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At least 109 records · Page 6

Surface enrichment dictates block copolymer orientation

Orientation of block copolymer (BCP) morphology in thin films is critical to applications as nanostructured coatings. Despite being well-studied, the ability to control BCP orientation across all possible block constituents remains challenging. Here, in this study, we deploy coarse-grained molecular dynamics simulations to study diblock copolymer ordering in thin films, focusing on chain makeup, substrate surface energy, and surface tension disparity between the two constituent blocks. We explore the multi-dimensional parameter space of ordering using a machine-learning approach, where an autonomous loop using a Gaussian process (GP) control algorithm iteratively selects high-value simulations to compute. The GP kernel was engineered to capture known symmetries. The trained GP model serves as both a complete map of system response, and a robust means of extracting material knowledge. We demonstrate that the vertical orientation of BCP phases depends on several counter-balancing energetic contributions, including entropic and enthalpic material enrichment at interfaces, distortion of morphological objects through the film depth, and of course interfacial energies. BCP lamellae are found more resistant to these effects, and thus more robustly form vertical orientations across a broad range of conditions; while BCP cylinders are found to be highly sensitive to surface tension disparity.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

On- and off-axis spectral emission features from laser-produced gas breakdown plasmas

Laser-heated gas breakdown plasmas or sparks emit profoundly in the ultraviolet and visible region of the electromagnetic spectrum with contributions from ionic, atomic, and molecular species. Laser created kernels expand into a cold ambient with high velocities during its early lifetime followed by confinement of the plasma kernel and eventually collapse. However, the plasma kernels produced during laser breakdown of gases are also capable of exciting and ionizing the surrounding ambient medium. Two mechanisms can be responsible for excitation and ionization of surrounding ambient: viz. photoexcitation and ionization by intense ultraviolet emission from the sparks produced during the early times of its creation and/or heating by strong shocks generated by the kernel during its expansion into the ambient. In this study, an investigation is made on the spectral features of on- and off-axis emission features of laser-induced plasma breakdown kernels generated in atmospheric pressure conditions with an aim to elucidate the mechanisms leading to ambient excitation and emission. Pulses from an Nd:YAG laser emitting at 1064 nm with 6 ns pulse duration are used to generate plasma kernels. Laser sparks were generated in air, argon, and helium gases to provide different physical properties of expansion dynamics and plasma chemistry considering the differences in laser absorption properties, mass density and speciation. Point shadowgraphy and time-resolved imaging were used to evaluate the shock wave and spark self-emission morphology at early and late times while space and time resolved spectroscopy is used for evaluating the emission features as well as for inferring plasma fundaments at on- and off-axis. Structure and dynamics of the plasma kernel obtained using imaging techniques are also compared to numerical simulations using computational fluid dynamics code. The emission from the kernel showed that spectral features from ions, atoms and molecules are separated in time with an early time temperatures and densities in excess of 35000 K and 4×10 18 /cm 3 with an existence of thermal equilibrium. However, the emission from the off-kernel positions from the breakdown plasmas showed enhanced ultraviolet radiation with the presence of N 2 bands and represented by non-LTE conditions. Finally, our results also highlight that the ultraviolet radiation emitted during early time of spark evolution is the predominant source of the photo-excitation of the surrounding medium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

WE-AB-207B-07: Dose Cloud: Generating “Big Data” for Radiation Therapy Treatment Plan Optimization Research

