We report on incoherent quasielastic neutron scattering measurements examining a self-diffusion process in two types of glass-forming liquids, namely a molecular liquid (3-methylpentane) and an ionic liquid [1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide]. We have experimentally demonstrated that both liquids exhibit two crossovers in the momentum transfer ($Q$) dependence of the self-correlation function, which is basically described by the stretched exponential function, $exp[-{(t/\tau )}^{\beta }]$. The first crossover point ($Q\approx 0.2{\AA }^{-1}$) corresponds to a crossover from Fickian ($\beta =1$) to non-Fickian ($\beta \ne 1$) diffusion attributed to dynamical correlation. On the other hand, the second one at $Q\approx 0.8{\AA }^{-1}$ is associated with the crossover from Gaussian to non-Gaussian behavior. It is remarkable that the stretching exponent $\beta$ gradually changes in between the two crossover points. We consider that the two crossovers are the universal feature for glass-forming liquids.

Previously we reported on the stable (i.e., minimal enthalpy) structures of soft monodisperse spheres in a long cylindrical channel. Here we present further simulations, which significantly extend the original phase diagram up to $D/d=2.714$ (ratio of cylinder and sphere diameters), where the nature of densest sphere packing changes. However, macroscopic systems of this kind are not confined to the ideal equilibrium states of this diagram. Consequently, we explore some of the structural transitions to be expected as experimental conditions are varied; these are in general hysteretic. We represent these transitions in a stability diagram for a representative case. Illustrative videos are included in the Supplemental Material.

When a classical fluctuating system in contact with a thermal bath undergoes a driven transformation in a finite time, a nonequilibrium distribution is created and an amount of energy is inevitably dissipated on average. It is known that the average dissipation and the extent of the out-of-equilibrium are mutually bounded. Here we elaborate the perspective of exploiting such a constraint to check the admissibility of the nonequilibrium distributions at a given amount of average dissipation. Namely, we focus on cyclic transformations and derive an upper bound for the statistical polarization that may be present, after the cycle, over an a priori unbiased periodic degree of freedom of the system. The finding is then applied to establish the maximum polarization that can be induced on the velocity of massive moieties in many-body molecular systems in response to generic cyclic transformations.

The depinning transition of elastic interfaces with an elastic interaction kernel decaying as $1/r^{d+\sigma }$ is characterized by critical exponents which continuously vary with $\sigma$. These exponents are expected to be unique and universal, except in the fully coupled ($-d<\sigma \le 0$) limit, where they depend on the “smooth” or “cuspy” nature of the microscopic pinning potential. By accurately comparing the depinning transition for cuspy and smooth potentials in a specially devised depinning model, we explain such peculiar limits in terms of the vanishing of the critical region for smooth potentials, as we decrease $\sigma$ from the short-range ($\sigma \ge 2$) to the fully coupled case. Our results have practical implications for the determination of critical depinning exponents and identification of depinning universality classes in concrete experimental depinning systems with nonlocal elasticity, such as contact lines of liquids and fractures.

The constraint relation for efficiency and power is crucial for the design of optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation regime. Such a constraint is validated with an example of a Carnot-like engine. Its microscopic dynamics is governed by the master equation. Based on the master equation, we connect the microscopic coupling strengths to the generic parameters in the phenomenological model. We find the usual assumption of low-dissipation is achieved when the coupling to thermal environments is stronger than the driving speed. Additionally, such a connection allows the design of a practical cycle to optimize the engine performance.

In this study we introduce small perturbations in the forms of graded intersite stiffnesses and graded on-site potentials to a lattice composed of bistable unit cells under elastic interactions. Based on a known soliton solution in the $\varphi$-4 model, we use a perturbation approach to approximate the effects of the perturbations on the propagation speeds of transition waves. Numerical validations follow on the exact discrete equations of motion, from which we observe eventual stoppage of transition waves in the periodic lattice under physical damping, unidirectional propagation of the waves in the direction of softening properties, and boomerang-like reflection of the waves in the stiffening direction. Finally, we present three-dimensional-printed experimental lattices, confirming the theoretical and numerical results. The observed behaviors imply the extreme controllability of solitary waves through slight engineering manipulations in material-level structures. We further find that both kink (rarefaction) and antikink (compression) waves are allowed at any site in the lattice, extending the functionality of the lattice in engineering applications such as energy harvesting.

