Effects of loading waveforms on rock damage using particle simulation method

The particle simulation method is used to study the effects of loading waveforms （i.e. square, sinusoidal and triangle waveforms） on rock damage at mesoscopic scale. Then some influencing factors on rock damage at the mesoscopic scale, such as loading frequency, stress amplitude, mean stress, confining pressure and loading sequence, are also investigated with sinusoidal waveform in detail. The related numerical results have demonstrated that： 1） the loading waveform has a certain effect on rock failure processes. The square waveform has the most damage within these waveforms, while the triangle waveform has less damage than sinusoidal waveform. In each cycle, the number of microscopic cracks increases in the loading stage, while it keeps nearly constant in the unloading stage. 2） The loading frequency, stress amplitude, mean stress, confining pressure and loading sequence have considerable effects on rock damage subjected to cyclic loading. The higher the loading frequency, stress amplitude and mean stress, the greater the damage the rock accumulated; in contrast, the lower the confining pressure, the greater the damage the rock has accumulated. 3） There is a threshold value of mean stress and stress amplitude, below which no further damage accumulated after the first few cycle loadings. 4） The high-to-low loading sequence has more damage than the low-to-high loading sequence, suggesting that the rock damage is loading-path dependent.

Computational modeling of free-surface slurry flow problems using particle simulation method

The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles.Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods,the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained.The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system.For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems,three examples involving slurry flow on three different types of river beds have been considered.The related particle simulation results obtained from these three examples have demonstrated that:1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields;2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed.

Magnetic Field Improvement in End Region of Rectangular Planar DC Magnetron Based on Particle Simulation

For a rectangular planar direct current （DC） magnetron, anomalous target erosion may occur in the curve-out region and inner side of the curved region. One key factor is that the magnetic field in the end region is weaker than that in the straight region, and another important factor may be that there is a circumferential component of the magnetic field in the curved region. Through a calculation of three-dimensional magnetic field for the rectangular magnetron, a magnet structure shimmed by permanent magnet bars and ferromagnetic bars is proposed to solve the above problems. Through a three-dimensional non-self-consistent particle simulation and the Yamamura/Tawara formula, the target erosion profile could be predicted. The simulation results show that for an improved uniformity in magnetic field, the entire target utilization could be much enhanced.

Test particle simulations of resonant interactions between energetic electrons and discrete, multi-frequency artificial whistler waves in the plasmasphere

Modulated high frequency （HF） heating of the ionosphere provides a feasible means of artificially generating ex- tremely low frequency （ELF）/very low frequency （VLF） whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high energy electrons. Combining the ray tracing method and test particle simulations, we evaluate the effects of energetic electron resonant scattering driven by the discrete, multi-frequency arti- ficially generated ELF/VLF waves. The simulation results indicate a stochastic behavior of electrons and a linear profile of pitch angle and kinetic energy variations averaged over all test electrons. These features are similar to those associated with single-frequency waves. The computed local diffusion coefficients show that, although the momentum diffusion of relativistic electrons due to artificial ELF/VLF whistlers with a nominal amplitude of ~ 1 pT is minor, the pitch angle scattering can be notably efficient at low pitch angles near the loss cone, which supports the feasibility of artificial triggering of multi-frequency ELF/VLF whistler waves for the removal of high energy electrons from the magnetosphere. We also investigate the dependences of diffusion coefficients on the frequency interval （△f） of the discrete, multi-frequency waves. We find that there is a threshold value of Af for which the net diffusion coefficient of multi-frequency whistlers is inversely proportional to △f （proportional to the frequency components Nw） when △f is below the threshold value but it remains unchanged with increasing Af when △f is larger than the threshold value. This is explained as being due to the fact that the resonant scattering effect of broadband waves is the sum of the effects of each frequency in the ＇effective frequency band＇. Our results suggest that the modulation frequency of HF heating of the ionosphere can be appropriately selected with reasonable frequency intervals so that better performance of controlled precipitation of high energy electrons in the plasmasphere by artificial ELF/VLF whistler waves can be achieved.

