Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model

Many kinds of simulation models have been developed to understand the complex plasma systems. However, these simulation models have been separately performed because the fundamental assumption of each model is different and restricts the physical processes in each spatial and temporal scales. On the other hand, it is well known that the interactions among the multiple scales may play crucial roles in the plasma phenomena (e.g. magnetic reconnection, collisionless shock), where the kinetic processes in the micro-scale may interact with the global structure in the fluid dynamics. To take self-consistently into account such multi-scale phenomena, we have developed a new simulation model by directly interlocking the fluid simulation of the magnetohyrdodynamics (MHD) model and the kinetic simulation of the particle-in-cell (PIC) model. The PIC domain is embedded in a small part of MHD domain. The both simulations are performed simultaneously in each domain and the bounded data are frequently exchanged each other to keep the consistency between the models. We have applied our new interlocked simulation to Alfvén wave propagation problem as a benchmark test and confirmed that the waves can propagate smoothly through the boundaries of each domain.     

Novel Kinetic Theory of the Classical Isotropic Oscillator Gas, the Flexible Shell Model

Ever since Chapman and Enskog first used the hard sphere model to evaluate the collision integral in the Boltzmann equation, more sophisticated models for molecular encounters have been sought. Rotation of molecules in kinetic theory has been pursued with a number of models, such as the spherocylinder or loaded sphere, to account for that aspect. As these efforts continued, more workers started to incorporate quantum mechanics methods in pursuit of solutions to the Boltzmann equation. Progress there with both rotational and vibrational features of molecules has been attained. Until now though, there has been no classical vibration model for molecules in kinetic theory. Far from standard kinetic theory, here a simple classical mechanics isotropic oscillator is combined, through a flexible shell, with the hard sphere model in a full Chapman Enskog procedure. The intent here has been to introduce the model, so items like translational-vibrational coupling have not been included. Still, the results compliment literature.     

Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model

Many kinds of simulation models have been developed to understand the complex plasma systems. However, these simulation models have been separately performed because the fundamental assumption of each model is different and restricts the physical processes in each spatial and temporal scales. On the other hand, it is well known that the interactions among the multiple scales may play crucial roles in the plasma phenomena (e.g. magnetic reconnection, collisionless shock), where the kinetic processes in the micro-scale may interact with the global structure in the fluid dynamics. To take self-consistently into account such multi-scale phenomena, we have developed a new simulation model by directly interlocking the fluid simulation of the magnetohyrdodynamics (MHD) model and the kinetic simulation of the particle-in-cell (PIC) model. The PIC domain is embedded in a small part of MHD domain. The both simulations are performed simultaneously in each domain and the bounded data are frequently exchanged each other to keep the consistency between the models. We have applied our new interlocked simulation to Alfvén wave propagation problem as a benchmark test and confirmed that the waves can propagate smoothly through the boundaries of each domain.     

Hydrogen-vacancy interactions in Ni-H solid solutions

The data for the solubility of hydrogen in nickel in equilibrium with H₂-gas at atmospheric pressure have been analyzed in terms of a model which considers H-vacancy interactions. This model has been shown to be compatible with both the thermodynamic and kinetic data for Ni-H system.     

Kinetic energy distributions around symmetric thermal fission of U234 and U236

The kinetic energy distributions have been measured at LOHENGRIN for symmetric fission of U²³⁴ and U²³⁶. The pre-neutron emission values for the average total kinetic energy and its rms width have been deduced using a Monte Carlo simulation for neutron evaporation. The total kinetic energy dip between symmetric and asymmetric divisions is 24 MeV for U²³⁴ and 29 MeV for U²³⁶. A strong peak in the initial rms width has been observed for masses 111–123 in U²³⁴ and for 111–125 in U²³⁶. A static scission point model is used to understand the origin of these features.     

Kinetic Models for Granular Flow

The generalization of the Boltzmann and Enskog kinetic equations to allow inelastic collisions provides a basis for studies of granular media at a fundamental level. For elastic collisions the significant technical challenges presented in solving these equations have been circumvented by the use of corresponding model kinetic equations. The objective here is to discuss the formulation of model kinetic equations for the case of inelastic collisions. To illustrate the qualitative changes resulting from inelastic collisions the dynamics of a heavy particle in a gas of much lighter particles is considered first. The Boltzmann–Lorentz equation is reduced to a Fokker–Planck equation and its exact solution is obtained. Qualitative differences from the elastic case arise primarily from the cooling of the surrounding gas. The excitations, or physical spectrum, are no longer determined simply from the Fokker–Planck operator, but rather from a related operator incorporating the cooling effects. Nevertheless, it is shown that a diffusion mode dominates for long times just as in the elastic case. From the spectral analysis of the Fokker–Planck equation an associated kinetic model is obtained. In appropriate dimensionless variables it has the same form as the BGK kinetic model for elastic collisions, known to be an accurate representation of the Fokker–Planck equation. On the basis of these considerations, a kinetic model for the Boltzmann equation is derived. The exact solution for states near the homogeneous cooling state is obtained and the transport properties are discussed, including the relaxation toward hydrodynamics. As a second application of this model, it is shown that the exact solution for uniform shear flow arbitrarily far from equilibrium can be obtained from the corresponding known solution for elastic collisions. Finally, the kinetic model for the dense fluid Enskog equation is described.     