We describe imbibition in real and artificial plant seeds, using a combination of experiments and theory. In both systems, our experiments demonstrate that liquid permeates the substrate at a rate which decreases gradually over time. Tomographic imaging of soy seeds is used to confirmed this by observation of the permeating liquid using an iodine stain. To rationalize the experimental data, we propose a model based on capillary action which predicts the temporal evolution of the radius of the wet front and the seed mass. The depth of the wetting front initially evolves as $t^{1/2}$ in accord with the Lucas-Washburn law. At later times, when the sphere is almost completely filled, the front radius scales as ${(1-t/t_{\text{max}})}^{1/2}$ where $t_{\text{max}}$ is the time required to complete imbibition. The data obtained on both natural and artificial seeds collapse onto a single curve that agrees well with our model, suggesting that capillary phenomena contribute to moisture uptake in soy seeds.

We report experiments, modeling, and numerical simulations of the self–assembly of particle patterns obtained from a nanometric metallic square grid. Initially, nickel filaments of rectangular cross section are patterned on a ${\mathrm{SiO}}_2$ flat surface, and then they are melted by laser irradiation with $\sim 18$-ns pulses. During this time, the liquefied metal dewets the substrate, leading to a linear array of drops along each side of the squares. The experimental data provide a series of SEM images of the resultant morphology as a function of the number of laser pulses or cumulative liquid lifetime. These data are analyzed in terms of fluid mechanical models that account for mass conservation and consider flow evolution with the aim to predict the final number of drops resulting from each side of the square. The aspect ratio, $\delta$, between the square sides' lengths and their widths is an essential parameter of the problem. Our models allow us to predict the $\delta$ intervals within which a certain final number of drops are expected. The comparison with experimental data shows a good agreement with the model that explicitly considers the Stokes flow developed in the filaments neck region that lead to breakup points. Also, numerical simulations that solve the Navier-Stokes equations along with slip boundary condition at the contact lines are implemented to describe the dynamics of the problem.

We present a boundary condition scheme for the lattice Boltzmann method that has significantly improved stability for modeling turbulent flows while maintaining excellent parallel scalability. Simulations of a three-dimensional lid-driven cavity flow are found to be stable up to the unprecedented Reynolds number $\mathrm{Re}=5\times {10}^4$ for this setup. Excellent agreement with energy balance equations, computational and experimental results are shown. We quantify rises in the production of turbulence and turbulent drag, and determine peak locations of turbulent production.

The nonlinear response of molecular systems undergoing Markovian stochastic reorientations is calculated up to fifth order in the amplitude of the external field. Time-dependent perturbation theory is used to compute the relevant response functions as in earlier treatments [G. Diezemann, Phys. Rev. E 85, 051502 (2012); Phys. Rev. E 96, 022150 (2017)]. Here, we consider the reorientational motion of isolated molecules and extend the existing calculations for the model of isotropic rotational diffusion to the model of anisotropic rotational diffusion and to the model of rotational random jumps. Depending on the values of some model parameters, we observe a hump in the modulus of the nonlinear susceptibility for either of these models. Interestingly, for the model of rotational random jumps, the appearance of this hump depends on the way the coupling to the external field is modeled in the master equation approach. If the model of anisotropic rotational diffusion is considered, the orientation of the diffusion tensor relative to the molecular dipole moment and additionally the amount of anisotropy in the rotational diffusion constants determine the detailed shape of the nonlinear response. In this case, the height of the observed hump is found to increase with increasing “diffusional anisotropy.” We discuss our results in relation to the features observed experimentally in supercooled liquids.

