The shear misfit model for highly viscous flow is based upon a theoretical prediction for its terminal stage in terms of irreversible Eshelby relaxations in five-dimensional shear space. The model is shown to predict a small $\delta$-function (Debye peak) in the dielectric spectrum, in agreement with experimental evidence. It is extended to density fluctuations, and a relation between adiabatic and isothermal compressibility jumps at the glass transition is derived. The model is applied to high-precision measurements of the shear, dielectric, and bulk relaxation data in two vacuum pump oils and in squalane, a short chain polymer with a strong secondary relaxation peak. The terminal stage of aging data in squalane demonstrates that the adiabatic density fluctuations contribute a fast component to the thermal expansion, explaining why the thermal expansion seems to equilibrate a bit faster than the dynamic heat capacity.

High-fidelity large-eddy simulation (LES) is performed of Rayleigh-Taylor (RT) mixing in three different configurations involving gravity reversal. In each configuration, LES results are compared with one-dimensional Reynolds-averaged Navier-Stokes (RANS) results, and a deficiency in a commonly used transport equation for the mass-flux velocity, $a_j$, is identified. In the first configuration, a classical two-component RT mixing layer is allowed to develop before it is subjected to rapid acceleration reversal. In the second configuration, a three-component RT mixing layer with an intermediate density layer is allowed to develop before being subjected to rapid acceleration reversal. Finally, in the third configuration, a light layer is interposed between two heavy layers; in this configuration, only one interface is RT-unstable at a time as it undergoes rapid acceleration reversal. In all cases, a commonly used buoyancy production closure in the $a_j$ transport equation is shown to lead to significant over-prediction of mixing layer growth after gravity reversal. An alternative formulation for this closure is then presented which is shown to more accurately capture the stabilization effect of gravity reversal.

We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or fragments, and subsampling each fragment (i.e., performing side walks) while freezing the environment. No bias is introduced and a zero-variance principle holds in the limit of separability, i.e., when the fragments are independent. In practice, the usual bottleneck of Monte Carlo calculations—the scaling of the statistical fluctuations as a function of the number of particles $N$—is relieved for extensive observables. We illustrate the method in variational Monte Carlo on the two-dimensional Hubbard model and on metallic hydrogen chains using Jastrow-Slater wave functions. A factor $\mathcal{O}\left(N\right)$ is gained in numerical efficiency.

In this Letter we investigate the concept of quantum work and its measurability from the viewpoint of quantum measurement theory. Very often, quantum work and fluctuation theorems are discussed in the framework of projective two-point measurement (TPM) schemes. According to a well-known no-go theorem, there is no work observable which satisfies both (i) an average work condition and (ii) the TPM statistics for diagonal input states. Such projective measurements represent a restrictive class among all possible measurements. It is desirable, both from a theoretical and experimental point of view, to extend the scheme to the general case including suitably designed unsharp measurements. This shifts the focus to the question of what information about work and its fluctuations one is able to extract from such generalized measurements. We show that the no-go theorem no longer holds if the observables in a TPM scheme are jointly measurable for any intermediate unitary evolution. We explicitly construct a model with unsharp energy measurements and derive bounds for the visibility that ensure joint measurability. In such an unsharp scenario a single work measurement apparatus can be constructed that allows us to determine the correct average work and to obtain free energy differences with the help of a Jarzynski equality.

We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, $J_2$ and $J_3$, respectively, in the presence of a magnetic field $h$ appropriately tuned. We find that when the pair interaction $J_2<0$ dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction $J_3$ dominates, the boundaries between the two cases being at $J_3=\pm J_2$. The exact ground-state crossover lines between the two distinct types of disorder remain identifiable crossover curves at finite temperatures. In the frustrated domain, the ground state of the three-parameter model is identical to the ground state of the prototype one-parameter ($J_2<0$) model of geometrical frustration. Towards further understanding the frustration domain of the three-parameter model, a closed-form approximation (exact at zero temperature) determines solutions on a two-parameter subspace for induced magnetization and parallel magnetic susceptibility at finite fields $h$ and temperatures $T$, the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact $T=0$ threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction $J_3$.

We study the steady states and the coarsening dynamics in a one-dimensional driven nonconserved system modeled by the so-called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In particular, we derive equations of motion for the phase boundaries in a phase ordering system obeying this equation using a nearest-neighbor interaction approach. Using the equations of motion we explore kink binary and ternary interactions and analyze how the average domain size scale with respect to time. Further, we employ numerical techniques to perform a bifurcation analysis of the one-period stationary solutions of the equation. We then investigate the linear stability of the two-period solutions and thereby identify and study various coarsening modes.