Kinetic Theory Model Research Articles

Analysis of one-dimensional electromagnetic wave transmission characteristics of plasma based on a kinetic theory model

This paper utilizes a kinetic theory model to gain the accurate electromagnetic (EM) wave characteristics in the plasma region, based on the solution of Maxwell-Boltzmann (MB) equation system. The system is solved by finite-difference time-domain (FDTD) algorithm, which gives the results of the electric field intensity and particle velocity distribution function. Furthermore, the validity and effectiveness of the proposed method is verified by comparing the results of reflection coefficient and transmission coefficient of the wave that impinges on plasma plate region with that of the analytic solution.

Understanding the bursty electron cyclotron emission during a sawtooth crash in the HT-7 tokamak

Bursts in electron cyclotron emission (ECE) were observed during sawtooth crashes in HT-7 in discharges with ion cyclotron resonance heating injected near the q = 1 rational surface (q is the safety factor). The local ECE measurement indicated that the bursty radiation is only observed on channels near but a little away outward from the q = 1 magnetic surface. In conjunction with the soft x-ray tomography analysis, it was determined that, for the first time, only a compression process survives in the later stage of fast magnetic reconnection but before prompt heat transport. The compression enhanced the electron radiation temperature, the increased amplitude of which agreed well with the estimation according to a kinetic compression theory model [R. J. Hastie and T. C. Hender, Nucl. Fusion 28, 585 (1988)]. This paper presents the experimental evidence that there indeed exists a transient compression phase which results in the bursty ECE radiation during a sawtooth crash.

ON A DISPERSIVE MODEL FOR THE UNZIPPING OF DOUBLE-STRANDED DNA MOLECULES

The paper deals with the analysis of a nonlinear Fokker–Planck equation modeling the mechanical unzipping of double-stranded DNA under the influence of an applied force. The dependent variable is the probability density of unzipping m base pairs. The nonlinear Fokker–Planck equation we propose here is obtained when we couple the model proposed in [D. K. Lubensky and D. R. Nelson, Pulling pinned polymers and unzipping DNA, Phys. Rev. Lett.85 (2000) 1572–1575] with a transcendental equation for the applied force. The resulting model incorporates nonlinear effects in a different way than the usual models in kinetic theory. We show the well-posedness of this model. For that we require a combination of techniques coming from second-order kinetic equations and compensated compactness arguments in conservation laws.

Molecular dynamics simulations of the diffusion and coalescence of helium in tungsten

Molecular dynamics (MD) simulations are performed on the diffusion and coalescence of helium in tungsten. A new method for determining the effective capture radii (ECRs) and the dissociation energies of helium-related defects is proposed in this work. It is observed that the ECR of an interstitial helium atom trapping helium interstitials (denoted as He–Hen, n=1–3) decreases with increasing temperature, except for He–He2 at T<400K. The traditional view that the ECR is approximately equal to the lattice constant, which has been widely used in kinetic Monte Carlo (KMC) and rate theory (RT) models, is only valid in some cases. However, the ECR between an interstitial helium atom and a substitutional helium atom (denoted as He–HeV) always approximates the third nearest-neighbor tetrahedral positions of the HeV. The diffusion coefficients Dn for helium clusters are also investigated. He2 migrates more quickly than a single He atom does at T<400K, whereas the diffusion path of He2 changes at higher temperatures. Another counterintuitive observation is that D5>D3>D4 at T<500K, which can be attributed to the disordered structure of He5. The Arrhenius relation describes the diffusion of Hen well in the temperature range from 300K to 550K, whereas the diffusion is not a standard thermally activated process at higher temperatures. Taken together, these results help elucidate the initial stage of helium bubble formation in tungsten as well as the requirements of long-term evolution methods such as KMC or RT models.