Study on electron stochastic motions in the magnetosonic wave field: Test particle simulations

Using the test particle simulation method, we investigate the stochastic motion of electrons with energy of 300 keV in a monochromatic magnetosonic(MS) wave field. This study is motivated by the violation of the quasi-linear theory assumption, when strong MS waves(amplitude up to ~1 nT) are present in the Earth's magnetosphere. First, electron motion can become stochastic when the wave amplitude exceeds a certain threshold. If an electron initially resonates with the MS wave via bounce resonance, as the bounce resonance order increases, the amplitude threshold of electron stochastic motion increases until it reaches the peak at about the 11 th order in our study, then the amplitude threshold slowly declines. Further, we find that the coexistence of bounce and Landau resonances between electrons and MS waves will significantly reduce the amplitude threshold. In some cases, the electron motion can become stochastic in the field of an MS wave with amplitudes below 1 nT. Regardless, if neither the bounce nor Landau resonance condition is satisfied initially, then the amplitude threshold of stochastic motion shows an increasing trend for lower frequencies and a decreasing trend for higher frequencies, even though the amplitude threshold is always very large(> 5 nT). Our study suggests that electron stochastic motion should also be considered when modeling electron dynamics regulated by intense MS waves in the Earth's magnetosphere.

Development of the PARASOL Code and Full Particle Simulation of Tokamak Plasma with an Open-Field SOL-Divertor Region Using PARASOL

The PARASOL code and the simulation by using PARASOL are introduced briefly. The PARASOL code with particle-in-cell （PIC） method and binary collision model was developed in JAERI and JAEA. Simulations using PARASOL code were carried out in order to investigate the power and particle control with diveror system in fusion reactors. The one-dimensional （1D） version of PARASOL was adopted to investigate the Bohm criterion, the supersonic flow, the SOL heat conduction, and so on. The heat propagation due to edge localized mode （ELM） was studied with the 1D-dynamic PARASOL. The two-dimensional version of PARASOL for the whole tokamak plasma including scrape-off-layer （SOL）-divertor region was useful for simulating the SOL flow pattern, the electric field formation etc. Based on PARASOL simulation results, improved physics modeling for the fluid simulation was built up.

Estimate of Lifetime of Ion Thruster Optics Based on Particle Simulation

A three-dimensional particle simulation of ion thruster optics with charge-exchange collision was developed in this study. The simulation code was based on tracking ions using the particle-in-cell method, and the Monte Carlo technique was used to model the charge-exchange collision. Simulations were performed for a 20 cm ion thruster optics. The results were compared with the corresponding experimental data from a test of the ion thruster optics for a duration of 800 hours. The Depth-From-Focus （DFF） method was used to measure the erosion depth of the downstream surface of the accelerator grid. The predicted erosion depth of the accelerator grid was consistent reasonably with the corresponding experimental data. The simulation results showed that the accelerator grid would be burned through after 1333 hours.

Particle Simulation of an Improved Axially Extracted Vircator

An axially extracted virtual cathode oscillator (vircator) with a feedback annulus is proposed and configured through particle-in-cell (PIC) simulation in Ref. [1]. In this paper, the effects of the feedback mechanism are studied through PIC method. The simulated results indicate that the improved new vircator can increase the output power twice large than that of the axially-extracted conventional vircator under the same condition. On the other hand, it can narrow the bandwidth and purify the modes.

DISCRETE PARTICLE SIMULATION OF SIZE SEGREGATION OF PARTICLE MIXTURES IN A GAS FLUIDIZED BED

This paper presents a study of the mixing/segregation behaviour of particle mixtures in a gas fluidized bed by use of the discrete particle simulation. Spherical particles with diameters 2 mm （jetsam） and 1 mm （flotsam） and density 2 500 kg.m^-3 are used as solid mixtures with different volume fractions. The particles are initially packed uniformly in a rectangular bed and then fluidized by gas uniformly injected at the bottom of the bed. The gas injection velocities vary to cover fixed, partially and fully fluidized bed conditions. Segregation/mixing behaviour is discussed in terms of flow patterns, solid concentration profile and mixing kinetics. The results show that segregation, as a transient fluidization process, is strongly affected by gas injection velocities for a given particle mixture. With the increase of the volume fraction of flotsam, size segregation appears at lower velocities.

Full Torus Electromagnetic Gyrokinetic Particle Simulations with Kinetic Electrons

The full torus electromagnetic gyrokinetic particle simulations using the hybrid model with kinetic electrons in the presence of magnetic shear is presented.The fluid-kinetic electron hybrid model employed in this paper improves numerical properties by removing the tearing mode,meanwhile,preserves both linear and nonlinear wave-particle resonances of electrons with Alfven wave and ion acoustic wave.

