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At least 1,603 records · Page 89

EVs-at-RISC: A Secure and Resilient Interoperable SCM Control System Architecture for Electric Vehicle’s-at-Scale (Final Technical Report)

The EVs-at-RISC project was a five-year research, development, and demonstration initiative to create foundational tools for utility-scale fleet aggregation and Smart Charge Management (SCM) of Electric Vehicles (EV), Electric Vehicle Charging Infrastructure (EVCI), and related Distributed Energy Resources (DER). Rather than seeking to develop and demonstrate highly perfected SCM algorithms and control strategies, this project instead focused on creating foundational software solutions that enable unprecedented digital interoperability across the communications technologies and vendor platforms used to manage EV , EVCI, and DER, as well as existing energy management infrastructure operated by utilities, grid operators, and aggregators. This project then extends these novel interoperability capabilities to develop and deploy powerful middleware abstractions across grid edge networks and EVCI/DER fleet aggregations incorporating modern software tools and best practices, such as CI/CD, to bring the immense capabilities of infrastructure-as-code and policy-as-code to modern grid edge network environments. This addresses the foremost systemic issues preventing realization of any net operational benefits from scaled deployment of behind-the-meter EV, EVCI, and DER assets in electric power grids and markets today. The results of this approach and project unlock massive potential for new SCM capabilities to be easily prototyped, evaluated, and deployed at-scale within the existing grid edge network infrastructure and EVCI/DER technology ecosystem. The EVs-at-RISC project achieves this by extending Open Field Message Bus (OpenFMB), a conceptual model for digital interoperability and distributed intelligence in traditional front-of-meter utility SCADA networks, validating our hypothesis that OpenFMB could be similarly used to solve systemic digital interoperability issues in behind-the-meter environments and unlock real-world utility-scale SCM capabilities without requiring any new proprietary vendor solutions or significant infrastructure reconfiguration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Data-driven quantum approximate optimization algorithm for power systems

Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems. It is especially promising for Distributed Energy Resources (DERs) dominant systems that have been widely developed to promote energy sustainability. In those systems, knowing the maximum sections of power and data delivery is essential for monitoring, operation, and control. However, high computational effort is required. By leveraging quantum resources, Quantum Approximate Optimization Algorithm (QAOA) provides a means to search for these sections efficiently. However, QAOA performance relies heavily on critical parameters, especially for weighted graphs. Here we present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. We verify the strategy with 39,774 expectation value calculations. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots its practical application to power systems in noisy intermediate-scale quantum devices.

Jing, Hang (ORCID:0000000256343489)↗

Enumeration reduction algorithm for the characterization of multi-primary LED systems

Multi-primary tunable LED lighting systems can generate a vast number of spectral outputs, with the exact number depending on the resolution of the control signal and number of LED primaries. Computing all combinations to identify optimal spectral power distributions (SPDs) with a specified chromaticity would require a tremendous amount of time and computational power. Here, an enumeration reduction (ER) algorithm is described to reduce the computation time by defining a bounding pyramid in the three-dimensional tristimulus space that maps to the circumscribed square of the target region in the chromaticity diagram. This method enables computing only the necessary amount of tristimulus values (and resulting chromaticity coordinates) for SPDs that fall into a user-defined target chromaticity area, reducing computation time by avoiding the need to generate each combination and calculate its chromaticity coordinates. The results show that the proposed ER algorithm can greatly reduce the time – up to 922 times in a series of tests – to determine a set of metamers compared to a full enumeration computation.

