Results for the kinetics of vapor-liquid transitions, following temperature quenches with different densities, are presented from molecular dynamics simulations of a Lennard-Jones system. For a critical density, bicontinuous liquid and vapor domains are observed which grow with time, obeying the predictions for the hydrodynamic mechanism. On the other hand, for quenches with density significantly below the critical one, phase separation progresses via nucleation and growth of liquid droplets. In the latter case, the Brownian diffusion and collision mechanism for the droplet growth is confirmed. We also discuss the possibility of interdroplet interaction leading to a different amplitude in the growth law. Arguments for faster growth, observed at early times, are also provided.

We use molecular dynamics simulations to study surface-directed spinodal decomposition in unstable binary $AB$ fluid mixtures at wetting surfaces. The thickness of the wetting layer $R_1$ grows with time $t$ as a power law ($R_1\sim t^{\theta }$). We find that hydrodynamic effects result in a crossover of the growth exponent from $\theta \simeq 1/3$ to 1. We also present results for the layerwise correlation functions and domain length scales.

Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when the number of particles $N$ is large. Accordingly, it fails close to the extinction transition, when the amplitude of stochastic fluctuations is comparable with the size of the population. Here we present a general scaling theory of the transition regime for spatially extended systems. We demonstrate this through a detailed study of two fundamental models for out-of-equilibrium phase transitions: the Susceptible-Infected-Susceptible (SIS) that belongs to the directed percolation equivalence class and the Susceptible-Infected-Recovered (SIR) model belonging to the dynamic percolation class. Implementing the Ginzburg criteria we show that the width of the fluctuation-dominated region scales like $N^{-\kappa }$, where $N$ is the number of individuals per site and $\kappa =2/(d_u-d)$, $d_u$ is the upper critical dimension. Other exponents that control the approach to the deterministic limit are shown to be calculable once $\kappa$ is known. The theory is extended to include the corrections to the front velocity above the transition. It is supported by the results of extensive numerical simulations for systems of various dimensionalities.

Estimating entropy from empirical samples of finite size is of central importance for information theory as well as the analysis of complex statistical systems. Yet, this delicate task is marred by intrinsic statistical bias. Here we decompose the entropy function into a polynomial approximation function and a remainder function. The approximation function is based on a Taylor expansion of the logarithm. Given $n$ observations, we give an unbiased, linear estimate of the first $n$ power series terms based on counting sets of $k$ coincidences. For the remainder function we use nonlinear Bayesian estimation with a nearly flat prior distribution on the entropy that was developed by Nemenman, Shafee, and Bialek. Our simulations show that the combined entropy estimator has reduced bias in comparison to other available estimators.

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results broadly applicable to any field in which correlation functions are employed.

We divide the circular boundary of a hyperbolic lattice into four equal intervals and study the probability of a percolation crossing between an opposite pair as a function of the bond occupation probability $p$. We consider the {7,3} (heptagonal), enhanced or extended binary tree (EBT), the EBT-dual, and the {5,5} (pentagonal) lattices. We find that the crossing probability increases gradually from 0 to 1 as $p$ increases from the lower $p_l$ to the upper $p_u$ critical values. We find bounds and estimates for the values of $p_l$ and $p_u$ for these lattices and identify the self-duality point $p^{*}$ corresponding to where the crossing probability equals $1/2$. Comparison is made with recent numerical and theoretical results.

We study the statistics of heat transferred in a given time interval $t_M$, through a finite harmonic chain, called the center, which is connected to two heat baths, the left $\left(L\right)$ and the right $\left(R\right)$, that are maintained at two temperatures. The center atoms are driven by external time-dependent forces. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, $Q_L$, based on the two-time quantum measurement concept and using the nonequilibrium Green's function method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of the CGF is valid in both transient and steady-state regimes. We consider three initial conditions for the density operator and show numerically, for a one-atom junction, how their transient behaviors differ from each other but, finally, approach the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution $P(Q_L,Q_R)$, and discuss the correlations between $Q_L$ and $Q_R$. We calculate the CGF for total entropy production in the reservoirs. In the steady state we explicitly show that the CGFs obey steady-state fluctuation theorems. We obtain classical results by taking $\hslash \to 0$. We also apply our method to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase and shifting the contour time, respectively.

