Particle Splitting Research Articles

A Kinetic-magnetohydrodynamic Model with Adaptive Mesh Refinement for Modeling Heliosphere Neutral-plasma Interaction

The charge exchange between the interstellar medium and the solar wind plasma is crucial for determining the structures of the heliosphere. Since both the neutral-ion and neutral–neutral collision mean free paths are either comparable to or larger than the size of the heliosphere, the neutral phase space distribution can deviate far away from the Maxwellian distribution. A kinetic description for the neutrals is crucial for accurately modeling the heliosphere. It is computationally challenging to run three-dimensional time-dependent kinetic simulations due to the large number of macroparticles. In this paper, we present the new highly efficient Solar Wind with Hydrogen Ion Exchange and Large-scale Dynamics-2 model with a kinetic model of neutrals and a magnetohydrodynamic model for the ions and electrons. To improve the simulation efficiency, we implement adaptive mesh refinement and particle splitting and merging algorithms for the neutral particles to reduce the particle number that is required for an accurate simulation. We present several tests to verify and demonstrate the capabilities of the model.

TOPAS simulation of photoneutrons in radiotherapy: accuracy and speed with variance reduction

Objective. We provide optimal particle split numbers for speeding up TOPAS Monte Carlo simulations of linear accelerator (linac) treatment heads while maintaining accuracy. In addition, we provide a new TOPAS physics module for simulating photoneutron production and transport. Approach. TOPAS simulation of a Siemens Oncor linac was used to determine the optimal number of splits for directional bremsstrahlung splitting as a function of the field size for 6 MV and 18 MV x-ray beams. The linac simulation was validated against published data of lateral dose profiles and percentage depth-dose curves (PDD) for the largest square field (40 cm side). In separate simulations, neutron particle split and the custom TOPAS physics module was used to generate and transport photoneutrons, called ‘TsPhotoNeutron’. Verification of accuracy was performed by comparing simulations with published measurements of: (1) neutron yields as a function of beam energy for thick targets of Al, Cu, Ta, W, Pb and concrete; and (2) photoneutron energy spectrum at 40 cm laterally from the isocenter of the Oncor linac from an 18 MV beam with closed jaws and MLC. Main results. The optimal number of splits obtained for directional bremsstrahlung splitting enhanced the computational efficiency by two orders of magnitude. The efficiency decreased with increasing beam energy and field size. Calculated lateral profiles in the central region agreed within 1 mm/2% from measured data, PDD curves within 1 mm/1%. For the TOPAS physics module, at a split number of 146, the efficiency of computing photoneutron yields was enhanced by a factor of 27.6, whereas it improved the accuracy over existing Geant4 physics modules. Significance. This work provides simulation parameters and a new TOPAS physics module to improve the efficiency and accuracy of TOPAS simulations that involve photonuclear processes occurring in high-Z materials found in linac components, patient devices, and treatment rooms, as well as to explore new therapeutic modalities such as very-high energy electron therapy.

The simulation of droplet impact on liquid film evaporation in horizontal falling film evaporator based on smoothed particle hydrodynamics

PurposeIn this paper, the complex flow evaporation process of droplet impact on the liquid film in a horizontal falling film evaporator is numerically studied based on smoothed particle hydrodynamics (SPH) method. The purpose of this paper is to present the mechanism of the water treatment problem of the falling film evaporation for the high salinity mine water in Xinjiang region of China.Design/methodology/approachTo effectively characterize the phase transition problem, the particle splitting and merging techniques are introduced. And the particle absorbing layer is proposed to improve the nonphysical aggregation phenomenon caused by the continuous splitting of gas phase particles. The multiresolution model and the artificial viscosity are adopted.FindingsThe SPH model is validated qualitatively with experiment results and then applied to the evaporation of the droplet impact on the liquid film. It is shown that the larger single droplet initial velocity and the smaller single droplet initial temperature difference between the droplet and liquid film improve the liquid film evaporation. The heat transfer effect of a single droplet is preferable to that of multiple droplets.Originality/valueA multiphase SPH model for evaporation after the droplet impact on the liquid film is developed and validated. The effects of different factors on liquid film evaporation, including single droplet initial velocity, single droplet initial temperature and multiple droplets are investigated.

