Modeling th dynamics of charged drop of one liquid in another under the action of an electric field

The work is devoted to the study of the features of the behavior of a group of droplets of one viscous liquid in another under the influence of various physical fields. When considering the dynamics of two drops under the action of an electric field, it is assumed that a drop in the form of a sphere with radius а will be placed in an electric field with an intensity , investigates how droplets will react to each other under the influence of an electric field. A mathematical model has been built and a computer program has been developed for the numerical solution of this problem. The behavior of several drops in an electric field is studied for different physical parameters of the material of the drops and the environment, as well as for different initial distributions of drops and the strength of the electric field. It is shown for the first time that emulsion droplets distributed in space, under the action of an electric field, begin to move and after a certain time a new stationary structure of droplets is formed. It was found that the relaxation time depends on the electric field strength, the size of the droplets and their initial distribution.

Subgeometric ergodicity and β-mixing

It is well known that stationary geometrically ergodic Markov chains are $\beta$ -mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$ -mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$ -mixing with subgeometrically decaying mixing coefficients. Although this result is simple, it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity cannot be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$ -mixing results for the self-exciting threshold autoregressive model.

Mean field approach to stochastic control with partial information

In our present article, we follow our way of developing mean field type control theory in our earlier works [4], by first introducing the Bellman and then master equations, the system of Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) equations, and then tackling them by looking for the semi-explicit solution for the linear quadratic case, especially with an arbitrary initial distribution; such a problem, being left open for long, has not been specifically dealt with in the earlier literature, such as [3, 13], which only tackled the linear quadratic setting with Gaussian initial distributions. Thanks to the effective mean-field theory, we propose a solution to this long standing problem of the general non-Gaussian case. Besides, our problem considered here can be reduced to the model in [2], which is fundamentally different from our present proposed framework.

Different Behavioral Types of Distributional Preferences Are Characterized by Distinct Neural Signatures

There are many situations where resources are distributed between two parties and where the deciding party has information about the initial distribution and can change its outcome, for example, the allocation of budget for funds or bonuses, where the deciding party might have self-interested motives. Although the neural underpinnings of distributional preferences of resources have been extensively studied, it remains unclear if there are different types of distributional preferences and if these types underlie different disposing neural signatures. We used source-localized resting EEG in combination with a data-driven clustering approach to participants' behavior in a distribution game in order to disentangle the neural sources of the different types of distributional preferences. Our findings revealed four behavioral types: Maximizing types always changed initial distributions to maximize their personal outcomes, and compliant types always left initial distributions unchanged. Disadvantage-averse types only changed initial distributions if they received less than the other party did, and equalizing types primarily changed initial distributions to fair distributions. These behavioral types differed regarding neural baseline activation in the right inferior frontal gyrus. Maximizing and compliant types showed the highest baseline activation, followed by disadvantage-averse types and equalizing types. Furthermore, maximizing types showed significantly higher baseline activation in the left OFC compared to compliant types. Taken together, our findings show that different types of distributional preferences are characterized by distinct neural signatures, which further imply differences in underlying psychological processes in decision-making.

Quantum relaxation in a system of harmonic oscillators with time-dependent coupling

In the context of the de Broglie–Bohm pilot-wave theory, numerical simulations for simple systems have shown that states that are initially out of quantum equilibrium—thus violating the Born rule—usually relax over time to the expected | ψ | 2 distribution on a coarse-grained level. We analyse the relaxation of non-equilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators in which the coupling depends explicitly on time through numerical simulations, focusing on the influence of different parameters such as the number of modes, the coarse-graining length and the coupling constant. We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters, particularly to the one related to the strength of the interaction. Possible implications on the detection of relic non-equilibrium systems are discussed.

Conditional particle filters with diffuse initial distributions

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.

Non-Homogeneous Markov Set Systems

A more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application.

A new weighted fraction Monte Carlo method for particle coagulation

Purpose The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method. Design/methodology/approach The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme. Findings Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated. Originality Value Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

Implementing Primordial Binaries in Simulations of Star Cluster Formation with a Hybrid MHD and Direct N-Body Method

The fraction of stars in binary systems within star clusters is important for their evolution, but what proportion of binaries form by dynamical processes after initial stellar accretion remains unknown. In previous work, we showed that dynamical interactions alone produced too few low-mass binaries compared to observations. We therefore implement an initial population of binaries in the coupled MHD and direct N-body star cluster formation code Torch. We compare simulations with, and without, initial binary populations and follow the dynamical evolution of the binary population in both sets of simulations, finding that both dynamical formation and destruction of binaries take place. Even in the first few million years of star formation, we find that an initial population of binaries is needed at all masses to reproduce observed binary fractions for binaries with mass ratios above the q ≥ 0.1 detection limit. Our simulations also indicate that dynamical interactions in the presence of gas during cluster formation modify the initial distributions towards binaries with smaller primary masses, larger mass ratios, smaller semi-major axes and larger eccentricities. Systems formed dynamically do not have the same properties as the initial systems, and systems formed dynamically in the presence of an initial population of binaries differ from those formed in simulations with single stars only. Dynamical interactions during the earliest stages of star cluster formation are important for determining the properties of binary star systems.

Planet formation and disc mass dependence in a pebble-driven scenario for low-mass stars

ABSTRACT Measured disc masses seem to be too low to form the observed population of planetary systems. In this context, we develop a population synthesis code in the pebble accretion scenario, to analyse the disc mass dependence on planet formation around low-mass stars. We base our model on the analytical sequential model presented by Ormel, Liu, and Schoonenberg and analyse the populations resulting from varying initial disc mass distributions. Starting out with seeds the mass of Ceres formed by streaming instability inside the ice-line, we grow the planets using the pebble accretion process and migrate them inwards using type I migration. The next planets are formed sequentially after the previous planet crosses the ice line. We explore different initial distributions of disc masses to show the dependence of this parameter with the final planetary population. Our results show that compact close-in resonant systems can be pretty common around M dwarfs between 0.09 and 0.2 M⊙ only when the discs considered are more massive than what is being observed by sub-mm disc surveys. The minimum disc mass to form a Mars-like planet is found to be about 2 × 10−3 M⊙. Small variations in the disc mass distribution also manifest in the simulated planet distribution. The paradox of disc masses might be caused by an underestimation of the disc masses in observations, by a rapid depletion of mass in discs by planets growing within 1 million years, or by deficiencies in our current planet formation picture.