Purpose: To provide a tool to generate large sets of realistic virtual patient geometries and beamlet doses for treatment optimization research. This tool enables countless studies exploring the fundamental interplay between patient geometry, objective functions, weight selections, and achievable dose distributions for various algorithms and modalities. Methods: Generating realistic virtual patient geometries requires a small set of real patient data. We developed a normalized patient shape model (PSM) which captures organ and target contours in a correspondence-preserving manner. Using PSM-processed data, we perform principal component analysis (PCA) to extract major modes of variation from the population. These PCA modes can be shared without exposing patient information. The modes are re-combined with different weights to produce sets of realistic virtual patient contours. Because virtual patients lack imaging information, we developed a shape-based dose calculation (SBD) relying on the assumption that the region inside the body contour is water. SBD utilizes a 2D fluence-convolved scatter kernel, derived from Monte Carlo simulations, and can compute both full dose for a given set of fluence maps, or produce a dose matrix (dose per fluence pixel) for many modalities. Combining the shape model with SBD provides the data needed for treatment plan optimization research. Results: We used PSM to capture organ and target contours for 96 prostate cases, extracted the first 20 PCA modes, and generated 2048 virtual patient shapes by randomly sampling mode scores. Nearly half of the shapes were thrown out for failing anatomical checks, the remaining 1124 were used in computing dose matrices via SBD and a standard 7-beam protocol. As a proof of concept, and to generate data for later study, we performed fluence map optimization emphasizing PTV coverage. Conclusions: We successfully developed and tested a tool for creating customizable sets of virtual patients suitable for large-scale radiation therapy optimization research.

60 APPLIED LIFE SCIENCES↗

The water factor in harvest-sprouting of hard red spring wheat

Sprouting in unthreshed, ripe, hard red spring wheat (Triticum aestivum L.) is induced by rain, but sprouting does not necessarily occur because the crop is wetted. The spike and grain water conditions conducive to sprouting were determined in a series of laboratory experiments. Sprouting did not occur in field growing wheat wetted to 110% water concentration until the spike water concentration was reduced to 12% and maintained at this concentration for 2 days before wetting. When cut at growth stage 11.3, Feekes scale, Saratovskaya 20 (USSR) sprouted after 4 days drying, Olaf and Alex between 7 and 15 days drying and Columbus, recognized for its resistance to harvest time sprouting, after more than 15 days drying. Sprouting potential was enhanced after 4 wetting drying cycles in which any wetted interval was too brief to permit sufficient water imbibition to initiate sprouting. At harvest ripeness, grain water concentration exceeded spike water concentration by 0.7 percentage units. Following 6 months storage, 20% of the kernels in 300 spike bundles (simulating windrows) sprouted within 28 hrs after initiation of wetting to saturation (150% water concentration). Ninety percent sprouting occurred within 8 days in bundles maintained at 75% water concentration and higher, but less sprouting occurred in bundles dried to 50% water concentration before resaturation.

Bauer, A.↗

Attribution of Chemistry-Climate Model Initiative (CCMI) Ozone Radiative Flux Bias from Satellites

The top-of-atmosphere (TOA) outgoing longwave flux over the 9.6-μm ozone band is a fundamental quantity for understanding chemistry-climate coupling. However, observed TOA fluxes are hard to estimate as they exhibit considerable variability in space and time that depend on the distributions of clouds, ozone (O3), water vapor (H2O), air temperature (Ta), and surface temperature (Ts). Benchmarking present day fluxes and quantifying the relative influence of their drivers is the first step for estimating climate feedbacks from ozone radiative forcing and predicting radiative forcing evolution. To that end, we constructed observational instantaneous radiative kernels (IRKs) under clear-sky conditions, representing the sensitivities of the TOA flux in the 9.6-μm ozone band to the vertical distribution of geophysical variables, including O3, H2O, Ta, and Ts based upon the Aura Tropospheric Emission Spectrometer (TES) measurements. Applying these kernels to present-day simulations from the Chemistry-Climate Model Initiative (CCMI) project as compared to a 2006 reanalysis assimilating satellite observations, we show that the models have large differences in TOA flux, attributable to different geophysical variables. In particular, model simulations continue to diverge from observations in the tropics, as reported in previous studies of the Atmospheric Chemistry Climate Model Inter-comparison Project (ACCMIP) simulations. The principal culprits are tropical mid and upper tropospheric ozone followed by tropical lower tropospheric H2O. Five models out of the eight studied here have TOA flux biases exceeding 100 mWm-2 attributable to tropospheric ozone bias. Another set of five models have flux biases over 50 mWm-2 due to H2O. On the other hand, Ta radiative bias is negligible in all models (no more than 30 mWm-2). We found that AM3 and CMAM have the lowest TOA flux biases globally but are a result of cancellation of opposite biases due to difference processes. Overall, the multi-model ensemble mean bias is –133±98 mWm-2, indicating that they are too atmospherically opaque due to trapping too much radiation in the atmosphere by overestimated tropical tropospheric O3 and H2O. Having too much O3 and H2O in the troposphere would have different impacts on the sensitivity of TOA flux to O3 and these competing effects add more uncertainties on the ozone radiative forcing. We find that the inter-model TOA outgoing longwave radiation (OLR) difference is well anti-correlated with their ozone band flux bias. This suggests that there is significant radiative compensation in the calculation of model outgoing longwave radiation.

