Based on the nonequilibrium evolution thermodynamics, the structure refinement of metals during severe plastic deformation is investigated. To describe the formation of stationary (limiting) submicrocrystalline or nanocrystalline structures, a two-defect approximation, including the grain boundaries and dislocations, is used. Introduction of the additive noise for the main parameters into the governing equations allowed us to describe the self-consistent behavior of structural defects during the stationary structure formation. Conditions of achieving the stationary state are investigated and possible scenarios of structure refinement modes are determined. Obtained grain boundary density distributions help to estimate the composition of grain structure in the bulk of metal sample quantitatively. The analysis of time evolution of the grain boundaries density shows the presence of correlated fluctuations. The autocorrelation function, describing the frequency characteristics of the structure refinement, is determined.

We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of the depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction ${\mu }_e$ encountered over six orders of magnitude of speeds. While a constant ${\mu }_e$ is found when the grain size, rod depth, and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze ${\mu }_e$ in terms of the inertial number $I$ and viscous number $J$ to understand the relative importance of inertia and viscous forces, respectively. For sufficiently high fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function ${\mu }_e={\mu }_o+k{J}^n$, where ${\mu }_o$ is the effective friction measured in the quasistatic limit, and $k$ and $n$ are material constants. The drag is then analyzed in terms of the effective viscosity ${\eta }_e$ and found to decrease systematically as a function of $J$. We further show that ${\eta }_e$ as a function of $J$ is directly proportional to the fluid viscosity and the ${\mu }_e$ encountered by the rod.

Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal $2\times 2$, $4\times 4$, and $6\times 6$ streaming-roll pattern in a shallow square cavity. We find that the high-frequency $6\times 6$ streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency $2\times 2$ streaming pattern, which is dominated by the boundary-driven streaming.

In this work, numerical simulations are performed to study the droplet response to the vertical vibration of the substrate, under various frequencies and amplitudes using the multiphase lattice Boltzmann method. First, the numerical results are validated against published experimental data. The effects of droplet size, surface wettability, amplitude, and frequency of the vibrating substrate on droplet detachment are studied. For high contact angles, regardless of the droplet size, when the vibration frequency matches the droplet resonance frequency the droplet is easily removed from the surface. For lower contact angles, the resonance frequency is higher and the detachment amplitude increases significantly. It was also found that viscous forces do not affect the resonance frequency, but have a noticeable impact on the detachment amplitude. The findings of this study can be useful in applications where droplet shedding is crucial, e.g., condensation heat transfer.

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.

The lattice Boltzmann method (LBM) facilitates efficient simulations of fluid turbulence based on advection and collision of local particle distribution functions. To ensure stable simulations on underresolved grids, the collision operator must prevent drastic deviations from local equilibrium. This can be achieved by various methods, such as the multirelaxation time, entropic, quasiequilibrium, regularized, and cumulant schemes. Complementing a part of a unified theoretical framework of these schemes, the present work presents a derivation of the regularized lattice Boltzmann method (RLBM), which follows a recently introduced entropic multirelaxation time LBM by Karlin, Bösch, and Chikatamarla (KBC). It is shown that both methods can be derived by locally maximizing a quadratic Taylor expansion of the entropy function. While KBC expands around the local equilibrium distribution, the RLBM is recovered by expanding entropy around a global equilibrium. Numerical tests were performed to elucidate the role of pseudoentropy maximization in these models. Simulations of a two-dimensional shear layer show that the RLBM successfully reproduces the largest eddies even on a $16\times 16$ grid, while the conventional LBM becomes unstable for grid resolutions of $128\times 128$ and lower. The RLBM suppresses spurious vortices more effectively than KBC. In contrast, simulations of the three-dimensional Taylor-Green and Kida vortices show that KBC performs better in resolving small scale vortices, outperforming the RLBM by a factor of 1.8 in terms of the effective Reynolds number.