Phase-field modeling of void evolution and swelling in materials under irradiation

Void swelling is an important phenomenon observed in both nuclear fuels and cladding materials in operating nuclear reactors. In this work we develop a phase-field model to simulate void evolution and void volume change in irradiated materials. Important material processes, including the generation of defects such as vacancies and self-interstitials, their diffusion and annihilation, and void nucleation and evolution, have been taken into account in this model. The thermodynamic and kinetic properties, such...     

THE CRITICAL DYNAMICS OF THE KINETIC ISING MODELS ON THE SYSTEMS WITH Rmin> 2

We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R_min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R_min >2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R_min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R_min=∞ exact TDRG calculationa are impossible. The complete new and interesting results are given.     

Spectral uncertainty quantification, propagation and optimization of a detailed kinetic model for ethylene combustion

The ability of a reaction model to predict the combustion behavior of a fuel relies on the rigorous quantification of the kinetic rate parameter uncertainty. Although the accuracy of a detailed kinetic model may be ensured, in principle, by a multi-parameter optimization, the inherent uncertainties in the fundamental combustion targets used for optimization cause the resulting optimized model to be characterized by a finite kinetic parameter space. In this work, spectral expansion techniques are developed and employed to quantify these uncertainties, using an as-compiled, detailed, H₂/CO/C₁-C₄ kinetic model for ethylene combustion as an example. Uncertainty was quantified for both the as-compiled model and the optimized model, and propagated into a wide variety of combustion experiment and conditions. Application of the spectral uncertainty method in mechanism reduction is also discussed.     

The direct exchange interaction for weakly delocalized multielectron systems in crystals

The multielectron theory of exchange interactions taking into account both electrostatic interactions between electrons (“potential” exchange) and electron transfer between magnetic centers (“kinetic” exchange) has been developed on the basis of Bogolubov's procedure using double irreducible operators. The final hamiltonian contains a number of isotropic and anisotropic terms. The exchange interaction parameter variations with the distance have been calculated. The terms determining the dependence on the occupancy of magnetic shells are shown to be of the same order of magnitude as the “potential” exchange and two orders of magnitude less than the “kinetic” exchange. It is shown that in the model adopted the mechanisms of direct exchange interactions always favour the antiferromagnetic spin ordering     

Anomalous Diffusion Equations with Multiplicative Acceleration

A generalization of the model of Lévy walks with traps is considered. The main difference between the model under consideration and the already existing models is the introduction of multiplicative particle acceleration at collisions. The introduction of acceleration transfers the consideration of walks to coordinate–momentum phase space, which allows both the spatial distribution of particles and their spectrum to be obtained. The kinetic equations in coordinate–momentum phase space have been derived for the case of walks with two possible states. This system of equations in a special case is shown to be reduced to ordinary Lévy walks. This system of kinetic equations admits of integration over the spatial variable, which transfers the consideration only to momentum space and allows the spectrum to be calculated. An exact solution of the kinetic equations can be obtained in terms of the Laplace–Mellin transform. The inverse transform can be performed only for the asymptotic solutions. The calculated spectra are compared with the results of Monte Carlo simulations, which confirm the validity of the derived asymptotics.     

High- and low-temperature ignition delay time study and modeling efforts on vinyl acetate

Although esters in general have received much attention over the last decade of combustion research, the combustion of vinyl esters have yet not been studied in detail. Recent studies on ethyl acetate show that vinyl acetate is a major intermediate but its combustion is not well understood. This may be due to the fact that vinyl acetate itself can presumably not be used as a fuel or fuel additive, but both the fundamental understanding of vinyl ester combustion and the improvement of the ethyl ester modeling motivate the present study. Building on the work on ethyl acetate, a first kinetic model for the high- and low-temperature combustion of vinyl acetate is proposed, which includes reactions and intermediates that have not been considered before. These reactions are based on low-level quantum mechanical calculations as well as analogies drawn to mainly ethyl acetate. Seven additional species are considered compared to the ethyl acetate study for which the thermochemical data is derived by ab-initio calculations. The vinyl acetate kinetic model is validated against ignition delay times obtained in a shock tube and a rapid compression machine at pressures of 20 and 40 bar and temperatures ranging from 850 to 1250 K. Overall, a satisfactory agreement between the predictions of the kinetic model and the experimental data was found for all investigated conditions. Rate of production and brute force sensitivity analyses were performed to identify the most relevant reaction pathways, which underline the strong connection between the vinyl acetate and ethyl acetate chemistry.     

