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At least 1,459 records · Page 81

Faster recovery of North Atlantic tropical cyclone-induced cold wakes in recent decades

Intense winds associated with tropical cyclones (TCs) generate surface ocean cooling in their wakes, which can persist for several weeks in their aftermath. While multi-decadal observations of the sea surface have shown a substantial warming of the ocean, long-term changes in cold wake recovery time remain largely unknown. Here we find a trend toward faster recovery of TC cold wakes in the Atlantic main development region (MDR) since 2001. This is due primarily to a decrease in the strength of the North Atlantic trade winds, which reduces evaporative cooling of the ocean. The faster damping of TC cold wakes has led to a significant increase in the intensification of subsequent TCs that encounter lingering wakes from prior TCs, with a magnitude that is about 9% of that from long-term warming of the ocean. Finally, earth system model simulations indicate that the observed decrease in the cold wake recovery time will likely continue into the future.

54 ENVIRONMENTAL SCIENCES↗

A modeling framework for optimal energy management of a residential building

Residential buildings are currently equipped with energy production facilities, e.g., solar rooftops and batteries, which in conjunction with smart meters, can function as smart energy hubs coordinating the loads and the resources in an optimal manner. This paper presents a mathematical model for the optimal energy management of a residential building and proposes a centralized energy management system (CEMS) framework for off-grid operation. The model of each component of the hub is integrated within the CEMS. The optimal decisions are determined in real-time by considering these models with realistic parameter settings and customer preferences. Model predictive control (MPC) is used to adapt the optimal decisions on a receding horizon to account for the deviations in the system inputs. Simulation results are presented to demonstrate the feasibility and effectiveness of the proposed CEMS framework. Results show that the proposed CEMS can reduce the energy cost and energy consumption of the customers by approximately 17% and 8%, respectively, over a day. In conclusion, using the proposed CEMS, the total charging cycles of the ESS were reduced by more than 50% in a day.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A new stepwise carbon cycle data assimilation system using multiple data streams to constrain the simulated land surface carbon cycle

Here, large uncertainties in land surface models (LSMs) simulations still arise from inaccurate forcing, poor description of land surface heterogeneity (soil and vegetation properties), incorrect model parameter values and incomplete representation of biogeochemical processes. The recent increase in the number and type of carbon cycle-related observations, including both in situ and remote sensing measurements, has opened a new road to optimize model parameters via robust statistical model–data integration techniques, in order to reduce the uncertainties of simulated carbon fluxes and stocks. In this study we present a carbon cycle data assimilation system that assimilates three major data streams, namely the Moderate Resolution Imaging Spectroradiometer (MODIS)-Normalized Difference Vegetation Index (NDVI) observations of vegetation activity, net ecosystem exchange (NEE) and latent heat (LE) flux measurements at more than 70 sites (FLUXNET), as well as atmospheric CO 2 concentrations at 53 surface stations, in order to optimize the main parameters (around 180 parameters in total) of the Organizing Carbon and Hydrology in Dynamics Ecosystems (ORCHIDEE) LSM (version 1.9.5 used for the Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations). The system relies on a stepwise approach that assimilates each data stream in turn, propagating the information gained on the parameters from one step to the next. Overall, the ORCHIDEE model is able to achieve a consistent fit to all three data streams, which suggests that current LSMs have reached the level of development to assimilate these observations. The assimilation of MODIS-NDVI (step 1) reduced the growing season length in ORCHIDEE for temperate and boreal ecosystems, thus decreasing the global mean annual gross primary production (GPP). Using FLUXNET data (step 2) led to large improvements in the seasonal cycle of the NEE and LE fluxes for all ecosystems (i.e., increased amplitude for temperate ecosystems). The assimilation of atmospheric CO 2 , using the general circulation model (GCM) of the Laboratoire de Météorologie Dynamique (LMDz; step 3), provides an overall constraint (i.e., constraint on large-scale net CO 2 fluxes), resulting in an improvement of the fit to the observed atmospheric CO 2 growth rate. Thus, the optimized model predicts a land C (carbon) sink of around 2.2 PgC yr -1 (for the 2000–2009 period), which is more compatible with current estimates from the Global Carbon Project (GCP) than the prior value. The consistency of the stepwise approach is evaluated with back-compatibility checks. The final optimized model (after step 3) does not significantly degrade the fit to MODIS-NDVI and FLUXNET data that were assimilated in the first two steps, suggesting that a stepwise approach can be used instead of the more “challenging” implementation of a simultaneous optimization in which all data streams are assimilated together. Most parameters, including the scalar of the initial soil carbon pool size, changed during the optimization with a large error reduction. This work opens new perspectives for better predictions of the land carbon budgets.