Kinetic theory of acoustic-like modes in nonextensive pair plasmas

The low-frequency acoustic-like modes in a pair plasma (electron-positron or pair-ion) is studied by employing a kinetic theory model based on the Vlasov and Poisson's equation with emphasizing the Tsallis's nonextensive statistics. The possibility of the acoustic-like modes and their properties in both fully symmetric and temperature-asymmetric cases are examined by studying the dispersion relation, Landau damping and instability of modes. The resultant dispersion relation in this study is compatible with the acoustic branch of the experimental data [W. Oohara, D. Date, and R. Hatakeyama, Phys. Rev. Lett. 95, 175003 (2005)], in which the electrostatic waves have been examined in a pure pair-ion plasma. Particularly, our study reveals that the occurrence of growing or damped acoustic-like modes depends strongly on the nonextensivity of the system as a measure for describing the long-range Coulombic interactions and correlations in the plasma. The mechanism that leads to the unstable modes lies in the heart of the nonextensive formalism yet, the mechanism of damping is the same developed by Landau. Furthermore, the solutions of acoustic-like waves in an equilibrium Maxwellian pair plasma are recovered in the extensive limit ($q\rightarrow1$), where the acoustic modes have only the Landau damping and no growth.

'과학1' 중학교 교과서의 물질의 상태 변화와 분자 운동 내용이 요구하는 인지 수준 분석(제III보)

우리나라 중학교 '과학1'에 실려 있는 '물질의 상태 변화'와 '분자의 운동'에 대한 서술 내용이 요구하는 인지 요구도를 분석하였다. '분자의 운동'에는 '확산과 증발', '기체의 압력과 부피', '기체의 온도와 부피', 그리고 '상태 변화와 열에너지' 개념이 포함된다. 인지 요구도 분석에 활용한 분석 준거는 영국에서 개발된 과학 교과 내용 분류틀에 있는 3종류 분석틀이다. 분석 대상인 6종 교과서 내용들이 요구하는 인지 수준들은 구체적 조작 수준과 형식적 조각 수준들이 다양하였다. 해당 내용에는 여러 인지 수준들이 있으나 그 중에서도 높은 인지 수준을 요구하는 내용들을 보면 다음과 같다. 첫째, 단원 초기에 물질의 세 가지 상태를 설명할 때에는 그 서술 내용이 요구하는 높은 인지 수준이 6종 모두 후기 구체적 조작 수준이다. 그러나 단원의 초기 이후부터는 이에 대한 설명이 모두 초기 형식적 수준이다. 분자 배열과 분자 모형에 관한 내용이 요구하는 높은 인지 수준은 모든 6종 교과서가 분자 운동으로 서술하고 있기 때문에 초기 형식적 조작 수준이다. 둘째, 확산과 증발 개념에 대한 내용이 요구하는 높은 인지 수준은 6종 교과서 모두 초기 형식적 조작 수준이다. 왜냐하면 상태 변화를 분자 운동론으로 서술하고 있어서 초기 형식적 조작 수준이다. 셋째, 기체의 압력과 부피, 기체의 온도와 부피 개념에 대한 내용이 요구하는 높은 인지 수준은 교과서 6종 모두 초기 형식적 조작 수준이다. 분자 운동을 이용한 형식적 모델을 이해해야 하고 그리고 그래프를 통해 보일 법칙과 샤를 법칙을 이해해야 하기 때문에 학생들은 고차식의 그래프를 해석해야 하며, 두 독립변수 사이의 관계를 발견해야 하므로 초기 형식적 조작 수준이다. 넷째, 상태 변화와 열에너지 개념에 대한 내용이 요구하는 높은 인지 수준은 교과서 6종 모두 초기 형식적 조작 수준이다. 물질의 끓는점과 어는점을 설명하는 고차식 그래프의 해석 능력을 요구하고 있기 때문에 초기 형식적 조작 수준이다. 물질의 상태 변화와 온도의 관계도 분자 운동론을 이용하여 서술하고 있기 때문에 초기 형식적 조작 수준이다. The purpose of this study is to analyze the cognitive demands level of the description about 'changes of state' and 'kinetic theory' on the 'science 1' textbooks by the 2007 revised curriculum. The three types of curriculum analysis taxonomy have been used to analyze the cognitive demands level of those contents on the 6 kinds of 'science 1' textbooks. The most higher level of cognitive demands about the concepts have been discussed here due to the focus of the concepts. The first, the cognitive demand level about 'three states of substances' depending on the motion of their particles in 6 textbooks is a early formal operational stage because of using by the application of kinetic theory. The second, the cognitive demand level about 'diffusion' and 'evaporation' is a early formal operational stage, because the particles move around faster so they can change their position. The third, the cognitive level of the pressure and volume in a gas is a early formal operational stage because of explaining only phenomena in simple correspondence with formal model of kinetic theory. And simple functional relationships beyond linear on the graph of the volume and pressure of gas, the volume and temperature of gas is also a early formal operational stage. The fourth, the cognitive level of the energy of heat by a change of the state is also a early formal operational stage because kinetic theory picture accepted as providing explanation by the change of the state. And functional relationships beyond linear on the graph of the explanation of boiling point of water in water is also a early formal operational stage.

