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At least 541 records · Page 30

Roofline Analysis in the Intel® Advisor to Deliver Optimized Performance for applications on Intel® Xeon Phi™ Processor

In this session we show, in two case studies, how the roofline feature of Intel Advisor has been utilized to optimize the performance of kernels of the XGC1 and PICSAR codes in preparation for Intel Knights Landing architecture. The impact of the implemented optimizations and the benefits of using the automatic roofline feature of Intel Advisor to study performance of large applications will be presented. This demonstrates an effective optimization strategy that has enabled these science applications to achieve up to 4.6 times speed-up and prepare for future exascale architectures. # Goal/Relevance of Session The roofline model [1,2] is a powerful tool for analyzing the performance of applications with respect to the theoretical peak achievable on a given computer architecture. It allows one to graphically represent the performance of an application in terms of operational intensity, i.e. the ratio of flops performed and bytes moved from memory in order to guide optimization efforts. Given the scale and complexity of modern science applications, it can often be a tedious task for the user to perform the analysis on the level of functions or loops to identify where performance gains can be made. With new Intel tools, it is now possible to automate this task, as well as base the estimates of peak performance on measurements rather than vendor specifications. The goal of this session is to demonstrate how the roofline feature of Intel Advisor can be used to balance memory vs. computation related optimization efforts and effectively identify performance bottlenecks. A series of typical optimization techniques: cache blocking, structure refactoring, data alignment, and vectorization illustrated by the kernel cases will be addressed. # Description of the codes ## XGC1 The XGC1 code [3] is a magnetic fusion Particle-In-Cell code that uses an unstructured mesh for its Poisson solver that allows it to accurately resolve the edge plasma of a magnetic fusion device. After recent optimizations to its collision kernel [4], most of the computing time is spent in the electron push (pushe) kernel, where these optimization efforts have been focused. The kernel code scaled well with MPI+OpenMP but had almost no automatic compiler vectorization, in part due to indirect memory addresses and in part due to low trip counts of low-level loops that would be candidates for vectorization. Particle blocking and sorting have been implemented to increase trip counts of low-level loops and improve memory locality, and OpenMP directives have been added to vectorize compute-intensive loops that were identified by Advisor. The optimizations have improved the performance of the pushe kernel 2x on Haswell processors and 1.7x on KNL. The KNL node-for-node performance has been brought to within 30% of a NERSC Cori phase I Haswell node and we expect to bridge this gap by reducing the memory footprint of compute intensive routines to improve cache reuse. ## PICSAR is a Fortran/Python high-performance Particle-In-Cell library targeting at MIC architectures first designed to be coupled with the PIC code WARP for the simulation of laser-matter interaction and particle accelerators. PICSAR also contains a FORTRAN stand-alone kernel for performance studies and benchmarks. A MPI domain decomposition is used between NUMA domains and a tile decomposition (cache-blocking) handled by OpenMP has been added for shared-memory parallelism and better cache management. The so-called current deposition and field gathering steps that compose the PIC time loop constitute major hotspots that have been rewritten to enable more efficient vectorization. Particle communications between tiles and MPI domain has been merged and parallelized. All considered, these improvements provide speedups of 3.1 for order 1 and 4.6 for order 3 interpolation shape factors on KNL configured in SNC4 quadrant flat mode. Performance is similar between a node of cori phase 1 and KNL at order 1 and better on KNL by a factor 1.6 at order 3 with the considered test case (homogeneous thermal plasma).