47 OTHER INSTRUMENTATION↗

WE-DE-BRA-09: Fast Megavoltage CT Imaging with Rapid Scan Time and Low Imaging Dose in Helical Tomotherapy

Purpose: Megavoltage computed tomography (MVCT) imaging has been widely used for daily patient setup with helical tomotherapy (HT). One drawback of MVCT is its very long imaging time, owing to slow couch speed. The purpose of this study was to develop an MVCT imaging method allowing faster couch speeds, and to assess its accuracy for image guidance for HT. Methods: Three cadavers (mimicking closest physiological and physical system of patients) were scanned four times with couch speeds of 1, 2, 3, and 4 mm/s. The resulting MVCT images were reconstructed using an iterative reconstruction (IR) algorithm. The MVCT images were registered with kilovoltage CT images, and the registration errors were compared with the errors with conventional filtered back projection (FBP) algorithm. Moreover, the fast MVCT imaging was tested in three cases of total marrow irradiation as a clinical trial. Results: Three-dimensional registration errors of the MVCT images reconstructed with the IR algorithm were significantly smaller (p < 0.05) than the errors of images reconstructed with the FBP algorithm at fast couch speeds (3, 4 mm/s). The scan time and imaging dose at a speed of 4 mm/s were reduced to 30% of those from a conventional coarse mode scan. For the patient imaging, a limited number of conventional MVCT (1.2 mm/s) and fast MVCT (3 mm/s) reveals acceptable reduced imaging time and dose able to use for anatomical registration. Conclusion: Fast MVCT with IR algorithm maybe clinically feasible alternative for rapid 3D patient localization. This technique may also be useful for calculating daily dose distributions or organ motion analyses in HT treatment over a wide area.

60 APPLIED LIFE SCIENCES↗

Correlative 3D X-ray fluorescence and ptychographic tomography of frozen-hydrated green algae

Accurate knowledge of elemental distributions within biological organisms is critical for understanding their cellular roles. The ability to couple this knowledge with overall cellular architecture in three dimensions (3D) deepens our understanding of cellular chemistry. Using a whole, frozen-hydrated Chlamydomonas reinhardtii cell as an example, we report the development of 3D correlative microscopy through a combination of simultaneous cryogenic x-ray ptychography and x-ray fluorescence microscopy. By taking advantage of a recently developed tomographic reconstruction algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE), we produce high-quality 3D maps of the unlabeled alga’s cellular ultrastructure and elemental distributions within the cell. We demonstrate GENFIRE’s ability to outperform conventional tomography algorithms and to further improve the reconstruction quality by refining the experimentally intended tomographic angles. As this method continues to advance with brighter coherent light sources and more efficient data handling, we expect correlative 3D x-ray fluorescence and ptychographic tomography to be a powerful tool for probing a wide range of frozen-hydrated biological specimens, ranging from small prokaryotes such as bacteria, algae, and parasites to large eukaryotes such as mammalian cells, with applications that include understanding cellular responses to environmental stimuli and cell-to-cell interactions.

59 BASIC BIOLOGICAL SCIENCES↗

Mastering Uncertainty and Risk at Multiple Time Scales in the Future Electrical Grid

Today's electrical grids enjoy a relatively clean separation of spatio-temporal scales yielding a compartmentalization of grid design, optimization, control and risk assessment allowing for the use of conventional mathematical tools within each area. In contrast, the future grid will incorporate time-intermittent renewable generation, operate via faster electrical markets, and tap the latent control capability at finer grid modeling scales; creating a fundamentally new set of couplings across spatiotemporal scales and requiring revolutionary advances in mathematics techniques to bridge these scales. One example is found in decade-scale grid expansion planning in which today's algorithms assume accurate load forecasts and well-controlled generation. Incorporating intermittent renewable generation creates fluctuating network flows at the hourly time scale, inherently linking the ability of a transmission line to deliver electrical power to hourly operational decisions. New operations-based planning algorithms are required, creating new mathematical challenges. Spatio-temporal scales are also crossed when the future grid's minute-scale fluctuations in network flows (due to intermittent generation) create a disordered state upon which second-scale transient grid dynamics propagate effectively invalidating today's on-line dynamic stability analyses. Addressing this challenge requires new on-line algorithms that use large data streams from new grid sensing technologies to physically aggregate across many spatial scales to create responsive, data-driven dynamic models. Here, we sketch the mathematical foundations of these problems and potential solutions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The application of complex network time series analysis in turbulent heated jets