A modified kinetic theory for frictional granular flows in dense and dilute regimes

Continuum modelingof granular and gas-solid flows generally involves the use of a kinetic-theory (KT) model for the particulate phase, and the most widely used KT models have been derived for dilute flows of smooth, frictionless spheres. In reality, however, granular particles are frictional and can achieve dense packing, and these features must be taken into account to improve rheological predictions in these flow scenarios. Existing approaches in the literature for producing closed-form KT-based models employ empirical modifications to adapt the original models for use in dense and frictional systems. In this article, we investigate the capacity for such modifications to improve the rheological predictions of the Garzó–Dufty (GD) KT model[V. Garzó and J. W. Dufty, “Dense fluid transport for inelastic hard spheres,” Phys. Rev. E59, 5895–5911 (1999)]10.1103/PhysRevE.59.5895. On the basis of molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional spheres, we propose a new expression for the radial distribution function at contact as well as modifications to the GD expressions for shear stress and energy dissipation rate. These changes account for dense-regime scalings observed in inertial-number models as well as the effects of interparticle friction while preserving the dynamic nature of the KT model.

Two-Scales Kinetic Theory Model of Short-Fibers Aggregates

This paper proposes a first attempt to define a two scales kinetic theory to describe concentrated suspensions involving short fibers, nano-fibers or nanotubes. In this case, fiber-fiber interactions can not be neglected and rich microstructures issued from these interactions can be observed, involving a diversity of fibers clusters or aggregates with complex kinematics, and different sizes and shapes. These clusters can interact to create larger clusters and also break because the flow induced hydrodynamic forces. In this paper we propose a double-scale model to describe such microstructure: at the finest scale we study the cluster kinematic based on the behaviour of the rods that constitute it, at a coarser scale, we use clusters distribution to derive the effect of the clusters presence on the suspensions properties.

KINETIC LIMITS FOR PAIR-INTERACTION DRIVEN MASTER EQUATIONS AND BIOLOGICAL SWARM MODELS

We consider a class of stochastic processes modeling binary interactions in an N-particle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair-interaction driven master equations. In the spatially homogeneous case, we prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well-known result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.

From Single-Scale to Two-Scales Kinetic Theory Descriptions of Rods Suspensions

This paper proposes a first attempt to define a two-scales kinetic theory description of suspensions involving short fibers, nano-fibers or nanotubes. We start revisiting the description of dilute enough suspensions for which microscopic, mesoscopic and macroscopic descriptions are available and all them have been successfully applied for describing the rheology of such suspensions. When the suspensions become too concentrated fiber-fiber interactions cannot be neglected and then classical dilute theories fail for describing the rich microstructure evolution. In the semi-concentrated regime some interaction mechanisms that mimetic the randomizing effect of fiber-fiber interactions were successfully introduced. Finally, when the concentration becomes high enough, richer microstructures can be observed. They involve a diversity of fiber clusters or aggregates with complex kinematics, and different sizes and shapes. These clusters can interact to create larger clusters and also break because the flow induced hydrodynamic forces. In this paper we propose a double-scale kinetic theory model that at the first scale consider the kinematics of the clusters, whose structure itself is described at the finest scale, the one related to the rods constituting the clusters.

From the Microscale to Collective Crowd Dynamics

This paper deals with the kinetic theory modeling crowd dynamics with the aim of showing how the dynamics at the microscale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations are treated by finite difference methods for hyperbolic equations. Some preliminary reasoning toward the modeling of panic conditions is proposed.