A molecular dynamics (MD) methodology based on Eyring theory of reaction rates is proposed for investigating solid-liquid interfacial properties crucial to the development of many nanotechnology applications. The method involves the calculation of activation energy required for the flow process directly from the MD trajectory information. We have applied this methodology to study the behavior of water in hydrophobic confinement in carbon nanotubes (CNTs) and also between graphene sheets. In the case of confined water molecules in CNTs and between graphene sheets the degree of confinement and curvature effects were found to have more influence on the solid-liquid interfacial friction, with almost negligible friction below a certain characteristic dimension in both the cases. This behavior of confined and unconfined water molecules is explained on the basis of molecular interactions and subsequent changes in the activation energy. Analysis based on this method also revealed that a finite amount of friction does exist at the channel entry and exit region. This could limit the flow of liquid molecules through the nanochannels and hence needs to be taken into account in the design of nanofluidic devices.

The effect of adding charged nonadsorbing polymers to electrostatically structured suspensions of charged liposomes has been experimentally studied by means of light scattering techniques. The static structure factor of the mixtures is analyzed using two polymers of different sizes. As the polymer concentration increases, the main peak of the structure factor decreases and shows an important shift to larger values of the scattering vector. Such displacement is the consequence of the electrostatic-enhanced depletion attraction induced by the polymers that counteracts the electrostatic repulsion. For the shorter polymer, the system remains stable for all studied polymer concentrations. However, for the long polymer chains, the effective attraction induced at the highest polymer density studied is strong enough to destabilize the mixture. In this case, the aggregation of the liposomes leads to clusters of nearly linear morphology. The PRISM theory is employed to calculate the effective pair potential between liposomes. The theoretical predictions are able to support the experimental observations, and provide an explanation of the interplay between the electrostatic repulsive interaction and the depletion attraction. In particular, they show that the depletion attraction is especially long ranged, and is dominated by electrostatic effects rather than entropic.

In this contribution, the yield behavior of a strongly flocculated colloidal structure subjected to a tensile-bending load is micromechanically modeled. The yielding of a cluster is assumed to be triggered by the failure of one bond (critical bond) and accompanied by massive breakage of further bonds. Thus, identifying the position of the critical bond and evaluating its yield force are the main goals of this study. Interparticle bonds are considered as flexible nanoscale bridges which fail when the force applied on them reaches a critical value. The yield of the critical bonds can result from both tensile and bending stresses. By means of the yield stresses in the critical bonds, the yield force of the whole cluster can be calculated.

In this paper we delineate the consequences of field-dependent solvent polarization in the electric double layer (EDL) electrostatic potential distribution, and the effective EDL thickness in narrow nanofluidic confinements with thick (or overlapping) EDLs. The EDL, formed at the interface between a charged substrate and an electrolyte solution, induces a large electric field spanning across few nanometer distances from the interface. As a result, a polar solvent like water gets polarized, making its relative permittivity a function of the EDL electric field. This affects the overall EDL electrostatic potential distribution and most importantly, leads to a significant reduction of the effective EDL thickness, with the extent of the reduction being dictated by the value of field independent EDL thickness, strength of the solvent polarization, and the substrate-liquid interfacial electrostatic potential. Such a finding will necessitate redefining the classical EDL thickness, which will be of overwhelming significance in nanofluidic transport.

A mechanism to form distorted helical structures in ferroelectric liquid crystals is presented. It is shown that the deformation of helical interlayer structures of thin smectic systems can be considered as a direct consequence of the surface-induced spatial inhomogeneity in the distribution of the azimuthal molecular orientation within smectic layers. The intralayer azimuthal nonuniformity occurring in helical phases is argued to generate a local depolarizing electric field of the strength varying not only in smectic layers but also between the layers. The resulting modulation of the depolarization level in the direction of helical axes is shown to lead to a distortion of helices. Using a simple model, including the depolarization interaction, it is demonstrated that the degree of the helix deformation strongly varies as parameters of the model are changed. It is also shown that strong deformations of extremely short helices, found for appropriate values of the parameters, reflect nonuniformity of helicoidal superstructures of respective smectic subphases in real liquid crystalline systems.