Aura Tropospheric Emission Spectrometer (TES) meas↗

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Macroscopic impacts of cloud and precipitation processes on maritime shallow convection as simulated by a large eddy simulation model with bin microphysics

This paper discusses impacts of cloud and precipitation processes on macrophysical properties of shallow convective clouds as simulated by a large eddy model applying warm-rain bin microphysics. Simulations with and without collision–coalescence are considered with cloud condensation nuclei (CCN) concentrations of 30, 60, 120, and 240 mg -1 . Simulations with collision–coalescence include either the standard gravitational collision kernel or a novel kernel that includes enhancements due to the small-scale cloud turbulence. Simulations with droplet collisions were discussed in Wyszogrodzki et al. (2013) focusing on the impact of the turbulent collision kernel. The current paper expands that analysis and puts model results in the context of previous studies. Despite a significant increase of the drizzle/rain with the decrease of CCN concentration, enhanced by the effects of the small-scale turbulence, impacts on the macroscopic cloud field characteristics are relatively minor. Model results show a systematic shift in the cloud-top height distributions, with an increasing contribution of deeper clouds for stronger precipitating cases. We show that this is consistent with the explanation suggested in Wyszogrodzki et al. (2013); namely, the increase of drizzle/rain leads to a more efficient condensate offloading in the upper parts of the cloud field. A second effect involves suppression of the cloud droplet evaporation near cloud edges in low-CCN simulations, as documented in previous studies (e.g., Xue and Feingold, 2006). We pose the question whether the effects of cloud turbulence on drizzle/rain formation in shallow cumuli can be corroborated by remote sensing observations, for instance, from space. Although a clear signal is extracted from model results, we argue that the answer is negative due to uncertainties caused by the temporal variability of the shallow convective cloud field, sampling and spatial resolution of the satellite data, and overall accuracy of remote sensing retrievals.

54 ENVIRONMENTAL SCIENCES↗

MO-A-BRD-10: A Fast and Accurate GPU-Based Proton Transport Monte Carlo Simulation for Validating Proton Therapy Treatment Plans

