Initial Particle Distribution Research Articles

Kinetic field theory applied to planetesimal formation I: Freely streaming dust particles

Abstract Planet formation in the solar system was started when the first planetesimals were formed from the gravitational collapse of pebble clouds. Numerical simulations of this process, especially in the framework of streaming instability, produce various power laws for the initial mass function for planetesimals. While recent advances have shed light on turbulence and its role in particle clustering, a comprehensive theoretical framework linking turbulence characteristics to particle cluster properties and planetesimal mass function remains incomplete. Recently, a kinetic field theory for ensembles of point-like classical particles in or out of equilibrium has been applied to cosmic structure formation. This theory encodes the dynamics of a classical particle ensemble by a generating functional specified by the initial probability distribution of particles in phase space and their equations of motion. Here, we apply kinetic field theory to planetesimal formation. A model for the initial probability distribution of dust particles in phase space is obtained from a quasi-initial state for a three-dimensional streaming-instability simulation that is a particle distribution with velocities for gas and particles from the Nakagawa relations. The equations of motion are chosen for the simplest case of freely streaming particles. We calculate the non-linearly evolved density power spectrum of dust particles and find that it develops a universal k−3 tail at small scales, suggesting scale-invariant structure formation below a characteristic and time-dependent length scale. Thus, the KFT analysis indicates that the initial state for streaming instability simulations does not impose a constraint on structure evolution during planetesimal formation.

Analysis and Application of Particle Backtracking Algorithm in Wind–Sand Two-Phase Flow Using SPH Method

Due to the high sensitivity of grid-based micro-scale wind–sand flow models to deformation and distortion, this study employs the Smooth Particle Hydrodynamics (SPH) method for numerical simulations. The advantage of the SPH method is that it can dynamically analyze the entire trajectory of the particles, thus allowing the initial positional distribution of sand-buried particles to be traced. This study utilizes the advantages of the SPH method. It develops particle backtracking algorithms based on the SPH method using the C language. It analyses the initial location distribution, concentration, velocity, and particle size distribution of sand-buried particles to formulate targeted measures to cope with wind–sand disasters. Meanwhile, this paper improves a particle modeling algorithm to realize arbitrary mixing particle size and mixing ratio by programming in C language and combining it with pixel recognition technology. In addition, this paper will use the particle backtracking algorithm to analyze the classical embankment wind and sand flow field and then propose adequate measures for embankment wind and sand disaster management by investigating sand particle movement characteristics.

A Novel Fast and Body-Fitted Particle Generation Technique for Large-Scale SPH Simulations

Particle generation is important for particle-based methods. The reasonable initial particle distribution has a profound impact on the computational accuracy and the stability of particle-based methods. We propose a particle generation method that generates the body-fitted and uniform particles fast. This method first generates initial body-fitted and locally uniformly distributed particles on the geometric facets, following the spatial partitioning, particle hashing, particle sorting, and particle merging. The surface particles become body-fitted and uniform. In addition, we combine several other generation methods of boundary-level particles and inner particles to provide a unified framework for the pre-processing process of the smoothed particle hydrodynamics (SPH) method. Some particle generation examples of complex geometric models demonstrate the feasibility and effectiveness of this method. The proposed method can generate large-scale particles of complex geometric models, improve the handling capacity of pre-processing techniques, and keep up with the scale of solvers.

Flocculation rate of locally densely distributed cohesive particles in Taylor–Green vortex flow

We employ the three-way coupled numerical simulations to investigate the flocculation of primary cohesive particles which are locally densely distributed in the Taylor–Green cellular vortex flow. The hydrodynamic and inertial forces as well as the direct contact, lubrication, and cohesion forces between particles during the growth, deformation, and breakup of flocs are captured in detail. The flocculation rate of the primary particles decreases gradually from its maximum value at the initial moment, then levels off during flocculation, yielding the flocculation and equilibrium stages. The flocculation rate is determined by the equilibrium floc size and a flocculation coefficient. A larger equilibrium floc size and a smaller value of the flocculation coefficient yield faster flocculation. An initially dense distribution of cohesive particles accelerates the growth of flocs during flocculation but has minor effects on the equilibrium floc size, compared to an initially dilute distribution. A larger particle-to-fluid density ratio, a smaller size ratio between the particle diameter and the Kolmogorov length scale, and stronger cohesion yield a larger equilibrium floc size and a higher flocculation coefficient. Their influence on the flocculation coefficient becomes more evident when the initial particle distribution becomes more concentrated, while their impact on the maximum flocculation rate is very limited. A simple new model is proposed to describe the flocculation process of unevenly distributed cohesive particles in turbulence.