Fission-mode calculations for 239U,a revision of the multi-modal random neck-rupture model

In the course of an experimental study of the fragment characteristics after neutron-induced fission of ²³⁸U with incident neutron energies between 1.2 and 5.8 MeV fission-mode calculations in the frame of the multi-modal random neck-rupture model have been performed. During these calculations some technical parts of the model have been revised. The identification of fission modes is now based on unequivocal and reproducible criteria. The Rayleigh criterion has consequently been applied to determine each possible scission configuration. The most remarkable new results are that all physically relevant fission modes branch off in the second potential minimum exhibiting different outer barriers, and that the total kinetic energy distribution of the fission fragments is a direct consequence of the Rayleigh criterion. The fragment characteristics as the mean mass, the mean total kinetic energy and the corresponding width obtained from the fission-mode calculations compare reasonably well with the experimental findings.For the first time the weighted fission cross sections through each particular fission mode have been analyzed simultaneously using a Hill-Wheeler type expression for the transmission through a double-humped fission barrier. The results support the picture of individual outer barriers with slightly different penetrabilities and a slightly lower inner barrier.     

Markovian description of irreversible processes and the time randomization

A certain class of kinetic equations, which describe the Markov-type irreversible evolution of the system, consistent with the second law of thermodynamics and with the relaxation postulate, has been distinguished. The physical meaning of these kinetic equations is that they describe thermally activated processes. The time asymmetry, observed on the macrolevel as the thermodynamical irreversibility of the process, is represented on the microlevel by the Markov-type randomization of the moments of the jump-like change of the microstates of the system. As an example, the thermodynamical interpretation of the one-particle stochastic model of the many-body system is discussed. The authors of this paper have agreed to not receive the proofs for correction     

AES: energy calibration of electron spectrometers. IV. A re-evaluation of the reference energies

Reference kinetic energies for Auger electrons were published by the National Physical Laboratory (NPL) in 1990. These energies are traceable via measurements of X-ray photoelectron binding energies, referenced to the Fermi level position in the spectrum, and values for the X-ray energies involved. Revised values of both the Fermi level position and the X-ray energies have now been obtained. Use of these new values leads to an increase of the recommended reference kinetic energies for AES by 0.07 eV from the previous values.     

Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior

This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a Fokker-Planck type equation posed in an extended phase-space involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results.     

Jet-stirred reactor and flame studies of propanal oxidation

There is a strong drive towards utilizing oxygenated biofuels in blends with existing fossil fuels. Improving the kinetic modeling of the oxidation of these bio-derived oxygenates requires further investigation of their key stable intermediates such as the aldehydes. In this study, an experimental and chemical kinetic modeling investigation of propanal oxidation was carried out. Experiments were conducted in a jet stirred reactor and in counterflow flames over a wide range of equivalence ratios, temperatures, and ambient pressures. Stable species concentration profiles were measured in the jet stirred reactor and laminar flame speeds were measured. A detailed chemical kinetic reaction model was validated using the present experimental results and existing literature data. The model was used also to provide insight into the controlling reaction pathways for propanal oxidation in both the low- and high-temperature kinetic regimes.     

Simulation of ball motion and energy transfer in a planetary ball mill

A kinetic model is proposed for simulating the trajectory of a single milling ball in a planetary ball mill, and a model is also proposed for simulating the local energy transfer during the ball milling process under no-slip conditions. Based on the kinematics of ball motion, the collision frequency and power are described, and the normal impact forces and effective power are derived from analyses of collision geometry. The Hertzian impact theory is applied to formulate these models after having established some relationships among the geometric, dynamic, and thermophysical parameters. Simulation is carried out based on two models, and the effects of the rotation velocity of the planetary disk and the vial-to-disk speed ratio ω/Ω on other kinetic parameters is investigated. As a result, the optimal ratio ω/Ω to obtain high impact energy in the standard operating condition at = 800 rpm is estimated, and is equal to 1.15.