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At least 235 records · Page 13

Techno-Economic Analysis and Life Cycle Assessment for the Separation of 2,3-Butanediol from Fermentation Broth Using Liquid–Liquid Extraction

It is energy-intensive to separate dilute 2,3-butanediol (2,3-BDO) (<10 wt %) from the aqueous phase of fermentation broth for sustainable aviation fuel (SAF) using conventional distillation. Liquid–liquid extraction (LLE) using oleyl alcohol as a solvent in a membrane extractor to extract BDO from water can significantly reduce the energy cost and minimize the potential emulsion. In an Aspen Plus model simulation, 95.2% BDO recovery and 97.1% BDO purity have been achieved using this LLE method with solvent recovery and heat integration. Here, the thermal energy cost was estimated to be 4.57 MJ/kg BDO, which is only about 16.8% of the lower heating value (LHV) of the BDO. This method consumes 81% less energy than the cascade distillation and reduces about $0.46/GGE (gasoline gallon equivalent) to the minimal fuel selling price. Meanwhile, the greenhouse gas (GHG) emission is 62% lower than petroleum-based jet fuel production and 34% less than using the cascade distillation.

09 BIOMASS FUELS↗

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗

Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations

The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction β eff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Effects-Based Monitoring of Geomagnetically-Induced Current Using a Convolutional Neural Network

Geomagnetically-induced current (GIC) due to space weather can flow in the power grid causing undesirable effects such as transformer overheating, misoperation of protection devices, and potential blackouts. It is therefore important to monitor GIC in the power grid to improve online situational awareness and decision-making of system operators during a geomagnetic disturbance. To avoid the costly installation of GIC monitors at transformers’ neutrals, it is desirable to find correlations between GIC and already-monitored parameters. Hence, this work proposed the use of a convolutional neural network (CNN) to compute GIC amplitudes from learned patterns in the time-series data of transformer even harmonic currents. Using an electromagnetic transient program, GIC injection simulations were performed for a modeled Dominion Energy Virginia (DEV) substation with two 504 MVA, 500/230 kV transformers. Data collected from these offline simulations were used to train the CNN to provide online GIC monitoring. Testing the CNN performance involved using real GIC measurements from published literature and from a physical GIC monitor in the DEV area. Finally, the results showed that the proposed method was able to provide GIC readings with a root mean squared error of 1.56 A/phase (equivalent to an average accuracy of 94%) for these real GIC waveforms.

42 ENGINEERING↗

Resilient Disaster Recovery Logistics of Distribution Systems: Co-Optimize Service Restoration With Repair Crew and Mobile Power Source Dispatch

Repair crews (RCs) and mobile power sources (MPSs) are critical resources for distribution system (DS) outage management after a natural disaster. However, their logistics have not been well investigated. We propose a resilient scheme for disaster recovery logistics to co-optimize DS restoration with the dispatch of RCs and MPSs. A novel co-optimization model is formulated to route RCs and MPSs in the transportation network, schedule them in the DS, and reconfigure the DS for microgrid formation coordinately, etc. The model incorporates different timescales of DS restoration and RC/MPS dispatch, the coupling of transportation and power networks, etc. To ensure radiality of the DS with variable physical structure and MPS allocation, we also model topology constraints based on the concept of spanning forest. The model is convexified equivalently and linearized into a mixed-integer linear programming. To reduce its computation time, preprocessing methods are proposed to preassign a minimal set of repair tasks to depots and reduce the number of candidate nodes for MPS connection. Resilient recovery strategies thus are generated to enhance service restoration, especially by dynamic formation of microgrids that are powered by MPSs and topologized by repair actions of RCs and network reconfiguration of the DS. Case studies demonstrate the proposed methodology.

Disaster recovery logistics↗

Improving the Estimation of the Atmospheric Water Vapor Pressure Using Interpretable Long Short-Term Memory Networks: Dataset, Python code, and trained models

Atmospheric water vapor pressure is an essential meteorological control on land surface and hydrologic processes. It is not as frequently observed as other meteorologic conditions, but often inferred through the August–Roche–Magnus formula by simply assuming dew point and daily minimum temperatures are equivalent or by empirically correlating the two temperatures using an aridity correction. The performance of both methods varies considerably across different regions and during different time periods; obtaining consistently accurate estimates across space and time remains a great challenge. We applied an interpretable Long Short-Term Memory (iLSTM) network conditioned on static, location specific attributes to estimate daily vapor pressure for 83 FLUXNET sites in the United States and Canada. This data package includes all raw data of the 83 FLUXNET sites, input data for model training/validation/test, trained models and results, and python codes for the manuscript "Improving the Estimation of the Atmospheric Water Vapor Pressure Using an Interpretable Long Short-term Memory Network". Specifically, it consists of five parts. - First, "1_Daymet_data_83sites.zip" includes raw data downloaded from Daymet for the 83 sites used in the paper according to their longitude and latitude, in which vapor pressure is used. It also includes a pre-processed CSV data file combining all data from the 83 sites which is specifically used for the paper. - Second, "2_Fluxnet2015_data_83sites.zip" includes raw half hourly data of the 83 sites downloaded from FLUXNET2015 data portal, pre-processed daily data of the 83 sites, a CSV file including combined pre-processed daily data of the 83 sites, and a CSV file including the information (site ID, site name, latitude, longitude, data available period) of the 83 sites. - Third, "3_MODIS_LAI_data_83sites_raw.zip" includes raw leaf area index (LAI) data downloaded from the AppEEARs data portal. - Fourth, "4_Scripts.zip" includes all scripts related to model training and post-processing of a trained model, and a jupyter notebook showing an example for model post-processing. Two typo errors in files titled "run2get_args.py" and "postprocess.py" were corrected on March 27, 2024 to avoid confusions. - Finally, "Trained_models_and_results.zip" includes three folders and three files with suffix ".npy", and each folder corresponds to one file with suffix ".npy" with the same title. Each of the three folders include all trained models associated with one iLSTM model configuration (35 models for each configuration, details are described in the paper). Each file with suffix ".npy" includes the post-processed results of the corresponding 35 models under one iLSTM model configuration.

54 ENVIRONMENTAL SCIENCES↗

Accuracy of HVAC Load Predictions: Validation of EnergyPlus and DOE-2 using FLEXLAB Measurements

The aim of the project reported here was to better understand the level of accuracy of three building energy simulation (BES) engines (‘engines’) — EnergyPlus™, DOE-2.1e, and DOE-2.2 — by identifying and investigating significant deviations between the performance predicted by these engines and actual performance as measured in the FLEXLAB® test facility at Lawrence Berkeley National Laboratory (LBNL). The specific test conditions included some of those prescribed in ANSI/ASHRAE Standard 140 - Standard Method of Test for the Evaluation of Building Energy Analysis Computer Programs. Detailed measurements of FLEXLAB performance, including indoor temperatures and heat fluxes and air-flow and water flow rates and temperatures in the Heating, Ventilating and Air Conditioning (HVAC) system, together with hourly weather data, were recorded and used in analyzing the simulation results from EnergyPlus v8.8, DOE-2.2 v3.65 and DOE-2.1e v127. These engines are commonly used in the United States for building energy code compliance, federal, state, and utility incentives programs, as well as energy efficient design of new buildings and energy retrofit of existing buildings. Seven conventional overhead mixing ventilation scenarios were tested and each engine was found to have a similar level of agreement with the measurements of space-level heating and sensible cooling loads. These results provide useful information regarding the accuracy of these engines in predicting the cooling and heating load elements of whole building energy performance. This information is intended for practitioners who are concerned about transitioning between simulation tools with different engines and for managers of utility programs leveraging these tools for evaluating and/or projecting measure savings to be incentivized under their programs. The results of the comparisons of simulated and measured performance indicate that the predictions from all three engines are not significantly different. The 24-hour average value of the absolute mean bias indicates the likely magnitude of the error in any particular case. The average mean bias is reduced by cancelation of overprediction in one case by underprediction in another. The daytime absolute mean biases, which may be more important for both energy performance and occupant comfort, are ~6%, presumably because of the greater complexity involved in simulating in the presence of solar radiation. EnergyPlus typically overpredicts the cooling load and/or underpredicts the heating load by ~1.5% and the DOE-2 engines typically underpredict the cooling load by approximately the same amount. The Root Mean Square Error is relatively more sensitive to shorter term variations in the difference between predicted and measured loads; the three engines have similar values, ~10%, suggesting that the uncertainties in their predictions of peak loads may also be similar in magnitude. The implication of these results is that users, both designers and program analysts, can use EnergyPlus, DOE-2.1e, or DOE-2.2 to model conventional commercial buildings equipped with overhead mixing ventilation with a similar level of confidence. Further work is required to better understand the variability in the level of agreement between the engine predictions and FLEXLAB measurements, where a particular engine will agree well with FLEXLAB in some cases and not so well in others and another engine will agree or disagree in different cases. As the sources of this variability are identified and eliminated or reduced significantly, it is recommended that the experimental capabilities and methods developed in the study reported here should be applied to validating heating and cooling load calculations for spaces with different types of furniture and miscellaneous loads. These methods should then be applied to low energy space conditioning systems in EnergyPlus including, in particular, radiant slab and radiant ceiling panel cooling and heating systems and ‘mixed mode’ systems that combine mechanical cooling and natural ventilation systems, focusing on controls, including control of thermal mass. The work reported here addresses the conventional method of heating and cooling occupied spaces; other methods, such as the use of radiant heating and cooling systems have the potential to provide equivalent occupant comfort, or better, with lower energy consumption. These systems are addressed more explicitly in EnergyPlus but there is a need for empirical validation to give users the same level of confidence in modeling these systems that they have, or should have, in modeling conventional systems, based on the results presented here.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

TEMPI: An Interposed MPI Library with Canonical Representation of MPI Datatypes [Poster]

TEMPI provides a transparent non-contiguous data-handling layer compatible with various MPIs. MPI Datatypes are a powerful abstraction for allowing an MPI implementation to operate on non-contiguous data. CUDA-aware MPI implementations must also manage transfer of such data between the host system and GPU. The non-unique and recursive nature of MPI datatypes mean that providing fast GPU handling is a challenge. The same noncontiguous pattern may be described in a variety of ways, all of which should be treated equivalently by an implementation. This work introduces a novel technique to do this for strided datatypes. Methods for transferring non-contiguous data between the CPU and GPU depends on the properties of the data layout. This work shows that a simple performance model can accurately select the fastest method. Unfortunately, the combination of MPI software and system hardware available may not provide sufficient performance. The contributions of this work are deployed on OLCF Summit through an interposer library which does not require privileged access to the system to use

97 MATHEMATICS AND COMPUTING↗

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

36 MATERIALS SCIENCE↗

Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are mappings from the microstructure space to the materials properties space. Due to the stochastic and random nature of microstructures, there is always some uncertainty associated with materials properties, for example, in homogenized stress-strain curves. For critical applications with strong reliability needs, it is often desirable to quantify the microstructure-induced uncertainty in the context of structure-property relationships. However, this uncertainty quantification (UQ) problem often incurs a large computational cost because many statistically equivalent representative volume elements (SERVEs) are needed. In this article, we apply a multi-level Monte Carlo (MLMC) method to CPFEM to study the uncertainty in stress-strain curves, given an ensemble of SERVEs at multiple mesh resolutions. By using the information at coarse meshes, we show that it is possible to approximate the response at fine meshes with a much reduced computational cost. We focus on problems where the model output is multi-dimensional, which requires us to track multiple quantities of interest (QoIs) at the same time. In conclusion, our numerical results show that MLMC can accelerate UQ tasks around 2.23x, compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.

36 MATERIALS SCIENCE↗

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗

Gray-Box Modeling for Distribution Systems With Inverter-Based Resources: Integrating Physics-Based and Data-Driven Approaches

Here, in this paper, we develop a novel gray-box modeling approach for distribution systems with inverter-based resources (IBRs). The proposed gray-box modeling method aims to improve estimation accuracy by taking advantages of both physics-based (white-box) and data-driven (black-box) modeling approaches. To this end, we utilize partial physical knowledge of the system, including the inverters’ structures and control diagrams, as well as the equivalent network model simplified through Kron reduction. The white-box model containing unknown parameters is then constructed with mathematical equations and an optimization-based method is subsequently employed to identify these unknown parameters within the white-box model. Next, the graybox modeling framework is then constructed by embedding the output variables of the white-box model into the input vector of a black-box model (represented using a neural network). Finally, the black-box section is trained using the collected input-output datasets and the gray-box model is then obtained. Furthermore, case studies demonstrate that our gray-box modeling approach effectively improves estimation accuracy compared to purely physics-based or data-driven methods.

42 ENGINEERING↗

A Life Cycle Decarbonization of Modular Building Solutions: Preprint

Off-site construction methods offer the opportunity to compress costs of net zero energy housing using the advantages of mass production. Blokable, LLC, a vertically integrated modular builder, wanted to know how the learning curves of mass production would help them decarbonize their existing modular housing prototype at a relative cost advantage. The method developed for this question looked at the life cycle assessment of an individual apartment and used learning curve efficiencies to approximate the relative advantage of construction-at-scale. Greenhouse gas emissions were quantified by a learning-affected, whole life carbon emissions model and demonstrated a path to a 60% reduction of whole life CO2-equivalent in the 2030 production year. The resultant roadmap considers a best-first approach to decarbonizing a modular building product line, and the method can be replicated for other modular builders.

decarbonization↗

Discovering causal structure with reproducing-kernel Hilbert space ε -machines

We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Suppression of Parasitic Voltage Oscillation in Power Modules by Turn-Off Current Zero Placement

This paper presents a frequency-domain analysis of the turn-off equivalent switching network of a hard-switched semiconductor switching cell. This paper also proposes a novel method to suppress parasitic voltage ringing by placing the turn-off current zero at the parasitic resonant frequency. The turn-off current was decomposed into ramp functions and a constant-valued function to facilitate obtaining the frequency components of the turn-off current using the Laplace transform of standard signals. The proposed frequency-domain modeling of the parasitic voltage ringing and the suppression were validated by detailed circuit simulation using parameters corresponding to prior literature with experimental validation.