58 GEOSCIENCES↗

Insights From the Software Design of a Multiphysics Multicomponent Scientific Code

Using simulations for scientific discovery requires that the software used in the simulations undergoes a rigorous design and development process similar to that of the lab instruments in the experimental sciences. To devise a good design methodology, it is critical to understand the requirements, constraints, and challenges. Furthermore, this article describes insights from the long-term stewardship of a multiphysics multicomponent software, FLASH, that was designed more than 20 years ago for astrophysics, now serves multiple communities, and has been successful in adapting to the changing world of high-performance computing.

97 MATHEMATICS AND COMPUTING↗

Verification Testing of OLI Systems Mixed Solvent Electrolyte Model for the Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 ) System to High Ionic Strength at 25°C

This technical report summarizes model verification results and summary statistics for 41 evaporite mineral solubility cases evaluated by Savannah River National Laboratory using OLI Systems’ aqueous electrolyte thermodynamic modeling software. The 41 verification cases containing a total of 60 solubility curves comprise mineral solubility data from low to high ionic strength at 25°C for the eight-component system Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 O as reported by Harvie et al. (1984). Thermodynamic calculations were executed using OLI Systems’ Stream Analyzer computation module within the OLI Studio software platform (Ver. 11.0, Rev. 11.0.1.9). The Mixed Solvent Electrolyte (MSE) thermodynamic framework was chosen for this investigation because of its superiority in modeling high ionic-strength inorganic salt solutions and actinide redox chemistry and solubility, both of which are relevant to the geological repository conditions at the Waste Isolation Pilot Plant in Carlsbad, New Mexico. Mineral solubility data in various inorganic salt solutions were digitized and extracted from figures generated by Harvie et al. (1984). For each of the 60 solubility curves, a case-specific chemistry model and input file were generated in OLI Studio using OLI Stream Analyzer and the MSE (H 3 O + ion) public databank provided by OLI Systems. Model simulation results were exported to Microsoft Excel to calculate summary statistics and to generate graphs comparing the OLI model predictions to the solubility data. Summary statistics include residuals (model – data) and concordance (accuracy × precision, where precision is indicated by the Pearson correlation coefficient and accuracy accounts for bias and scale differential). Private databanks were not developed, and activity coefficient model regressions were not performed to improve OLI model fits to the data. Of the 41 model verification plots, 83% have a mean of the percent residuals less than or equal to 25%. Similarly, 75% display a concordance greater than or equal to 0.75. Only seven of the 41 verification plots fail to show good agreement between the model and data. Of these seven, three are relevant to the WIPP repository because they involve the Mg-OH-Cl-SO 4 -CO 3 aqueous system. The remaining four address salt solubilities at the pH extremes (strong acid and strong base). It should be noted that in two of the three Mg-OH-Cl-SO 4 -CO 3 system cases, the regressed Harvie et al. (1984) solubility curve also deviated from the data. Lack of agreement between the OLI model-predicted solubility curves and the data is attributable to one or more of the following: specific solid species are not included in the OLI MSE databank; there is significant variation among the different solubility datasets chosen by Harvie et al. (1984); the OLI MSE model’s thermodynamic parameters were determined using different solubility datasets; and the activity coefficient parameters for certain relevant ion-ion and ion-molecule pairs have not been optimized via data regression. Two recommendations for future work are to (1) evaluate solubility data for the Mg-OH-Cl-SO 4 -CO 3 system at high ionic strength and, if necessary, develop a private OLI MSE database that includes missing species and, where necessary, regressed standard state properties and interaction parameters; (2) perform similar verification testing of the OLI model for actinide solubility data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Hardware-in-the-Loop (HIL) Simulations for Smart Grid Impact Studies

Hardware-in-the-loop (HIL) simulations are increasingly employed in power engineering as more inverter-based generation and smart appliances are connected to the electric grid. HIL techniques allow for the co-simulation of analytical models with actual devices whose complex behavior is computationally inefficient or difficult to model. They also allow for testing the behavior of these devices under adverse conditions that rarely occur in the field but are important to evaluate. This paper provides an overview of how HIL simulations have been used to date and proposes that HIL simulations should play an important role in evaluating new control strategies, especially at the distribution level, that are being proposed to allow for continued affordable and reliable operation of the electric grid. We present a new capability that was developed to evaluate the interactions between residential loads and the smart grid: smart home hardware-in-the-loop. The paper includes results from an HIL experiment that incorporates multiple technologies and controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Development of a Trip Energy Estimation Model Using Real-World Global Positioning System Driving Data: Preprint

A data-driven technique for estimation of energy requirements for a proposed vehicle trip has been developed. Based on over 700,000 miles of driving data, the technique has been applied to generate a model that estimates trip energy requirements. The model uses a novel binning approach to categorize driving by road type, traffic conditions, and driving profile. The trip-level energy estimations can easily be aggregated to any higher-level transportation system network desired. The model has been tested and validated on the Austin, Texas, data set used to build this model. Ground-truth energy consumption for the data set was obtained from Future Automotive Systems Technology Simulator (FASTSim) vehicle simulation results. The energy estimation model has demonstrated 12.1 percent normalized total absolute error. The energy estimation from the model can be used to inform control strategies in routing tools, such as change in departure time, alternate routing, and alternate destinations, to reduce energy consumption. The model can also be used to determine more accurate energy consumption of regional or national transportation networks if trip origin and destinations are known. Additionally, this method allows the estimation tool to be tuned to a specific driver or vehicle type.

33 ADVANCED PROPULSION SYSTEMS↗

Study of beam transverse properties of a thermionic electron gun for application to a compact THz free electron laser

A novel thermionic electron gun adopted for use in a high power THz free electron laser (FEL) is proposed in this paper. By optimization of the structural and radiofrequency (RF) parameters, the physical design of the gun is performed using dynamic calculations. Velocity bunching is used to minimize the bunch's energy spread, and the dynamic calculation results indicate that high quality beams can be provided. The transverse properties of the beams generated by the gun are also analyzed. The novel RF focusing effects of the resonance cavity are investigated precisely and are used to establish emittance compensation, which enables the injector length to be reduced. In addition, the causes of the extrema of the beam radius and the normalized transverse emittance are analyzed and interpreted, respectively, and slice simulations are performed to illustrate how the RF focusing varies along the bunch length and to determine the effects of that variation on the emittance compensation. Finally, by observation of the variations of the beam properties in the drift tube behind the electron gun, prospective assembly scenarios for the complete THz-FEL injector are discussed, and a joint-debugging process for the injector is implemented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Smart Ventilation for Advanced California Homes

This project investigated smart ventilation approaches to minimize energy use for providing indoor air quality (IAQ) in high performance new California homes. Evaluation criteria included annual ventilation-related energy, peak energy and time-of-use savings, and the indoor air quality relative to a minimally code-compliant ventilation system. The simulations used CONTAM’s air flow and contaminant transport model, combined with the EnergyPlus building loads model. House types representing the default California Energy Code compliance homes were investigated for four California climate zones, covering a wide range of climate types. Both single and multi-zone smart ventilation controls were investigated. Contaminant sources included contaminants emitted continuously and varying with time, temperature and relative humidity, episodic emissions from occupant activities and outdoor particles. Single-zone ventilation controls that varied ventilation depending on outdoor temperatures were able to consistently save half of ventilation-related energy without compromising long-term IAQ. Ventilation strategies that tracked occupancy were less successful, because this work included generic contaminants with constant background emission rates. Energy performance for occupancy controls improved with a one-hour pre-occupancy flush out strategy. The addition of zoning ventilation controls did not offer significant IAQ to energy improvements compared to non-zonal versions of the same ventilation system type. The best controls had HVAC energy savings of 10-20%, with individual cases reaching up to 40% savings. However, these savings cannot be achieved without worsening personal exposures for at least one contaminant. A metric is needed to assess the competing changes in exposure to different contaminants in order to determine the net-health impacts of a control strategy. Controls that directly sensed contaminants and controlled them to acceptable levels showed that the California OEHHA limit for formaldehyde completely dominates system performance, with homes not able to meet the limit even with continuous operation of a fan sized to twice the current code minimum.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Eye tracking studies based on attentional-resource effectiveness - 310

In the majority of cases, the primary means of information input to operators in nuclear power plants (NPPs) control rooms is through the visual channel. In this study, eye movement patterns of NPP operators are analyzed with eye tracking data obtained from simulator-based experimental studies. Two eye tracking measures of attentional-resource effectiveness in monitoring and detection tasks in NPPs which had been developed by the authors are introduced and several applications with the two eye tracking measures are discussed for the use of the measures. The underlying principle of the measures is that information sources should be selectively attended according to their importance. One of the two measures is the fixation to importance ratio (FIR), which represents attentional resource (eye fixations) spent on an information source compared to the importance of the information source. The other measure is selective attention effectiveness (SAE), which incorporates the FIRs of all information sources. The FIR represents the effectiveness on an information source, whereas the SAE represents the overall effectiveness on all information sources. Frequency and the duration of eye fixations of an operator on information sources are used as attentional resource. Finally feasible future applications with eye tracking data were discussed in terms of plant systems automation and operator training. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multi-Scale Thermal Analysis for Design of SiC-Based Medium Voltage Motor Drive: Preprint

This paper describes a multi-scale thermal analysis approach for the design of an air-cooled 1.7-kV SiC MOSFET-based medium-voltage variable-speed motor drive. The National Renewable Energy Laboratory supported the project objectives by providing thermal management design support to the project partner The Ohio State University (OSU). The scope of the models and limited resources required efficient and flexible thermal models to be developed. Two modeling techniques are described that significantly reduced model run time and enabled more complex models to be run faster while retaining needed accuracy. The first technique uses the effectiveness-NTU method to extract convection boundary conditions from a computational fluid dynamics (CFD) model that can be applied to a fast-running finite element analysis model. The second is a porous media technique that enables system-level CFD simulations that incorporate effects from heat exchangers (e.g., pin fin heat sinks) that run in a fraction of the time required for fully resolved CFD simulations. The multi-scale approach to the thermal analysis enabled fast and accurate simulation for the converter design ranging from the die level up to the full system with 36 submodules. The modeling results were validated against experimental data from system tests performed by OSU.

DIRECT ENERGY CONVERSION↗

Code modernization strategies for short-range non-bonded molecular dynamics simulations

Modern HPC systems are increasingly relying on greater core counts and wider vector registers. Thus, applications need to be adapted to fully utilize these hardware capabilities. One class of applications that can benefit from this increase in parallelism are molecular dynamics simulations. In this paper, we describe our efforts at modernizing the ESPResSo++ simulation package for molecular dynamics by restructuring its particle data layout for efficient memory accesses and applying vectorization techniques to benefit the calculation of short-range non-bonded forces, which results in an overall three times speedup and serves as a baseline for further optimizations. We also implement fine-grained parallelism for multi-core CPUs through HPX, a C++ runtime system which uses lightweight threads and an asynchronous many-task approach to maximize concurrency. Our goal is to evaluate the performance of an HPX-based approach compared to the bulk-synchronous MPI-based implementation. This requires the introduction of an additional layer to the domain decomposition scheme that defines the task granularity. On spatially inhomogeneous systems, which impose a corresponding load-imbalance in traditional MPI-based approaches, we demonstrate that by choosing an optimal task size, the efficient work-stealing mechanisms of HPX can overcome the overhead of communication resulting in an overall 1.4 times speedup compared to the baseline MPI version.