Purpose: To build a GPU-based Monte Carlo (MC) simulation of proton transport with detailed modeling of elastic and non-elastic (NE) protonnucleus interactions, for use in a very fast and cost-effective proton therapy treatment plan verification system. Methods: Using the CUDA framework, we implemented kernels for the following tasks: (1) Simulation of beam spots from our possible scanning nozzle configurations, (2) Proton propagation through CT geometry, taking into account nuclear elastic and multiple scattering, as well as energy straggling, (3) Bertini-style modeling of the intranuclear cascade stage of NE interactions, and (4) Simulation of nuclear evaporation. To validate our MC, we performed: (1) Secondary particle yield calculations in NE collisions with therapeutically-relevant nuclei, (2) Pencil-beam dose calculations in homogeneous phantoms, (3) A large number of treatment plan dose recalculations, and compared with Geant4.9.6p2/TOPAS. A workflow was devised for calculating plans from a commercially available treatment planning system, with scripts for reading DICOM files and generating inputs for our MC. Results: Yields, energy and angular distributions of secondaries from NE collisions on various nuclei are in good agreement with the Geant4.9.6p2 Bertini and Binary cascade models. The 3D-gamma pass rate at 2%–2mm for 70–230 MeV pencil-beam dose distributions in water, soft tissue, bone and Ti phantoms is 100%. The pass rate at 2%–2mm for treatment plan calculations is typically above 98%. The net computational time on a NVIDIA GTX680 card, including all CPU-GPU data transfers, is around 20s for 1×10{sup 7} proton histories. Conclusion: Our GPU-based proton transport MC is the first of its kind to include a detailed nuclear model to handle NE interactions on any nucleus. Dosimetric calculations demonstrate very good agreement with Geant4.9.6p2/TOPAS. Our MC is being integrated into a framework to perform fast routine clinical QA of pencil-beam treatment plans. Hardware for such a system will cost under $5000. This work was funded in part by a grant from Varian Medical Systems, Inc.

61 RADIATION PROTECTION AND DOSIMETRY↗

Post-irradiation 1600°C Heating Test of AGR-1 UCO Fuel Kernels

Five bare kernels were selected from the U.S. Advanced Gas Reactor (AGR) 1 irradiation experiment Compact 5-3-1 to perform post-irradiation safety tests. The safety test involved heating the kernels in the Fuel Accident Condition Simulator (FACS) furnace in the inert atmosphere to a peak temperature of 1600°C and isothermally holding at this temperature for about 47 hours while collecting fission products released. This test was to assess the retention of fission products in bare kernels without the effects of the other TRISO layers (buffer, IPyC, SiC, and OPyC) or the graphitic matrix material. The bare kernels released nearly 100% of cesium and antimony, while they were able to maintain about 30% of europium, 50% of strontium, and the majority of cerium and ruthenium. In addition, about 48% of the calculated inventory of Kr-85 released during the test, indicating that kernels were capable of retaining a considerable fraction of fission gas K-85 during irradiation.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Computational Fluid Dynamics Modeling of Low Temperature Ignition Processes From a Nanosecond Pulsed Discharge at Quiescent Conditions

Recent interest in nonequilibrium plasma discharges as sources of ignition for the automotive industry has not yet been accompanied by the availability of dedicated models to perform this task in computational fluid dynamics (CFD) engine simulations. The need for a low-temperature plasma (LTP) ignition model has motivated much work in simulating these discharges from first principles. Most ignition models assume that an equilibrium plasma comprises the bulk of discharge kernels. LTP discharges, however, exhibit highly nonequilibrium behavior. In this work, a method to determine a consistent initialization of LTP discharge kernels for use in engine CFD codes like CONVERGE is proposed. The method utilizes first principles discharge simulations. Such an LTP kernel is introduced in a flammable mixture of air and fuel, and the subsequent plasma expansion and ignition simulation is carried out using a reacting flow solver with detailed chemistry. Finally, the proposed numerical approach is shown to produce results that agree with experimental observations regarding the ignitability of methane-air and ethylene-air mixtures by LTP discharges.

33 ADVANCED PROPULSION SYSTEMS↗

STEPS: A Portable Numerical Simulation Toolkit for Electrical Power System Dynamic Studies

Numerical simulation is the key technique for large scale power system analysis. Redistribution of global renewable power via international interconnections requires new simulation tools to study the interconnected systems with different nominal frequencies as a whole. In this paper we introduce an open source simulation toolkit for electrical power systems (STEPS) which is hosted at Github. Its kernel is coded in C++ with major functions of power flow and electro-mechanical dynamic simulation. Flexible options are provided and configurable to improve power flow solution and dynamic simulation. Common devices and models are supported in STEPS for AC/DC hybrid system studies. Studies of interconnected systems with different nominal frequencies is supported in STEPS for research of international interconnection. Application program interfaces are provided and wrapped with Python to enable high-level interfaces for general applications. STEPS is thread safe and parallel computation is supported in both kernel and script levels to accelerate simulation. It is portable and works on Windows and GNU/Linux platforms. Cases from small to large scale systems are thoroughly tested to validate the toolkit with commercial packages as benchmarks.