Chaos and anomalous transport in a semiclassical Bose-Hubbard chain.

We study chaotic dynamics and anomalous transport in a Bose-Hubbard chain in the semiclassical regime (the limit when the number of particles goes to infinity). We find that the system has mixed phase space with both regular and chaotic dynamics, even for long chains with up to 100 wells. The consequence of the mixed phase space is strongly anomalous diffusion in the space of occupation numbers, with a discrete set of transport exponents. After very long times the system crosses over to the hydrodynamic regime with normal diffusion. Anomalous transport is quite universal and almost completely independent of the parameters of the model (Coulomb interaction and chemical potential): It is mainly determined by the initial distribution of particles along the chain. We corroborate our findings by analytical arguments: scaling analysis for the anomalous regime and the Langevin equationfor the normal diffusion regime.

On the partition noise in chosen particle weighted methods and its consequences for weakly-compressible flow models

The Meshless Finite Volume (MFV) method, which is a member of the particle weighted methods (PWM) family, is analysed in the context of the so-called partition noise problem. This issue is inherent to PWM-type discretisation which is based on compact support kernel functions and particle sampling. The partition noise exhibits itself as spurious oscillations observed in the solution; they are caused by unphysical source terms in the discretised equations and approximate local volumes computation. Unfortunately, decreasing the discrete length scale which controls the spatial resolution reduces the partition noise only weakly (and never completely). When choosing numerical schemes, a special care is required since in naive implementations the partition noise may even lead to loss of stability. However, even when stability is assured, PWM does not fulfil the assumptions of the Lax equivalence theorem (i.e. the discretised equations are not consistent), therefore convergence in the classical meaning cannot be guaranteed.As an example of a problematic use of MFV, we investigate its application to the solution of fluid flow equations at low Mach numbers, aiming to mimic truly incompressible flow conditions. Taken here as isothermal Euler equations, they are the basis of the so-called weakly-compressible (WC) flow models. Such modelling does not involve any elliptic-type equation and, due to the algorithmic and computational reasons, seems to be well-suited for particle methods. The WC flow model imposes, however, a serious challenge for PWM since: (i) the method is not gauge invariant and the disparity between the speed of sound and the convective velocity scale causes a significant spurious source of momentum; (ii) the inaccuracy in the local volumes approximation leads to errors in the computed density which are comparable to physically relevant slight variations, inherent to the WC approach. We propose specific numerical and modelling measures: controlled relaxation of initial particle distribution, particle volumes computation using an optimal kernel function, a choice of gradient limiting techniques and a carefully chosen background pressure. Although these improvements significantly increase the accuracy (however at remarkably increased computational cost), the theoretical 2nd-order convergence is achieved only at lower spatial resolutions when the truncation errors dominate. The accuracy of mesh-based methods is achieved in PWM only for the pressure field; the errors in the velocity field are much larger and convergence is at most 1st-order. We point some contradictory requirements of the model equations and the numerical method. One of the conclusions is that it is doubtful to construct a convergent truly Lagrangean method of PWM type at reasonable computational cost. The present findings also apply to conservative variants of the weakly-compressible Smoothed Particle Hydrodynamics which, being first order consistent in the best case, suffers from the partition noise even more severely than the considered MFV approach which is theoretically second order consistent. The conclusions pose a question about a rationale for the use of WC-PWM approach in chosen applications, in particular free surface and interfacial flows.

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

The exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes. Given the nonlinear nature of the governing equation, only a limited number of analytical solutions for the number density function corresponding to empirical kernels are available in the literature. This article introduces a semi-analytical approach using the homotopy perturbation method to obtain series solutions for the nonlinear collisional fragmentation equation. The method presented here can be readily adapted to solve both linear and nonlinear integral equations, eliminating the need for domain discretization. To gain deeper insights intothe accuracy of the proposed method, a convergence analysis is conducted. This analysis employs the concept of contractive mapping within the Banach space, a well-established technique universally acknowledged for ensuring convergence. Various collisional kernels (product and polymerization kernels), breakage distribution functions (binary and multiple breakage) and various initial particle distributions are considered to obtain the new series solutions. The obtained results are successfully compared against finite volume method [26] solutions in terms of number density functions and their moments. The error between the exact and obtained series solutions is shown in plots and tables to confirm the applicability and accuracy of the proposed method.