A parallel multi-resolution Smoothed Particle Hydrodynamics model with local time stepping

Smoothed Particle Hydrodynamics (SPH) model has exhibited remarkable efficacy in addressing strongly nonlinear large deformation problems. However, the expensive computational cost could limit its application. To address this, we propose a novel parallel multi-resolution SPH model with a local time step strategy. This model integrates the multi-resolution model with a Message Passing Interface-based parallelization framework, wherein subdomains discretize the computational domain at varying resolutions. Meanwhile, a local fourth-order Runge-Kutta time integration scheme is introduced, enabling different subdomains to use different time steps. Subdomains of varying resolutions are devoid of overlapping regions, and changes in particle resolution at interfaces are achieved through a dynamic strategy involving particle merging and splitting. Besides that, we conducted a comparative analysis of different SPH discretization formats concerning their impact on the accuracy of multi-resolution particle discretization. Finally, several numerical tests were conducted to validate the accuracy and efficiency of the present multi-resolution SPH model.

Comparative Study and Evaluation of Sediment Deposition and Migration Characteristics of New Sustainable Filter Media in Micro-Irrigation Sand Filters

The quartz sand filter medium used in micro-irrigation media filters has the disadvantages of short filtration cycle, surface filtration, and mining pollution. Selecting resources as new filter media is essential to improve the performance of the media filter and boost sustainable development. In this study, the traditional quartz sand filter medium and two new filter media were selected, and their corresponding filtration performances were comparatively studied. The influence of the type, particle size, and height of the filter medium on filtration performance was evaluated. The sediment content and distribution based on the size of particles in quartz sand, crushed glass, and glass bead filter layers was measured and analyzed. The hydraulic performance of different filter columns was analyzed. The results showed that for a given particle size, quartz sand exhibits the best sediment retention ability. This promoted the aggregation of small sediment particles into larger ones, whereas the crushed glass and bead glass filter layers promoted the splitting of large sediment particles into smaller ones, which enabled the reduction of blockage during the micro-irrigation process. The filtration rate of the quartz sand filter column exhibited the least fluctuation relative to crushed glass and glass bead filter media, and the pressure in each column exhibited a linear incremental change. In summary, glass microbeads are not suitable as filter material, crushed glass is suitable for general micro-irrigation systems, and quartz sand is suitable for micro-irrigation systems with elaborate filtration requirements. The findings of this study can provide theoretical guidance for the selection of the micro-irrigation filter material.

Evaluation of Upscaling the Selective Electrophoretic Deposition of Reduced Graphene Oxide on Miniaturized Au Interdigital Electrodes from Chip-to Wafer-Level

Today’s novel materials challenge the research industry to enhance the performance and to reduce the power consumption of microchips as well as to develop new sensor principles. All this applies pressure on the investigation of new economical mass production technologies for the integration into standard process sequences or on top of state-of-the-art CMOS devices. Since the discovery of graphene in 2004, many different variations have been investigated, thus the number of publications of graphene-based content grew from a few in 2004 exponential to 1.2 million only in 2019, according to Google Scholar analysis. The deposition of graphene-based materials at wafer-level is still difficult to do economically on standard SEMI wafers up to 8” diameter. In this publication, the selective electrophoretic deposition (EPD) of reduced graphene oxide flakes (rGO) will be shown. This technique is a very promising deposition method for large scale fabrication. The EPD of rGO particles is the only known way to create 3D surface topologies for an enhanced sensing area of electrochemical sensor applications e.g. biosensors. The electrical and chemical properties of this novel material provides a broad range of applications for possible sensor solutions [1, 2]. Firstly, the deposition will be shown on chip scale to gain optimum parameters in suspension preparation and EPD deposition time/voltage for a uniform particle deposition over the sensor area. Shortcuts from particles between the transmission lines or co-deposition on reference electrodes have to be avoided. This leads to a high selectivity in rGO particle deposition on Au-structures. Afterwards designs and experiments have been made on array level and a proof of concept wafer-level deposition with a low volume suspension is demonstrated. In previous work, the adhesion of rGO on Au structures in electrochemical sensors with a liquid flow, showed a migration of the deposited particles with the friction of the liquid [3]. Therefore, standard separation of particle agglomeration or splitting of primary particles with ultra sonic sonotrodes are not sufficient to gain highly concentrated suspensions with homogenous target particle distributions (< 0,5µm ≤ 1µm ≥ 5µm). For this reason, a novel particle crushing preparation by ball milling is introduced and enhanced selectivity with an improved adhesion is demonstrated. A full process of the preparation of the colloidal suspension with the definition of target particle sizes with an optimum zeta potential will be provided and the cathodic electrophoretic deposition shown [4, 5]. For the evaluation of the deposition experiments, stereo microscopy is used to reveal the selectivity on the interdigital electrode (IDE) structures (sensor area) and scanning electron microscopy (SEM) analysis is used to characterize particle sizes and 3D topography, in terms of primary and secondary particles (agglomerates). For this study, IDE structures with 15 different geometry variations (3µm to 15µm lines and spaces) are used that were manufactured [6] to evaluate the rGO deposition on chip level. A novel multisensory array design with eight sensing areas are presented, combined with wafer-level deposition as a proof of concept on a 200mm wafer.