We present basic characteristics and a model of photoinduced anchoring of liquid crystals (LCs) on a chalcogenide surface. It was found that characteristics of the alignment strongly depend on the LC material for the same chalcogenide glass. The photoalignment is partially reversible and can be controlled by changing the light polarization direction. We propose a model in which the existence of dichroic units on the chalcogenide surface and competition between two mechanisms of the photoalignment is suggested. The first mechanism is related to the light-induced anisotropy on the chalcogenide surface and results in an easy orientation axes of a LC parallel to the polarization of the incident light. The second mechanism is attributed to an energy transfer from the dichroic units after the light absorption to the LC molecules adsorbed on the chalcogenide surface. The transferred energy causes polarization-sensitive desorption of the LC molecules from the chalcogenide surface and the light-induced easy orientation axis of a LC perpendicular to the incident light polarization. The competition between these mechanisms leads to the observed change of the direction of the easy axis with the exposure.

The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed at the expense of (i) overtwist or (ii) supercoils. Recent work has shown that the supercoiling mechanism results in a picture similar to Bose-Einstein condensation where a macroscopic loop appears at $T_c$ and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above $T_c$, with a cusp at the critical point.

A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of $S$ local attractor states. The internal neuronal dynamics of the patch is not described by the model, rather it is subsumed into an effective description in terms of graded Potts units, with adaptation effects both specific to each attractor state and generic to the patch. If each unit, or patch, receives effective (tensor) connections from $C$ other units, the network has been shown to be able to store a large number $p$ of global patterns, or network attractors, each with a fraction $a$ of the units active, where the critical load $p_c$ scales roughly like $p_c\approx C{S}^2/a\ln (1/a)$ (if the patterns are randomly correlated). Interestingly, after retrieving an externally cued attractor, the network can continue jumping, or latching, from attractor to attractor, driven by adaptation effects. The occurrence and duration of latching dynamics is found through simulations to depend critically on the strength of local attractor states, expressed in the Potts model by a parameter $w$. Here we describe with simulations and then analytically the boundaries between distinct phases of no latching, of transient and sustained latching, deriving a phase diagram in the plane $w-T$, where $T$ parametrizes thermal noise effects. Implications for real cortical dynamics are briefly reviewed in the conclusions.

Formulas are derived for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the distribution of ions near cell membranes more accurately than by using Poisson-Boltzmann theory or its linearized version. Here I use them to discuss the electric field of a uniformly charged membrane, the image charges of an ion, the distribution of salt ions near a charged membrane, the energy of a zwitterion near a lipid slab, and the effect of including the phosphate head groups as thin layers of high electric permittivity.

Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean-field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

We report on wind-tunnel measurements of particle velocity distribution in aeolian transport. By performing extended statistics, we show that for saltation occurring over an erodible bed the vertical lift-off velocity distributions deviate significantly from a Gaussian law and exhibit a long tail accurately described by a lognormal law. In contrast, saltation over a rigid bed produces Gaussian velocity distributions. These results strongly suggest that the deviation from Gaussian distributions is a consequence of the splash process which is exclusively present in saltation transport over an erodible bed. We further suggest that the non-Gaussian statistics is intimately related to the statistical properties of a single splash event which produces ejection of particles with lift-off velocities distributed according to a lognormal law. This lognormal behavior can be simply inferred from the propagation process of the impact energy through the granular bed which can be viewed as the analog of a fragmentation process. These findings emphasize the crucial role of the splash process in saltation transport.

The pattern of over- and under-representations of three-node subgraphs has become a standard method of characterizing complex networks and evaluating how this intermediate level of organization contributes to network function. Understanding statistical properties of subgraph counts in random graphs, their fluctuations, and their interdependences with other topological attributes is an important prerequisite for such investigations. Here we introduce a formalism for predicting subgraph fluctuations induced by perturbations of unidirectional and bidirectional edge densities. On this basis we predict the over- and under-representation of subgraphs arising from a density mismatch between a network and the corresponding pool of randomized graphs serving as a null model. Such mismatches occur, for example, in modular and hierarchical graphs.

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power blackouts which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its “generalized strength,” a measure of the ability of a node to attract walkers. The generalized strength is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of generalized strength, on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of generalized strength.