97 MATHEMATICS AND COMPUTING↗

Preliminary results from the first round of post-irradiation heating tests of fuel compacts from the US AGR-3/4 irradiation

Three post-irradiation heating tests of fuel compacts from the US AGR-3/4 irradiation experiment. In addition to TRISO-coated driver fuel, each compact contained 20 particles with UCO fuel kernels coated only in pyrocarbon to simulate exposed kernels. Tests at 1600/1700°C, 1400°C, and 1200°C were performed to measure fission product releases as a function of time and temperature. Silver releases were highest in the 1200°C test, supporting the observation that silver release rates are highest in the temperature range of 1100-1300°C. Except for Ag-110m (which was released in multiple particle equivalents) releases of Cs, Kr, Eu, and Sr were all less than one particle inventory per compact. This suggests that exposed kernels retain little Cs and Kr after irradiation. Despite these low releases, compared to tests of compacts with no exposed kernels, the Cs and Kr releases were noticeably higher, and at 1600°C the exposed kernels contributed noticeably more Eu and Sr than in AGR-1 compacts with no exposed kernels. These data can be used to make inferences on retention of fission products in exposed kernels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Physics-constrained Gaussian process model for prediction of hydrodynamic interactions between wave energy converters in an array

To improve the efficiency of wave farms and achieve maximum power generation, the layout of wave energy converters (WECs) in an array needs to be carefully designed so that the hydrodynamic interactions can be positively exploited. For this, the hydrodynamic characteristics of the WEC array in different layouts need to be calculated. However, such calculations using numerical models usually entail significant computational cost, especially for large arrays of WECs. To address the computational challenge, a physics-constrained Gaussian process (GP) model is proposed to replace the original expensive numerical model and predict the hydrodynamic characteristics of the WECs for any array layout. By exploring the relationship between the WEC array (i.e., the input) and different hydrodynamic characteristics (i.e., the output), here we summarize a set of physical constraints/features, including invariance, symmetry, and additivity. This prior knowledge about the input-output relationship is then directly embedded in the constructed GP model through the design of physics-constrained kernels. In particular, a double-sum invariant kernel is first developed to incorporate the invariance and symmetry features, and then an additive kernel is developed to incorporate the additive feature of the problem. The invariant kernel and the additive kernel are then integrated to construct the physics-constrained GP model. Compared to the standard GP model, the proposed physics-constrained GP models require less training data to achieve the desired accuracy in predicting the hydrodynamic characteristics and are also less vulnerable to the curse of dimensionality (i.e., good scalability for large arrays) due to the use of an additive kernel. The efficiency, accuracy, and scalability of the proposed approach are demonstrated through an application to predict the hydrodynamic characteristics for WEC arrays of different sizes and layouts.

16 TIDAL AND WAVE POWER↗

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↗

MO-G-17A-05: PET Image Deblurring Using Adaptive Dictionary Learning

Purpose: The aim of this work is to deblur PET images while suppressing Poisson noise effects using adaptive dictionary learning (DL) techniques. Methods: The model that relates a blurred and noisy PET image to the desired image is described as a linear transform y=Hm+n where m is the desired image, H is a blur kernel, n is Poisson noise and y is the blurred image. The approach we follow to recover m involves the sparse representation of y over a learned dictionary, since the image has lots of repeated patterns, edges, textures and smooth regions. The recovery is based on an optimization of a cost function having four major terms: adaptive dictionary learning term, sparsity term, regularization term, and MLEM Poisson noise estimation term. The optimization is solved by a variable splitting method that introduces additional variables. We simulated a 128×128 Hoffman brain PET image (baseline) with varying kernel types and sizes (Gaussian 9×9, σ=5.4mm; Uniform 5×5, σ=2.9mm) with additive Poisson noise (Blurred). Image recovery was performed once when the kernel type was included in the model optimization and once with the model blinded to kernel type. The recovered image was compared to the baseline as well as another recovery algorithm PIDSPLIT+ (Setzer et. al.) by calculating PSNR (Peak SNR) and normalized average differences in pixel intensities (NADPI) of line profiles across the images. Results: For known kernel types, the PSNR of the Gaussian (Uniform) was 28.73 (25.1) and 25.18 (23.4) for DL and PIDSPLIT+ respectively. For blinded deblurring the PSNRs were 25.32 and 22.86 for DL and PIDSPLIT+ respectively. NADPI between baseline and DL, and baseline and blurred for the Gaussian kernel was 2.5 and 10.8 respectively. Conclusion: PET image deblurring using dictionary learning seems to be a good approach to restore image resolution in presence of Poisson noise. GE Health Care.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Approaches to reducing photon dose calculation errors near metal implants