The totally asymmetric simple exclusion process was originally introduced as a model for the trafficlike collective movement of ribosomes on a messenger RNA (mRNA) that serves as the track for the motorlike forward stepping of individual ribosomes. In each step, a ribosome elongates a protein by a single unit using the track also as a template for protein synthesis. But, prefabricated functionally competent ribosomes are not available to begin synthesis of protein; a subunit directionally scans the mRNA in search of the predesignated site where it is supposed to bind with the other subunit and begin the synthesis of the corresponding protein. However, because of “leaky” scanning, a fraction of the scanning subunits miss the target site and continue their search beyond the first target. Sometimes such scanners successfully identify the site that marks the site for initiation of the synthesis of a different protein. In this paper, we develop an exclusion model with three interconvertible species of hard rods to capture some of the key features of these biological phenomena and study the effects of the interference of the flow of the different species of rods on the same lattice. More specifically, we identify the mean time for the initiation of protein synthesis as appropriate mean first-passage time that we calculate analytically using the formalism of backward master equations. Despite the approximations made, our analytical predictions are in reasonably good agreement with the numerical data that we obtain by performing Monte Carlo simulations.

We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.

We study a variant of the voter model with multiple opinions; individuals can imitate each other and also change their opinion randomly in mutation events. We focus on the case of a population with all-to-all interaction. A noise-driven transition between regimes with multimodal and unimodal stationary distributions is observed. In the former, the population is mostly in consensus states; in the latter, opinions are mixed. We derive an effective death-birth process, describing the dynamics from the perspective of one of the opinions and use it to analytically compute marginals of the stationary distribution. These calculations are exact for models with homogeneous imitation and mutation rates and an approximation if rates are heterogeneous. Our approach can be used to characterize the noise-driven transition and to obtain mean switching times between consensus states.

Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good estimators provably do not exist. We focus on the estimator introduced by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)] based on the statistics of distances between neighboring data points, which empirically works for a wide class of underlying probability distributions. First, we illustrate pitfalls of naively applying bootstrapping to estimate the variance of the mutual information estimate. Then we improve this estimator by (1) expanding its range of applicability and by providing (2) a self-consistent way of verifying the absence of bias, (3) a method for estimation of its variance, and (4) guidelines for choosing the values of the free parameter of the estimator. We demonstrate the performance of our estimator on synthetic data sets, as well as on neurophysiological and systems biology data sets.

How cells regulate the number of organelles is a fundamental question in cell biology. While decades of experimental work have uncovered four fundamental processes that regulate organelle biogenesis, namely, de novo synthesis, fission, fusion, and decay, a comprehensive understanding of how these processes together control organelle abundance remains elusive. Recent fluorescence microscopy experiments allow for the counting of organelles at the single-cell level. These measurements provide information about the cell-to-cell variability in organelle abundance in addition to the mean level. Motivated by such measurements, we build upon a recent study and analyze a general stochastic model of organelle biogenesis. We compute the exact analytical expressions for the probability distribution of organelle numbers, their mean, and variance across a population of single cells. It is shown that different mechanisms of organelle biogenesis lead to distinct signatures in the distribution of organelle numbers which allow us to discriminate between these various mechanisms. By comparing our theory against published data for peroxisome abundance measurements in yeast, we show that a widely believed model of peroxisome biogenesis that involves de novo synthesis, fission, and decay is inadequate in explaining the data. Also, our theory predicts bimodality in certain limits of the model. Overall, the framework developed here can be harnessed to gain mechanistic insights into the process of organelle biogenesis.

Active Ornstein-Uhlenbeck particles (AOUPs) are overdamped particles in an interaction potential subject to external Ornstein-Uhlenbeck noises. They can be transformed into a system of underdamped particles under additional velocity dependent forces and subject to white noise forces. There has been some discussion in the literature on whether AOUPs can be in equilibrium for particular interaction potentials and how far from equilibrium they are in the limit of small persistence time. By using a theorem on the time reversed form of the AOUP Langevin-Ito equations, I prove that they have an equilibrium probability density invariant under time reversal if and only if their smooth interaction potential has zero third derivatives. In the limit of small persistence Ornstein-Uhlenbeck time $\tau$, a Chapman-Enskog expansion of the Fokker-Planck equation shows that the probability density has a local equilibrium solution in the particle momenta modulated by a reduced probability density that varies slowly with the position. The reduced probability density satisfies a continuity equation in which the probability current has an asymptotic expansion in powers of $\tau$. Keeping up to $O\left(\tau \right)$ terms, this equation is a diffusion equation, which has an equilibrium stationary solution with zero current. However, $O\left({\tau }^2\right)$ terms contain fifth- and sixth-order spatial derivatives and the continuity equation no longer has a zero current stationary solution. The expansion of the overall stationary solution now contains odd terms in the momenta, which clearly shows that it is not an equilibrium.