In the present study, we applied the methodology of the complex network-based time series analysis to experimental temperature time series from a vertical turbulent heated jet. More specifically, we approach the hydrodynamic problem of discriminating time series corresponding to various regions relative to the jet axis, i.e., time series corresponding to regions that are close to the jet axis from time series originating at regions with a different dynamical regime based on the constructed network properties. Applying the transformation phase space method (k nearest neighbors) and also the visibility algorithm, we transformed time series into networks and evaluated the topological properties of the networks such as degree distribution, average path length, diameter, modularity, and clustering coefficient. The results show that the complex network approach allows distinguishing, identifying, and exploring in detail various dynamical regions of the jet flow, and associate it to the corresponding physical behavior. In addition, in order to reject the hypothesis that the studied networks originate from a stochastic process, we generated random network and we compared their statistical properties with that originating from the experimental data. As far as the efficiency of the two methods for network construction is concerned, we conclude that both methodologies lead to network properties that present almost the same qualitative behavior and allow us to reveal the underlying system dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

MANCINTAP: Time and space dependent neutron activation tool algorithm improvement and analysis of a PWR nozzle gallery

MANCINTAP [1], a fully automated tool for determining the activation patterns in complex 4D scenarios and evaluating the distribution of the ensuing radiation fields, has been improved. The constraint of forcing the user to define a single global mesh in order to approximate the whole problem, a limitation which prevented an accurate description of detail-rich geometries, has been overcome. The algorithm was improved and many limitations were relaxed. MANCINTAP is now capable of handling many different geometry elements in a given area at once, even if they have very different geometries and characteristic dimensions, thus allowing a vastly more complete and detailed analysis. Different meshes can be superimposed to the 3D geometry, allowing for an appropriate, dedicated treatment of all the relevant features of the problem, and the results are automatically combined in order to provide a global perspective. These new capabilities were accurately tested by applying the tool to the study of time-dependent radiation levels during shutdown in the upper reactor cavity and nozzle gallery regions of a 2-loop PWR reactor. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Characterization of Fuel Cladding Chemical Interaction on a High Burnup U-10Zr Metallic Fuel via Electron Energy Loss Spectroscopy Enhanced by Machine Learning

Fuel cladding chemical interaction (FCCI) is one of the main performance limiting factors for metallic nuclear fuels. The interaction destabilizes the martensitic microstructure and deteriorates mechanical properties of HT-9 cladding. The detection of low atomic number elements (Z<10) and overlapping of elemental peaks can be problematic in interpreting energy dispersive X-ray spectroscopy (EDS) data. Electron energy loss spectroscopy (EELS) provides precise elemental edge energy values and can detect elements with a low atomic number. This work utilizes EELS to study the distribution of lanthanides and light elements at the interaction region. The sample was prepared from the FCCI region of a U-10Zr (wt.%) solid fuel with HT-9 cladding, irradiated to a burnup of 13.2 at.%. Processing the EELS data included three major steps: 1) enhance the signal to noise ratio by denoising the spectrum with principal component analysis (PCA) method, removing background and performing deconvolution; 2) identify chemical elements with core energy loss edges; 3) confirm different phases using a popular machine learning method, K-means. This work presents qualitative assessment of lanthanides and light elements like carbon (C) and oxygen (O) enhanced by the application of machine learning algorithms. By comparing with EDS elemental maps, EELS provides higher resolution chemical maps, reveals the distribution of carbon at the interaction region supporting the formation of zirconium carbide, a rind-like microstructure feature that was proposed to mitigate the chemical interaction. Furthermore, the plasmon peak map was also found to indicate an energy shift associated with the formation of phases/compounds. K-means clustering method was used on the processed electron energy loss (EEL) spectrum to automatically reveal different phases. The resulting clustered maps from K-means clustering align well with elemental maps confirming certain phases, especially Fe-Ce and Zr-C, in the FCCI region.