A fracture-based discrete model for simulating creep in quartz sands

Creep of granular soils is frequently accompanied by grain breakage. Stress corrosion driven grain breakage offers a micromechanically based explanation for granular creep. This study incorporates that concept into a new model based on the discrete element method (DEM) to simulate creep in sands. The model aims for conceptual simplicity, computational efficiency and ease of calibration. To this end a new form of normalized Charles power law is incorporated into a DEM model for rough-crushable sands based on the particle splitting technique. The model is implemented using a controlled on-off computational strategy. The model is validated by simulating creep in quartz sands in oedometric and triaxial conditions. Model predictions are shown to compare favourably with experimental results in terms of creep strain, creep strain rates and particle breakage. The model proposed would facilitate the calibration of phenomenological continuum models, but may be also useful to directly investigate structural scale phenomena, such as pile ageing.

Smectite-bitumen interactions in non-aqueous bitumen extraction process

The non-aqueous extraction (NAE) is an alternative to the commercial water-based extraction technology used to liberate bitumen from oil sands. Although the impact of kaolinite, illite, chlorite, illite-smectite and montmorillonite on NAE process has been previously studied, the effect of different types of smectites has not been fully understood yet. In this work, mixtures of bitumen with bentonites dominated by saponite, hectorite, nontronite, beidellite and montmorillonite were reacted for several days and then washed with solvent (cyclohexane) to remove bitumen from the bentonites. The main goal was to better understand the impact of different smectites properties (specific surface area, pore structure characteristics, particle size, crystallite thickness, swelling ability, cation exchange capacity, layer charge and crystal-chemistry of smectites) on NAE process. The results showed that the porosity, particle size and swelling ability were the key parameters affecting the solvent-based bitumen recovery under the studied conditions. Samples with larger initial total pore volume and smaller particle size displayed reduced solvent bitumen extractability. The particle size of studied samples was affected primarily by swelling of smectites during the solvent bitumen extraction experiments. Smectites were swelling in water but not in cyclohexane. Swelling of smectite caused splitting of larger clay particles into many smaller particles. As a consequence, the efficiency of solvent bitumen extraction was significantly lower for fine grained samples, consisting of thin delaminated smectite particles, in which the bitumen was distributed among small-sized clay particles.

Direct Formation of Massive Black Holes via Dynamical Collapse in Metal-enriched Merging Galaxies at z ∼ 10: Fully Cosmological Simulations