Earthquake time series are widely used to characterize the main features of regional seismicity and to provide useful insights into earthquake dynamics. Properties such as intermittency and nonstationary clustering are common in earthquake time series, highlighting the complex nature of the earthquake generation process. In the present work we introduce a stochastic model with memory effects that reproduces the temporal scaling behavior observed in regional seismicity. For nonstationary earthquake activity, where the average seismic rate fluctuates, the solution of the stochastic model is the $q$-generalized gamma function that presents two power-law regimes for short and long waiting times, respectively, while for stationary activity it reduces to the standard gamma function. To validate the derived model, we study nonstationary earthquake time series from Southern California and Japan. The analysis shows that for various threshold magnitudes and spatial areas and after rescaling with the mean waiting time, the normalized probability density functions fall onto a unique curve, which is characterized by two power-law regimes for short and long waiting times, respectively, a scaling behavior that can exactly be recovered by the derived $q$-generalized gamma function. The results show the validity of the stochastic model and the derived scaling function, further signifying both short- and long-term clustering effects and memory in the evolution of seismicity.

We systematically study heat current $J$ that flows through a few one-dimensional nonlinear lattices, each of which consists of two identical segments that are coupled by a weak interface. Existing theoretical analyses expect that $J$ is generally proportional to the square of the interface strength when the temperature drop is fixed and small. However, we observe two completely different classes in our numerical simulations. One follows the original expectation. In the other class, however, $J$ follows a power-law decay with the strength and the detailed power exponent depends on the details of the lattices and the interface interaction. Further theoretical analyses reveal that in the former class the interface potential energy decays with the interface strength linearly, which is commonly observed. In the latter class, the interface potential energy approaches a constant that is independent of the interaction strength. The detailed power exponents are then well explained.

Random processes have attracted much attention due to their broad applications. Despite the many varieties of random processes, it is proposed that there can be universal properties, e.g., the cover-time distributions for noncompact random walks. In this work, we investigate experimentally the cover-time distribution in random processes of granular gases. In particular, the trajectory of a tracer particle in the granular gases is read out by a high-speed camera, which forms a random process that is specific to granular gas systems. Analysis of the covering process of this trajectory is then carried out to get the cover-time distribution. The direct results of cover-time distribution deviates from the universal law, which can be attributed to two main factors: the attracting effect at the boundary and the nonperiodic boundary condition due to the fixed boundaries. By efficiently removing these effects step by step, the cover-time distribution recovers to the universal law approximately, which also reveals that the attracting effect at the boundary is the most dominant factor leading to the discrepancy. We have carried out three distinct experiments with different granular gas circumstances, and all agreed well with the universal distribution after removing the boundary effects.

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy of a minimal ecosystem on a lattice in which two species struggle for survival. The method quantitatively reproduces the scale-free law of the prey shoals size, where the simpler mean-field approach fails: the direct near-neighbor correlations are found to be the fundamental ingredient describing the system self-organized behavior. Furthermore, entropy allows the measurement of structural ordering we found to be a key ingredient in characterizing two different coexistence behaviors, one where predators form localized patches in a sea of preys and another where species display more complex patterns. The general nature of the introduced method paves the way for its application in many other systems of interest.

We investigate structural and dynamical properties of a self-propelled filament using coarse-grained Brownian dynamics simulations. A self-propulsion force is applied along the bond vectors, i.e., tangent to the filament and their locations are considered in two different manners. In case one, force is applied to all beads of the filament, which is termed as homogeneous self-propulsion. Here we obtain a monotonic decrease in the stiffness of the filament with Péclet number, hence, radius of gyration also displays the same trend. Moreover, the radius of gyration of the filament shows universal dependence for various bending rigidities with flexure number. The effective diffusivity of the filament shows enhancement with the active force, and it increases linearly with force, and bending rigidity. In case two, self-propulsion force is applied only to a few bond vectors. The location of active forces is chosen in a periodic manner starting from the tail of the filament and leaving the front end without force. In this case, the filament acquires various structures such as the rodlike, helical, circular, and folded states. The transition from several states is understood in terms of tangent-tangent correlation, bending energy, and torsional order parameter. The helical state is identified through a crossover from exponential to oscillatory behavior of the tangent-tangent correlation. A sudden increase in the bending energy separates a helical state to a folded state of the filament.

