Molecular model for the VLE p- T-x relationships of binary mixtures

An analytical expression for the pressure-temperature-composition relations in the vapour - liquid equilibrium of non-polar binary mixtures is proposed. The model is based on a simple analytical expression for the vapour pressure of pure non-polar fluids, which, for a given temperature, requires as input only the Lennard- Jones molecular parameters and the acentric factor of the substance. The equilibrium mixture pressure is then expressed as a function of the vapour pressure of each component and of a mixture contribution. The molecular parameters required for this mixture contribution are related to the molecular parameters of the pure component through a modified Lorentz-Berthelot mixing rule, where the interaction parameters are given as simple functions of the temperature and composition, with eight appropriate constants for each binary mixture. We show that the model permits one to reproduce or predict in a simple way the pressure (for a given liquid mole fraction) or the liquid composition (for a given pressure).     

Molecular dynamics study of phase separation kinetics in thin films

We use molecular dynamics to simulate experiments where a symmetric binary fluid mixture (AB), confined between walls that preferentially attract one component (A), is quenched from the one-phase region into the miscibility gap. Surface enrichment occurs during the early stages, yielding a B-rich mixture in the film center with well-defined A-rich droplets. The droplet size grows with time as l(t) proportional t(2/3) after a transient regime. The present atomistic model is also compared to mesoscopic coarse-grained models for this problem.     

Dynamic heterogeneity of relaxations in glasses and liquids

We report an investigation of the heterogeneity in supercooled liquids and glasses using the non-Gaussianity parameter. We simulate selenium and a binary Lennard-Jones system by molecular dynamics. In the non-Gaussianity three time domains can be distinguished: an increase on the ps scale due to the vibrational (ballistic) motion of the atoms, followed by a growth, due to local relaxations ( beta relaxation) at not too high temperatures, and finally a slow drop at long times. The non-Gaussianity follows in the intermediate time domain a sqrt[t] law. This is explained by collective hopping and dynamic heterogeneity. We support this finding by a model calculation.     

Perfect Simulation of Autoregressive Models with Infinite Memory

In this paper we consider the problem of determining the law of binary stochastic processes from transition kernels depending on the whole past. These kernels are linear in the past values of the process. They are allowed to assume values close to both 0 and 1, preventing the application of usual results on uniqueness. We give sufficient conditions for uniqueness and non-uniqueness; in the former case a perfect simulation algorithm is also given.     

Variational Quantum Algorithm Applied to Collision Avoidance of Unmanned Aerial Vehicles

Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs’ collision avoidance model.     

The elliptical motion of stars in close binary systems with a conservative mass exchange

The problem of the motion of a star in a close binary system with a conservative mass exchange is considered. In contrast to the well-known Paczynski-Huang model, a new model is used that defines the motion of close binary systems in the case of an elliptical orbit. The reactive forces and the force of gravity of stars by the overflowing jet are accounted for in the elliptic motion of the star. The calculations of elliptical orbits of close binary stars show that the effect of the reactive force on the evolution of the star orbit can be different. The changes of the major axis and eccentricity of the orbit of the second star are defined. The results are applied to the BF Aurigae star system and are given in the form of figures.     

Binary Systems Around a Black Hole

We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry given by the main source. For this purpose, the motion equations are obtained in two different but equivalent ways. The particles can either be considered as a zeroth order (static) perturbation to the given metric or as an external Newtonian force in the geodesic equations. After obtaining the motion equations we perform simulations of two and three interacting particles moving around a black hole, i.e., in a Schwarzschild geometry. We also compare with the equivalent Newtonian problem and note differences in the stability, e.g., binary systems are found only in the general relativistic approach.     

Molecular dynamics simulations of surface-controlled phase separation of binary fluid mixtures confined in slit pores - Online only

When binary mixtures are confined into nanoscopic slit pores, an intricate interplay between surface enrichment (wetting) of one component and lateral phase separation occurs. After a brief review of the static equilibrium phase diagram of such systems, a discussion of the kinetics of phase separation is given. Considering quenches from an initially homogeneous distribution of the two species in the slit, it is shown by molecular dynamics simulation that typically in the initial stages a stratified structure develops, with enrichment layers of the preferred component at the walls of the slit pore. Then this laterally homogeneous structure breaks up into domains, which coarsen with time according to a power law with a 2/3 exponent. This growth law must be attributed to a hydrodynamic mechanism, since corresponding simulations of a diffusive Ginzburg-Landau model yield an exponent of 1/3 only. The relation to spinodal decomposition in d=2 space dimensions is briefly discussed.     

Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models

We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size distribution and related statistics obtained from the model. There are three well known statistical features obtained from the panel study of the firms i.e., the power law in size (in terms of income and/or employment), the Laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size. First, we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents. When the number of interacting agents is in the order of the system itself, it is possible to decouple the model. We provide exact results on the distributions which are not known yet for binary interactions. Our model easily reproduces the power law for the size distribution of firms (Zipf’s law). The fluctuations in the growth rate falls with increasing size following a power law (though the exponent does not match with the data). However, the distribution of the difference of the firm size in this model has Laplace distribution whereas the real data suggests that the difference of the log of sizes has the same distribution.     

Velocity selection problem in the presence of the triple junction

Melting of a bicrystal along the grain boundary is discussed. A triple junction plays a crucial role in the velocity selection problem in this case. In some range of the parameters an entirely analytical solution of this problem is given. This allows us to present a transparent picture of the structure of the selection theory. We also discuss the selection problem in the case of the growth of a "eutectoid dendrite."     