We present the results of the first fully cosmological hydrodynamical simulations studying the merger-driven model for massive black hole (BH) seed formation via direct collapse. Using the zoom-in technique as well as particle splitting, we achieve a final spatial resolution of 2 pc. We show that the major merger of two massive galaxies at redshift z ∼ 8 results in the formation of a nuclear supermassive disk (SMD) of only 4 pc in radius, owing to a prodigious gas inflow sustained at 100–1000 M ⊙ yr−1. The core of the merger remnant is metal-rich, well above solar abundance, and the SMD reaches a gaseous mass of 3 × 108 M ⊙ in less than a million years after the merger, despite a concurrent prominent nuclear starburst. Dynamical heating as gas falls into the deepest part of the potential well, and heating and stirring by supernova blastwaves, generate a turbulent multiphase interstellar medium, with a gas velocity dispersion exceeding 100 km s−1. As a result, only moderate fragmentation occurs in the inner 10–20 pc, despite the temperature falling below 1000 K. The SMD is Jeans-unstable as well as bar-unstable and will collapse further adiabatically, becoming warm and ionized. We show that the SMD, following inevitable contraction, will become general-relativistic-unstable and directly form a supermassive BH of mass in the range 106–108 M ⊙, essentially skipping the stage of BH seed formation. These results confirm that mergers between the most massive galaxies at z ∼ 8–10 can naturally explain the rapid emergence of bright high-redshift quasars.

Optimal Monte Carlo particle splitting for neutron transport equation

Global tallying problem is hard to be solved efficiently when using Monte carlo method to simulate neutron transport equation, especially for sys- tem with big scale and/or strong imbalanced characteristics. Among numerous global variance reduction methods, particle splitting is an easy-to-implement method, but the efficiency is hard to be satisfying for practical problems. The essential challenge lies in the fact there are too many parameters to be opti- mized. In this paper, a systematic approach for setting all splitting parameters is proposed based on maximization of some global efficiency indicator. Results of two models show this approach can increase the global efficiency indicator up to two orders of magnitude while keeping the results unbiased.

Coupling of smoothed particle hydrodynamics and finite volume method for electrohydrodynamic droplet deformation simulation

In the numerical simulation of droplet electrohydrodynamic deformation, the grid-based method is difficult to handle the large topological deformation of the droplet interface, while the meshless method is challenging in the enforcement of boundary conditions. Therefore, a coupling method of the smoothed particle hydrodynamics (SPH) method and the finite volume method (FVM) is developed in this paper. In the present coupling method, the SPH method is used to solve the governing equations of the two-phase flow, while the FVM is used to solve the governing equations of the electric field. The realization of the coupling method is based on the information transfer between particles and grids. In order to accurately transfer the electric field force of interface grid nodes to SPH particles, a particle splitting interpolation method is developed. The influences of electrical capillary number, electrical conductivity ratio, and permittivity ratio on droplet deformation are studied. The simulation results are in good agreement with the theoretical predictions, and the coupling method can obtain more accurate numerical results than the pure SPH method. The coupling method can provide a reliable way to investigate complex electrohydrodynamic problems.

A particle refinement technique with dynamic splitting and coalescing pattern for fluid-structure interaction problem

With the increasing demand of large scale computation, multi-resolution particle methods have been paid much attention by many researchers. In multi-resolution method, high resolution is applied in local area to reduce the whole computational costs and maintain the local accuracy. However, there are still many challenges in the stability and accuracy of multi-resolution particle methods. In this research, an efficient variable particle size (VSP) multi-resolution method, using particle splitting and coalescing techniques, is developed in moving semi-implicit particle (MPS) method. Particles split or coalesce in dynamic five steps to avoid particle overlap and clustering. The mixed splitting mechanism by combining hexagonal splitting pattern and pair splitting pattern are proposed in the five-step splitting algorithm. Pair splitting and coalescing techniques with variable particle size are proposed to strictly ensure the conservation of mass and momentum and avoid particle clustering. To solve the non-linear fluid-structure interaction problem, the VSP algorithm is introduced in MPS-DEM method. The numerical results are compared with the analytical solutions and experimental results. It shows that the proposed VSP algorithm cannot only maintain the local accuracy, but also improve the computational efficiency by avoiding unnecessary chain operations between particle splitting and coalescing.

Investigating the role of electric fields on flow harmonics in heavy-ion collisions

Using the blast-wave model, we explore the effect of electric fields on spectra and flow harmonics (especially the elliptic flow) for charged pions and protons. We incorporate the first-order correction to the single-particle distribution function due to the electric fields and the dissipative effect while calculating the invariant yields of hadrons in the Cooper–Frye prescription at the freezeout hypersurface. We find a noticeable correction to the directed and elliptic flow of pions and protons for unidirectional and azimuthal asymmetric electric fields of a magnitude in the transverse plane. Further, we observe mass dependency of the directed flow generated due to the electric fields. The splitting of particle and antiparticle’s elliptic flow due to the electric fields is also discussed.