42 ENGINEERING↗

Reconstruction of the primordial power spectrum of curvature perturbations using multiple data sets

Detailed knowledge of the primordial power spectrum of curvature perturbations is essential both in order to elucidate the physical mechanism ('inflation') which generated it, and for estimating the cosmological parameters from observations of the cosmic microwave background and large-scale structure. Hence it ought to be extracted from such data in a model-independent manner, however this is difficult because relevant cosmological observables are given by a convolution of the primordial perturbations with some smoothing kernel which depends on both the assumed world model and the matter content of the universe. Moreover the deconvolution problem is ill-conditioned so a regularisation scheme must be employed to control error propagation. We demonstrate that 'Tikhonov regularisation' can robustly reconstruct the primordial spectrum from multiple cosmological data sets, a significant advantage being that both its uncertainty and resolution are then quantified. Using Monte Carlo simulations we investigate several regularisation parameter selection methods and find that generalised cross-validation and Mallow's C{sub p} method give optimal results. We apply our inversion procedure to data from the Wilkinson Microwave Anisotropy Probe, other ground-based small angular scale CMB experiments, and the Sloan Digital Sky Survey. The reconstructed spectrum (assuming the standard ΛCDM cosmology) is not scale-free but has an infrared cutoff at k∼<5 × 10{sup −4} Mpc{sup −1} (due to the anomalously low CMB quadrupole) and several features with ∼ 2σ significance at k/Mpc{sup −1} ∼ 0.0013–0.0025, 0.0362–0.0402 and 0.051–0.056, reflecting the 'WMAP glitches'. To test whether these are indeed real will require more accurate data, such as from the Planck satellite and new ground-based experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-E-T-31: A Fast Finite Size Pencil Beam (FSPB) Convolution Algorithm for a New Co-60 Arc Therapy Machine

Purpose: Present a fast Finite Size Pencil Beam (FSPB) convolution algorithm for a new Co-60 arc therapy machine. The FSPB algorithm accounts for (i) strong angular divergence (short SAD), (ii) heterogeneity effect for primary attenuation, and (iii) source energy spectrum. Methods: The FSPB algorithm is based on a 0.5×0.5-cm2 dose kernel calculated using the GEPTS (Gamma Electron and Positron Transport System) Monte Carlo code. The dose kernel is tabulated using a thin XYZ mesh (0.1 mm steps in lateral directions) for radius less than 1 cm and using an RZ mesh (with varying steps) for larger radial distance. To account for SSD effect, 11 dose kernels with SSDs varying between 30 cm to 80 cm are calculated. Maynord factor and “lateral stretching” are applied to account for differences between closest and actual SSD. Appropriate rotations and second order interpolation are used to calculate the dose from a given beamlet to a point. Results: Accuracy: Dose distributions in water with 80 cm SSD are calculated using the new FSPB convolution algorithm and full Monte Carlo simulation (gold standard). Figs 1–4 show excellent agreements between FSPB and Monte Carlo calculations for different field sizes and at different depths. The dose distribution for a prostate case is calculated using FSPB (Fig.5). Sixty conformal beams with rectum blocking are assumed. Figs 6–8 show the comparison with Monte Carlo simulation based on the same beam apertures. The excellent agreement demonstrates the accuracy of the new algorithm in handling SSD variation, oblique incidence, and scatter contribution.Speed: The FSPB convolution algorithm calculates 28 million dose points per second using a single 2.2-GHz CPU. The present algorithm is seven times faster than a similar algorithm from Gu et al. (Phys. Med. Biol. 54, 2009, 6287–6297). Conclusion: A fast and accurate FSPB convolution algorithm was developed and benchmarked.

