Particle Splitting Research Articles

STAR FORMATION AT VERY LOW METALLICITY. V. THE GREATER IMPORTANCE OF INITIAL CONDITIONS COMPARED TO METALLICITY THRESHOLDS

The formation of the first stars out of metal-free gas appears to result in stars at least an order of magnitude more massive than in the present-day case. We here consider what controls the transition from a primordial to a modern initial mass function. It has been proposed that this occurs when effective metal line cooling occurs at a metallicity threshold of Z/Z_sun > 10^{-3.5}. We study the influence of low levels of metal enrichment on the cooling and collapse of initially ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations with particle splitting. Our initial conditions represent protogalaxies forming within a previously ionized H ii region that has not yet had time to cool and recombine. These differ considerably from those used in simulations predicting a metallicity threshold, where the gas was initially cold and only partially ionized. In the centrally condensed potential that we study here, a wide variety of initial conditions for the gas yield a monolithic central collapse. Our models show no fragmentation during collapse to number densities as high as 10^5 cm^{-3}, for metallicities reaching as high as 10^{-1} Z_sun in one rotating case, far above the threshold suggested by previous work. Rotation allows for the formation of gravitationally stable gas disks over large fractions of the local Hubble time. Turbulence slows the growth of the central density slightly, but both spherically symmetric and turbulent initial conditions collapse and form a single sink particle. We therefore argue that fragmentation at moderate density depends on the initial conditions for star formation more than on the metal abundances present.

An efficient, robust, domain-decomposition algorithm for particle Monte Carlo

A previously described algorithm [T.A. Brunner, T.J. Urbatsch, T.M. Evans, N.A. Gentile, Comparison of four parallel algorithms for domain decomposed implicit Monte Carlo, Journal of Computational Physics 212 (2) (2006) 527–539] for doing domain decomposed particle Monte Carlo calculations in the context of thermal radiation transport has been improved. It has been extended to support cases where the number of particles in a time step are unknown at the beginning of the time step. This situation arises when various physical processes, such as neutron transport, can generate additional particles during the time step, or when particle splitting is used for variance reduction. Additionally, several race conditions that existed in the previous algorithm and could cause code hangs have been fixed. This new algorithm is believed to be robust against all race conditions. The parallel scalability of the new algorithm remains excellent.

Alteration of swelling clay minerals by acid activation

The bulk material of six dioctahedral and two trioctahedral swellable clay minerals was leached in H 2SO 4 and HCl at concentrations of 1.0, 5.0 and 10.0 M at 80 °C for several hours. Alteration of the clay mineral structures was dependent on the individual character of each mineral (chemical composition and initial particle size). Acid attack dissolved the octahedral sheets by interlayer and edge attack. The number of substitutions by Mg or Fe in the octahedral sheet of the clay minerals promoted the dissolution of these layers and the formation of a silica phase. The dissolution of the octahedral cations occurred in the following order: Mg > Fe > Al. The dioctahedral smectites were more stable than the trioctahedral smectites and vermiculites; the behavior of trioctahedral smectites against acid was similar to that of vermiculites. The acid activated smectites displayed still the ability to exchange cations. The obtained materials had a lower layer charge, lower CEC and higher specific surface area than the crude materials but still adsorbed very large organic cations like dodecylammonium ions. The reaction with the acid caused particle splitting within the octahedral sheet. A model of dissolution and particle splitting is proposed.

The energy partitioning of non-thermal particles in a plasma: the Coulomb logarithm revisited

The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated exactly to leading and next-to-leading accuracy in the plasma density by Brown, Preston and Singleton (BPS). Since the calculational techniques of BPS might be unfamiliar to some, and since the same methodology can also be used for other energy transport phenomena, we will review the main ideas behind the calculation. BPS used their stopping power calculation to derive a Fokker–Planck equation, also accurate to leading and next-to-leading orders, and we will also review this. We use this Fokker–Planck equation to compute the electron–ion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion—more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fractional energy loss to electrons and ions as accurately as possible. One method by which one calculates the electron–ion energy splitting of a charged particle traversing a plasma involves integrating the stopping power dE/dx. However, as the charged particle slows down and becomes thermalized into the background plasma, this method of calculating the electron–ion energy splitting breaks down. As a result, it suffers a systematic error that may be as large as T/E0, where T is the plasma temperature and E0 is the initial energy of the charged particle. The formalism presented here is designed to account for the thermalization process and it provides results that are near-exact.