Mass-velocity Formula and Mass-energy Relation Cannot Be Derived Based on Lorentz Velocity Transformation

The most important achievement of the Einstein's special relativity was to derive the mass-velocity formula and the famous mass-energy relation from the Lorentz velocity transformation formula. Based on the mass-velocity formula, the dynamics of special relativity was established. In this paper, six derivation methods of the mass-velocity formula in special relativity are re-analyzed, including the elastic collision and the inelastic collision of two particles, the particle splitting processes, and the force moment balance methods based on the Lorentz velocity transformation formula, as well as the method to consider the symmetry principle without using the Lorentz transformation formula. It is pointed out that all of them have serious problems so that they cannot hold actually. Besides, it is pointed out that the method of Hamiltonian action to derive the mass-velocity has nothing to do with the Lorentz velocity transformation and does not belong to the category of special relativity. Therefore, the conclusion of this paper is that it is impossible to derive the mass-velocity formula and the mass-energy relation based on the Lorentz velocity transformation formula. The mass-velocity formula can only be considered as an empirical formula which cannot be derived in theory and have nothing to do with special relativity. If the mass-velocity formula and the mass-energy relationship are correct, it just means that Einstein's special relativity is not true.

Modified replica exchange-based MCMC algorithm for estimation of structural reliability based on particle splitting method

We consider the problem of evaluation of the reliability integral when the limit state functions could have complicating features such as (a) discontinuity/rapid changes in values of GU in the space spanned by U, (b) existence of multiple, possibly unimportant, regions of failure with rapid changes in performance function near one or more of the important regions, and (c) multiple regions of failure with substantial contributions to failure probability. We tackle this problem by using the particle splitting framework and introduce an improved Markov chain Monte Carlo sampler based on replica exchange strategy. This is shown to enhance the capacity of samples to detect and explore important regions of failure. The application of the bootstrap technique to deduce the sampling variance of the estimator of the probability of failure is developed. Also given are a few examples of problems in structural mechanics where limit state functions with the aforementioned difficulties arise. The performance of the proposed method in dealing with these difficulties is compared with those of existing methods.

FLEKS: A flexible particle-in-cell code for multi-scale plasma simulations

The magnetohydrodynamics with embedded particle-in-cell (MHD-EPIC) model has been successfully applied to global magnetospheric simulations in recent years. However, the PIC region was restricted to be one or more static boxes, which is not always sufficient to cover the whole physical structure of interest efficiently. The FLexible Exascale Kinetic Simulator (FLEKS), which is a new PIC code and allows a dynamic PIC region of any shape, is designed to break this restriction. FLEKS is usually used as the PIC component of the MHD with adaptively embedded particle-in-cell (MHD-AEPIC) model. FLEKS supports dynamically activating or deactivating cells to fit the regions of interest during a simulation. An adaptive time-stepping scheme is also introduced to improve the accuracy and efficiency of a long simulation. The particle number per cell may increase or decrease significantly and lead to load imbalance and large statistical noise in the cells with fewer particles. A particle splitting scheme and a particle merging algorithm are designed to limit the change of the particle number and hence improve the accuracy of the simulation as well as load balancing. Both particle splitting and particle merging conserve the total mass, momentum, and energy. FLEKS also contains a test-particle module to enable tracking particle trajectories due to the time-dependent electromagnetic field that is obtained from a global simulation.