EELS↗

Latent uncertainties of the precalculated track Monte Carlo method

Purpose: While significant progress has been made in speeding up Monte Carlo (MC) dose calculation methods, they remain too time-consuming for the purpose of inverse planning. To achieve clinically usable calculation speeds, a precalculated Monte Carlo (PMC) algorithm for proton and electron transport was developed to run on graphics processing units (GPUs). The algorithm utilizes pregenerated particle track data from conventional MC codes for different materials such as water, bone, and lung to produce dose distributions in voxelized phantoms. While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from the limited number of unique tracks in the pregenerated track bank is missing from the paper. With a proper uncertainty analysis, an optimal number of tracks in the pregenerated track bank can be selected for a desired dose calculation uncertainty. Methods: Particle tracks were pregenerated for electrons and protons using EGSnrc and GEANT4 and saved in a database. The PMC algorithm for track selection, rotation, and transport was implemented on the Compute Unified Device Architecture (CUDA) 4.0 programming framework. PMC dose distributions were calculated in a variety of media and compared to benchmark dose distributions simulated from the corresponding general-purpose MC codes in the same conditions. A latent uncertainty metric was defined and analysis was performed by varying the pregenerated track bank size and the number of simulated primary particle histories and comparing dose values to a “ground truth” benchmark dose distribution calculated to 0.04% average uncertainty in voxels with dose greater than 20% of D{sub max}. Efficiency metrics were calculated against benchmark MC codes on a single CPU core with no variance reduction. Results: Dose distributions generated using PMC and benchmark MC codes were compared and found to be within 2% of each other in voxels with dose values greater than 20% of the maximum dose. In proton calculations, a small (≤1 mm) distance-to-agreement error was observed at the Bragg peak. Latent uncertainty was characterized for electrons and found to follow a Poisson distribution with the number of unique tracks per energy. A track bank of 12 energies and 60000 unique tracks per pregenerated energy in water had a size of 2.4 GB and achieved a latent uncertainty of approximately 1% at an optimal efficiency gain over DOSXYZnrc. Larger track banks produced a lower latent uncertainty at the cost of increased memory consumption. Using an NVIDIA GTX 590, efficiency analysis showed a 807 × efficiency increase over DOSXYZnrc for 16 MeV electrons in water and 508 × for 16 MeV electrons in bone. Conclusions: The PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty of 1% with a large efficiency gain over conventional MC codes. Before performing clinical dose calculations, models to calculate dose contributions from uncharged particles must be implemented. Following the successful implementation of these models, the PMC method will be evaluated as a candidate for inverse planning of modulated electron radiation therapy and scanned proton beams.

07 ISOTOPE AND RADIATION SOURCES↗

Model-based iterative reconstruction with adaptive regularization for artifact reduction in electron tomography

Obtaining high-quality 3D reconstructions from electron tomography of crystalline particles embedded in lighter support elements is crucial for various material systems such as catalysts for fuel cell applications. However, significant challenges arise due to the limited tilt range, sparse and low signal-to-noise ratio of the measurements. In addition, small metal particles can cause strong streaking and shading artifacts in the 3D reconstructions when using conventional reconstruction algorithms due to the presence of Bragg diffraction and the large scattering cross-section difference between the materials of the particles and the background support regions. These artifacts lead to errors in the downstream characterization affecting extraction of critical features such as the size of the metal particles, their distribution and the volume of the lighter support regions. In this paper, we present a two-stage algorithm based on metal artifact reduction, utilizing model-based iterative reconstruction methods with adaptive adjustment of regularization parameters. Our approach yields high-quality 3D reconstructions compared to traditional algorithms, accurately capturing both the metal particles as well as the background support. We demonstrate the effectiveness of our algorithm through simulated and experimental bright-field electron tomography data, showing significant improvements in reconstruction quality compared to traditional methods.