An initial assessment of a mechanistic model, GRASS-SST, in U–Pu–Zr metallic alloy fuel fission-gas behavior simulations

A mechanistic kinetic rate theory model originally developed for the prediction of fission gas behavior in oxide nuclear fuels under steady-state and transient conditions has been assessed to investigate its applicability to model fission gas behavior in U–Pu–Zr metallic alloy fuel. In order to capture and validate the underlying physics for irradiated U–Pu–Zr fuels, the mechanistic model was applied to evaluate fission gas release, fission gas and fission product induced swelling, and detailed gas bubble size distributions in three different fuel zones: the outer α-U, the intermediate, and the inner γ-U zones.Due to its special microstructural features, the α-U zone in U–Pu–Zr fuels is believed to contribute the largest fraction of fission gas release among the different fuel zones. It is shown that with the use of small effective grain sizes, the mechanistic model can predict fission gas release that is in reasonable consistence with (though slightly lower than) experimentally measured data. These simulation results are comparable to the experimentally measured fission gas release since the mechanism of fission gas transport through the densely distributed laminar porosity in the α-U zone is analogous to the mechanism of fission gas transport through the interconnected gas bubble porosity utilized in the mechanistic model.Detailed gas bubble size distributions predicted with the mechanistic model in both the intermediate zone and the high temperature γ-U zone of U–Pu–Zr fuel are also compared to experimental measurements from available SEM micrographs. These comparisons show good agreement between the simulation results and experimental measurements, and therefore provide crucial guidelines for the selection of key physical parameters required for modeling these two zones. Material properties such as fuel grain size and thermal diffusivity of gas and model parameters such as di-atom nucleation probability and gas bubble re-solution constant are predicted by these comparisons. In addition, the results of parametric studies for several parameters are presented for both the intermediate zone and the γ-U zone simulations in order to clarify the sensitivities of simulation results on these parameters.

An adiabatic piston in a temperature gradient

The steady states of two gases of hard spheres or disks separated by an adiabatic piston in the presence of a temperature gradient are discussed. The temperature field is generated by two thermal walls at different temperatures, each of them in contact with one of the gases. The presence of the piston strongly affects the hydrodynamic fields, inducing a jump in its vicinity. A simple kinetic theory model is formulated. Its predictions are shown to be in good agreement with molecular dynamics simulation results. The applicability of the minimum entropy production principle is analyzed, and it is found that it only provides an accurate description of the system in the limit of a small temperature gradient.

Observed Mixing Behavior of Single Particles in a Bubbling Fluidized Bed of Higher-Density Particles

We report experimental observations of the dynamic behavior of single, magnetically tagged 3—4 mm particles varying in density from 0.55 g/cm 3 to 1.2 g/cm 3 as they migrate freely in a bubbling air-fluidized bed of 177—250 μm glass beads of 2.5 g/cm 3 density over a range of air flows. The densities of the tracer particles (made by imbedding small magnets in wooden particles) were chosen to span a range typical for many biomass materials and exhibited both segregated and well-mixed behavior. Using high-speed measurements from externally mounted magnetic probes, we were able to reconstruct three-dimensional spatial and temporal information about the tracers' trajectories over periods of five minutes. Based on this information, we describe general trends in how the tracers moved and redistributed themselves as functions of their density, fluidization air flow, and the overall concentration of low density particles present. One key finding was that the time average vertical probability distribution of the tracer particles locations is consistent with a Weibull distribution. The effective Weibull parameters appear to vary systematically with the degree of fluidization and particle density. Also, we observed that temporal autocorrelations in the vertical position of the tracer particles vary systematically with fluidization intensity and reveal important information about the dominant bed circulation time scales. Our results suggest that it may be possible to develop relatively simple statistical models or correlations for describing the spatial distribution and circulation of mm sized particles in bubbling beds of this type. Such tools should be useful for simulating some types of fluidized biomass processing and for validating kinetic-theory models of fluidized bed systems.

