Large-eddy simulation of a temporally evolving Kelvin-Helmholtz (KH) mixing layer is performed with the tenth-order compact difference code miranda to examine the steady-state behavior of a passive scalar in a shear-driven mixing layer. It is shown that the integral behavior of scalar variance in a KH mixing layer behaves similarly to the integral behavior of scalar variance in a Rayleigh-Taylor (RT) mixing layer, and mixedness of the simulated KH shear layer tends towards a value of about 0.8. It is further shown that if the $k\text{−}L\text{−}a\text{−}V$ Reynolds-averaged Navier-Stokes (RANS) model [B. E. Morgan et al., Phys. Rev. E 98, 033111 (2018)], calibrated to reproduce steady-state mixing in an RT layer, is applied to simulate a KH mixing layer, the RANS model will significantly overpredict the magnitude of scalar variance in the KH layer. A straightforward addition to the $k\text{−}L\text{−}a\text{−}V$ model is then suggested, and self-similarity analysis is applied to determine constraints on model coefficients. It is shown that with the addition of a buoyancy production term in the model equation for scalar variance, it becomes possible to eliminate the model deficiency and match steady-state mixedness in simulations of both RT and KH mixing layers with a single model calibration.

Interfacial fluid mixing induced by successive waves, such as shock, rarefaction, and compression waves, plays a fundamental role in engineering applications, e.g., inertial confinement fusion, and in natural phenomena, e.g., supernova explosion. These waves bring nonuniform, unsteady external forces into the mixing zone, which leads to a complex mixing process. The growth rate of the mixing width is analyzed by decomposing the turbulent flow field into the averaged field and the fluctuating counterpart. The growth rate is thus divided into three parts: (i) the stretching or compression (S(C)) effect induced by the averaged-velocity difference between two ends of the mixing zone, (ii) the penetration effect induced by the fluctuations which represent the penetration of the two species into each other, and (iii) the diffusive effect, which is induced by the molecular diffusion and is negligible in high-Reynolds-number flows at Schmidt number of order unity. The penetration effect is further divided into the Richtmyer-Meshkov (RM) effect, which is induced by fluctuations that were deposited by earlier wave interactions, and the Rayleigh-Taylor (RT) effect, which is caused by the fluctuations that arise in an overall acceleration of the mixing zone. During the passage of the rarefaction waves, the mixing zone is stretched, while during the passage of the compression waves or shock waves, the mixing zone is compressed. To illustrate these effects, a physical model of RM mixing with reshock is used. By combining the S(C), RM, and RT effects, the entire evolution of mixing width is restructured, which agrees well with numerical simulations for problems with a wide range of density ratios.

Recent experiments have shown that self-propelled millimetric walking droplets bouncing on a vibrating liquid surface exhibit phenomena, such as interference or tunneling, that so far were thought to be possible only in the microscopic realm. Here we present calculations showing that the surface wave satisfies, in the long-memory limit, a Bohr-Sommerfeld quantization-like relation. This strongly suggest the possibility of a novel fundamental type of quantization in these experiments, which can simultaneously explain their emulation of the quantum behavior and, more importantly, shed light into some of the interpretational difficulties of the standard quantum theory.

A vector order parameter phase field model derived from a grand potential functional is presented as an alternative approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit. In addition, it is shown that grain boundary energy and solute back-diffusion are quantitatively consistent with earlier theoretical work, with grain boundary energy being controlled through a simple solid-solid interaction parameter. Moreover, when considering polycrystalline aggregates and their coarsening, we show that the kinetics follow the expected parabolic growth law. Finally, we demonstrate how this vector order parameter model can be used to describe nucleation in polycrystalline systems via thermal fluctuations of the vector order parameter, a process that cannot be treated consistently with multiphase or multi-order-parameter based phase field models. The presented vector order parameter model serves as a practical and efficient computational tool for simulating polycrystalline materials. We also discuss the extension of the order parameter to higher dimensions as a simple method for modeling multiple solid phases.

Increasingly important photomechanical materials produce stress and mechanical work when illuminated. We propose experimentally accessible performance metrics for photostress and photowork, enabling comparison of materials performance. We relate these metrics to material properties, providing a framework for the design and optimization of photomechanical materials.

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has recently achieved success in detecting structural transitions in material science, such as the glass-liquid transition. However, data obtained from physical states may not have explicit shapes as structural materials. We thus propose a general framework, termed “topological persistence machine,” to construct the shape of data from correlations in states, so that we can subsequently decipher phase transitions via qualitative changes in the shape. Our framework enables an effective and unified approach in phase transition analysis. We demonstrate the efficacy of the approach in detecting the Berezinskii-Kosterlitz-Thouless phase transition in the classical XY model and quantum phase transitions in the transverse Ising and Bose-Hubbard models. Interestingly, while these phase transitions have proven to be notoriously difficult to analyze using traditional methods, they can be characterized through our framework without requiring prior knowledge of the phases. Our approach is thus expected to be widely applicable and will provide practical insights for exploring the phases of experimental physical systems.

We propose a procedure to implement Dirichlet velocity boundary conditions for complex shapes that use data from a single node only, in the context of the lattice Boltzmann method. Two ideas are at the base of this approach. The first is to generalize the geometrical description of boundary conditions combining bounce-back rule with interpolations. The second is to enhance them by limiting the interpolation extension to the proximity of the boundary. Despite its local nature, the resulting method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well-established Bouzidi's scheme for curved walls [M. Bouzidi, M. Firdaouss, and P. Lallemand, Phys. Fluids 13, 3452 (2001)]. Among the infinite number of possibilities, we identify several meaningful variants of the method, discerned by their approximation of the second-order nonequilibrium terms and their interpolation coefficients. For each one, we provide two parametrized versions that produce viscosity independent accuracy at steady state. The method proves to be suitable to simulate moving rigid objects or surfaces moving following either the rigid body dynamics or a prescribed kinematic. Also, it applies uniformly and without modifications in the whole domain for any shape, including corners, narrow gaps, or any other singular geometry.

The study of hyperuniform states of matter is an emerging multidisciplinary field, impinging on topics in the physical sciences, mathematics, and biology. The focus of this work is the exploration of quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes as well as the crossover point between them in terms of the “volume” coefficient $A$ and “surface-area” coefficient $B$ associated with the local number variance ${\sigma }^2\left(R\right)$ for a spherical window of radius $R$. The larger the ratio $B/A$, the larger the hyperuniform scaling regime, which becomes of infinite extent in the limit $B/A\to \infty$. To complement the known direct-space representation of the coefficient $B$ in terms of the total correlation function $h\left(\mathbf{r}\right)$, we derive its corresponding Fourier representation in terms of the structure factor $S\left(\mathbf{k}\right)$, which is especially useful when scattering information is available experimentally or theoretically. We also demonstrate that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio $B/A$, as well as other diagnostic measures of hyperuniformity, including the hyperuniformity index $H$ and the direct-correlation function length scale ${\xi }_c$, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. Specifically, we analyze equilibrium systems of hard rods and “sticky” hard-sphere systems in arbitrary space dimension $d$ as a function of density. We also examine low-temperature excited states of many-particle systems interacting with “stealthy” long-ranged pair interactions as the temperature tends to zero, where the ground states are disordered, hyperuniform, and infinitely degenerate. We demonstrate that our various diagnostic hyperuniformity measures are positively correlated with one another. The same diagnostic measures can be used to detect the degree to which imperfections in nearly hyperuniform systems cause deviations from perfect hyperuniformity. Moreover, the capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally or computationally generated samples that are necessarily of finite size.

Biological and synthetic microswimmers display a wide range of swimming trajectories depending on driving forces and torques. In this paper we consider a simple overdamped model of self-propelled particles with a constant self-propulsion speed but an angular velocity that varies in time. Specifically, we consider the case of both deterministic and stochastic angular velocity reversals, mimicking several synthetic active matter systems, such as propelled droplets. The orientational correlation function and effective diffusivity is studied using Langevin dynamics simulations and perturbative methods.

The lattice-Boltzmann method is convenient for simulating flow fields in porous media. However, due to its lattice characteristics, the velocity near a solid surface is not accurate, which results in significant errors when simulating colloid transport in porous media. Based on the general properties of a flow field close to a solid surface, we propose an alternative velocity interpolation method in which the velocity at a solid surface is strictly zero. Numerical simulation results show that the proposed method can give more accurate results than the usual bilinear interpolation. In addition, we use this method to simulate the contact efficiency of colloids in porous media and obtain a new power-law form of the contact efficiency.

Destruction of the quantum mechanical features of matter by decoherence restricts the applicability of quantum technologies. The limited information of the quantum features (such as coherence) in the basis-dependent observations urges the use of a basis-independent quantity for a better understanding. In this context, the state purity of a quantum system (composed of quantized pigments immersed in a noisy protein environment) is studied with a numerically exact hierarchical equations of motion approach over the wide range of the parameter domain (with the main focus on the nonzero-energy gradient). It is noted that the state purity does not necessarily reflect any significant information about the persistence of quantum features (in the dissipative environment), even when the quantum coherence survives at the steady state in both the localized and the eigenstate basis.

