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At least 559 records · Page 31

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

HALOGAS Observations of NGC 4559: Anomalous and Extraplanar H i and its Relation to Star Formation

We use new deep 21 cm H i observations of the moderately inclined galaxy NGC 4559 in the HALOGAS survey to investigate the properties of extraplanar gas. We use TiRiFiC to construct simulated data cubes to match the H i observations. We find that a thick-disk component of scale height ∼2 kpc, characterized by a negative vertical gradient in its rotation velocity (lag) of ∼13 ± 5 km s{sup −1} kpc{sup −1} is an adequate fit to extraplanar gas features. The tilted ring models also present evidence for a decrease in the magnitude of the lag outside R {sub 25}, and a radial inflow of ∼10 km s{sup −1}. We extracted lagging extraplanar gas through Gaussian velocity profile fitting. From both the 3D models and extraction analyses we conclude that ∼10%–20% of the total H i mass is extraplanar. Most of the extraplanar gas is spatially coincident with regions of star formation in spiral arms, as traced by H α and GALEX FUV images, so it is likely due to star formation processes driving a galactic fountain. We also find the signature of a filament of a kinematically “forbidden” H i feature, containing ∼1.4 × 10{sup 6} M {sub ⊙} of H i, and discuss its potential relationship to a nearby H i hole. We discover a previously undetected dwarf galaxy in H i located ∼0.°4 (∼58 kpc) from the center of NGC 4559, containing ∼4 × 10{sup 5} M {sub ⊙}. This dwarf has counterpart sources in SDSS with spectra typical of H ii regions, and we conclude that it is two merging blue compact dwarf galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Effect of Clouds on Shuttle Imaging

This report describes the results of the AMU's task for determining the effect of clouds on optical imaging of the Space Shuttle launch vehicle during its ascent phase from lift-off to Solid Rocket Booster (SRB) Separation. This effort was motivated by Recommendation R3.4-1 from the Columbia Accident Investigation Board Report. The AMU developed a 3-dimensional (3D) model to forecast the probability that at any time from lift-off to SRB separation, at least three of the ascent imaging cameras would have a view of the Shuttle unobstructed by cloud. Because current observational and modeling capabilities do not permit accurate forecasts of cloud morphology and location, the AMU simulated obscuration of the lines-of-sight (LOS) from a network of cameras to the Shuttle by idealized cloud-fields placed randomly within the 3D domain. For each random realization of numerous cloud-field scenarios the number of simultaneous views of the Shuttle was computed from the LOS data between lift-off and SRB separation. The percent of time with 3 simultaneous views was averaged from 100 random realizations of each scenario. Analyses of the percent of time viewable were made to determine its sensitivity to cloud amount, cloud base height, cloud thickness, cloud horizontal dimensions, and an upgrade of the camera network.

Short, David A.↗

Some Observations on the Current Status of Performing Finite Element Analyses

Aerospace structures are complex high-performance structures. Advances in reliable and efficient computing and modeling tools are enabling analysts to consider complex configurations, build complex finite element models, and perform analysis rapidly. Many of the early career engineers of today are very proficient in the usage of modern computers, computing engines, complex software systems, and visualization tools. These young engineers are becoming increasingly efficient in building complex 3D models of complicated aerospace components. However, the current trends demonstrate blind acceptance of the results of the finite element analysis results. This paper is aimed at raising an awareness of this situation. Examples of the common encounters are presented. To overcome the current trends, some guidelines and suggestions for analysts, senior engineers, and educators are offered.

Raju, Ivatury S.↗

Recent Improvement of Measurement Instrumentation to Supervise Nuclear Operations and to Contribute Input Data to 3D Simulation Code - 13289

The CEA has developed many compact characterization tools to follow sensitive operations in a nuclear environment. Usually, these devices are made to carry out radiological inventories, to prepare nuclear interventions or to supervise some special operations. These in situ measurement techniques mainly take place at different stages of clean-up operations and decommissioning projects, but they are also in use to supervise sensitive operations when the nuclear plant is still operating. In addition to this, such tools are often associated with robots to access very highly radioactive areas, and thus can be used in accident situations. Last but not least, the radiological data collected can be entered in 3D calculation codes used to simulate the doses absorbed by workers in real time during operations in a nuclear environment. Faced with these ever-greater needs, nuclear measurement instrumentation always has to involve on-going improvement processes. Firstly, this paper will describe the latest developments and results obtained in both gamma and alpha imaging techniques. The gamma camera has been used by the CEA since the 1990's and several changes have made this device more sensitive, more compact and more competitive for nuclear plant operations. It is used to quickly identify hot spots, locating irradiating sources from 50 keV to 1500 keV. Several examples from a wide field of applications will be presented, together with the very latest developments. The alpha camera is a new camera used to see invisible alpha contamination on several kinds of surfaces. The latest results obtained allow real time supervision of a glove box cleaning operation (for {sup 241}Am contamination). The detection principle as well as the main trials and results obtained will be presented. Secondly, this paper will focus on in situ gamma spectrometry methods developed by the CEA with compact gamma spectrometry probes (CdZnTe, LaBr{sub 3}, NaI, etc.). The radiological data collected is used to quantify the activity of hot spots and can also then be entered in 3D models of nuclear plants to simulate intervention scenarios. Recent developments and results will be presented regarding this. Finally, thanks to a large amount of feedback, the interest of using complementary measurements will be discussed. In fact, the recent use of 3D simulation codes requires very accurate knowledge of nuclear plant radiological data. The use of coupled devices such as imaging devices, (gamma and alpha cameras), gamma spectrometry, dose rate mapping, collimated / un-collimated measurements and many other physical values gives an approach to the radiological knowledge of a process or plant with the lowest possible uncertainty. In line with this, the paper will conclude with the future developments and trials that could be assessed in that field of application. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effective Long-term Monitoring Strategies by Integrating Reactive Transport Models with In situ Geochemical Measurements - 16212