Localization for Linear Stochastic Evolutions

We consider a discrete-time stochastic growth model on the d-dimensional lattice with non-negative real numbers as possible values per site. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of the binary contact path process. We show the equivalence between the slow population growth and a localization property in terms of “replica overlap”. The main novelty of this paper is that we obtain this equivalence even for models with positive probability of extinction at finite time. In the course of the proof, we characterize, in a general setting, the event on which an exponential martingale vanishes in the limit.     

The Problems of Quantifying Mineral Liberation: A review

A review is given of recent publications concerning the theory of liberation of component B from AB material as particle size is reduced, with a view to combining models of liberation with models of size reduction. Although a number of approaches are promising, it is concluded that there is no adequate model of liberation of binary systems suitable for incorporation into a mill model.     

Using Background Knowledge from Preceding Studies for Building a Random Forest Prediction Model: A Plasmode Simulation Study

There is an increasing interest in machine learning (ML) algorithms for predicting patient outcomes, as these methods are designed to automatically discover complex data patterns. For example, the random forest (RF) algorithm is designed to identify relevant predictor variables out of a large set of candidates. In addition, researchers may also use external information for variable selection to improve model interpretability and variable selection accuracy, thereby prediction quality. However, it is unclear to which extent, if at all, RF and ML methods may benefit from external information. In this paper, we examine the usefulness of external information from prior variable selection studies that used traditional statistical modeling approaches such as the Lasso, or suboptimal methods such as univariate selection. We conducted a plasmode simulation study based on subsampling a data set from a pharmacoepidemiologic study with nearly 200,000 individuals, two binary outcomes and 1152 candidate predictor (mainly sparse binary) variables. When the scope of candidate predictors was reduced based on external knowledge RF models achieved better calibration, that is, better agreement of predictions and observed outcome rates. However, prediction quality measured by cross-entropy, AUROC or the Brier score did not improve. We recommend appraising the methodological quality of studies that serve as an external information source for future prediction model development.     

Analytical model of dislocation nucleation on a near-surface void under tensile surface stress

We have analyzed in detail the mechanism leading to tip growth on a surface which operates via nucleation of dislocations on a near-surface void under tensile surface stress. We derived a simplified analytical model describing the relevant physical factors related to the observed linearity between the void radius and the maximum depth of the void for the growth to occur. The model is based on the direct numerical calculation of atomic level stresses in the simulated system. Based on the present model we can estimate this maximum depth for a void of a certain size under a given stress in the size range which is beyond the feasibility of the molecular dynamics simulation method.     

Crowd Computing as a Cooperation Problem: An Evolutionary Approach

Cooperation is one of the socio-economic issues that has received more attention from the physics community. The problem has been mostly considered by studying games such as the Prisoner’s Dilemma or the Public Goods Game. Here, we take a step forward by studying cooperation in the context of crowd computing. We introduce a model loosely based on Principal-agent theory in which people (workers) contribute to the solution of a distributed problem by computing answers and reporting to the problem proposer (master). To go beyond classical approaches involving the concept of Nash equilibrium, we work on an evolutionary framework in which both the master and the workers update their behavior through reinforcement learning. Using a Markov chain approach, we show theoretically that under certain----not very restrictive—conditions, the master can ensure the reliability of the answer resulting of the process. Then, we study the model by numerical simulations, finding that convergence, meaning that the system reaches a point in which it always produces reliable answers, may in general be much faster than the upper bounds given by the theoretical calculation. We also discuss the effects of the master’s level of tolerance to defectors, about which the theory does not provide information. The discussion shows that the system works even with very large tolerances. We conclude with a discussion of our results and possible directions to carry this research further.     

Molecular dynamics simulations of the penetration lengths: application within the fluctuation theory for diffusion coefficients

Mutual diffusion in condensed phases is a theoretically and practically important subject of active research. One of the most rigorous and theoretically advanced approaches to the problem is a recently developed approach based on the concept of penetration lengths (Physica A 320 (2003) 211; Physica A 322 (2004) 151). In the current study, a fast molecular dynamics scheme has been developed to determine the values of the penetration lengths in Lennard–Jones binary systems. Results deduced from computations provide a new insight into the concept of penetration lengths. It is shown for four different binary liquid mixtures of non-polar components that computed penetration lengths, for various temperatures and compositions, are consistent with those deduced from experiments in the framework of the formalism of the fluctuation theory. Moreover, the mutual diffusion coefficients obtained from a coupled fluctuation theory and molecular dynamics scheme exhibit consistent trends and average deviations from experimental data around 10–20%.     

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where “surface fields” may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.     

Bounds on the mixing enhancement for a stirred binary fluid

The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss stirring strategies that homogenize the binary fluid. By measuring fluctuations of the composition away from its mean value, we quantify the amount of homogenization achievable. We find upper and lower bounds on our measure of homogenization using only the Cahn-Hilliard equation and the incompressibility of the advecting flow. We compare these theoretical bounds with numerical simulations for two model flows: the constant flow, and the random-phase sine flow. Using the sine flow as an example, we show how our bounds on composition fluctuations provide a measure of the effectiveness of a given stirring protocol in homogenizing a phase-separating binary fluid.     

Binary Level Set Methods for Dynamic Reservoir Characterization by Operator Splitting Scheme

In this paper, operator splitting scheme for dynamic reservoir characterization by binary level set method is employed. For this problem, the absolute permeability of the two-phase porous medium flow can be simulated by the constrained augmented Lagrangian optimization method with well data and seismic time-lapse data. By transforming the constrained optimization problem in an unconstrained one, the saddle point problem can be solved by Uzawas algorithms with operator splitting scheme, which is based on the essence of binary level set method. Both the simple and complicated numerical examples demonstrate that the given algorithms are stable and efficient and the absolute permeability can be satisfactorily recovered.