A GPU-based general numerical framework for plasma simulations in terms of microscopic kinetic equations with full collision terms

We have proposed a general numerical framework for plasma simulations on graphics processing unit clusters based on microscopic kinetic equations with full collision terms.Our numerical algorithm consistently deals with both long-range(classical forces in the Vlasov term)and short-range(quantum processes in the collision term)interactions.Providing the relevant particle masses,charges and types(classical,fermionic or bosonic),as well as the external forces and the matrix elements(in the collisional integral),the algorithm consistently solves the coupled multi-particle kinetic equations.Currently,the framework is being tested and applied in the field of relativistic heavy-ion collisions;extensions to other plasma systems are straightforward.Our framework is a potential and competitive numerical platform for consistent plasma simulations.

Kinetic equations characterizing double reversible transformations in heating CuZnAlMnNi shape memory alloy

The apparent activation energies and frequency factors of thedouble reversible transformations occurring in heating CuZnAlMnNIshape memory alloy (SMA) were deduced as ΔE_x→M = 62. 597 8 KJ/mol, ΔE_M → A = 153. 92 KJ/Mol, A_x→M = 5.2232 × 10~9S^-1, andA_ M → A = 2.3251 × 10~23 S^-1, respectively. The kinetic equationsof the two transformations due- Ing heating were establishedsimultaneously.

Kinetic Equation for Internal Oxidation of Cu-Al Alloy Spheres

The kinetics of internal oxidation of Cu-Al alloy spheres, containing up to 2.214% mole fraction Al was investigated in the temperature range 1 023 K to 1 273 K, and the depth of internal oxidation was measured in the microscopy. A kinetic equation was derived to describe the internal oxidation of Cu-A1 alloy spheres, which was checked experimentally by means of oxidation depth measurements. The results show that the derived equation is exact enough to describe the kinetics of internal oxidation of Cu-Al alloy spheres. Based on this equation and the oxidation depth measurements, the permeability of oxygen in solid copper has been obtained. Investigation also shows that in the process of internal oxidation, there is no evidence for preferential diffusion along grain boundaries.

KINETIC EQUATIONS WITH VARIATION OF LIQUID REACTANT CONCENTRATION

For two common types of liquid-solid heterogeneous reactions,the kinetic equations have been established which involved both the variation of liquid reactant concentration and the va- riation of solid reactant geornetry with the reaction time.The experimental results show that the kinetic equations are more accurate and reasonable than those appeared in previous litera- tures.Moreover,they are also suitable for gas-solid heterogeneous reactions in principle.

Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma

By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ionsare recombined into neutral molecules and atoms of hydrogen isotopes. These speciesrecycle back into the plasma volume and participate, in particular, in charge–exchange(cx) collisions with ions. As a result, hot atoms with chaotically directed velocities aregenerated and some of them hit the wall. Statistical Monte Carlo methods often usedto model the behavior of cx atoms are too time-consuming for comprehensive parameter studies. Recently1 an alternative iteration approach to solve one-dimensional kineticequation2 has been significantly accelerated, by a factor of 30–50, by applying a passmethod to evaluate the arising integrals from functions, involving the ion velocity distribution. Here, this approach is used by solving a two-dimensional kinetic equation,describing the transport of cx atoms in the vicinity of an opening in the wall, e.g.,the entrance of a duct guiding to a diagnostic installation. To assess the erosion rateand lifetime of the installation, one need to know the energy spectrum of hot cx atomsescaping from the plasma into the duct. Calculations are done for a first mirror of molybdenum under plasma conditions expected in a fusion reactor like DEMO.3,4 The resultsof kinetic modeling are compared with those found by using a diffusion approximation5relevant for cx atoms if the time between cx collisions with ions is much smaller thanthe time till the ionization of atoms by electrons. The present more exact kinetic consideration predicts a mirror erosion rate by a factor of 2 larger than the approximatediffusion approach.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integra- tion method can be developed and adopted to attack complex flows with different Mach numbers. HPF paral- lel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarilywith massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System （MEMS）.