Purpose: Dose calculation errors near metal implants are caused by limitations of the dose calculation algorithm in modeling tissue/metal interface effects as well as density assignment errors caused by imaging artifacts. The purpose of this study was to investigate two strategies for reducing dose calculation errors near metal implants: implementation of metal-based energy deposition kernels in the convolution/superposition (C/S) dose calculation method and use of metal artifact reduction methods for computed tomography (CT) imaging. Methods: Both error reduction strategies were investigated using a simple geometric slab phantom with a rectangular metal insert (composed of titanium or Cerrobend), as well as two anthropomorphic phantoms (one with spinal hardware and one with dental fillings), designed to mimic relevant clinical scenarios. To assess the dosimetric impact of metal kernels, the authors implemented titanium and silver kernels in a commercial collapsed cone C/S algorithm. To assess the impact of CT metal artifact reduction methods, the authors performed dose calculations using baseline imaging techniques (uncorrected 120 kVp imaging) and three commercial metal artifact reduction methods: Philips Healthcare’s O-MAR, GE Healthcare’s monochromatic gemstone spectral imaging (GSI) using dual-energy CT, and GSI with metal artifact reduction software (MARS) applied. For the simple geometric phantom, radiochromic film was used to measure dose upstream and downstream of metal inserts. For the anthropomorphic phantoms, ion chambers and radiochromic film were used to quantify the benefit of the error reduction strategies. Results: Metal kernels did not universally improve accuracy but rather resulted in better accuracy upstream of metal implants and decreased accuracy directly downstream. For the clinical cases (spinal hardware and dental fillings), metal kernels had very little impact on the dose calculation accuracy (<1.0%). Of the commercial CT artifact reduction methods investigated, the authors found that O-MAR was the most consistent method, resulting in either improved dose calculation accuracy (dental case) or little impact on calculation accuracy (spine case). GSI was unsuccessful at reducing the severe artifacts caused by dental fillings and had very little impact on calculation accuracy. GSI with MARS on the other hand gave mixed results, sometimes introducing metal distortion and increasing calculation errors (titanium rectangular implant and titanium spinal hardware) but other times very successfully reducing artifacts (Cerrobend rectangular implant and dental fillings). Conclusions: Though successful at improving dose calculation accuracy upstream of metal implants, metal kernels were not found to substantially improve accuracy for clinical cases. Of the commercial artifact reduction methods investigated, O-MAR was found to be the most consistent candidate for all-purpose CT simulation imaging. The MARS algorithm for GSI should be used with caution for titanium implants, larger implants, and implants located near heterogeneities as it can distort the size and shape of implants and increase calculation errors.