QCD splitting/joining functions at finite temperature in the deep Landau-Pomeranchuk-Migdal regime

There exist full leading-order-in-${\ensuremath{\alpha}}_{\mathrm{s}}$ numerical calculations of the rates for massless quarks and gluons to split and join in the background of a quark-gluon plasma through hard, nearly collinear bremsstrahlung and inverse bremsstrahlung. In the limit of partons with very high energy $E$, where the physics is dominated by the Landau-Pomeranchuk-Migdal effect, there are also analytic leading-log calculations of these rates, where the logarithm is $\mathrm{ln}(E/T)$. We extend those analytic calculations to next-to-leading-log order. We find agreement with the full result to within roughly 20% for ${E}_{<}\ensuremath{\gtrsim}10T$, where ${E}_{<}$ is the energy of the least energetic parton in the splitting/joining process. We also discuss how to account for the running of the coupling constant in the case that $E/T$ is very large. Our results are also applicable to isotropic nonequilibrium plasmas if the plasma does not change significantly over the formation time associated with particle splitting.

Phase-field study for the splitting behaviour of precipitate under applied stress

This paper employs the phase-field method to study the splitting behaviour of a single coherent particle under an applied uniaxial stress. It finds that the splitting behaviour is greatly influenced by the initial shape of precipitates, the bulk free energy condition, the degree of supersaturation and the ratio of the interfacial energy to the elastic strain energy, etc. The simulated results demonstrate that the aspect ratio of the particle determines whether the splitting can occur and how many split plates can be obtained. The splitting of particle is sensitive to the interfacial energy, i.e. the splitting becomes more and more difficult with increasing the ratio of the interfacial energy to the elastic strain energy. And increasing the magnitude of the applied stress is favourable to the splitting. The splitting process is also explained from the point of view of the corresponding diffusion potential.

Study of Continuos Settling Vessels Operating with Suspensions Previously Floculated

The settling vessels are equipment destined to solid-liquid separation; usually have continuous operation, with a circular section, presenting one conic and one cylindrical part. They are very used in chemical industries: wastewater treatment, minerals industries; to concentrate or to remove the solids. The solid particle splitting with small granular becomes difficult through the operation of conventional sedimentation. An expedient very used in the industry is the flocculant substance addition, whose objective is to promote the precipitation of particles, with decantation speed is upper than the single one. The present work aim the study of the burst operational conditions that influence the formation and the stability of these aggregates, the flake, the effect of pH and the concentration of flocculant using kaolin suspension and genfloc, that contains aluminum sulfate, as a flocculant; and the capacity of conventional settling vessel, which area of the transversal remains constant, considering this operational conditions.

Robust single-particle tracking in live-cell time-lapse sequences

Single particle tracking (SPT) is often the rate-limiting step in live cell imaging studies of sub-cellular dynamics. Here we present a tracking algorithm that addresses the principal challenges of SPT, namely high particle density, particle motion heterogeneity, temporary particle disappearance, and particle merging and splitting. The algorithm first links particles between consecutive frames and then links the resulting track segments into complete trajectories. Both steps are formulated as global combinatorial optimization problems whose solution identifies the overall most likely set of particle trajectories throughout the movie. Using this approach, we show that the GTPase dynamin differentially affects the kinetics of long and short-lived endocytic structures, and that the motion of CD36 receptors along cytoskeleton-mediated linear tracks increases their aggregation probability. Both applications indicate the requirement for robust and complete tracking of dense particle fields to dissect the mechanisms of receptor organization at the level of the plasma membrane.