97 MATHEMATICS AND COMPUTING↗

Optimal Load Ensemble Control in Chance-Constrained Optimal Power Flow

Distribution system operators (DSOs) world-wide foresee a rapid roll-out of distributed energy resources. From the system perspective, their reliable and cost effective integration requires accounting for their physical properties in operating tools used by the DSO. This work describes an decomposable approach to leverage the dispatch flexibility of thermostatically controlled loads (TCLs) for operating distribution systems with a high penetration level of photovoltaic resources. Each TCL ensemble is modeled using the Markov Decision Process (MDP). The MDP model is then integrated with a chance constrained optimal power flow that accounts for the uncertainty of PV resources. Since the integrated optimization model cannot be solved efficiently by existing dynamic programming methods or off-the-shelf solvers, this paper proposes an iterative Spatio-Temporal Dual Decomposition algorithm (ST-D2). Finally, we demonstrate the merits of the proposed integrated optimization and ST-D2 algorithm on the IEEE 33-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Bayesian inverse modeling of the atmospheric transport and emissions of a controlled tracer release from a nuclear power plant

Probability distribution functions (PDFs) of model inputs that affect the transport and dispersion of a trace gas released from a coastal California nuclear power plant are quantified using ensemble simulations, machine-learning algorithms, and Bayesian inversion. The PDFs are constrained by observations of tracer concentrations and account for uncertainty in meteorology, transport, diffusion, and emissions. Meteorological uncertainty is calculated using an ensemble of simulations of the Weather Research and Forecasting (WRF) model that samples five categories of model inputs (initialization time, boundary layer physics, land surface model, nudging options, and reanalysis data). The WRF output is used to drive tens of thousands of FLEXPART dispersion simulations that sample a uniform distribution of six emissions inputs. Machine-learning algorithms are trained on the ensemble data and used to quantify the sources of ensemble variability and to infer, via inverse modeling, the values of the 11 model inputs most consistent with tracer measurements. We find a substantial ensemble spread in tracer concentrations (factors of 10 to 10 3 ), most of which is due to changing emissions inputs (about 80%), though the cumulative effects of meteorological variations are not negligible. The performance of the inverse method is verified using synthetic observations generated from arbitrarily selected simulations. When applied to measurements from a controlled tracer release experiment, the inverse method satisfactorily determines the location, start time, duration and amount. In a 2 km × 2 km area of possible locations, the actual location is determined to within 200m. The start time is determined to within 5min out of 2h, and the duration to within 50min out of 4h. Over a range of release amounts of 10 to 1000kg, the estimated amount exceeds the actual amount of 146kg by only 32kg. The inversion also estimates probabilities of different WRF configurations. In conclusion, to best match the tracer observations, the highest-probability cases in WRF are associated with using a late initialization time and specific reanalysis data products.

54 ENVIRONMENTAL SCIENCES↗

KIVA-Update June 2012

Development of a fractional step, a Predictor-Corrector Split (PCS), or what is often known as a projection method combining hp-adaptive system in a Finite Element Method (FEM) for combustion modeling has been achieved. This model will advance the accuracy and range of applicability of the KIVA combustion model and software used typically for internal combustion engine modeling. This abstract describes a PCS hp-adaptive FEM model for turbulent reactive flow spanning all velocity regimes and fluids that is being developed for the new KIVA combustion algorithm, particularly for internal combustion engines. The method and general solver is applicable to Newtonian and non- Newtonian fluids and also for incompressible solids, porous media, solidification modeling, and fluid structure interaction problems. The fuel injection and injector modeling could easily benefit from the capability of solving the fluid structure interaction problem in an injector, helping to understand cycle to cycle variation and cavitation. This is just one example where the new algorithm differs from the old, in addition to handling Conjugate Heat Transfer (CHT), although there a numerous features that makes the new system more robust and accurate. In these ways, the PCS hp-adaptive algorithm does not compete with commercial software packages, those often used in conjunction with the currently distributed KIVA codes for engine combustion modeling. In addition, choosing a local ALE method on immersed moving parts represented by overset grid that is 2nd order spatially accurate, allows for easy grid generation from CAD to fluid grid while also provide for robustness in handling any possible moving parts configuration without any code modifications. The combined methods employed produce a minimal amount of computational effort as compared to fully resolved grids at the same accuracy. We demonstrate the solver on benchmark problems for the all flow regimes as follows: (1) 2-D backward-facing step using h-adaption, (2) 2-D driven cavity, (3) 2-D natural convection in a differentially heat cavity with h-adaptation, (4) NACA 0012 airfoil in 2-D, (5) supersonic flows over compression ramps, (6) 2-D natural convection in a differentially heat cavity with hp-adaptation, (7) 3-D natural convection in a differentially heat sphere with hp-adaptation. In addition, we show the new moving parts algorithm for working for a 2-D piston; the immersed moving parts method also for valves and pistons, vanes, etc... The movement is performed using an overset grid method and is 2nd order accurate in space, and never produces a tangle grid, that is, robust system at any resolution and any parts configuration. We also show CHT for the currently distributed KIVA-4mpi software and some fairly automatic grid generation using Sandia's Cubit unstructured grid generator. A new electronic web-based manual for KIVA-4 has been developed as well.

