Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008)], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the behavior of daughter droplets is significantly different in both branch channels. Also, it is found that the contact angle hysteresis is strengthened with decreasing the viscosity ratio, leading to an earlier droplet breakup and a decrease in the maximum length that the droplet can reach before the breakup. These simulation results manifest that the present multiphase LBM can be a useful substitute to Ba et al. [Phys. Rev. E 88, 043306 (2013)] for modeling the contact angle hysteresis, and it can be easily implemented with higher computational efficiency.

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.

It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property.

This paper is a report of the experimental evidence of suppression of vibrational higher-order harmonics in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies in the phenomenon of vibrational resonance when an optimal amount of white, Gaussian noise is applied. A quantitative characterization of the suppression is given on the basis of the coefficient of nonlinear distortions. The behavior of the coefficient of nonlinear distortions is studied in wide ranges of the added noise intensity, the dc current, and the amplitude of the harmonic signals. The experimental results are compared with a numerical simulation of a Langevin model showing good agreement.

We demonstrate the synthesis of sparse sampling and dimensionality reduction to characterize and model nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper orthogonal decomposition in order to expose the dominant low-rank coherent structures. Here, libraries of the nonlinear terms are also constructed in order to take advantage of the discrete empirical interpolation method and projection that allows for the approximation of nonlinear terms from a sparse number of grid points. The selected grid points are shown to be effective sensing and measurement locations for characterizing the underlying dynamics, stability, and bifurcations of nonlinear dynamical systems. The use of empirical interpolation points and sparse representation facilitates a family of local reduced-order models for each physical regime, rather than a higher-order global model, which has the benefit of physical interpretability of energy transfer between coherent structures. The method advocated also allows for orders-of-magnitude improvement in computational speed and memory requirements. To illustrate the method, the discrete interpolation points and nonlinear modal libraries are used for sparse representation in order to classify and reconstruct the dynamic bifurcation regimes in the complex Ginzburg-Landau equation. It is also shown that point measurements of the nonlinearity are more effective than linear measurements when sensor noise is present.

Two symmetrically coupled populations of $N$ oscillators with inertia $m$ display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite lifetimes diverging as a power law with $N$ and $m$. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.

We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of non-negative contributions from all the possible frustration-free loop configurations. We then compute the loop corrections using different approximations for the nonlocal loop interactions induced by the spin correlations in the tree graph. For distant loopy interactions, we can exploit the exponential decay of correlations in the tree interaction graph to compute loop corrections within an independent-loop approximation. Higher orders of the approximation are obtained by considering the correlations between the nearby loopy interactions involving larger number of spin variables. In particular, the sum over the loop configurations can be computed “exactly” by the belief propagation algorithm in the low orders of the approximation as long as the loopy interactions have a tree structure. These results might be useful in developing more accurate and convergent message-passing algorithms exploiting the structure of loopy interactions.

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of $V_o/(k_{B}T/e)$, where $V_o$ is the amplitude of the driving voltage and $k_{B}T/e$ is the thermal voltage with $k_B$ as Boltzmann's constant, $T$ as the temperature, and $e$ as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, $D/{\lambda }_{D}L$, where $D$ is the ion diffusivity, ${\lambda }_D$ is the Debye layer thickness, and $L$ is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is $O\left(V_o^3\right)$ which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in $V_o$. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing $V_o$. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

The microscopic structure and dynamics of an excess proton in water constrained in narrow graphene slabs between 0.7 and 3.1 nm wide has been studied by means of a series of molecular dynamics simulations. Interaction of water and carbon with the proton species was modeled using a multistate empirical valence bond Hamiltonian model. The analysis of the effects of confinement on proton solvation structure and on its dynamical properties has been considered for varying densities. The system is organized in one interfacial and a bulk-like region, both of variable size. In the widest interplate separations, the lone proton shows a marked tendency to place itself in the bulk phase of the system, due to the repulsive interaction with the carbon atoms. However, as the system is compressed and the proton is forced to move to the vicinity of graphene walls it moves closer to the interface, producing a neat enhancement of the local structure. We found a marked slowdown of proton transfer when the separation of the two graphene plates is reduced. In the case of lowest distances between graphene plates (0.7 and 0.9 nm), only one or two water layers persist and the two-dimensional character of water structure becomes evident. By means of spectroscopical analysis, we observed the persistence of Zundel and Eigen structures in all cases, although at low interplate separations a signature frequency band around 2500 ${\mathrm{cm}}^{-1}$ suffers a blue shift and moves to characteristic values of asymmetric hydronium ion vibrations, indicating some unstability of the typical Zundel-Eigen moieties and their eventual conversion to a single hydronium species solvated by water.

A molecular dynamics study on the collisional dynamics of soft and sticky single face-centered cubic crystal nanoparticles is presented. The softness and stickiness of the nanoparticles are controlled by varying parameters in the Lennard-Jones potential that is used to describe the interatomic interactions. Softening of nanoparticles due to extensive plastic deformations is observed as was previously found in hard nanoparticles. Further, two primary plastic deformation modes, slip and twinning, of the nanoparticles are found to play important roles in the temperature dependence of the coefficient of restitution. Additionally, we observe the effects of surface roughness, facets, and edges in the collisional behaviors of the sticky nanoparticles in low-velocity collisions. Nevertheless, the Johnson-Kendall-Roberts theory for macroscopic adhesive bodies still remains valid in nearly spherical nanoparticles.

Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.

The motions of a red blood cell in Poiseuille flows in a range of channel widths are simulated using a two-dimensional model. For a range of initial off-centerline distances in a 12-$\mu \mathrm{m}$ channel, cell trajectories converge to a specific off-centerline position and exhibit tank-treading motions. This behavior coexists with initial positions that lead to migration towards the centerline. The predicted off-centerline focusing effect is shown to depend on the curvature of the flow profile and on interactions with both solid boundaries.

The twist-bend nematic phase, $N_{\mathrm{TB}}$, may be viewed as a heliconical molecular arrangement in which the director $\mathbf{n}$ precesses uniformly about an extra director field, $\mathbf{t}$. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which $K_{22}>K_{33}$. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative $K_{33}$ in agreement with recent experimental data that yield $K_{33}>0$. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

We investigate the coupled dynamics of the local hydrodynamics and global electric response of an electrodialysis system, which consists of an electrolyte solution adjacent to a charge selective membrane under electric forcing. Under a dc electric current, counterions transport through the charged membrane while the passage of co-ions is restricted, thereby developing ion concentration polarization (ICP) or gradients. At sufficiently large currents, simultaneous measurements of voltage drop and flow field reveal several distinct dynamic regimes. Initially, the electrodialysis system displays a steady Ohmic voltage difference $(\mathrm{\Delta }{V}_{\text{ohm}})$, followed by a constant voltage jump $\left(\mathrm{\Delta }{V}_c\right)$. Immediately after this voltage increase, microvortices set in and grow both in size and speed with time. After this growth, the resultant voltage levels off around a fixed value. The average vortex size and speed stabilize as well, while the individual vortices become unsteady and dynamic. These quantitative results reveal that microvortices set in with an excess voltage drop (above $\mathrm{\Delta }{V}_{\text{ohm}}+\mathrm{\Delta }{V}_c$) and sustain an approximately constant electrical conductivity, destroying the initial ICP with significantly low viscous dissipation.

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

We consider the critical system with a point defect and study the variation of thermodynamic quantities, which are the differences between those with and without the defect. Within renormalization group theory, we show generally that the critical exponent of the internal energy variation is the specific heat exponent of a pure system, and the critical exponent of the heat capacity variation is that for the temperature derivative of specific heat of a pure system. This conclusion is valid for the isotropic systems with a short-range interaction. As an example we solve the two-dimensional Ising model with a point defect numerically. The variations of the free energy, internal energy, and specific heat are calculated with the bond propagation algorithm. At the critical point, the internal energy variation diverges with the lattice size logarithmically and the heat capacity variation diverges with size linearly. Near the critical point, the internal energy variation behaves as $ln\left|t\right|$ and the heat capacity variation behaves as ${\left|t\right|}^{-1}$, where $t$ is the reduced temperature.

We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions.

In experiments two-dimensional systems are realized mainly on solid substrates, which introduce quenched disorder due to some inherent defects. The defects of substrates influence the melting scenario of the systems and have to be taken into account in the interpretation of experimental results. We present the results of molecular dynamics simulations of a two-dimensional system with a core-softened potential in which a small fraction of the particles is pinned, inducing quenched disorder. Ppotentials of this type are widely used for the qualitative description of systems with waterlike anomalies. In our previous publications it was shown that the system demonstrates an anomalous melting scenario: at low densities the system melts through two continuous transitions in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory with an intermediate hexatic phase, while at high densities the conventional first-order melting transition takes place. We find that the well-known disorder-induced widening of the hexatic phase occurs at low densities, while in the high-density part of the phase diagram random pinning transforms the first-order melting into two transitions: a continuous KTHNY-like solid-hexatic transition and a first-order hexatic–isotropic liquid transition.

Reduction of a mesoscopic level to a level with fewer details is made by the time evolution during which the entropy increases. An extension of a mesoscopic level is a construction of a level with more details. In particular, we discuss extensions in which extra state variables are found in the vector fields appearing on the level that we want to extend. Reductions, extensions, and compatibility relations among them are formulated first in an abstract setting and then illustrated in specific mesoscopic theories.

We studied the collective motion of particles forced to move along a circular path in water by utilizing an optical vortex. Their collective motion, including the spontaneous formation of clusters and their dissociation, was observed. The observed temporal patterns depend on the number of particles on the path and the variation of their sizes. The addition of particles with different sizes suppresses the dynamic formation and dissociation of clusters and promotes the formation of specific stationary clusters. These experimental findings are reproduced by numerical simulations that take into account the hydrodynamic interaction between the particles and the radial trapping force confining the particles to the circular path. A transition between stationary and nonstationary clustering of the particles was observed by varying their size ratio in the binary-size systems. Our simulation reveals that the transition can be either continuous or discontinuous depending on the number of different-size particles. This result suggests that the size distribution of particles has a significant effect on the collective behavior of self-propelled particles in viscous fluids.