SU‐GG‐T‐311: A Distributed‐Computing Platform for Monte Carlo Dose Calculations and Beam‐Weight Optimization

Purpose: Monte carlo (MC) algorithms remain the gold standard in dose calculation routines. However, their long calculation times generally make them infeasible for clinical implementation, especially for IMRT optimization which requires rapid pencil‐beam dose computation. In a preliminary study, we are investigating how high‐throughput computing may be employed to perform MC dose calculations and rudimentary optimization using non‐commercial software. Method and Materials: Two non‐commercial software packages were used for this project, VMC++ and CERR. VMC++ is an MC dose calculation package which is more efficient than general‐purpose MC routines due to its use of variance reduction techniques. A combination of particle splitting and Russian Roulette methods is employed in VMC++ for photon transport modeling, which enhances the efficiency and speed of the calculation, making it approximately 50 times faster than the BEAMnrc code. CERR is an open‐source environment for radiotherapy calculations. We used the data‐importation and beam‐shaping features of CERR in conjunction with the dose‐calculation routines of VMC++ to perform dose computation on a 4‐field 3D CRT prostate case. We then optimized the beam weights using DVH‐based constraints and the Nelder‐Mead simplex technique, a multidimensional unconstrained nonlinear minimization algorithm. Collaborating with members of an academic supercomputing facility enabled us to perform the calculations on a subset of a cluster of 1000 dual‐core Linux‐based computers. Results: The dose calculation and optimization, involving several million particle histories, required only a few minutes to complete. The resulting plan was optimal based on the constraints provided to the system, and indicated that additional constraints may be necessary for clinical feasibility. Conclusion: We have shown that, using a distributed‐computing platform, an MC routine may be employed for treatment planning in a reasonable amount of time. This work will be extended to IMRT and beam‐angle optimization by combining a variety of Techniques.

Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

A discrete framework is introduced for simulating the particulate physical systems governed by population balance equations (PBE) with particle splitting (breakage) and aggregation based on accurately conserving (from theoretical point of view) an unlimited number of moments associated with the particle size distribution. The basic idea is based on the concept of primary and secondary particles, where the former is responsible for distribution reconstruction while the latter is responsible for different particle interactions such as splitting and aggregation. The method is found to track accurately any set of low-order moments with the ability to reconstruct the shape of the distribution. The method is given the name: the sectional quadrature method of moments (SQMOM) and has the advantage of being not tied to the inversion of large sized moment problems as required by the classical quadrature method of moments (QMOM). These methods become ill conditioned when a large number of moments are needed to increase their accuracy. On the contrary, the accuracy of the SQMOM increases by increasing the number of primary particles while using fixed number of secondary particles. Since the positions and local distributions for two secondary particles are found to have an analytical solution, no large moment inversion problems are anymore encountered. The generality of the SQMOM is proved by showing that all the related sectional and quadrature methods appearing in the literature for solving the PBE are merely special cases. The method has already been extended to bivariate PBEs.

Splitting for rare event simulation: A large deviation approach to design and analysis

Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set B before another set A , and it is assumed that this probability satisfies a large deviation scaling. A notion of subsolution is defined for the related calculus of variations problem, and two main results are proved under mild conditions. The first is that the number of particles generated by the algorithm grows subexponentially if and only if a certain scalar multiple of the importance function is a subsolution. The second is that, under the same condition, the variance of the algorithm is characterized (asymptotically) in terms of the subsolution. The design of asymptotically optimal schemes is discussed, and numerical examples are presented.

Modeling weathering pathways and processes of the fragmentation of salt weathered quartz‐chlorite schist

The relationship between the rate of rock breakdown and environmental and geological factors must be understood in order to establish the conditions under which weathering limits erosion. In this study qualitative and quantitative models of the rock fragmentation process are fitted to previously published data obtained from laboratory salt weathering trials of quartz‐chlorite schist. Weathering was modeled as a combination of (1) a fragmentation event that fragments the parent particle into a number of daughter particles while preserving mass, and (2) a fracture probability, that determines the probability that a fragmentation event will occur in a given time period. We show that observations of the complex breakdown of salt weathered schist are consistent with model assumptions of a simple fracture geometry model and an increase in fracture probability with time. For the fragmentation geometry the best fit to the experimental data was achieved by assuming that each fragmentation event involves splitting of the parent particle into two daughter fragments of equal volume. For the fragmentation rate the data could best be described with a fracture probability, and hence the weathering rate, that increased linearly with time. This paper shows that it is possible to use a physically based fragmentation model to infer the process of fragmentation for individual particles using a time evolving particle size distribution for the weathering rock fragments.

