In the present work, an in-depth analysis of the theoretical structure of the smoothed-particle hydrodynamics (hereinafter SPH) is provided for an inviscid, weakly compressible, and barotropic flow in the presence of a free surface. The role of the free surface in the SPH scheme is indeed little addressed in literature. In the present analysis, the general continuous formulation of the SPH method is considered. A detailed description of the free-surface influence on the smoothed differential operators is supplied. New and existing forms are analyzed in detail, in terms of convergence and conservation properties. The proposed analysis is based on the principle of virtual works, which permits to exhibit the link with the enforcement of the dynamic free-surface boundary condition. Finally, possible SPH formulations resulting from this analysis are investigated, in terms of consistency, conservation, and dynamic free-surface boundary condition.

To prevent the flocculation and phase separation of nanoparticles in solution, nanoparticles are often functionalized with short chain surfactants. Here we present fully atomistic molecular dynamics simulations which characterize how these functional coatings affect the interactions between nanoparticles and with the surrounding solvent. For 5-nm-diameter silica nanoparticles coated with poly(ethylene oxide) (PEO) oligomers in water, we determined the hydrodynamic drag on two approaching nanoparticles moving through solvent and on a single nanoparticle as it approaches a planar surface. In most circumstances, macroscale fluid theory accurately predicts the drag on these nanoscale particles. Good agreement is seen with Brenner’s analytical solutions for wall separations larger than the soft nanoparticle radius. For two approaching coated nanoparticles, the solvent-mediated (velocity independent) and lubrication (velocity-dependent) forces are purely repulsive and do not exhibit force oscillations that are typical of uncoated rigid spheres.

In this work, we propose a method to stabilize a nucleus in the framework of lattice density-functional theory (LDFT) by imposing a suitable constraint. Using this method, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. As an application of this method, we study the nucleation behavior of vapor-liquid transition in nanosquare pores with infinite length and relate the observed hysteresis loop on an adsorption isotherm to the nucleation mechanism. According to the dependence of hysteresis and the nucleation mechanism on the fluid-wall interaction, $w$, in this work, we have classified $w$ into three regions ($w>0.9$, $0.1\le w\le 0.9$, and $w<0.1$), which are denoted as strongly, moderately, and weakly attractive fluid-wall interaction, respectively. The dependence of hysteresis on the fluid-wall interaction is interpreted by the different nucleation mechanisms. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be considered if morphological transition of nuclei exists during a nucleation process.

The observation of a first order phase transition between two fluid phases, reported by R. Angelini et al. [Phys. Rev. E 78, 020502(R) (2008)], is not supported by the measurements and is shown to be caused by the loss of solubility of alpha-cyclodextrin in the water–4-methylpyridine solvent.

In their comment, Plazanet, Johnson, and Trommsdorff [Phys. Rev. E 79, 053501 (2009)] point out inconsistencies of our work [Angelini, Ruocco, and De Panfilis, Phys. Rev. E 78, 020502(R) (2008)] with previous measurements performed in solutions composed of $\alpha$-cyclodextrin, water, and 4-methylpyridine. In particular, they state that the phase transition observed between two fluid phases is simply due to a loss of solubility of the solutions. In this reply, we underline that our work, on the contrary, represents an extension in concentration and temperature ranges with respect to previous studies and that, how explicitly discussed in the same work, the most intimate nature of the high temperature fluid phase has never been defined homogeneous as objected to in the comment.

The diameter of columnar joints forming in cooling basalt and drying starch increases with decreasing growth rate. This observation can be reproduced with a linear-elastic three-dimensional fracture mechanics bifurcation analysis, which has been done for a periodic array of hexagonal columnar joints by considering a bifurcation mode compatible with observations on drying starch. In order to be applicable to basalt columns, the analysis has been carried out with simplified stationary temperature fields. The critical diameter differs from the one derived with a two-dimensional model by a mere factor of 1/2. By taking into account the latent heat released at the solidification front, the results agree fairly well with observed column diameters.

We study a discrete model described by coupled excitable elements following the monostable FitzHugh-Nagumo equations. Our model has a weakly coupled activator and a strongly coupled inhibitor. For two-coupled excitable elements, we show that the trivial state always exists stably, while nontrivial stable states appear depending on the coupling strengths. In a one-dimensional array, only the elements near the initial condition step remain at nontrivial states. We discuss stationary pattern formation in a one-dimensional array and a two-dimensional lattice using the analytical results of a two-coupled system.

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and numerically in terms of a random sawtooth potential and a periodically varying driving force. Precise conditions for the occurrence of transition between these two transport regimes are derived and analyzed in detail.

The precision of biochemical signaling is limited by randomness in the diffusive arrival of molecules at their targets. For proteins binding to specific sites on DNA and regulating transcription, the ability of the proteins to diffuse in one dimension by sliding along the length of the DNA, in addition to their diffusion in bulk solution, would seem to generate a larger target for DNA binding, consequently reducing the noise in the occupancy of the regulatory site. Here we show that this effect is largely canceled by the enhanced temporal correlations in one-dimensional diffusion. With realistic parameters, sliding along DNA has surprisingly little effect on the physical limits to the precision of transcriptional regulation.

Based on information theory, we present a method to determine an optimal Markov approximation for modeling and prediction from time series data. The method finds a balance between minimal modeling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples, and the consequences for prediction are evaluated by means of the root-mean-squared prediction error for point prediction.