60 APPLIED LIFE SCIENCES↗

Production of LEU fully ceramic microencapsulated fuel for irradiation testing

The Advanced Fuels Campaign of the US DOE Fuel Cycle Research/Development program is currently engaged in production of FCM fuel for irradiation testing in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL). FCM fuel production is a serial process with 3 major steps namely kernel, TRISO, and compact production. The first step in the kernel process is production of air-dried UO{sub 3} gel spheres with suspended carbon particles. These spheres, roughly 2 mm in size, are then calcined to produce a mixture of UO{sub 2} and carbon. This calcination step may be performed in either argon, hydrogen, or mixtures of these gases. Once the calcination step is complete, temperature is increased (>1400 Celsius degrees) to convert this mixture to UO{sub 2} + UC{sub x}. Once dense oxide-carbide kernels are available, the inert environment is switched to a nitrogen containing one to facilitate carbothermic reduction of kernels and production of UN. Essentially, the oxygen and carbon in the oxide-carbide kernels react with one another to produce CO and are replaced with nitrogen inside the lattice. The TRISO step in fuel production is incorporation of a porous carbon buffer layer, a dense inner pyrolytic carbon layer (IPyC), a SiC layer, and finally and outer pyrolytic carbon layer (OPyC) onto the UN kernels. The coating layer deposition step is carried out inside a graphite furnace using a fluidized bed chemical vapor deposition (CVD) process. In essence, a mixture of reactant and inert gasses flow from the bottom through a bed of particles that are in turn fluidized by the gas stream. The particles undergo CVD and once a different coating layer is to be incorporated, the furnace temperature is adjusted and the reactant gases are changed. The final step in the series of fuel production activities is the consolidation of UN TRISO particles inside the SiC matrix to produce cylindrical pellets. It entails 3 critical areas: SiC powder mixing, over-coating of particles, and high-temperature densification. Optimal execution of the powder mixing step is vital to achieve a fully dense SiC matrix at the end of the process. The SiC matrix is consolidated using a special form of liquid phase sintering (LPS) involving nano-powder feedstock that is designated as the NITE process. The SiC nano-powder slurry is sprayed directly onto the particle surface using a piezoelectric nozzle. Once the over-coated particles are available, final consolidation step at high temperatures (1875 Celsius degrees) is carried out.

36 MATERIALS SCIENCE↗

Methods for multitasking among real-time embedded compute tasks running on the GPU: Methods for Multitasking Real-time Embedded GPU Computing Tasks

Here, we provide an extensive survey on wide spectrum of scheduling methods for multitasking among graphics processing unit (GPU) computing tasks. We then design several schedulers and explain in detail the selected methods we have developed to implement our scheduling strategies. Next, we compare the performance of schedulers on various workloads running on Fermi and Kepler architectures and arrive at the following major conclusions: (1) Small kernels benefit from running kernels concurrently. (2) The combination of small kernels, high-priority kernels with longer runtimes, and lower-priority kernels with shorter runtimes benefits from a CPU scheduler that dynamically changes kernel order on the Fermi architecture. (3) Because of limitations of existing GPU architectures, currently CPU schedulers outperform their GPU counterparts. We also provide results and observations obtained from implementing and evaluating our schedulers on the NVIDIA Jetson TX1 system-on-chip architecture. We observe that although TX1 has the newer Maxwell architecture, the mechanism used for scheduler timings behaves differently on TX1 compared to Kepler leading to incorrect timings. In this paper, we describe our methods that allow us to report correct timings for CPU schedulers running on TX1. Lastly, we propose new research directions involving the investigation of additional scheduling strategies.

97 MATHEMATICS AND COMPUTING↗

Generalizations of the double-copy: the KLT bootstrap

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the “KLT algebra” and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy in addition to locality constraints. We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a ‘heterotic’-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order ∇ 10 R 4 . Finally, we initiate a search for new double-copy kernels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗

LaRIS: Targeting Portability and Productivity for LAPACK Codes on Extreme Heterogeneous Systems by Using IRIS

In keeping with the trend of heterogeneity in high-performance computing, hardware manufacturers and vendors are developing new architectures and associated software stacks (e.g., libraries) to harness the best possible performance from commonly used kernels (e.g., linear algebra kernels). However, kernels tuned for one architecture are not portable to others. Moreover, the coexistence of different architectures in a single node makes orchestration difficult. To address these challenges, we introduce LaRIS, a portable framework for LAPACK functionalities. LaRIS ensures a separation between linear algebra algorithms and vendor-library kernels by using the IRIS run time and IRIS-BLAS library. Such abstraction at the algorithm level makes the implementation completely agnostic to the vendor library and architecture. LaRIS uses the IRIS run time to dynamically select the vendor-library kernel and suitable processor architecture at run time. Through LU factorization, we demonstrate that LaRIS can fully utilize different heterogeneous systems by launching and orchestrating different vendor-library kernels without any change in the source code.