A major stumbling block for statistical physics and materials science has been the lack of a universal principle that allows us to understand and predict elementary structural, morphological, and dynamical properties of nonequilibrium amorphous states of matter. The recently developed nonequilibrium self-consistent generalized Langevin equation theory, however, has been shown to provide a fundamental tool for the understanding of the most essential features of the transformation of liquids into amorphous solids, such as their aging kinetics or their dependence on the protocol of fabrication. In this work we focus on the predicted kinetics of one of the main fingerprints of the formation of gels by arrested spinodal decomposition of suddenly and deeply quenched simple liquids, namely, the arrest of structural parameters associated with the morphological evolution from the initially uniform fluid, to the dynamically arrested spongelike amorphous material. The comparison of the theoretical predictions (based on a simple specific model system), with simulation and experimental data measured on similar but more complex materials, suggests the universality of the predicted scenario.

A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control strategies are mathematically involved and contain peculiar and counterintuitive features. We show that optimal driving protocols determined by means of linear-response theory exhibit the same step and $\delta$-peak-like structures that were previously found from solving the full optimal control problem. However, our method is significantly less involved, since only a minimum of a quadratic form has to be determined. In addition, our findings suggest that optimal protocols from linear-response theory are applicable far outside their actual range of validity.

In this paper, we present the construction of statistical models of gas-wall collision based on data issued from molecular dynamics (MD) simulations and use them to predict the velocity slip and temperature jump coefficients at the gas-solid interface. The Gaussian mixture (GM) model, an unsupervised learning technique, is chosen for this purpose. The model shares some similarities with the well-known Cercignani-Lampis model in kinetic theory but it is more robust due to the unlimited number of Gaussian functions used and the ability to deal with correlated data of high dimensions. Applications to real gas-wall systems (argon-gold and helium-gold) confirm the good performance of the model. The trained GM model predicts physical and statistical properties including accommodation, friction, and thermal conductance coefficients in excellent agreement with the MD model.

We study anomalous transport in a finite one-dimensional system with two conserved quantities in the presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two-point correlations in steady state as well as in the nonstationary state where the latter describe the relaxation to the steady state. In contrast to the Fourier heat equation in the diffusive case, here we show that the evolution of the temperature profile is governed by a nonlocal anomalous heat equation. We provide numerical verifications of our results.

An integrable nonlocal nonlinear Schrödinger (NLS) equation with clear physical motivations is proposed. This equation is obtained from a special reduction of the Manakov system, and it describes Manakov solutions whose two components are related by a parity symmetry. Since the Manakov system governs wave propagation in a wide variety of physical systems, our nonlocal equation has clear physical meanings. Solitons and multisolitons in this nonlocal equation are also investigated in the framework of Riemann-Hilbert formulations. Surprisingly, symmetry relations of discrete scattering data for this equation are found to be very complicated, where constraints between eigenvectors in the scattering data depend on the number and locations of the underlying discrete eigenvalues in a very complex manner. As a consequence, general $N$-solitons are difficult to obtain in the Riemann-Hilbert framework. However, one- and two-solitons are derived, and their dynamics investigated. It is found that two-solitons are generally not a nonlinear superposition of one-solitons, and they exhibit interesting dynamics such as meandering and sudden position shifts. As a generalization, other integrable and physically meaningful nonlocal equations are also proposed, which include NLS equations of reverse-time and reverse-space-time types as well as nonlocal Manakov equations of reverse-space, reverse-time, and reverse-space-time types.