Sample size adaptive strategy for time-dependent Monte Carlo particle transport simulation

When multiphysics coupling calculations contain time-dependent Monte Carlo particle transport simulations, these simulations often account for the largest part of the calculation time, which is insufferable in certain important cases. This study proposes an adaptive strategy for automatically adjusting the sample size to fulfil more reasonable simulations. This is realized based on an extension of the Shannon entropy concept and is essentially different from the popular methods in timeindependent Monte Carlo particle transport simulations, such as controlling the sample size according to the relative error of a target tally or by experience. The results of the two models show that this strategy can yield almost similar results while significantly reducing the calculation time. Considering the efficiency, the sample size should not be increased blindly if the efficiency cannot be enhanced further. The strategy proposed herein satisfies this requirement.

Numerical simulation of flocculation and settling behavior of whole-tailings particles in deep-cone thickener

Rapid dewatering and thickening of whole-tailings with ultrafine particles is one of the most important processes for the whole-tailings paste preparation. Deep-cone thickener, a kind of such process for the flocculation and settling of whole-tailings, is particularly necessary to study. However, there exist many problems in observing the flocculation and settling process of whole-tailings, as well as the particle size distribution(PSD) of whole-tailings floccules in deep-cone thickener. Population balance model(PBM) is applied to predict the PSD in deep-cone thickener, and LUO model and GHADIRI model are employed to study the aggregation and fragmentation mechanism of the whole-tailings particles, respectively. Through three-dimensional numerical simulation on the whole-tailings flocculation and settling in deep-cone thickener using computational fluid dynamics(CFD)-PBM, the distribution of density and turbulent kinetic energy in deep-cone thickener were obtained, at the same time the spatio-temporal changes of whole-tailings floccules particle size distribution are analyzed. Finally, the major flocculation position in deep-cone thickener is found and the flocculation settling rules of whole-tailings are achieved.

DEM simulation of particle flow on a single deck banana screen

A mathematical study of particle flow on a banana screen deck using the discrete element method (DEM) was presented in this paper. The motion characteristics and penetrating mechanisms of particles on the screen deck were studied. Effects of geometric parameters of screen deck on banana screening process were also investigated. The results show that when the values of inclination of discharge and increment of screen deck inclination are 10° and 5° respectively, the banana screening process get a good screening performance in the simulation. The relationship between screen deck length and screening efficiency was further confirmed. The conclusion that the screening efficiency will not significantly increase when the deck length L≥430 mm (L/B ≥ 3.5) was obtained, which can provide theoretical basis for the optimization of banana screen.

Potential application of particle based simulations in reservoir security management

In order to model the movement progress in case of risks such as dam collapse and coastal inundation, particle-based simulation methods, including the discrete-element method and smoothed particle hydrodynamics, which have specific advantages in modeling complex three-dimensional environmental fluid and particulate flows, are adopted as an effective way to illustrate environmental applications possibly happening in the real world. The theory of these methods and their relative advantages compared with traditional methods are discussed. Examples of 3-D flows on realistic topography including the flooding of a river valley as a result of a dam collapse and coastal inundation by a tsunami are introduced. Issues related to validation and quality data availability are also discussed. The results show that the simulations provide a valuable insight in a given situation for the security management of reservoir dams. Validation can only be performed where both the initial and final states can be very well characterized.

Physical Simulation of Nonmetallic Particle Movement in Al Melt under Electromagnetic Field

Physical simulation is used to study the movement of nonmetallic particles in Al melt in electro- magnetic field. It is found that the terminal velocity of particles in different Reynolds number range has different functions. By confirming drag force coefficient of nonmetallic particles with Reynolds number in the range of 0.2-10 and 10-25 respectively, two functions of terminal ve- locity for spherical nonmetallic particles have been got accordingly, which provide a theoretical basis for separating nonmetallic inclusions from Al melt in electromagnetic field.