Monil, M. A. H.↗

Toward Evaluating High-Level Synthesis Portability and Performance between Intel and Xilinx FPGAs

Offloading computation from a CPU to a hardware accelerator is becoming a more common solution for improving performance because traditional gains enabled by Moore’s law and Dennard scaling have slowed. GPUs are often used as hardware accelerators, but field-programmable gate arrays (FPGAs) are gaining traction. FPGAs are beneficial because they allow hardware specific to a particular application to be created. However, they are notoriously difficult to program. To this end, two of the main FPGA manufacturers, Intel and Xilinx, have created tools and frameworks that enable the use of higher level languages to design FPGA hardware. Although Xilinx kernels can be designed by using C/C++, both Intel and Xilinx support the use of OpenCL C to architect FPGA hardware. However, not much is known about the portability and performance between these two device families other than the fact that it is theoretically possible to synthesize a kernel meant for Intel to Xilinx and vice versa.In this work, we evaluate the portability and performance of Intel and Xilinx kernels. We use OpenCL C implementations of a subset of the Rodinia benchmarking suite that were designed for an Intel FPGA and make the necessary modifications to create synthesizable OpenCL C kernels for a Xilinx FPGA. We find that the difficulty of porting certain kernel optimizations varies, depending on the construct. Once the minimum amount of modifications is made to create synthesizable hardware for the Xilinx platform, more nontrivial work is needed to improve performance. However, we find that constructs that are known to be performant for an FPGA should improve performance regardless of the platform; the difficulty comes in deciding how to invoke certain kernel optimizations while also abiding by the constraints enforced by a given platform’s hardware compiler.

Cabrera, Anthony↗

Greggd

greg(g)d - Global runtime for eBPF-enabled gathering (w/ gumption) daemon Recently the linux kernel has added support for low-level kernel monitoring and profiling through a in-kernel virtual machine. The tooling around these new features (the extended Berkley Packet Filter or eBPF for short) is not mature and is difficult to use. Benefits from eBPF are especially hard to realize while trying to do large scale deployments and integrate with existing metric analysis stacks. A tool was needed to enable loading and collecting data from eBPF programs on large scale HPC systems. Given the problems above it was obvious we needed some wrapper program to compile, load, and collect data from eBPF programs running in the kernel. This tool needed to be lightweight without a heavy set of dependencies, relatively stable between different kernel versions, and integrate nicely with existing widely used metric collection tools. We wrote a program that wraps the eBPF tooling and sends data to our metric gathering tool. eBPF programs are either compiled using the host compiler stack, or loaded in the kernel directly from an object file. These programs are then attached to the system calls that we want to profile. Whenever these system calls are run, the eBPF program collects information of interest and writes that to memory. Our wrapper program polls these memory locations, reads and formats the data, then sends the information to a local unix socket. Our other monitoring tools are configured to read from that socket and send it to the rest of our metric monitoring stack for analysis.

Voss, Joseph [Oak Ridge National Lab. (ORNL), Oak ↗

Automated Defect Identification For Triso Fuels

The developed code is to be used to identify manufacturing defects of nuclear fuel kernels using image processing methods. Past batches of TRi-structural ISOtropic particle (TRISO) fuel kernels have on occasion contained fissures that result in the fuel batch not meeting specifications. The developed code automates the inspection process of these kernels. The code analyzes micrographs of TRISO fuel kernels and outputs a count of total kernels in the sample, a count of the number of defective particles in the sample, as well as processed images for more effective manual inspection. This information output will be used to help identify if defective kernels are present in a fuel batch and quantify the countable fissure fraction.

