We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the mechanism is different from that of the critical slowing-down encountered in conventional molecular dynamics or Monte Carlo simulations. When trapped, the random walker misses the entire or even several stages of Wang-Landau modification factor reduction, leading to inadequate sampling of the configuration space and a rough density of states, even though the modification factor has been reduced to very small values. Trapping is dependent on specific systems, the choice of energy bins, and the Monte Carlo step size, making it highly unpredictable. A general, simple, and effective solution is proposed where the configurations of multiple parallel Wang-Landau trajectories are interswapped to prevent trapping. We also explain why swapping frees the random walker from such traps. The efficacy of the proposed algorithm is demonstrated.

The pseudopotential lattice Boltzmann model (PP-LBM) is a very popular model for simulating multiphase systems. In this model, phase separation occurs via a short-range attraction between different phases when the interaction potential term is properly chosen. Therefore, the potential term is expected to play a significant role in the model and to affect the accuracy and the stability of the computations. The original PP-LBM suffers from some drawbacks such as being capable of dealing with low density ratios only, thermodynamic inconsistency, and spurious velocities. In this paper, we aim to analyze the PP-LBM with the view to simulate single-component (non-)isothermal multiphase systems at large density ratios and in spite of the presence of spurious velocities. For this purpose, the performance of two popular potential terms and of various implementation schemes for these potential terms is examined. Furthermore, the effects of different parameters (i.e., equation of state, viscosity, etc.) on the simulations are evaluated, and, finally, recommendations for a proper simulation of (non-)isothermal multiphase systems are presented.

We examine fluctuations in particle density in the restricted-height, conserved stochastic sandpile (CSS). In this and related models, the global particle density is a temperaturelike control parameter. Thus local fluctuations in this density correspond to disorder; if this disorder is a relevant perturbation of directed percolation (DP), then the CSS should exhibit non-DP critical behavior. We analyze the scaling of the variance $V_{\ell }$ of the number of particles in regions of ${\ell }^d$ sites in extensive simulations of the quasistationary state in one and two dimensions. Our results, combined with a Harris-like argument for the relevance of particle-density fluctuations, strongly suggest that conserved stochastic sandpiles belong to a universality class distinct from that of DP.

In a microcanonical ensemble (constant $NVE$, hard reflecting walls) and in a molecular dynamics ensemble (constant $NVE\mathbf{PG}$, periodic boundary conditions) with a number $N$ of smooth elastic hard spheres in a $d$-dimensional volume $V$ having a total energy $E$, a total momentum $\mathbf{P}$, and an overall center of mass position $\mathbf{G}$, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on $d, N, E$, the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in $d$ dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of $N$.

Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively pertain to a finite-size sample in a periodic box, as they are washed out in the bulk limit. Below the critical density, at each pressure jump the shape of the liquid drop undergoes a morphological transition, changing from spherical to cylindrical to slablike as the density is increased. We formulate a simple theory of these shape transitions, which is adapted from a calculation originally developed by Binder and coworkers [L. G. MacDowell, P. Virnau, M. Muller, and K. Binder, J. Chem. Phys. 120, 5293 (2004)]. Our focus is on the pressure equation of state (rather than on the chemical potential, as in the original work) and includes an extension to elongated boxes. Predictions based on this theory well agree with extensive Monte Carlo data for the cut-and-shifted Lennard-Jones fluid. We further discuss the thermodynamic stability of liquid drops with shapes other than the three mentioned above, like those found deep inside the liquid-vapor region in simulations starting from scratch. Our theory classifies these more elaborate shapes as metastable.

When a granular mixture involving grains of different sizes is shaken, sheared, mixed, or left to flow, grains tend to separate by sizes in a process known as size segregation. In this study, we explore the size segregation mechanism in granular chute flows in terms of the pressure distribution and granular microstructure. Therefore, two-dimensional discrete numerical simulations of bidisperse granular chute flows are systematically analyzed. Based on the theoretical models of J. M. N. T. Gray and A. R. Thornton [Proc. R. Soc. A 461, 1447 (2005)] and K. M. Hill and D. S. Tan [J. Fluid Mech. 756, 54 (2014)], we explore the stress partition in the phases of small and large grains, discriminating between contact stresses and kinetic stresses. Our results support both gravity-induced and shear-gradient-induced segregation mechanisms. However, we show that the contact stress partition is extremely sensitive to the definition of the partial stress tensors and, more specifically, to the way mixed contacts (i.e., involving a small grain and a large grain) are handled, making conclusions on gravity-induced segregation uncertain. By contrast, the computation of the partial kinetic stress tensors is robust. The kinetic pressure partition exhibits a deviation from continuum mixture theory of a significantly higher amplitude than the contact pressure and displays a clear dependence on the flow dynamics. Finally, using a simple approximation for the contact partial stress tensors, we investigate how the contact stress partition relates to the flow microstructure and suggest that the latter may provide an interesting proxy for studying gravity-induced segregation.