Refinement of Adaptive Dynamical Simulation of Quantum Mechanical Double Slit Interference Phenomenon

We applied adaptive dynamics to double slit interference phenomenon using particle model and obtained partial successful results in our previous report. The patterns qualitatively corresponded well with experiments. Several properties such as concave single slit pattern and large influence of slight displacement of the emission position were different from the experimental results. In this study we tried other slit conditions and obtained consistent patterns with experiments. We do not claim that the adaptive dynamics is the principle of quantum mechanics, but the present results support the probability of adaptive dynamics as the candidate of the basis of quantum mechanics. We discuss the advantages of the adaptive dynamical view for foundations of quantum mechanics.

Thermo-mechanical coupled particle model for rock

A thermo-mechanical coupled particle model for simulation of thermally-induced rock damage based on the particle simulation method was proposed.The simulation results of three verification examples,for which the analytical solutions are available,demonstrate the correctness and usefulness of the thermo-mechanical coupled particle model.This model is applied to simulating an application example with two cases：one is temperature-independent elastic modulus and strength,while the other is temperature-dependent elastic modulus and strength.The related simulation results demonstrate that microscopic crack initiation and propagation process with consideration of temperature-independent and temperature-dependent elastic modulus and strength are different and therefore,the corresponding macroscopic failure patterns of rock are also different.On the contrary,considering the temperature-dependent elastic modulus and strength has no or little effect on the heating conduction behavior.Numerical results,which are obtained by using the proposed model with temperature-dependent elastic modulus and strength,agree well with the experimental results.This also reveals that the rock subjected to heating experiences much more cracking than the rock subjected to cooling.

Simulation of rock deformation and mechanical characteristics using clump parallel-bond models

To properly simulate hard rock with a high ratio of the uniaxial compressive strength to tensile strength(UCS/TS) and realistic strength-failure envelope,the rock deformation and mechanical characteristics were discussed in detail when the particle simulation method with the clump parallel-bond model(CPBM) was used to conduct a series of numerical experiments at the specimen scale.Meanwhile,the effects of the loading procedure and crack density on the mechanical behavior of a specimen,which was modeled by the particle simulation method with the CPBM,were investigated.The related numerical results have demonstrated that:1) The uniaxial compressive strength(UCS),tensile strength(TS) and elastic modulus are overestimated when the conventional loading procedure is used in the particle simulation method with the CPBM; 2) The elastic modulus,strength and UCS/TS decrease,while Poisson ratio increases with the increase of the crack density in the particle simulation method with the CPBM; 3) The particle simulation method with the CPBM can be used to reproduce a high value of UCS/TS(>10),as well as a high friction angle and reasonable cohesion strength; 4) As the confining pressure increases,both the peak strength of the simulated specimen and the number of microscopic cracks increase,but the ratio of tensile cracks number to shear cracks number decreases in the particle simulation method with the CPBM; 5) Compared with the conventional parallel-bond model,the CPBM can be used to reproduce more accurate results for simulating the rock deformation and mechanical characteristics.

Simulation to Predict Target Erosion of Planar DC Magnetron

Plasma properties in a planar DC magnetron system are simulated by a non-self- consistent particle method in two dimensions. Through tracing the trajectories of the energetic electrons in the specified electric field and the magnetic field, and treating the collision process by Monte Carlo method, the spatial profile of ionization events can be obtained conveniently. Assuming that the ions speed up from the ionization points and bombard the target with the energy at these points, and according to the Yamamura/Tawara method, the target erosion can be predicted. The magnetic field is calculated by the finite element method, and the electric field is estimated according to the self-consistent simulation and measured results. The influence of the time step size on the target erosion profile is analysed first to find a proper step size. Then the influence of electric field estimated on the erosion profile is discussed. The erosion profile may become narrower if the sheath thickness is increased. Finally, considering the dynamic erosion process, the erosion profile may get wider over time for the magnetron with shunt bar.

Numerical Simulation of Ion Extraction Through Ion Thruster Optics

Based on the particle-in-cell （PIC） method, a two-dimensional numerical scheme was developed to investigate the ion beam extraction phenomena through the ion thruster optics. According to the calculated results, the plasma sheath upstream of the screen grid, the electric field in the calculation domain, and the ion and electron spatial distributions are obtained for different accelerator grid voltages. The results indicate that the accelerator grid voltage affects the plasma sheath upstream of the screen grid significantly. It is found that a moderate accelerator grid voltage results in an ion optical performance better than either a higher or lower voltage, from a point of ion extraction from the discharge chamber and erosion mitigation of the accelerator grid due to the direct ion impingement.