Oncken, JosephE.↗

Improving Block-level Efficiency with scsi-mq

Current generation solid-state storage devices are exposing a new bottlenecks in the SCSI and block layers of the Linux kernel, where IO throughput is limited by lock contention, inefficient interrupt handling, and poor memory locality. To address these limitations, the Linux kernel block layer underwent a major rewrite with the blk-mq project to move from a single request queue to a multi-queue model. The Linux SCSI subsystem rework to make use of this new model, known as scsi-mq, has been merged into the Linux kernel and work is underway for dm-multipath support in the upcoming Linux 4.0 kernel. These pieces were necessary to make use of the multi-queue block layer in a Lustre parallel filesystem with high availability requirements. We undertook adding support of the 3.18 kernel to Lustre with scsi-mq and dm-multipath patches to evaluate the potential of these efficiency improvements. In this paper we evaluate the block-level performance of scsi-mq with backing storage hardware representative of a HPC-targerted Lustre filesystem. Our findings show that SCSI write request latency is reduced by as much as 13.6%. Additionally, when profiling the CPU usage of our prototype Lustre filesystem, we found that CPU idle time increased by a factor of 7 with Linux 3.18 and blk-mq as compared to a standard 2.6.32 Linux kernel. Our findings demonstrate increased efficiency of the multi-queue block layer even with disk-based caching storage arrays used in existing parallel filesystems.

Cluster Computing↗

Efficient track-before detect algorithm with minimal prior knowledge

Apparatus, system and method for tracking an image target in a system, wherein a system receives an image comprising a plurality of pixels. The received image is processed via a plurality of different recursive motion model kernels in parallel to provide a plurality of kernel outputs, wherein each of the motion model kernels may include a respective pixel mask. Per-pixel energy is estimated of at least some of the plurality of kernel outputs. Velocity of at least one of the image pixels may also be estimated by generating a directional energy vector for each motion model kernel. The per-pixel energy and velocity estimates are fused to produce a fused estimate representing at least some of the motion model kernels for the image.

42 ENGINEERING↗

Evaluation of recycle pathways for out-of-specification uranium microspheres from the internal gelation process

During the production of uranium oxide microspheres with carbon using internal gelation, a small fraction of microspheres will not meet the required size or sphericity specification. The uranium microspheres with carbon can be rejected after they have been air-dried or converted into uranium carbide and uranium oxide (UCO) kernels. The next step for the rejected spheres was an air oxidation for carbon removal. The air-dried spheres became triuranium octoxide (U 3 O 8 ) spheres, which were sometimes ground into powder. The UCO kernels became U 3 O 8 powder during the air oxidation. The next recycle step was nitric acid dissolution of the U 3 O 8 spheres or powders to produce acid-deficient uranyl nitrate (ADUN) solutions, which were used to make new uranium oxide microspheres with carbon and subsequently UCO kernels. Finaly, the kinetics of the acid dissolution process were compared, and the impurity levels in the different ADUN solutions were determined. X-ray diffraction results for the UCO kernels from the initial and recycled ADUN solutions indicate that changes in the impurity levels can impact the uranium carbide to uranium dicarbide ratio in the UCO kernels.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Application of stochastic weighted algorithms to a multidimensional silica particle model

Highlights: •Stochastic weighted algorithms (SWAs) are developed for a detailed silica model. •An implementation of SWAs with the transition kernel is presented. •The SWAs’ solutions converge to the direct simulation algorithm’s (DSA) solution. •The efficiency of SWAs is evaluated for this multidimensional particle model. •It is shown that SWAs can be used for coagulation problems in industrial systems. -- Abstract: This paper presents a detailed study of the numerical behaviour of stochastic weighted algorithms (SWAs) using the transition regime coagulation kernel and a multidimensional silica particle model. The implementation in the SWAs of the transition regime coagulation kernel and associated majorant rates is described. The silica particle model of Shekar et al. [S. Shekar, A.J. Smith, W.J. Menz, M. Sander, M. Kraft, A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles, Journal of Aerosol Science 44 (2012) 83–98] was used in conjunction with this coagulation kernel to study the convergence properties of SWAs with a multidimensional particle model. High precision solutions were calculated with two SWAs and also with the established direct simulation algorithm. These solutions, which were generated using large number of computational particles, showed close agreement. It was thus demonstrated that SWAs can be successfully used with complex coagulation kernels and high dimensional particle models to simulate real-world systems.

97 MATHEMATICS AND COMPUTING↗