Recently, shear rate gradients and associated gradients in velocity fluctuations (e.g., granular temperatures or kinetic stresses) have been shown to drive segregation of different-sized particles in a manner that reverses at relatively high solids fractions $\left(\langle f\rangle >0.50\right)$. Here we investigate these effects in mixtures of particles differing in material density through computational and theoretical studies of particles sheared in a vertical chute where we vary the solids fraction from $\langle f\rangle =0.2$ to 0.6. We find that in sparse flows, $\langle f\rangle =0.2$ to 0.4, the heavier (denser) particles segregate to lower shear rates similarly to the heavier (larger) particles in mixtures of particles differing only in size. However, there is no segregation reversal at high $f$ in mixtures of particles differing in density. At all solids fractions, heavier (denser) particles segregate to regions of lower shear rates and lower granular temperatures, in contrast with segregation of different-sized particles at high $f$, where the heavier (larger) particles segregate to the region of higher shear rates. Kinetic theory predicts well the segregation for both types of systems at low $f$ but breaks down at higher $f$'s. Our recently proposed mixture theory for high $f$ granular mixtures captures the segregation trends well via the independent partitioning of kinetic and contact stresses between the two species. In light of these results, we discuss possible directions forward for a model framework that encompasses segregation effects more broadly in these systems.

The origin of Debye-like relaxation in some hydrogen-bonded liquids is a matter of hot debate over the past decade. While a relatively clear picture of the issue has been established for monohydroxy alcohols, the Debye-type dynamics in other glass-forming systems still remains a not fully understood phenomenon. In this paper we present the results of dielectric measurements performed in the frequency interval ${10}^{-1}$ to ${10}^9\mathrm{Hz}$, both in the supercooled and normal liquid state of etoricoxib anti-inflammatory agent. Our investigations reveal the presence of slow Debye-like relaxation with features similar to that found for another active pharmaceutical ingredient, ibuprofen. Our results provide a fresh insight into the molecular nature of Debye-type relaxation in H-bonded pharmaceutically relevant materials and thus may stimulate the academic community for further discussion concerning the molecular dynamics of hydrogen-bonded fluids in general.

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

The dynamics of regular clusters of many nontouching particles falling under gravity in a viscous fluid at low Reynolds number are analyzed within the point-particle model. The evolution of two families of particle configurations is determined: two or four regular horizontal polygons (called “rings”) centered above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated in which the long-lasting clusters are centered around periodic solutions for the relative motions, and they are surrounded by regions of chaotic scattering in a similar way to what was observed by Janosi et al. [Phys. Rev. E. 56, 2858 (1997)] for three particles only. These findings suggest that we should consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid.

We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to $48\times 48$ sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, $y_t=1.804\left(5\right)$, $y_g=0.80\left(1\right)$, and $y_h=1.925\left(3\right)$, provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.

The time evolution of a random graph with varying number of edges and vertices is considered. The edges and vertices are assumed to be added at random by one at a time with different rates. A fresh edge connects either two linked components and forms a new component of larger order $g$ (coalescence of graphs) or increases (by one) the number of edges in a given linked component (cycling). Assuming the vertices to have a finite valence (the number of edges connected with a given vertex is limited) the kinetic equation for the distribution of linked components of the graph over their orders and valences is formulated and solved exactly by applying the generating function method for the case of coalescence of trees. The evolution process is shown to reveal a phase transition: the emergence of a giant linked component whose order is comparable to the total order of the graph. The time dependencies of the moments of the distribution of linked components over their orders and valences are found explicitly for the pregelation period and the critical behavior of the spectrum is analyzed. It is found that the linked components are $\gamma$ distributed over $g$ with the algebraic prefactor $g^{-5/2}$. The coalescence process is shown to terminate by the formation of the steady-state $\gamma$ spectrum with the same algebraic prefactor.

The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as $d_L=2.520$ for a family of hierarchical lattices, from an essentially exact (correlation coefficent $R^2=0.999999$) near-linear fit to 23 different diminishing fractional dimensions. To obtain this result, the phase transition temperature between the disordered and spin-glass phases, the corresponding critical exponent $y_T$, and the runaway exponent $y_R$ of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered.