Order, Chaos and Born’s Distribution of Bohmian Particles

We study order, chaos and ergodicity in the Bohmian trajectories of a 2D quantum harmonic oscillator. We first present all the possible types (chaotic, ordered) of Bohmian trajectories in wavefunctions made of superpositions of two and three energy eigenstates of the oscillator. There is no chaos in the case of two terms and in some cases of three terms. Then, we show the different geometries of nodal points in bipartite Bohmian systems of entangled qubits. Finally, we study multinodal wavefunctions and find that a large number of nodal points does not always imply the dominance of chaos. We show that, in some cases, the Born distribution is dominated by ordered trajectories, something that has a significant impact on the accessibility of Born’s rule P=|Ψ|2 by initial distributions of Bohmian particles with P0≠|Ψ0|2.

The Particle Generation Method Utilizing an Arbitrary 2D Model for Smoothed Particle Hydrodynamics Modeling and Its Application in the Field of Snowdrift

This paper uses the SPH method to study snow disasters, including the snow flow model of a vertical water diffusion equation and heat balance equation. The advantage of the SPH method is that it can capture particles’ positions, which can be used to track the initial position distribution of hazardous particles. At the same time, a particle modeling method based on pixel value is proposed, which has certain advantages in dealing with the boundary modeling of different materials. In addition, snow disaster prevention and the control of classic embankment and cutting procedures were carried out. The final treatment results showed that the number of snow particles on the subgrade surface was reduced by about 90%. The validity and feasibility of the snow disaster simulation software based on the SPH method are verified by comparison with the experimental results.

Transformation of CuO and Cu2O particles into CuxS within the polymeric matrix of anion exchangers, and its structural and morphological implications

The study demonstrates the process of anion exchanger modification in order to obtain a reactive organic polymer containing CuxS dispersed within its matrix. As starting materials, two strongly basic commercial anion exchangers were used – macroreticular and gel-type – previously modified by deposition of cuprite or tenorite within their structure. The pre-formed composites were sulphidated using an Na2S solution to obtain materials containing CuxS (5.3–6.7 wt% Cu and 4.5–6.7 wt% S), which were further studied using Raman and XPS spectroscopy, and XRD and SEM/EDS analyses. Depending on the sulphidation precursor, Cu2O or CuO, its distribution within the polymeric matrix, and the porous structure of the supporting anion exchanger, products with different CuxS content were obtained. The main sulphidation product – covellite – was accompanied by admixtures of copper-rich phases such as digenite and djurleite, but products of sulphide oxidation were also identified. The conversion of Cu2O into CuS was more efficient and selective in comparison to CuO. The sulphidation process remained within the initial distribution of the precursor particles within the polymeric matrix. The morphology of the obtained covellite particles was strongly dependent on the porous structure of the supporting anion exchanger. The conversion of the Cu2O and CuO within the macroporous matrix led respectively to spiky burr-like CuS and more densely packed elongated needle-shaped CuS particles, while the CuS particles obtained in the gel-type matrix were spherical. The spherical particles obtained from Cu2O conversion exhibited a hollow structure, which was the result of solid-state diffusion during the sulphidation, the so-called Kirkendall effect.

A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems.

We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for the Casimir invariants. This has restricted studies of Lynden-Bell's violent relaxation theory to only a very small class of initial conditions of a very simple waterbag form, for which the entropy maximization can be performed numerically. In the present approach, an arbitrary initial distribution is discretized into density levels which are then evolved using an efficient Monte Carlo algorithm towards the final equilibrium state. A comparison is also made between the LB equilibrium and explicit Molecular Dynamics simulations. We find that for most initial distributions, relaxation is incomplete and the system is not able to reach the state of maximum LB entropy. In particular, we see that the tail of the stationary particle distribution is very different from the one predicted by the theory of violent relaxation, with a hard cutoff instead of an algebraic decay predicted by LB's theory.

Modelling of particulate contamination redistribution inside purged cavities

Sophisticated instruments on-board most of satellite payloads, especially scientific ones, are sensitive to particulate contamination since their performance can be affected in terms of straylight or surface obscuration. The surface cleanliness levels have to be minimized on ground. However, even if the deposition rate is controlled in cleanroom, the hardware is continuously exposed to particles and fibers, moving in the airflow and settling according to their various sizes and matter compositions. Thus, depending on the initial surface cleanliness level, the redistribution of particulate contamination can be a concern during integration and tests activities until launch, when venting and/or vibrations occur which results in more or less random fallout of particles. Previous studies identified different steps for the transfer mechanism such as detachment, transport and interaction with the surface (with or without bounce). Therefore, it is paramount to understand the physical phenomena of particle resuspension that happens either inside purged cavities of spacecraft or under fairing in order to be able to model them as for molecular contamination. After performing a state of the art of the existing detachment models, a Computational Fluid Dynamics software, scSTREAM, has been chosen among the most relevant ones for a feasibility study to simulate particles redistribution. This tool was particularly interesting due to the possibility to add specific functions for computation. For the purpose, the Rock’n’Roll (R’n’R) model has been implemented to consider particle resuspension. In parallel, some simple test configurations have been defined and a mock-up with several adjacent cavities has been used to compare theory and experiment when a purging under dry nitrogen was applied in the vicinity of a pre-contaminated surface. The relocation of FluoDust particles, as the source of contamination, deposited on a specific substrate has been evaluated thanks to many collector plates disseminated in one or two cavities and the levels quantified. The impact of different test conditions (flow rate, material of the substrate, presence of leakage, initial contamination level…) has been investigated. This paper presents the comparative results that confirmed the redistribution of the particulate contamination with similar trajectories but also some discrepancies due to the limitations of the R’n’R model and depending on experimental parameters such as initial distribution of particles, adherence force to the substrate…