Electromagnetic particle-in-cell simulations on magnetic reconnection with adaptive mesh refinement

The electromagnetic particle-in-cell (EM-PIC) model using the adaptive mesh refinement (AMR) is reconsidered so that it is properly and efficiently applied to the current sheet evolution associated with magnetic reconnection. It is very important to adequately select the refinement criteria for cell splitting. It is demonstrated that fine cells have to be distributed not only in the region where the electron Debye length is small, but also in the region where the electron-scale structure is expected to be significant. While the AMR reduces the number of cells drastically, the total simulation cost is also controlled by the number of particles. In order to reduce the total number of particles in the entire system, the present code controls the local number of particles per cell by splitting or coalescing particles. It is shown that the particle splitting and coalescence are quite effective as well as the AMR to enhance the efficiency of the EM-PIC simulations. A new 3D code extended from the 2D code is also introduced. The code is checked against the tearing instability and the lower hybrid drift instability, and it is confirmed that the code has been successfully developed. It is also found that the 3D simulations can gain more efficiency by using the AMR than the 2D simulations.

High-resolution simulations of clump-clump collisions using SPH with particle splitting

We investigate, by means of numerical simulations, the phenomenology of star formation triggered by low-velocity collisions between low-mass molecular clumps. The simulations are performed using an SPH code which satisfies the Jeans condition by invoking On-the-Fly Particle Splitting. Clumps are modelled as stable truncated (non-singular) isothermal, i.e. Bonnor-Ebert, spheres. Collisions are characterised by M_0 (clump mass), b (offset parameter, i.e. ratio of impact parameter to clump radius), and M (Mach Number, i.e. ratio of collision velocity to effective post-shock sound speed). The gas subscribes to a barotropic equation of state, which is intended to capture (i) the scaling of pre-collision internal velocity dispersion with clump mass, (ii) post-shock radiative cooling, and (iii) adiabatic heating in optically thick protostellar fragments. The efficiency of star formation is found to vary between 10% and 30% in the different collisions studied and it appears to increase with decreasing M_0, and/or decreasing b, and/or increasing M. For b ~ 5 x 10^5 cm^{-3}, are sufficient that they could be mapped in NH_3 or CS line radiation, in nearby star formation regions.

Phase Field Study for Self-Assemble of the Second Phase Particles in Coherent Phase Transition

We present a phase field model for coherent phase transition and its application to the self-assembled arrangement of second phase particles in coherent phase transition. The model developed here is free from the interface instability due to the contribution of chemical free energy and correctly describes elastically inhomogeneous system. It is observed that coherent misfit strain and anisotropy of elastic constants induce the interface instability that brings about the particle splitting and the self-assembled alignment of second phase particles. Their arrangement to the elastically soft direction occurs only in the system where the elastic contant of the precipitates is larger than that of the matrix phase.

One-dimensional model for QCD at high energy

We propose a stochastic particle model in ( 1 + 1 ) dimensions, with one dimension corresponding to rapidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of pomeron loops. The model evolves via non-linear particle splitting, with a non-local splitting rate which is constrained by boost-invariance and multiple scattering. The splitting rate saturates at high density, so like the gluon emission rate in the JIMWLK evolution. In the mean field approximation obtained by ignoring fluctuations, the model exhibits the hallmarks of the BK equation, namely a BFKL-like evolution at low density, the formation of a traveling wave, and geometric scaling. In the full evolution including fluctuations, the geometric scaling is washed out at high energy and replaced by diffusive scaling. It is likely that the model belongs to the universality class of the reaction–diffusion process. The analysis of the model sheds new light on the pomeron loops equations in QCD and their possible improvements.

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.