Galigekere, Veda Prakash↗

A remote sensing algorithm for vertically resolved cloud condensation nuclei number concentrations from airborne and spaceborne lidar observations

Cloud condensation nuclei (CCN) are mediators of aerosol–cloud interactions (ACIs), contributing to the largest uncertainties in the understandings of global climate change. We present a novel remote-sensing-based algorithm that quantifies the vertically resolved CCN number concentrations (N CCN ) using aerosol optical properties measured by a multiwavelength lidar. The algorithm considers five distinct aerosol subtypes with bimodal size distributions. The inversion used the lookup tables developed in this study, based on the observations from the Aerosol Robotic Network, to efficiently retrieve optimal particle size distributions from lidar measurements. The method derives dry aerosol optical properties by implementing hygroscopic enhancement factors in lidar measurements. The retrieved optically equivalent particle size distributions and aerosol-type-dependent particle composition are utilized to calculate critical diameters using κ-Köhler theory and N CCN at six supersaturations ranging from 0.07 % to 1.0 %. Sensitivity analyses indicate that uncertainties in extinction coefficients and relative humidity greatly influence the retrieval error in N CCN . The potential of this algorithm is further evaluated by retrieving N CCN using airborne lidar from the NASA ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) campaign and is validated against simultaneous measurements from the CCN counter. The independent validation with robust correlation demonstrates promising results. Furthermore, the N CCN has been retrieved for the first time using a proposed algorithm from spaceborne lidar – Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) – measurements. The application of this new capability demonstrates the potential for constructing a 3D CCN climatology at a global scale, which helps to better quantify ACI effects and thus reduce the uncertainty in aerosol climate forcing.

54 ENVIRONMENTAL SCIENCES↗

Decarbonization During Predevelopment of Modular Building Solutions

Off-site construction methods offer the opportunity to compress costs of net-zero energy (NZE) housing using the advantages of mass production. There has been limited investigation on trade-offs between site-built and industrialized construction from the perspective of reducing the incremental cost of NZE strategies and reducing greenhouse gas emissions during embodied and operational stages. Blokable, LLC, a vertically integrated modular builder, wanted to know how the learning curves of mass production would help them decarbonize their existing modular housing prototype at a relative cost advantage. The method developed for this question looked at the life cycle assessment of an individual apartment and used learning-curve efficiencies to approximate the relative advantage of construction-at-scale. Greenhouse gas emissions were quantified by a learning-affected, whole-life carbon emissions model and demonstrated a path to a 60% reduction of whole-life CO2-equivalent in the 2030 production year. The resultant roadmap considers a best-first approach to decarbonizing a modular building product line, and the method can be replicated for other modular builders.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Data Processing Workflow for Fixed-wing Drone Based Radiation Mapping in the Chornobyl Exclusion Zone (CEZ) - 20119

April 2020 marks the 34. anniversary of the high-profile radiological release from the Chornobyl Nuclear Power Plant (ChNPP). The release of radioactive material from reactor number four began on the 26 April 1986 and continued over a period of about 10 days, releasing approximately 1700 PBq of radioactive material (including 85 PBq of 137-Cs) into the environment. To this day, the accident remains the most significant release of radioactive material since civil nuclear power generation began. In the years since the accident, automated and remote radiation monitoring technologies have advanced significantly in their capabilities. One such example of this is the use of unmanned aerial vehicles (UAVs) in radiation mapping investigations. In April 2019, a team of scientists from the University of Bristol showcased a novel radiation mapping system within the CEZ, specifically aiming to map radiation over a large portion of the area immediately surrounding the ChNPP. Over six days of data collection, the system flew a total distance of 583.8 km, covering an area of 14.6 sq.km with an exceptional spatial resolution (sub 20 m/pixel). The work presented herein outlines and explains the data processing procedure to convert the raw data into 137-Cs activity (kBq/sq.m) and cesium-equivalent dose-rate (CED) at 1 m above ground level (μSv/hr). A demonstration of the validity of the method is demonstrated through the successful reduction of the raw data into a single linear relationship between the measured {sup 137}Cs net peak intensity and the {sup 137}Cs activity. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