We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Bénard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by free-slip planes at the top and bottom and with periodic side walls. The turbulence is inhomogeneous with respect to the vertical direction. This manifests in different lateral and vertical two-particle dispersion and in a dependence of the dispersion on the initial tracer position for short and intermediate times. Similar to homogeneous isotropic turbulence, the dispersion properties depend in addition to the initial pair separation and yield a short-range Richardson-like scaling regime of two-particle dispersion for initial separations close to the Kolmogorov dissipation length. The Richardson constant is about half the value of homogeneous isotropic turbulence. The multiparticle statistics is very close to the homogeneous isotropic case. Clusters of four Lagrangian tracers show a clear trend to form flat, almost coplanar, objects in the long-time limit and deviate from the Gaussian prediction. Significant efforts have been taken to resolve the statistics of the acceleration components up to order four correctly. We find that the vertical acceleration is less intermittent than the lateral one. The joint statistics of the vertical acceleration with the local convective and conductive heat flux suggests that rising and falling thermal plumes are not associated with the largest acceleration magnitudes. It turns out also that the Nusselt number which is calculated in the Lagrangian frame converges slowly in time to the standard Eulerian one.

The density fluctuations below the onset of convection in the Rayleigh-Bénard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows ($\text{Kn}=0.01$ and $\text{Kn}=0.005$). Furthermore, the physical nature for no convection in the Rayleigh-Bénard problem under large Knudsen number conditions $\left(\text{Kn}>0.028\right)$ is explained based on the dynamics of fluctuations.

An anisotropically forced passive vector model is analyzed at scales much smaller and larger than the forcing scale by solving exactly the equation for the pair correlation function. The model covers the cases of magnetohydrodynamic turbulence, the linear pressure model, and the linearized Navier-Stokes equations by choice of a simple parameter. We determine whether or not the anisotropic injection mechanism induces dominance of the anisotropic effects at the asymptotic scaling regimes. We also show that under very broad conditions, both scaling regimes exhibit anomalous scaling due to the existence of nontrivial zero modes.

The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas.

We simulate a relaxation process of non-Brownian particles in a sheared viscous medium; the system is subject to the small shear strain and then undergoes relaxation. We estimate the exponents with which the relaxation time and the correlation length diverge as the density approaches the jamming density from below. In particular, the dynamic critical exponent is estimated as 4.6(2). It is also found that shear stress undergoes power-law decay at the jamming density, which is reminiscent of critical slowing down.

We investigate numerically and analytically the effects of conservation of total translational and angular momentum on the distribution of kinetic energy among particles in microcanonical particle systems with small number of degrees of freedom, specifically microclusters. Molecular dynamics simulations of microclusters with constant total energy and momenta, using Lennard-Jones, Morse, and Coulomb plus Born-Mayer-type potentials, show that the distribution of kinetic energy among particles can be inhomogeneous and depend on particle mass and position even in thermal equilibrium. Statistical analysis using a microcanonical measure taking into account of the additional conserved quantities gives theoretical expressions for kinetic energy as a function of the mass and position of a particle with only $O\left(1/N^2\right)$ deviation from the Maxwell-Boltzmann distribution. These expressions fit numerical results well. Finally, we propose an intuitive interpretation for the inhomogeneity of the kinetic energy distributions.

The ability to independently dictate the shape and crystal orientation of islands in electrocrystallization remains a significant challenge. The main reason for this is that the complex interplay between the substrate, nucleation, and surface chemistry is not fully understood. Here we report on the kinetics of island growth for copper on ruthenium oxide. The small nucleation overpotential leads to enhanced lateral growth and the formation of hexagonal disk-shaped islands. The amorphous substrate allows the nuclei to achieve the thermodynamically favorable orientation, i.e., a $⟨111⟩$ surface normal. Island growth follows power law kinetics in both lateral and vertical directions. At shorter times, the two growth exponents are equal to $\frac{1}{2}$ whereas at longer times lateral growth slows down while vertical growth speeds up. We propose a growth mechanism, wherein the lateral growth of disk-shaped islands is initiated by attachment of Cu adatoms on the ruthenium oxide surface onto the island periphery while vertical growth is initiated by two-dimensional nucleation on the top terrace and followed by lateral step propagation. These results indicate three criteria for enhanced lateral growth in electrodeposition: (i) a substrate that leads to a small nucleation overpotential, (ii) fast adatom surface diffusion on substrate to promote lateral growth, and (iii) preferential anion adsorption to stabilize the basal plane.

In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing nonequilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between nonequilibrium and classical equilibrium networks.

We consider the algorithmic problem of selecting a set of target nodes that cause the biggest activation cascade in a network. In case when the activation process obeys the diminishing return property, a simple hill-climbing selection mechanism has been shown to achieve a provably good performance. Here we study models of influence propagation that exhibit critical behavior and where the property of diminishing returns does not hold. We demonstrate that in such systems the structural properties of networks can play a significant role. We focus on networks with two loosely coupled communities and show that the double-critical behavior of activation spreading in such systems has significant implications for the targeting strategies. In particular, we show that simple strategies that work well for homogenous networks can be overly suboptimal and suggest simple modification for improving the performance by taking into account the community structure.

Recently, a new mechanism leading to purely quantum directed transport in the asymmetric multibaker map has been presented. Here, we show a comprehensive characterization of the finite asymptotic current behavior with respect to the $h$ value, the shape of the initial conditions, and the features of the spectrum. We have considered different degrees of asymmetry in these studies and we have also analyzed the classical and quantum phase-space distributions for short times in order to understand the mechanisms behind the generation of the directed current.