Numerical simulation of metal evaporation based on the kinetic model equation and the direct simulation Monte Carlo method

Metal evaporation on the basis of the kinetic model equations(BGK and S-model) and the direct simulation Monte Carlo(DSMC) method was investigated computationally under the circumstances of collimators existing or not. Numerical data of distributions of number density, bulk velocity and temperature were reported over a wide range of evaporation rate.It was shown that these results reached a good agreement for the case of small evaporation rate, while the deviations became increasingly obvious with the increase of evaporation rate, especially when the collimators existed. Moreover, the deposition thickness over substrate obtained from the kinetic model equations were inaccurate even though the evaporation rate was small. All of the comparisons showed the reliability of the kinetic model equations, which require less computational cost at small evaporation rate and simple structure.

Asymptotic Solutions of the Kinetic Boltzmann Equation and Multicomponent Non-Equilibrium Gas Dynamics

In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asym- ptotic) method for solution of the system of kinetic Boltzmann equations.

An Algorithm to Optimize the Calculation of the Fourth Order Runge-Kutta Method Applied to the Numerical Integration of Kinetics Coupled Differential Equations

The kinetic electron trapping process in a shallow defect state and its subsequent thermal- or photo-stimulated promotion to a conduction band, followed by recombination in another defect, was described by Adirovitch using coupled rate differential equations. The solution for these equations has been frequently computed using the Runge-Kutta method. In this research, we empirically demonstrated that using the Runge-Kutta Fourth Order method may lead to incorrect and ramified results if the numbers of steps to achieve the solutions is not “large enough”. Taking into account these results, we conducted numerical analysis and experiments to develop an algorithm that determines the smallest non-critical number of steps in an automatic way to optimize the application of the Runge-Kutta Fourth Order method. This algorithm was implemented and tested in a variety of situations and the results have shown that our solution is robust in dealing with different equations and parameters.

Preparation of nano-TiO_2/diatomite-based porous ceramics and their photocatalytic kinetics for formaldehyde degradation

Diatomite-based porous ceramics were adopted as carriers to immobilize nano-TiO2 via a hydrolysis-deposition technique. The thermal degradation of as-prepared composites was investigated using thermogravimetric-differential thermal analysis, and the phase and microstructure were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, and transmission electron microscopy. The results indicated that the carriers were encapsulated by nano-TiO2 with a thickness of 300-450 nm. The main crystalline phase of TiO2 calcined at 650~C was anatase, and the average grain size was 8.3 nm. The FT-IR absorption bands at 955.38 cm1 suggested that new chemical bonds among Ti, O, and Si had formed in the composites. The photocatalytic （PC） activity of the composites was investigated un- der UV irradiation. Furthermore, the photodegradation kinetics of formaldehyde was investigated using the composites as the cores of an air cleaner. A kinetics study showed that the reaction rate constants of the gas-phase PC reaction of formaldehyde were k = 0.576 mg＇m3·min^-1 and K = 0.048 m3/mg.

LESSER KNOWN MIRACLES OF BURGERS EQUATION

This article is a short introduction to the surprising appearance of Burgers equation in some basic probabilistic models.

Kinetic analysis of austenite transformation for B1500HS high-strength steel during continuous heating

The dilatometric curves of B1500HS high-strength steel at different heating rates were measured by a Gleeble-3800 thermal simulator and analyzed to investigate the effect of heating rate on austenitization.Results show that the value of starting temperature and ending temperature of austenite transformation increase with the rise of heating rates,whereas the temperature interval of austenite formation decreases.The kinetic equation of austenite transformation was solved using the Johnson–Mehl–Avrami model,and the related parameters of the equation were analyzed by the Kissinger method.For those calculations,the activation energy of austenite transformation is 1.01×10^6 J/mol,and the values of kinetic parameters n and ln k0 are 0.63 and 103.03,respectively.The relationship between the volume fraction of austenite and the heating time at different heating rates could be predicted using the kinetic equation.The predicted and experimental results were compared to verify the accuracy of the kinetic equation.The microstructure etched by different corrosive solutions was analyzed,and the reliability of kinetic equation was further verified from the microscopic perspective.