97 MATHEMATICS AND COMPUTING↗

Flower‐Type Organized Trade‐Wind Cumulus: A Multi‐Day Lagrangian Large Eddy Simulation Intercomparison Study

Shallow cumulus cloud fields in subtropical marine trade wind environments, particularly over the tropical Atlantic Ocean, show distinct organizational patterns. Among these, Flower‐type clouds are characterized by expansive stratiform cloud patches surrounded by regions of scattered convection. The objectives of this study were (a) to construct a case study of a time period during the EUREC 4 A/ATOMIC field campaign when Flower‐type organization was observed, (b) to evaluate the fidelity of a multi‐model ensemble of large eddy simulations of that case, and (c) to analyze the interaction between cloud and precipitation processes and mesoscale organization in the simulations. The simulations follow a quasi‐Lagrangian trajectory, allowing mesoscale features to develop over time in a domain that follows the boundary‐layer airmass. The results show a broad agreement in simulated thermodynamic properties across different LES codes, with Flower‐type cloud patches appearing within hours of each other. The consensus among models is consistent with observations made during the EUREC 4 A/ATOMIC field campaign on the specific day of interest. The cloud structure reveals three distinct peaks in the joint probability densities of cloud base and cloud top height, with the dominant peak at any given time influenced by the stage of cloud organization. The simulated cloud system evolution reveals consistent occurrence of maxima in liquid water path and rain rate before Flower reaches its maximum length scale. Targeted sensitivity tests reveal a weak relationship between Cloud Droplet Number concentration and the extent/degree/type of organization.

EUREC4A↗

High Performance Computing Facility Operational Assessment, 2012 Oak Ridge Leadership Computing Facility

Oak Ridge National Laboratory’s Leadership Computing Facility (OLCF) continues to deliver the most powerful resources in the United States for open science. At 2.33 petaflops peak performance, the Cray XT Jaguar delivered more than 1.4 billion core hours in calendar year (CY) 2012 to researchers around the world for performing computational simulations relevant to national and energy security; advancing the frontiers of knowledge in physical sciences and areas of biological, medical, environmental, and computer sciences; and providing world-class research facilities for the nation’s science enterprise. OLCF users achieved numerous wide-ranging research accomplishments and technological innovations in 2012. It is not possible to fully summarize the breadth and impact of their productivity within this brief report—OLCF researchers published more than 300 research articles in 2012 alone. Here we identify selected accomplishments that advance the state of the art in science and engineering research and development. The work was recognized through peer-review publications in notable journals such as Science, Nature, and The Proceedings of the National Academy of Sciences (PNAS), among the many noted in this report. Exploration of the nuclear landscape carried out by Innovative and Novel Computational Impact on Theory and Experiment (INCITE) researchers and their theoretical prediction of isotopes were featured in Nature in 2012 (see Section 3.2.2). On the other end of the physical-scale spectrum, researchers executed a 22,000-year transient Earth System Model simulation that explained the misleading lag of carbon dioxide behind Antarctic temperature records and pointed to carbon dioxide’s role in driving global climate change over glacial cycles. This deglaciation study and related work by OLCF users were featured in Nature and PNAS in 2012 (see Section 3.2.3). Other representative achievements by OLCF users include generation of spectroscopic and photometric data for more accurate distance measurements, necessary for planning future National Science Foundation and Department of Energy (DOE) missions such as the Large Synoptic Survey Telescope and the Palomar Transient Factory; calculations to enable the experimental verification of Bose glass; and screening of 2 million compounds against a targeted receptor in a matter of days, as opposed to the months that would be required for computing clusters, creating a vast library of molecular compounds that can be used for future screenings of potential drug candidates. These and other accomplishments are described in Section 3.

OA↗

Lessons from a large-scale systems dynamics modeling project: the example of the biomass scenario model

The biomass scenario model (BSM) is a dynamic model of the biomass-to-biofuels supply chain in the U.S.A., developed during a multi-year analysis effort conducted by the National Renewable Energy Laboratory (NREL), under sponsorship from the United States Department of Energy (DOE) Bioenergy Technologies Office (BETO). The BSM project, which received the 2018 Applications Award by the International System Dynamics Society, has supported collaborative analyses, developed scenarios for industry development and facilitated stakeholder engagement. We summarize insights gained from the BSM project that may be useful to other large-scale dynamic modeling efforts. We summarize the project focus, the analysis process, key outcomes and observations on successful execution of such a product. Key points include the value of a multidisciplinary team with clear roles, engagement of experts and stakeholders, and use and reuse of simple, modular structures. As a result, the overall effort suggests that these practices may aid long-term, team-focused, multi-stakeholder modeling efforts.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

plexos-coad (Plexos Class-Object-Attribute Data manipulation tool)