We consider absorption refrigerators consisting of simultaneously operating Carnot-type heat engine and refrigerator. Their maximum efficiency at given power (MEGP) is given by the product of MEGPs for the internal engine and refrigerator. The only subtlety of the derivation lies in the fact that the maximum cooling power of the absorption refrigerator is not limited just by the maximum power of the internal refrigerator, but, due to the first law, also by that of the internal engine. As a specific example, we consider the simultaneous absorption refrigerators composed of low-dissipation (LD) heat engines and refrigerators, for which the expressions for MEGPs are known. The derived expression for maximum efficiency implies bounds on the MEGP of LD absorption refrigerators. It also implies that a slight decrease in power of the absorption refrigerator from its maximum value results in a large nonlinear increase in efficiency, observed in heat engines, whenever the ratio of maximum powers of the internal engine and the refrigerator does not diverge. Otherwise, the increase in efficiency is linear as observed in LD refrigerators. Thus, in all practical situations, the efficiency of LD absorption refrigerators significantly increases when their cooling power is slightly decreased from its maximum.

Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this topic is far from being understood. There is no unique way to measure localization, and individual measures can reflect different aspects of the same quantum state. Here we present a general scheme to define localization in measure spaces, which is based on what we call Rényi occupations, from which any measure of localization can be derived. We apply this scheme to the four-dimensional unbounded phase space of the interacting spin-boson Dicke model. In particular, we make a detailed comparison of two localization measures based on the Husimi function in the regime where the model is chaotic, namely, one that projects the Husimi function over the finite phase space of the spin and another that uses the Husimi function defined over classical energy shells. We elucidate the origin of their differences, showing that in unbounded spaces the definition of maximal delocalization requires a bounded reference subspace, with different selections leading to contextual answers.

The flexibility and the extension along the direction of the force are shown to be related to the bubble number fluctuation and the average number of bubbles, respectively, when the strands of the DNA are subjected to a force along the same direction, here called a stretching force. The force-temperature phase diagram shows the existence of a tricritical point, where the first-order force-induced zipping transition becomes continuous. On the other hand, when the forces are being applied in opposite directions, here called an unzipping force, the transition remains first order, with the possibility of vanishing of the low-temperature reentrant phase for a semiflexible DNA. Moreover, we found that the bulk elasticity changes only if an external force penetrates the bound phase and affects the bubble states.

Recurrent neural networks are machine learning algorithms that are well suited to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-Bénard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations to obtain training and test data for the algorithm. Both sets are preprocessed by a proper orthogonal decomposition (POD) using the snapshot method to reduce the amount of data. Training data comprise long time series of the first 150 most energetic POD coefficients. The reservoir is subsequently fed by these data and predicts future flow states. The predictions are thoroughly validated by original simulations. Our results show good agreement of the low-order statistics. This incorporates also derived statistical moments such as the cloud cover close to the top of the convection layer and the flux of liquid water across the domain. We conclude that our model is capable of learning complex dynamics which is introduced here by the tight interaction of turbulence with the nonlinear thermodynamics of phase changes between vapor and liquid water. Our work opens new ways for the dynamic parametrization of subgrid-scale transport in larger-scale circulation models.

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this Letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.

Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting step by introducing a random resetting amplitude such that the diffusing particle may be only partially reset towards the trajectory origin or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) and population dynamics or financial markets, as well as generic search processes.

Centrality, which quantifies the “importance” of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given purpose and network. Here we identify two categories of centrality parameters. Reach parameters control the attenuation of influence flows between distant nodes. Grasp parameters control the centrality's tendency to send influence flows along multiple, often nongeodesic paths. Combining these categories with Borgatti's centrality types [Borgatti, Soc. Networks 27, 55 (2005)], we arrive at a classification system for parametrized centralities. Using this classification, we identify the notable absence of any centrality measures that are radial, reach parametrized, and based on acyclic, conserved flows of influence. We therefore introduce the ground-current centrality, which is a measure of precisely this type. Because of its unique position in the taxonomy, the ground-current centrality differs significantly from similar centralities. We demonstrate that, compared to other conserved-flow centralities, it has a simpler mathematical description. Compared to other reach-parametrized centralities, it robustly preserves an intuitive rank ordering across a wide range of network architectures, capturing aspects of both the closeness and betweenness centralities. We also show that it produces a consistent distribution of centrality values among the nodes, neither trivially equally spread (delocalization) nor overly focused on a few nodes (localization). Other reach-parametrized centralities exhibit both of these behaviors on regular networks and hub networks, respectively. We compare the properties of the ground-current centrality with several other reach-parametrized centralities on four artificial networks and seven real-world networks.