Studies on Kinetics of Chlorination Reaction of Polyethylene

Through kinetic method, the reaction mechanism and the rate equations of chlorination of polyethylene are suggested in this paper. The rate of chlorination is second order with respect to the concentration of methylene remained and chlorine, respectively. Apparent changes in crystallinity during chlorination processes were determinated by differential scanning calorimetry(DSC). The mathematical model relating crystallinety with kinetic parameters and function of sequence length distribution are derived.

A KINETIC APPROACH TO SCALAR MULTI-DIMENSIONAL CONSERVATION LAWS

This paper gives the kinetic formation of multi-dimensional conservation laws and proves the compactness of velocity averages by employing the compactness theorem in L(loc)(1)(R(n) x R(t)). As a by product, the existence and uniqueness of the generalized solution is obtained.

The effect of forced oscillations on the kinetics of wave drift in an inhomogeneous plasma

The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the drift of electromagnetic waves in a cold ionized plasma in the absence of a magnetic field(Erofeev 2015 Phys. Plasmas 22 092302) and the drift of long Langmuir waves in a cold magnetized plasma(Erofeev 2019 J. Plasma Phys. 85 905850104). It is shown that the traditional concept of the wave kinetic equation does not account for the effects of the forced plasma oscillations that are excited when the waves propagate in an inhomogeneous plasma.Terms are highlighted that account for these oscillations in the kinetic equations of the abovementioned highly informative wave drift scenarios.

Aging kinetics of 14H-LPSO precipitates in Mg-Zn-Y alloy

Alloys with long-period stacking ordered structures(LPSO)have good properties and are highly regarded.Mg-Zn-Y alloy containing LPSO phase was prepared by the traditional casting method,and the aging heat treatment was performed at different temperatures and times.The microstructure and phase constitutions of the alloy were observed by means of optical microscopy and scanning electron microscopy methods.Results show the microstructure of as-cast Mg95.5Zn1.5Y3 mainly consists ofα-Mg,W phases and LPSO phases.During the aging treatment,fine lamellar-shaped 14H-LPSO phase is formed at the grain boundaries and precipitates from the supersaturated magnesium matrix,and the volume fraction increases as the aging time increases.By controlling the aging time,Mg-Zn-Y alloys with different volume fractions of 14H-LPSO phase were prepared.The aging kinetics equation of the 14H-LPSO phase is summarized,that is f=1-exp(-0.2705 t 0.6368).The phase transformation mechanism of 14H-LPSO in Mg95.5Zn1.5Y3 alloy can be described as the change of dislocation energy.

Two stages kinetics of municipal solid waste inoculation composting processes

In order to understand the key mechanisms of the composting processes, the municipal solid waste(MSW) composting processes were divided into two stages, and the characteristics of typical experimental scenarios from the viewpoint of microbial kinetics was analyzed. Through experimentation with advanced composting reactor under controlled composting conditions, several equations were worked out to simulate the degradation rate of the substrate. The equations showed that the degradation rate was controlled by concentration of microbes in the first stage. The degradation rates of substrates of inoculation Run A, B, C and Control composting systems were 13 61 g/(kg·h), 13 08 g/(kg·h), 15 671 g/(kg·h), and 10 5 g/(kg·h), respectively. The value of Run C is around 1 5 times higher than that of Control system. The decomposition rate of the second stage is controlled by concentration of substrate. Although the organic matter degradation rates were similar to all Runs, inoculation could reduce the values of the half velocity coefficient K \-m and could be more efficient to make the composting stable. Particularly, for Run C, the degradation rate is high in the first stage, and K \-m is low in the second stage. The results indicated that the inoculation was efficient for the composting processes.

Developed mathematical technique for fractional stochastic point kinetics model in nuclear reactor dynamics

Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.

Non-Maxwellian Kinetic Modelling of City Size Distribution

To extend the kinetic formulation of city size distribution introduced in [1], the non-Maxwellian kinetic modeling is introduced in the present study, in which a variable collision kernel is used in the underlying kinetic equation of Boltzmann type. By resorting to the well-known grazing asymptotic, a kinetic Fokker-Planck counterpart is obtained. The equilibrium of the Fokker-Planck equation belongs to the class of generalized Gamma distributions. Numerical test shows good fit of the generalized Gamma distribution with the city size distribution of China.