An efficient algorithm for scalar PDF modelling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micro-mixing models

In this paper, we investigate the application of probability density function (PDF) Monte Carlo methods to scalar release from small sources in a turbulent flow spanning a large physical domain. This is a typical situation encountered when modeling the dispersion of a gaseous substance in the atmosphere. Monte Carlo PDF methods have recently been applied to atmospheric modeling responding to the need for predicting the higher statistics and the concentration PDF generated by the continuous release of reactive and non-reactive substances. In this work we introduce some optimized numerical techniques based on the paradigm that the main field of interest is the scalar field and not the fluid dynamic field; the scalar are considered dynamically passive and the statistical characteristics of the turbulence velocity field are assumed known. These techniques are a block-structured grid coupled with a particle splitting/erasing algorithm and a localized time stepping. The proposed technique is different from others presented before since the particle splitting and erasing is done in a more straightforward and consistent manner. This method has been applied to the study of scalar dispersion from localized line sources in a canopy generated boundary layer. The line source has been treated as a point source in a two-dimensional space but the extension to three dimensions is straightforward. Our framework allows for an evaluation of the effects induced by different levels of discretization in the velocity space of the involved micro-mixing model, starting from the interaction by the exchange with the mean (IEM) toward the more physically consistent interaction by exchange with the conditional mean (IECM). Therefore, aside from the algorithm description and a complete numerical analysis of the code, a comparison between the IEM and IECM micro-mixing models has been investigated.

A generation mechanism of electrostatic waves and subsequent electron heating in the plasma sheet–lobe boundary region during magnetic reconnection

A generation mechanism of high‐energy electrons in the plasma sheet–lobe boundary region associated with magnetic reconnection is studied by using 2‐1/2‐dimensional kinetic simulations in a large system. Our simulation code employs the adaptive mesh refinement technique and the particle splitting algorithm to the conventional particle‐in‐cell code, which enable us to perform large‐scale kinetic simulations. It is shown that the electron two‐stream instability arising between the cold background electrons and the intense beam electrons with high temperature is responsible for the formation of the flat‐topped electrons, which have been often observed in the boundary region when magnetic reconnection has occurred. Electrons are quickly heated along the ambient magnetic field due to the trapping effect in the electrostatic potential wells, and the shoulder energy of the flat‐topped electron distribution reaches a few keV, consistent with satellite observations. The intense beam consists of high‐ and low‐energy electrons in the perpendicular direction. The former electrons come from the lobe region through the vicinity of the X line, while the latter originate from the opposite boundary region of the plasma sheet. The electron two‐stream instability in association with magnetic reconnection is also responsible for the generation of the electrostatic solitary waves that have been frequently detected in the boundary region. This indicates that the electrostatic turbulence should play an important role in strong electron energization in the plasma sheet–lobe boundary region during magnetic reconnection.

Time evolution of the electron diffusion region and the reconnection rate in fully kinetic and large system

Time evolutions of the electron diffusion region embedded in the ion-scale diffusion region and the reconnection rate associated with magnetic reconnection are investigated using 2-1/2 dimensional full kinetic simulations in a large system, so that any effects of the downstream boundary conditions are negligible. The simulation code employs the adaptive mesh refinement technique and the particle splitting algorithm to the conventional particle-in-cell code, which enable us to perform large-scale full particle simulations. It is shown that the reconnection rate increases associated with magnetic reconnection and reaches a peak value large enough for fast reconnection, but then it decreases as time goes on, even though the effects of the system boundary are negligible. The key process responsible for slowing the reconnection processes is the extension of the electron diffusion region in association with the enhancement of the polarization electric field directing toward the neutral sheet in the electron inflow region. The polarization electric field is caused by the inertia difference between ions and electrons, and enhanced by the meandering motions of the background ions. In order to confirm the role of the polarization electric field, we compare the simulation results with mi∕me=1 and 100. It is found that (1) a quasi-steady reconnection is achieved in the system where the polarization electric field does not arise, (2) a large reconnection rate is obtained, even in the system without the Hall effects. It is suggested that the anomalous resistivity due to the Buneman-type instability might be required to support a steady-state fast reconnection.