02 PETROLEUM↗

Distributed out-of-memory NMF on CPU/GPU architectures

We propose an efficient distributed out-of-memory implementation of the non-negative matrix factorization (NMF) algorithm for heterogeneous high-performance-computing systems. The proposed implementation is based on prior work on NMFk, which can perform automatic model selection and extract latent variables and patterns from data. In this work, we extend NMFk by adding support for dense and sparse matrix operation on multi-node, multi-GPU systems. The resulting algorithm is optimized for out-of-memory problems where the memory required to factorize a given matrix is greater than the available GPU memory. Memory complexity is reduced by batching/tiling strategies, and sparse and dense matrix operations are significantly accelerated with GPU cores (or tensor cores when available). Input/output latency associated with batch copies between host and device is hidden using CUDA streams to overlap data transfers and compute asynchronously, and latency associated with collective communications (both intra-node and inter-node) is reduced using optimized NVIDIA Collective Communication Library (NCCL) based communicators. Benchmark results show significant improvement, from 32X to 76x speedup, with the new implementation using GPUs over the CPU-based NMFk. Good weak scaling was demonstrated on up to 4096 multi-GPU cluster nodes with approximately 25,000 GPUs when decomposing a dense 340 Terabyte-size matrix and an 11 Exabyte-size sparse matrix of density 10 -6 .

97 MATHEMATICS AND COMPUTING↗

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Distributed Power Allocation for 6-GHz Unlicensed Spectrum Sharing via Multi-agent Deep Reinforcement Learning

We consider the problem of power allocation over the 6 GHz Unlicensed National Information Infrastructure (UNII)- 5 spectrum. We propose a novel deep Reinforcement Learning (DRL)-based distributed power allocation scheme which utilizes the multi-agent Deep Deterministic Policy Gradient (MADDPG) algorithm. In particular, we model the base stations (BSs) as DRL agents that simultaneously determine the transmit powers to their scheduled user equipment (UE) in a synchronized manner. The power decision of each BS is based on its own observation of the radio environment, which consists of several local interference measurements and a limited amount of information obtained from other BSs. One advantage of the proposed scheme is that it addresses the single-agent non-stationarity problem of RL in the multi-agent scenario by incorporating the actions and observations of other BSs into each BS’s own critic which helps it to gain a more accurate perception of the overall radio environment. A centralized-training-distributed execution framework is used to train the policies where the critics are trained over the joint actions and observations of all BSs while the actor of each BS only takes the local observation as input in order to produce the transmit power. Simulation shows that the proposed power allocation scheme can achieve better throughput performance than several state-of-the-art approaches.

99 GENERAL AND MISCELLANEOUS↗

Estimating consistent biased source probabilities over arbitrary bins - 25621

This paper describes computational algorithms for estimating consistent biased source probabilities for the CADIS and FW-CADIS methods that are compatible with most of the general fixed-source capabilities of the MCNP continuous-energy transport code. The basic algorithm is a novel Monte Carlo sampling technique that enables the straightforward estimation of biased source probabilities over arbitrarily complex distribution trees. In recent work, a method has been developed for generating correct biased spatial source probabilities in the presence of rejection from an arbitrary number of geometry cells. Two numerical test problems that demonstrate the correctness of this new algorithm are presented, including a simplified model of a cooling water system with an N-17 neutron source. (authors)

07 ISOTOPE AND RADIATION SOURCES↗