Colloidal particles are essential materials for modern inkjet printing and coating. Here we demonstrate a versatile method to achieve hexagonal deposits of colloidal particles through droplet evaporation on hexagonal micropillar arrays. We identify how colloidal fluids turn into hexagonal deposits during evaporation with x-ray tomography. Interestingly, evaporation-driven hexagonal deposits are quite crack-free uniform. We attribute hexagonal deposit shape control to local contact line pinning by colloidal particles and geometric constraints by micropillar arrays. This deposition strategy offers a feasibility for high-quality evaporation-driven crack-free uniform polygonal deposits of colloidal particles for diverse applications.

We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free energy, in the thermodynamic limit, follows from its semiclassical limit. Analysis of singularities of the equations of state reveals the occurrence of phase transitions of nematic type at not zero external fields and allows for an interpretation of the phase transitions in terms of shock dynamics in the space of thermodynamic variables. The approach is shown at work in the case of a $q$-state model for $q=3$ but the method generalizes to arbitrary $q$. Critical asymptotics of magnetization, susceptibility, specific heat and relative critical exponents $\beta ,\gamma$, and $\alpha$ are also provided.

We study a finite spin-$\frac{1}{2}$ Ising chain with a spatially alternating transverse field of period 2. By means of a Jordan-Wigner transformation for even and odd sites, we are able to map it into a one-dimensional model of free fermions. We determine the ground-state energies in the positive- and negative-parity subspaces (subspaces with an even or odd total number of down spins, respectively) and compare them in order to establish the ground-state energy for the entire Hamiltonian. We derive closed-form expressions for this energy gap between the different parity subspaces and analyze its behavior and dependence on the system size in the various regimes of the applied field. Finally, we suggest an expression for the correlation length of such a model that is consistent with the various values found in the literature for its behavior in the vicinity of critical points.

Integrable quantum many-body systems are considered to equilibrate to generalized Gibbs ensembles (GGEs) characterized by the expectation values of integrals of motion. We study the dynamics of exactly solvable quadratic bosonic systems in the thermodynamic limit, and show a general mechanism for the relaxation to GGEs, in terms of the diagonal singularity. We show analytically and explicitly that a free bosonic system relaxes from a general (not necessarily Gaussian) initial state under certain physical conditions to a Gaussian GGE. We also show the relaxation to a Gaussian GGE in an exactly solvable coupled system, a harmonic oscillator linearly interacting with bosonic reservoirs.

Various systems in the real world can be nonlinear and stochastic, but because nonlinear time series analysis has been developed to distinguish nonlinear deterministic systems from linear stochastic systems, there have been no appropriate methods developed so far for testing the nonlinear stochasticity for a given system. Thus, here we propose a set of two hypothesis tests, one for the nonlinearity and one for the stochasticity, independent of each other. The test for the linearity is based on Fourier-transform-based surrogate data with a nonlinear test statistic, while the test for determinism depends on the theory of ordinal patterns or permutations recently developed intensively. We demonstrate the proposed set of tests with time series generated from toy models. In addition, we show that both a foreign exchange market and a temperature series in Tokyo could be nonlinear and stochastic, as well as sometimes with determinism beyond pseudoperiodicity.

We present a method based on a Lagrangian descriptor for revealing the high-dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include a normally hyperbolic invariant manifold and its stable and unstable manifolds, which act as codimension-1 barriers to phase space transport. In this article, finding the invariant manifolds in high-dimensional phase space will constitute identifying coordinates on these invariant manifolds. The method of Lagrangian descriptor is demonstrated by applying to classical two and three degrees of freedom Hamiltonian systems which have implications for myriad applications in chemistry, engineering, and physics.

Metapopulation epidemic models describe epidemic dynamics in networks of spatially distant patches connected via pathways for migration of individuals. In the present study, we deal with a susceptible-infected-recovered (SIR) metapopulation model where the epidemic process in each patch is represented by an SIR model and the mobility of individuals is assumed to be a homogeneous diffusion. We consider two types of patches including high-risk and low-risk ones under the assumption that a local patch is changed from a high-risk one to a low-risk one by an intervention. We theoretically analyze the intervention threshold which indicates the critical fraction of low-risk patches for preventing a global epidemic outbreak. We show that an intervention targeted to high-degree patches is more effective for epidemic control than a random intervention. The theoretical results are validated by Monte Carlo simulations for synthetic and realistic scale-free patch networks. The theoretical results also reveal that the intervention threshold depends on the human mobility network and the mobility rate. Our approach is useful for exploring better local interventions aimed at containment of epidemics.