A conservative particle splitting and merging technique with dynamic pattern and minimum density error

Splitting and merging technique is one of the effective refinement tools to increase the resolution in particle methods. However, it still has many challenges in stability, accuracy and conservation issues. In this research, a pair splitting technique with minimum density error, as well as with mass, momentum and energy conservations, is proposed. Instead of using a fixed splitting pattern adopted in previous researches, the splitting angle and distance in this research are dynamically obtained by achieving the total minimum density error of splitting particles and their surrounding particles. Regarding the merging algorithm, a triplet particle merging model with two small particles and one large particle is proposed to maintain angular momentum conservation. A minimum merging distance limitation is developed to ensure mass, momentum and energy conservations at the same time. A set of cases are investigated to validate the effectiveness, stability and conservation of the present splitting and merging model. The results show that the present model decreases large oscillations and avoids sudden disturb caused by irregular particle distribution due to splitting and merging.

Elastic Strain Relaxation of Phase Boundary of α' Nanoscale Phase Mediated via the Point Defects Loop under Normal Strain.

Irradiation-induced point defects and applied stress affect the concentration distribution and morphology evolution of the nanophase in Fe-Cr based alloys; the aggregation of point defects and the nanoscale precipitates can intensify the hardness and embrittlement of the alloy. The influence of normal strain on the coevolution of point defects and the Cr-enriched α' nanophase are studied in Fe-35 at.% Cr alloy by utilizing the multi-phase-field simulation. The clustering of point defects and the splitting of nanoscale particles are clearly presented under normal strain. The defects loop formed at the α/α' phase interface relaxes the coherent strain between the α/α' phases, reducing the elongation of the Cr-enriched α' phase under the normal strains. Furthermore, the point defects enhance the concentration clustering of the α' phase, and this is more obvious under the compressive strain at high temperature. The larger normal strain can induce the splitting of an α' nanoparticle with the nonequilibrium concentration in the early precipitation stage. The clustering and migration of point defects provide the diffusion channels of Cr atoms to accelerate the phase separation. The interaction of point defect with the solution atom clusters under normal strain provides an atomic scale view on the microstructure evolution under external stress.

A partition-coupled Eulerian–Lagrangian method for large-deformation simulation of compressible fluid

We present a partition-coupled Eulerian–Lagrangian method (PCELM) for accurately tracking a free interface and a contact discontinuity of the compressible fluid with large deformation. This method tracks the interface by arranging splittable Lagrangian particles on an Eulerian grid and adopts a partition-weighted bidirectional mapping between particles and grids using a cubic B-spline as interpolation function. PCELM suppresses oscillation of the discontinuous surface by this partition-weighted remapping method and solves the problem of numerical fracture by a particle splitting method. A virtual particle method is also proposed to deal with discontinuity of particle flow at the boundary and to maintain interpolation accuracy at the boundary. The conservation of mass, momentum, and energy of PCELM is proved by conservation analysis. Accuracy tests and simulations of discontinuous surfaces and free interfaces are performed to verify the accuracy and stability of PCELM. The results show that PCELM has strong energy conservation and low energy dissipation and that it is not only better at suppressing oscillations than the original method, but can also simulate a compressible fluid with large deformation more accurately than weighted essentially nonoscillatory schemes.

Cascades of high-energy SM particles in the primordial thermal plasma

High-energy standard model (SM) particles in the early Universe are generated by the decay of heavy long-lived particles. The subsequent thermalization occurs through the splitting of high-energy primary particles into lower-energy daughters in primordial thermal plasma. The principal example of such processes is reheating after inflation caused by the decay of inflatons into SM particles. Understanding of the thermalization at reheating is extremely important as it reveals the origin of the hot Universe, and could open up new mechanisms for generating dark matter and/or baryon asymmetry. In this paper, we investigate the thermalization of high-energy SM particles in thermal plasma, taking into account the Landau-Pomeranchuk-Migdal effect in the leading-log approximation. The whole SM particle content and all the relevant SM interactions are included for the first time, i.e., the full gauge interactions of SU(3)c×SU(2)L×U(1)Y and the top Yukawa interaction. The distribution function of each SM species is computed both numerically and analytically. We have analytically obtained the distribution function of each SM species after the first few splittings. Furthermore, we demonstrate that, after a sufficient number of splittings, the particle distributions are asymptotic to certain values at low momentum, independent of the high-energy particles injected by inflaton decay. The results are useful to calculate the DM abundance produced during the pre-thermal phase. An example is provided to illustrate a way to calculate the DM abundance from the scattering between the thermal plasma and high-energy particles in the cascade.