We study an open-boundary version of the on-off zero-range process introduced in Hirschberg et al. [Phys. Rev. Lett. 103, 090602 (2009)]. This model includes temporal correlations which can promote the condensation of particles, a situation observed in real-world dynamics. We derive the exact solution for the steady state of the one-site system, as well as a mean-field approximation for larger one-dimensional lattices, and also explore the large deviation properties of the particle current. Analytical and numerical calculations show that, although the particle distribution is well described by an effective Markovian solution, the probability of rare currents differs from the memoryless case. In particular, we find evidence for a memory-induced dynamical phase transition.

Phase transitions in one-dimensional classical fluids are usually ruled out by using van Hove's theorem. A way to circumvent the conclusions of the theorem is to consider an interparticle potential that is everywhere bounded. Such is the case of, e.g., the generalized exponential model of index 4 (GEM-4 potential), which in three dimensions gives a reasonable description of the effective repulsion between flexible dendrimers in a solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4 model [S. Prestipino, Phys. Rev. E 90, 042306 (2014)] has recently provided evidence of an infinite sequence of low-temperature cluster phases, however, also suggesting that upon pushing the simulation forward what seemed a true transition may eventually prove to be only a sharp crossover. We hereby investigate this problem theoretically by use of three different and increasingly sophisticated approaches (i.e., a mean-field theory, the transfer matrix of a lattice model of clusters, and the exact treatment of a system of point clusters in the continuum) to conclude that the alleged transitions of the one-dimensional GEM-4 system are likely just crossovers.

A quantum-mechanical analysis of hyperfast (faster than ballistic) diffusion of a quantum wave packet in random optical lattices is presented. The main motivation of the presented analysis is experimental demonstrations of hyperdiffusive spreading of a wave packet in random photonic lattices [L. Levi et al., Nature Phys. 8, 912 (2012)]. A rigorous quantum-mechanical calculation of the mean probability amplitude is suggested, and it is shown that the power-law spreading of the mean-squared displacement (MSD) is $\langle x^2\left(t\right)\rangle \sim t^{\alpha }$, where $2<\alpha \le 3$. The values of the transport exponent $\alpha$ depend on the correlation properties of the random potential $V(x,t)$, which describes random inhomogeneities of the medium. In particular, when the random potential is $\delta$ correlated in time, the quantum wave packet spreads according Richardson turbulent diffusion with the MSD $\sim t^3$. Hyperdiffusion with $\alpha =12/5$ is also obtained for arbitrary correlation properties of the random potential.

We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics and thus produce useful information about a variety of granular phenomena, including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.

When a suspension containing particles of different sizes flows through a confined geometry a size gradient can be established, with large particles accumulating in the channel center. Such size separation driven by hydrodynamic interactions is expected to facilitate membrane filtration and may lead to the design of novel and innovative separation techniques. For this, a wide range of particle concentrations has to be investigated, in order to clarify whether shear-induced migration can be utilized at concentrations close to or above the colloidal glass transition, where particle motion is severely hindered and hydrodynamic interactions are screened. We explore this scenario by studying the flow of binary mixtures of soft colloidal microgels, well above their liquid-solid transition, through narrow microchannels. We find that, even though the flow becomes strongly heterogeneous, in both space and time, characterized by a large cooperativity length, size segregation still occurs. This suggests that even above the glass transition shear-induced diffusion could still be used as a fractionation mechanism, which is of great relevance for process intensification purposes.

The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapor phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid-liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect ratio of thickness compared to radius, because radial growth is much faster than axial growth. We calculate numerically how fast disk-shaped crystals grow in both pure and binary melts, accounting for the comparatively slow axial growth, the effect of dissolved solute in the fluid phase, and the difference in thermal properties between solid and fluid phases. We identify the main physical mechanisms that control crystal growth and show that the diffusive removal of both the latent heat released and the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parametrizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10–100 for low aspect ratio disks, and we provide a parametrization for use in models of ice crystal growth in environmental settings.

The flexoelectric polarization $\left(P_f\right)$ of four bent-core nematic liquid crystals (LCs) has been measured using the pyroelectric effect. Hybrid aligned nematic cells are fabricated for measuring the pyroelectric response over the entire range of the nematic phase. It is found that the magnitude of flexoelectric polarization $P_f$ and the sum of the flexoelectric coefficients $|e_1+e_3|$ for the bent-core LCs studied here are three to six times higher than for the calamitics. $P_f$ is found to depend on the transverse dipole moment of LC molecules. However, $|e_1+e_3|$ values are by no means giant as $|e_3|$ alone had been reported for a bent-core nematic system previously. The dependence of the sum of “splay and bend flexoelectric coefficients” is discussed in terms of the shape of the molecule and of the dipole moment directed normal to the molecular axis.