Thermal Conductivity of Diameter-Modulated Silicon Nanowires Within a Frequency-Dependent Model for Phonon Boundary Scattering

Modulated nanowires have been proposed as candidates for efficient thermoelectric applications. It has been previously shown within the low-temperature ballistic regime of phonon transport that the thermal conductivity can be significantly reduced when the width of the nanowire is modulated. Here, we report on the thermal conductivity of modulated Si nanowires calculated within a kinetic theory model. The size dependence is taken into account through the sampling of k-points in the first Brillouin zone and a frequency-dependent calculation of the boundary scattering length. It has been found that the thermal conductivity of modulated nanowires can be drastically reduced compared with that of nanowires with constant width. Interestingly, the thermal conductivity is even smaller than that of corresponding straight wires with width equal to the smallest width in the modulated nanowires. The dramatic decrease of the thermal conductivity of modulated nanowires is attributed to their small transmissivity.

Pressure-driven flow through a single nanopore

We have measured the flow of gas through single ion track pores in a polymer film using a mass spectroscopy technique. The pores are 12 μm long with diameters in the range of 50-1000 nm, and the flow was driven by pressure drops in the range 0-30 atm. When the mean free path is large compared to the pore diameter (large Knudsen number Kn), the flow rate is proportional to the pressure drop and the pore radius R cubed, and is consistent with a model of diffusive scattering at the pore walls. For Kn≤0.1, the hydrodynamic conductance increases, as predicted by standard kinetic theory models, and finally approaches the conventional Poiseuille value with zero slip length.

Viscosity of pure fluids—Enskog-2σ model

In this work, we propose a new kinetic theory model (Enskog-2σ model) to analyze and predict the viscosity of simple fluids. The model is based on the Enskog formulation and makes use of two effective diameters to represent two aspects of molecular interactions in Enskog's treatment; namely, the effective diameter representing the excluded volume of a molecule and the effective diameter accounting for the increased probability of collision in comparison to the dilute gas. We have tested the model by analyzing the viscosity of five simple fluids (Ar, CH4, N2, CO2 and SF6) of increasing complexity at supercritical temperatures. The new Enskog-2σ model outperforms previous approaches based on Enskog theory in terms of its correlative ability. We demonstrate that the effective diameter associated with the excluded volume exhibits a universal behaviour as a function of reduced temperature. The conformal behaviour can be achieved by means of a single fluid-dependent length scaling parameter. We make use of this finding to develop a general model that allows the prediction of the viscosity of one fluid from the knowledge of the viscosity of a reference fluid, which in this work was chosen to be Ar. The accuracy of the predicted viscosity depends on the way in which the length scaling parameter was estimated. If the length scaling parameter is obtained from the knowledge of viscosity along a single isotherm, the accuracy of the predicted viscosity is similar to the uncertainty of the original correlation over its entire supercritical range. If a single viscosity value is used to estimate the length scaling parameter, the viscosities of supercritical CH4, N2, CO2 and SF6 are predicted with the maximum deviation of 3.3%, 4.2%, 9.9% and 10.5% respectively over the entire range of validity of the Enskog-2σ model.

Quantum kinetic theory model of a continuous atom laser

We investigate the feasible limits for realising a continuously evaporated atom laser with high-temperature sources. A plausible scheme for realising a truly continuous atom laser is to outcouple atoms from a partially condensed Bose gas, whilst continuously reloading the system with non-condensed thermal atoms and performing evaporative cooling. Here we use quantum kinetic theory to model this system and estimate feasible limits for the operation of such a scheme. For sufficiently high temperatures, the figure of merit for the source is shown to be the phase-space flux. The dominant process limiting the usage of sources with low phase-space flux is the three-body loss of the condensed gas. We conclude that certain double-magneto-optical trap (MOT) sources may produce substantial mean condensate numbers through continuous evaporation, and provide an atom laser source with a narrow linewidth and reasonable flux.

Kinematics Analysis of the Driving Cylinder for Dual-Rotor Piston Engine

The engine is the most common power source in our life. For a long time, people never stopped research it. Kinematics analysis study the relationship among the position, velocity and acceleration. In recent years, with computer technology, graphics technology and automatic modeling techniques together, much kinematics analysis software came into the world, which makes the engine kinematics analysis more quickly and easily. The article base on the idea of a novel dual-rotor piston engine, describe the structure and movement principle of the driving cylinder, build the kinetic theory model of the key components, and then expand the simulation study, discuss their kinematics properties.

Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology

Kinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks.