Methods Of Kinetic Theory Research Articles

Four-way coupled second-order method of two-fluid model for gas-particle flow and the numerical simulation in horizontal channels

In this study, a four-way coupled second-order method of Eulerian-Eulerian two-fluid model is proposed to numerically investigate the gas-particle flow, where exist particle-particle collisions, however, the particle turbulence is far from equilibrium to satisfy the Boussinesq approximation. The second-order two-fluid model is developed by coupling the gas phase model of Reynolds-averaged Navier-Stokes method closed by the second-order Reynolds stress turbulence model with the particle simulation equations of second-order moment method of kinetic theory of granular flow. The four-way coupling method is established considering the particle-particle collisions and fluid-particle interactions, which are represented by the momentum exchange between two phases, fluid turbulence generation and/or dissipation due to the presence of particles, and the particle fluctuation due to drag fluctuations. Furthermore, the model is applied to the pneumatic conveying in a horizontal channel to demonstrate the Eulerian-Eulerian two-fluid modeling of the gas-particle flow in the median concentration of the particles. The model is found superior to the two-way coupled method and the classic isotropic method of kinetic theory of granular flow. The simulation results are in good agreement with the experimental results.

Diffusion, Trapping, and Dissociation Behaviours of Helium at the Σ5 Grain Boundary in Tungsten: A Molecular Dynamics Study

Tungsten (W) is a promising candidate for plasma-facing materials in future fusion devices because of its excellent properties. Quantitatively understanding and describing the behaviours of helium (He) in polycrystalline W is important for determining the long-term structural evolution of these materials under extreme operating conditions. However, there exist some intrinsic difficulties in the determination of the key parameters to describe various dynamical processes via static methods. Therefore, it is necessary to extend new models based on molecular dynamics (MD) simulations to abstract the dynamical parameters. In this study, the diffusion, trapping, and dissociation behaviours of He at the Σ5<100>(310) symmetric tilt grain boundaries (GBs) in W were systematically investigated using MD simulations. The key parameters, including the diffusion coefficients of He in bulk W (bulk He) and He trapped by GB (GB-He), the dissociation coefficients of GB-He, and absorbing probability of He by GB were firstly identified using mean square displacement, a coarse-grained model, and a continuous diffusion theory (CDT)-based model. The temperature effect on the diffusivity of GB-He and the dissociation coefficient of GB-He can be described by the Arrhenius relationship, but the temperature effect on the diffusion of bulk He is non-Arrhenius. The diffusion of GB-He is significantly anisotropic; the GB is a strong sink for interstitial He and acts as an inhibitor of He diffusion. The migration of He in the GB can be frequent before the dissociation of GB-He when the temperature increases. The trapping behaviour of He by the GB is described by one CDT-based model, which means that GB can be modelled as an absorbing layer that absorbs He atoms with one probability when the He atoms migrate to the impurity-free zone near the GB plane. This work not only presents a systematic study on the interaction between He atom and GB in W, but also provides some extended models to abstract the key dynamical parameters describing the behaviours of He atom near the GB in W and these abstracted transport parameters for the long-term simulation methods, such as kinetic Monte Carlo and rate theory method. Furthermore, this work gives a good example of supporting the long-term simulation methods by offering transport coefficients from MD simulations.

A hybrid thermostatted kinetic framework for the modeling of a hybrid multisource system with storage

The planning and development of a hybrid energy source network is based on an optimal analysis which takes into account the connection costs and the production facilities. This paper aims at modeling a hybrid multisource system by employing the methods of the thermostatted kinetic theory. Specifically a network of energy sources is allocated into a geographical domain, which is divided into different regions each of them containing different energy sources. A hybrid kinetic theory framework is proposed where the energy source is identified by a quality parameter which can attain discrete values, whereas the energy supplied by the source is modeled by defining a continuous variable. The mathematical framework consists into a system of partial integro-differential equations with quadratic type nonlinearities whose parameters are interaction rates and probability density functions. The storage system is also modeled by introducing an external force field coupled with a mathematical thermostat for ensuring the conservation of the activation energy of the energy network. The existence and uniqueness of the solution is investigated by employing fixed point arguments and integration along the characteristic curves. A critical analysis and research perspectives conclude the paper showing that the proposed thermostatted kinetic theory frameworks can be considered as general paradigms for the derivation of specific models.