Clean energy systems including the future power grid are enabled via the development, analysis and application of advanced simulation of complex systems based on large datasets. The ability to handle and enable the simulation of complex systems allows researchers and analysts to address significant problems with greater confidence and greater levels of integrity. Parallel execution of complex systems is paramount to addressing increasing complexity. Programmatic interfaces for software configuration and parallel execution enable handling greater complexity and improving simulation integrity. The Class Object Attribute Data (COAD) software is written as a programmatic interface to the PLEXOS dataset that enables the decomposition of the dataset in time and execution in parallel without loss of integrity. COAD also enable the recomposition of solution datasets that are the output of distributed parallel execution of the core simulator.

Jones, Wes↗

Toward quantitative modeling of silicon phononic thermocrystals

The wealth of technological patterning technologies of deca-nanometer resolution brings opportunities to artificially modulate thermal transport properties. A promising example is given by the recent concepts of 'thermocrystals' or 'nanophononic crystals' that introduce regular nano-scale inclusions using a pitch scale in between the thermal phonons mean free path and the electron mean free path. In such structures, the lattice thermal conductivity is reduced down to two orders of magnitude with respect to its bulk value. Beyond the promise held by these materials to overcome the well-known “electron crystal-phonon glass” dilemma faced in thermoelectrics, the quantitative prediction of their thermal conductivity poses a challenge. This work paves the way toward understanding and designing silicon nanophononic membranes by means of molecular dynamics simulation. Several systems are studied in order to distinguish the shape contribution from bulk, ultra-thin membranes (8 to 15 nm), 2D phononic crystals, and finally 2D phononic membranes. After having discussed the equilibrium properties of these structures from 300 K to 400 K, the Green-Kubo methodology is used to quantify the thermal conductivity. The results account for several experimental trends and models. It is confirmed that the thin-film geometry as well as the phononic structure act towards a reduction of the thermal conductivity. The further decrease in the phononic engineered membrane clearly demonstrates that both phenomena are cumulative. Finally, limitations of the model and further perspectives are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A PARALLEL MONTE CARLO CODE FOR SIMULATING COLLISIONAL N-BODY SYSTEMS

We present a new parallel code for computing the dynamical evolution of collisional N-body systems with up to N {approx} 10{sup 7} particles. Our code is based on the Henon Monte Carlo method for solving the Fokker-Planck equation, and makes assumptions of spherical symmetry and dynamical equilibrium. The principal algorithmic developments involve optimizing data structures and the introduction of a parallel random number generation scheme as well as a parallel sorting algorithm required to find nearest neighbors for interactions and to compute the gravitational potential. The new algorithms we introduce along with our choice of decomposition scheme minimize communication costs and ensure optimal distribution of data and workload among the processing units. Our implementation uses the Message Passing Interface library for communication, which makes it portable to many different supercomputing architectures. We validate the code by calculating the evolution of clusters with initial Plummer distribution functions up to core collapse with the number of stars, N, spanning three orders of magnitude from 10{sup 5} to 10{sup 7}. We find that our results are in good agreement with self-similar core-collapse solutions, and the core-collapse times generally agree with expectations from the literature. Also, we observe good total energy conservation, within {approx}< 0.04% throughout all simulations. We analyze the performance of the code, and demonstrate near-linear scaling of the runtime with the number of processors up to 64 processors for N = 10{sup 5}, 128 for N = 10{sup 6} and 256 for N = 10{sup 7}. The runtime reaches saturation with the addition of processors beyond these limits, which is a characteristic of the parallel sorting algorithm. The resulting maximum speedups we achieve are approximately 60 Multiplication-Sign , 100 Multiplication-Sign , and 220 Multiplication-Sign , respectively.

79 ASTRONOMY AND ASTROPHYSICS↗