60 APPLIED LIFE SCIENCES↗

Using kernel-based statistical distance to study the dynamics of charged particle beams in particle-based simulation codes

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as numerical diagnostics for simulations involving charged-particle beams. Related measures of statistical dependence are also described. The resulting diagnostics provide sensitive measures of dynamical processes important for beams in nonlinear or high-intensity systems, which are otherwise difficult to characterize. Here, the focus is on kernel-based methods such as maximum mean discrepancy, which have a well-developed mathematical foundation and reasonable computational complexity. Several benchmark problems and examples involving intense beams are discussed. While the focus is on charged-particle beams, these methods may also be applied to other many-body systems such as plasmas or gravitational systems.

47 OTHER INSTRUMENTATION↗

Using Numba for GPU acceleration of Neutron Beamline Digital Twins

Digital twins of neutron instruments using Monte Carlo ray tracing have proven to be useful in neutron data analysis and verifying instrument and sample designs. However, these simulations can become quite complex and computationally demanding with tens of billions of neutrons. In this paper, we present a GPU accelerated version of MCViNE using Python and Numba to balance user extensibility with performance. Numba is an open-source just-in-time (JIT) compiler for Python using LLVM to generate efficient machine code for CPUs and GPUs with NVIDIA CUDA. The JIT nature of Numba allowed complex instrument kernels to be generated easily. Initial simulations have shown a speedup between 200-1000x over the original CPU implementation. The performance gain with Numba enables more sophisticated data analysis and impacts neutron scattering science and instrument design.

Kendrick, Coleman↗

Physics and Components syntax to enable a systems-based approach to multiphysics

Simulations in MOOSE have traditionally used kernel and boundary condition classes to describe the equations. Downstream applications leveraged a system called Actions to define a pre-packaged discretization of the equations they solve. Unfortunately, the Action base class was very limited, and most applications implemented the same concepts in their Actions. This led to an increased maintenance burden and a reduction in coupling opportunities, save for the use of MultiApps which renders each input mostly independent. With the introduction of multi-system capabilities in MOOSE, there is growing interest in defining entire simulations of complex multiphysics systems in a single input file. By introducing a new Physics system, with its dedicated syntax and a new base class providing wide-ranging capabilities, we are now able to define multiple equations in a single input file in a compact and user-friendly way. With new interactions between Physics and the Component system, these equations can be defined on each component of a complex system. In this talk, we will present the capabilities of these new systems, their interactions, and how to define complex systems multiphysics simulations with Physics and Components.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluating Climate Model Simulations of the Radiative Forcing and Radiative Response at Earth’s Surface

In this work, we analyze the radiative forcing and radiative response at Earth’s surface, where perturbations in the radiation budget regulate the atmospheric hydrological cycle. By applying a radiative kernel-regression technique to CMIP5 climate model simulations where CO 2 is instantaneously quadrupled, we evaluate the intermodel spread in surface instantaneous radiative forcing, radiative adjustments to this forcing, and radiative responses to surface warming. The cloud radiative adjustment to CO 2 forcing and the temperature-mediated cloud radiative response exhibit significant intermodel spread. In contrast to its counterpart at the top of the atmosphere, the temperature-mediated cloud radiative response at the surface is found to be positive in some models and negative in others. Also, the compensation between the temperature-mediated lapse rate and water vapor radiative responses found in top-of-atmosphere calculations is not present for surface radiative flux changes. Instantaneous radiative forcing at the surface is rarely reported for model simulations; as a result, intermodel differences have not previously been evaluated in global climate models. We demonstrate that the instantaneous radiative forcing is the largest contributor to intermodel spread in effective radiative forcing at the surface. We also find evidence of differences in radiative parameterizations in current models and argue that this is a significant, but largely overlooked, source of bias in climate change simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing

This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