Simulation and analysis of physical characteristics of a molecular beam in a collimator using methods of kinetic theory

The paper is dedicated to the study of gas outflow from a vessel for the case of a simple collimator and to the determination of molecular beam and collimator characteristics enabling a maximum reduction in the beam width. A software system was developed for studying gas flow in various geometries using the GP-GPU.

Nonlinear Electrophysical Phenomena in Ionic Dielectrics with a Complicated Crystal Structure

The methods of quasi-classical kinetic theory are used to study the phenomena of nonlinear relaxation polarization in ionic dielectrics with a complicated crystal lattice structure (layered crystals, ceramics, perovskites, vermiculites, etc.) characterized by high ionic conductivity. A special case of materials of this class are proton semiconductors and dielectrics (mica, talc, pyrophyllite, etc.) characterized by high proton conductivity in fairly wide ranges of field parameters (100 kV/m – 1000 MV/m) and temperatures (1–1500 K). Based on the continuity equation for the ion current, a generalized kinetic equation is constructed that describes transfer of electric charge in ionic dielectrics in an alternating polarizing field with blocking electrodes. The nonlinearity of the mathematical model is ensured by the dependences of the diffusion coefficients and ion mobility on the parameters of the inhomogeneous electric field in the dielectric. It is shown that the Fokker–Planck equation, known in the kinetic theory, is a zero approximation of the generalized nonlinear kinetic equation with respect to a small dimensionless parameter. The dielectric polarization is written from the solution of the Fokker–Planck equation in the infinite approximation of the perturbation theory (k = 1, 2, 3, ...) for an arbitrary value of the multiplicity factor r over the alternating field frequency. The spectra of a complex dielectric permittivity constructed at the fundamental frequency of the alternating field (r = 1) taking into account all subsequent (starting from the second one) approximations of the perturbation theory (k > 1) differ significantly from the classical laws of the Debye dispersion (corresponding to the first approximation of the perturbation theory (k = 1)). The theoretical foundations have been laid for the program algorithms of computer prediction of properties and parameters of electrical materials for the functional elements of the microelectronic device circuits, isolation technology, and non-volatile high-speed memory devices.

Determination of the vapor film thickness at steady superfluid helium film boiling

Heat mass transfer processes at superfluid helium boiling is considered for different conditions. Mathematical description is formulated with taking into account the peculiarities of superfluid helium. System of equations is based on the methods of continuum mechanics and molecular kinetic theory. Pressure distribution in the liquid is determined by the hydrostatic difference. At the vapor-liquid interface the Laplace formula is used. The vapor pressure in the film is determined by the non-equilibrium effects in the vapor near the interface. Heat transfer in a liquid is described by the Gorter-Mellink semi-empirical theory. Experimental data on the stationary boiling of superfluid helium under various conditions are interpreted based on the formulated mathematical model. For all cases in the considered range of parameters, the qualitative and in some cases quantitative agreement between the calculated and experimental values of the vapor film thickness were obtained.

Determination of the recovery heat flux at superfluid helium film boiling in different conditions

The calculation of the recovery heat flux density is considered for different conditions to investigate heat mass transfer processes. System of equations is based on the methods of continuum mechanics and molecular kinetic theory. Pressure distribution in the liquid is determined by the hydrostatic difference. At the vapor-liquid interface the Laplace formula is used. The vapor pressure in the film is determined by the non-equilibrium effects in the vapor near the interface. Heat transfer in a liquid is described by the Gorter-Mellink semi-empirical theory. Experimental data on the boiling of superfluid helium under various conditions are interpreted based on the formulated mathematical model. For all cases in the considered range of parameters, the qualitative and in some cases quantitative agreement between the calculated and experimental values of the recovery heat flux were obtained.

Kinetic Modeling of Alcohol Consumption

In most countries, alcohol consumption distributions have been shown to possess universal features. Their unimodal right-skewed shape is usually modeled in terms of the Lognormal distribution, which is easy to fit, test, and modify. However, empirical distributions often deviate considerably from the Lognormal model, and both Gamma and Weibull distributions appear to better describe the survey data. In this paper we explain the appearance of these distributions by means of classical methods of kinetic theory of multi-agent systems. The microscopic variation of alcohol consumption of agents around a universal \emph{social} accepted value of consumption, is built up introducing as main criterion for consumption a suitable value function in the spirit of the prospect theory of Kahneman and Twersky. The mathematical properties of the value function then determine the unique macroscopic equilibrium which results to be a generalized Gamma distribution. The modeling of the microscopic kinetic interaction allows to clarify the meaning of the various parameters characterizing the generalized Gamma equilibrium.

Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives

This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of the kinetic models developed in the last 10 years on the aforementioned topics so that overlapping with previous reviews can be avoided. Although the main focus of this paper lies on the mesoscopic models for collective dynamics, we provide a brief overview on the corresponding micro and macroscopic models, and discuss intermediate role of mesoscopic model between them. Moreover, we provide a number of selected challenging research perspectives for readers’ attention.

Simulation of Transport Coefficients of Aerosols and Nanofluids with Hollow Nanoparticles

Diffusion of hollow nanoparticles in low-density and rarefied gases and the viscosity of aerosols with such particles are studied using the previously developed kinetic theory and molecular dynamics method. Nitrogen-based aerosols with hollow and solid aluminum and uranium nanoparticles are considered at a temperature of 300 K and atmospheric pressure. Diameter of the nanoparticles was varied from 5 to 100 nm; the thickness of walls of hollow nanoparticles was 1 nm. It is shown that the diffusion coefficients of hollow nanoparticles always exceed those of solid particles of the same size and the same material, but this difference does not exceed 1%. The viscosity of aerosols with hollow nanoparticles is always lower than of aerosols with solid particles. Using the molecular dynamics method, the diffusion coefficients of hollow and solid nanoparticles of the same diameter and the same material in dense argon are found to be equal.

On the Complex Interaction between Collective Learning and Social Dynamics

This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed. Our work focuses on the study of the interactions between learning dynamics and other types of dynamics which can be modeled by kinetic theory methods. The contents are presented in three parts. First, a general description of different theories of learning dynamics within the framework of cognitive sciences is critically analyzed with the aim of capturing the main features of the system towards modeling. Subsequently, the class of systems which are the object of the modeling approach is defined by showing how the previous structure can be developed, thanks to new conceptual ideas, including the concept of symmetric and asymmetric learning, towards modeling. Finally, some applications are selected to show how the approach can be methodologically applied.

A Critical Analysis of Behavioural Crowd Dynamics—From a Modelling Strategy to Kinetic Theory Methods

This paper proposes a critical analysis of the literature addressed to modelling and simulations of human crowds with the aim of selecting the most appropriate scale out of the microscopic (individual based), mesoscopic (kinetic), and macroscopic (hydrodynamical) approaches. The selection is made focusing on possible applications of the model. In particular, model validation and safety problems, where validation consists of studying the ability of models to depict empirical data and observed emerging behaviors. The contents of the paper look forward to computational applications related to the flow crowds on the Jamarat bridge.

Chemical Equilibration in Hadronic Collisions

We study chemical equilibration in out-of-equilibrium quark-gluon plasma using the first principles method of QCD effective kinetic theory, accurate at weak coupling. In longitudinally expanding systems-relevant for relativistic nuclear collisions-we find that for realistic couplings chemical equilibration takes place after hydrodynamization, but well before local thermalization. We estimate that hadronic collisions with final state multiplicities dN_{ch}/dη≳10^{2} live long enough to reach approximate chemical equilibrium, which is consistent with the saturation of strangeness enhancement observed in proton-proton, proton-nucleus, and nucleus-nucleus collisions.

Аналитическое исследование нелинейных электрофизических процессов в протонных полупроводниках и диэлектриках

This paper presents the investigation of the mechanism of nonlinear proton-relaxation polarization in hydrogen-bonded crystals (HBC), classified by their electrophysical properties as proton semiconductors and dielectrics (PSCD), by quasi-classical kinetic theory methods. The generalized kinetic equation that is nonlinear in the field and based on the continuity equation for proton flow is developed to describe the proton relaxation in HBC for a wide range of temperatures (1-1500 К) and electric field strengths (100 kV/m - 1000 MV/m). The proposed scheme (the model) allows to build numerical solutions of the generalized nonlinear Fokker - Planck equation together with the Poisson equation by using the method of successive approximations (at small dimensionless parameter). A scientific and practical significance of the received results consists in the applicability of this mathematical model (with respect to some experimental assumptions) to investigate the mechanism of ion-relaxation polarization and conductivity in heterogeneous dielectric materials (mica, ceramics, perovskites, KDP, DKDP, etc.) which is of high demand in various areas of modern industry. Further research goals are to promote the proposed methods as a theoretical basis for computer algorithms of numerical optimization and prediction of properties and parameters of functional elements and components of industrial equipment and systems working in wide ranges of fields and temperatures.