Unstable Points, Ergodicity and Born's Rule in 2d Bohmian Systems.

We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of the moving nodal points, in cases with 1, 2 and multiple nodal points. Then, we find the contributions of the ordered and chaotic trajectories in the Born distribution, and when the latter is accessible by an initial particle distribution which does not satisfy Born's rule.

Multiscale analysis of Ni-YSZ and Ni-CGO anode based SOFC degradation: From local microstructural variation to cell electrochemical performance

Nickel based fuel electrodes are widely used for commercial solid oxide fuel cells showing a high catalytic activity, despite of involving severe microstructural changes which reduce the system lifetime. Needing a detailed knowledge of such phenomena, the authors compare the behaviour of two state-of-the-art planar cells, Ni-YSZ based anode supported cell and Ni-CGO based electrolyte supported cell, working for 1000 hours under a galvanostatic operation with H2 rich feed. Following a multiscale approach, the system was analysed in terms of both global performance and local properties. Experimental observations through electrochemical characterization and microstructural analysis laid the basis for developing a physics-based model able to predict the cell operation at reference and aged status. Indeed, the kinetics was expressed as a function of microstructural features and considers the time evolution of some parameters. Ni-based electrode was identified as the first source of degradation due to Ni instability resulting in a reduction of catalytic activity and conductivity, correlated mainly to Ni particle coarsening and migration respectively. Each degradation mechanism prevailed depending on the material structure (i.e., initial particle size and distribution) and imposed working conditions (i.e., temperature, load and gas composition).

Kinetics of a Reaction-Diffusion Mtb/SARS-CoV-2 Coinfection Model with Immunity

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and Mycobacterium tuberculosis (Mtb) coinfection has been observed in a number of nations and it is connected with severe illness and death. The paper studies a reaction–diffusion within-host Mtb/SARS-CoV-2 coinfection model with immunity. This model explores the connections between uninfected epithelial cells, latently Mtb-infected epithelial cells, productively Mtb-infected epithelial cells, SARS-CoV-2-infected epithelial cells, free Mtb particles, free SARS-CoV-2 virions, and CTLs. The basic properties of the model’s solutions are verified. All equilibrium points with the essential conditions for their existence are calculated. The global stability of these equilibria is established by adopting compatible Lyapunov functionals. The theoretical outcomes are enhanced by implementing numerical simulations. It is found that the equilibrium points mirror the single infection and coinfection states of SARS-CoV-2 with Mtb. The threshold conditions that determine the movement from the monoinfection to the coinfection state need to be tested when developing new treatments for coinfected patients. The impact of the diffusion coefficients should be monitored at the beginning of coinfection as it affects the initial distribution of particles in space.

Indoor Localization Method for a Mobile Robot Using LiDAR and a Dual AprilTag

Global localization is one of the important issues for mobile robots to achieve indoor navigation. Nowadays, most mobile robots rely on light detection and ranging (LiDAR) and adaptive Monte Carlo localization (AMCL) to realize their localization and navigation. However, the reliability and performance of global localization only using LiDAR are restricted due to the monotonous sensing feature. This study proposes a global localization approach to improve mobile robot global localization using LiDAR and a dual AprilTag. Firstly, the spatial coordinate system constructed with two neighboring AprilTags is applied as the reference basis for global localization. Then, the robot pose can be estimated by generating precise initial particle distribution for AMCL based on the relative tag positions. Finally, in pose tracking, the count and distribution of AMCL particles, evaluating the certainty of localization, is continuously monitored to update the real-time position of the robot. The contributions of this study are listed as follows. (1) Compared to the localization method only using LiDAR, the proposed method can locate the robot’s position with a few iterations and less computer power consumption. (2) The failure localization issues due to the many similar indoor features can be solved. (3) The error of the global localization can be limited to an acceptable range compared to the result using a single tag.