Solid solution decomposition and Guinier-Preston zone formation in Al-Cu alloys: A kinetic theory with anisotropic interactions

Using methods of statistical kinetic theory parametrized with first-principles interatomic interactions that include chemical and strain contributions, we investigated the kinetics of decomposition and microstructure formation in Al-Cu alloys as a function of temperature and alloy concentration. We show that the decomposition of the solid solution forming platelets of copper, known as Guinier-Preston (GP) zones, includes several stages and that the transition from GP1 to GP2 zones is determined mainly by kinetic factors. With increasing temperature, the model predicts a gradual transition from platelet-like precipitates to equiaxial ones and at intermediate temperatures both precipitate morphologies may coexist.

Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods

ABSTRACTThis paper deals with the modelling of pedestrian dynamics at the entry of a metro station by means of the thermostatted kinetic theory framework. Specifically, the model depicts the time evolution of the pedestrian dynamics at the turnstiles under no panic conditions. The modelling of the microscopic interactions is based on the stochastic game theory and reflects the decision dynamics of the turnstiles pursued by pedestrians. A qualitative analysis is addressed to the equilibrium solutions by means of the classical stability theory of perturbations. Numerical simulations aim at showing the emerging behaviours captured by the model. In particular the model validation is obtained by performing a sensitivity analysis on the parameters and on the initial conditions. Further refinements and research perspective, including the modelling under panic conditions, are discussed in the last section of the paper.

Validation of vibration-dissociation coupling models in hypersonic non-equilibrium separated flows

The validation of recently developed models of vibration-dissociation coupling is discussed in application to numerical solutions of the Navier–Stokes equations in a two-temperature approximation for a binary N2/N flow. Vibrational-translational relaxation rates are computed using the Landau–Teller formula generalized for strongly non-equilibrium flows obtained in the framework of the Chapman–Enskog method. Dissociation rates are calculated using the modified Treanor–Marrone model taking into account the dependence of the model parameter on the vibrational state. The solutions are compared to those obtained using traditional Landau–Teller and Treanor–Marrone models, and it is shown that for high-enthalpy flows, the traditional and recently developed models can give significantly different results. The computed heat flux and pressure on the surface of a double cone are in a good agreement with experimental data available in the literature on low-enthalpy flow with strong thermal non-equilibrium. The computed heat flux on a double wedge qualitatively agrees with available data for high-enthalpy non-equilibrium flows. Different contributions to the heat flux calculated using rigorous kinetic theory methods are evaluated. Quantitative discrepancy of numerical and experimental data is discussed.

Generalized Boltzmann-Type Equations for Aggregation in Gases

The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker–Doring-type equation). The transition to a continuum description is performed.

Kinetic theory simulation of LiNbO3 thin films deposition distribution by pulsed laser deposition

ABSTRACTIn this paper, the progress of LiNbO3 thin films formation was simulated by kinetic theory method. The whole Plused Laser Deposition (PLD for short) process was considered: LiNbO3 particles were sublimated to high density plasma after laser erosion and propagated into space and then deposited into thin films. And the thickness of LiNbO3 thin films was discussed, which reflected the surface roughness and crystal type.The particles speed and distribution in the plasma were considered and discussed, and the roughness distribution of the films along the radius has been discussed. The thickness change could indicate the growth mode of the films along the radius. The detailed explanation of the PLD experiment was established.

Determination of Parameters of Endurance Limit Distribution Law of Material by the Methods of Nonparametric Statistics and Kinetic Theory of High-Cycle Fatigue

The paper considers the first developed algorithm of processing the data of specimen life tests based on the kinetic theory of mechanical fatigue and methods of nonparametric statistics. It makes it possible to determine the distribution density function of the material endurance limit. Implementation of the algorithm is illustrated on example of processing the data obtained in fatigue tests of steel 50 specimens.