Developed molecular dynamics method of dissipative particle dynamics for the bench mark numerical simulation of fluid flow inside a rectangular chamber,,

The fluid flow inside the chamber with a moving wall is simulated by developed Dissipative Particle Dynamics (DPD) method which implies the developed molecular dynamics (MD) appraoch. In this benchmark problem, the chamber is filled with a fluid with a certain initial temperature and its cover is moving at a constant speed. One of the most important issues in DPD method, is creating solid walls and then applying related boundary conditions. Hence by freezing several layers of DPD particles, solid walls were created to prevent DPD particles from leaving the area. Then, by applying the boundary condition of parallel reflection, the penetration of fluid particles into the solid wall was prevented, and the no-slip condition was applied to the walls. Next, the effect of parameters such as initial distribution of fluid particles, their initial velocity, geometry of the problem, boundary conditions, Reynolds number and different weighting functions, were investigated. It was showed that increasing Reynolds number to more than 800 in addition to eliminating the incompressibility property caused particles exit from the solution domain and diverge. It is also possible to increase the Schmidt number of DPD fluid by applying a suitable weighting function.

Simulating Grain Shape Effects and Damage in Granular Media Using PeriDEM

We provide a numerical platform for the analysis of particle shape and topology on the bulk behavior of granular media using a peridynamic based discrete element method, where the deformation and damage of individual particles are taken into account. To accommodate arbitrary particle shapes including nonconvex ones as well as particle topology, a method is developed to detect peridynamic bonds that extend outside the domain boundary. To avoid numerical oscillation on contact, Coulomb's law is modified for small velocity and a node-level damping is introduced. Particle contact with the rigid boundary wall is computed analytically to avoid treating the wall a peridynamic domain to improve simulation. Moreover, to generate an initial jammed particle distribution, a optimization-based method is used.

Simulation of van der Waals liquid droplets within a hot air atmosphere using the smoothed particle hydrodynamics method

The mass and heat transfer of van der Waals liquid droplets within a hot air atmosphere in microgravity have been studied using adaptive Smoothed Particle Hydrodynamics by assuming that the gas atmosphere is in contact with a thermal reservoir for a single-component two-dimensional system. A better definition of the diffuse interface between the phases was obtained through the introduction of a Korteweg tensor. As in previous works, the best initial particle distribution was obtained using the process of spinodal decomposition. The temperature obtained from the van der Waals cycle was compared with the temperature that arises from the integration of the conservation laws that contain the heat-flux vector. The calculated temperature profiles are the same for both the liquid and gas phases. The interface satisfies the condition of coexistence between the phases. In addition, the mass and heat transfer rates as well as the decrease of the drop radius were obtained for the three temperatures studied, finding that these are enhanced as the temperature of the reservoir is increased. Finally, it was possible to observe a damped oscillatory behavior of the temperature between the liquid phase and the interface for the first instants of time. We conclude that this is the mechanism by which the areas with lower temperature within the drop are heated before starting the mass transfer between the liquid and the gas phase.

Importance of Initial Particle Distribution in Modeling Dam Break Analysis with SPH

Smoothed-Particle Hydrodynamics (SPH) has drawn a great deal of attention in recent years to model various phenomena in engineering and science. SPH is a Lagrangian model in which moving particles represent the fluid body during simulation. Therefore, the initial distribution of particles may affect the model results along with the simulation, and a good initial condition can minimize numerical errors or increase the computational efficiency. Since SPH model particle distributions need a flow pattern, the dam break flow as a classic benchmark SPH problem is selected in this study, and the best initial particle distribution for this case has to be found. Different results, including the mean density of particles, hydrostatic and dynamic pressures and surge front position, are considered the main model results for the adequacy of different initial particle distributions to be discussed. All models are verified at first by simulating different test cases and comparing the results with analytical and experimental data. Acceptable agreements between these data show the model's capability in well predicting the dam break flows. Then, the effects of initial particle distribution on the results are investigated by considering five different particle distributions. For this purpose, Body-Centered Cubic (BCC), Simple Cubic (SC), Greedy, Voronoi Tessellation and Fibonacci algorithms for particle distributions have been modeled. To get reliable conclusions, these distributions have been utilized in models with different kernel functions as well as with different particle spacings. Based on the results, irregular arrangements such as Greedy distribution perform better than regular SC and BCC distributions in modeling dam-break flow. In addition, both Voronoi and Fibonacci distributions perform almost the same with a moderate level of accuracy. Regarding mentioned arrangements, the main outcome of this study, is that the initial particle distribution is an important issue in SPH models, which clearly affects the results.