Long-term monitoring of contaminant transport in groundwater is expected to account for a large fraction of future life-cycle cleanup costs at the DOE sites. The Attenuation-Based Remedies in the Subsurface Applied Field Research Initiative (ABRS AFRI) is developing an innovative approach for cost-effective in situ long-term monitoring. The approach is based on strategically adding the measurements of controlling variables (such as pH, redox potential, electrical conductivity, and groundwater level), which control the plume mobility and its spatial and temporal distribution. In situ measurements of these variables - supplemented with a reduced number of standard periodic groundwater samples - are expected to lead to more cost-effective monitoring, and can also serve as an early warning system for detecting unexpected plume migration. The objective of this study is to support the development of such a long-term monitoring approach through the application of advanced computational methods, including (1) statistical data mining and analysis, and (2) three-dimensional flow and reactive chemical transport modeling. We have performed the statistical data analysis of historical and current monitoring data at the Savannah River Site (SRS) F-Area to quantify the correlations between the controlling variables and radioactive contaminant concentrations. In parallel, we have used 3D modeling of flow and contaminant transport to provide the prediction of the contaminant plume evolution. The results of both data analysis and modeling confirmed that the correlations between controlling variables and contaminant concentrations are significant. Modeling results also suggest that the correlation parameters will change in the future, which is important to assess the long-term efficacy of the proposed monitoring approach. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Validation of a Simple RELAP5-3D Point Kinetics Model of the Full-Slotted MARCH Core in TREAT

A simple RELAP5-3D point kinetics model of the TREAT facility was validated using data from three unshaped transients in the MARCH full-slotted core. These transients were initiated with near step insertions of reactivity of about 1.7%, 2.9%, and 3.9%, respectively. The RELAP5-3D calculations were in reasonable agreement with the measured results. The calculated energy depositions were within the scatter of the data or were slightly conservative for all three transients.

97 MATHEMATICS AND COMPUTING↗

Three-dimensional analysis of microbunched electron cooling

Microbunched electron cooling (MBEC, Ratner, ), a special category of coherent electron cooling, has been under consideration as a candidate method for the strong hadron cooling component of the Electron Ion Collider (EIC) at BNL. Most of the theoretical treatments of this scheme so far have been based on simplified models for the key space charge effect in which electrons and/or hadrons are approximated by charged disks. Although such disk-based models provide a flexible tool that captures a good part of the underlying physics, they lack the fidelity and robustness of a rigorous analysis that explicitly treats the hadron and cooler electron beams as collections of point charges. In this paper, we present such a rigorous, three-dimensional (3D) model, both from a theory-based and a simulation perspective. Specifically, we calculate the generalized wakefield (or Green’s function) of the cooling system—a crucial quantity that determines the overall performance—paying special attention to the dependence of the wake on the hadron transverse positions. Additionally, our treatment takes into account previously neglected 3D effects that can cause damping of the plasma oscillations in the amplification section of the cooler, such as focusing and the angular spread of the electron beam. Published by the American Physical Society 2025

43 PARTICLE ACCELERATORS↗

SU-F-E-13: Design and Fabrication of Gynacological Brachytherapy Shielding & Non Shielding Applicators Using Indigenously Developed 3D Printing Machine

Purpose: In this innovative work we have developed Gynecological Brachytherapy shielding & Non Shielding Applicators and compared with the commercially available applicators by using the indigenously developed 3D Printing machine. Methods: We have successfully indigenously developed the 3D printing machine. Which contain the 3 dimensional motion platform, Heater unit, base plate, ect… To fabricate the Gynecological Brachytherapy shielding & non shielding applicators the 3D design were developed in the computer as virtual design. This virtual design is made in a CAD computer file using a 3D modeling program. Separate programme for the shielding & non shielding applicators. We have also provided the extra catheter insert provision in the applicator for the multiple catheter. The DICOM file of the applicator were then converted to stereo Lithography file for the 3D printer. The shielding & Non Shielding Applicators were printed on a indigenously developed 3D printer material. The same dimensions were used to develop the applicators in the acrylic material also for the comparative study. A CT scan was performed to establish an infill-density calibration curve as well as characterize the quality of the print such as uniformity and the infill pattern. To commission the process, basic CT and dose properties of the printing materials were measured in photon beams and compared against water and soft tissue. Applicator were then scanned to confirm the placement of multiple catheter position. Finally dose distributions with rescanned CTs were compared with those computer-generated applicators. Results: The doses measured from the ion Chamber and X-Omat film test were within 2%. The shielded applicator reduce the rectal dose comparatively with the non shielded applicator. Conclusion: As of submission 3 unique cylinders have been designed, printed, and tested dosimetrically. A standardizable workflow for commissioning custom 3D printed applicators was codified and will be reported.

60 APPLIED LIFE SCIENCES↗

System Modeling of the HTTR and Economic Dispatch Model of the Secondary System

High Temperature Gas-cooled Reactors (HTGRs) can be used for the generation of electricity and their process heat can be used to improve the efficiency of chemical processes such as hydrogen production. The JAEA-operated High-Temperature engineering Test Reactor (HTTR-GT/H2) is exploring using the reactor for electricity and hydrogen production. A RELAP5-3D model of the HTTR-GT/H2 secondary system has been developed using design information. The various components and heat exchangers in the secondary system were modeled and results were compared to the design conditions. The results for the sole-power generation mode were shown to fit the design conditions very well. The largest temperature difference was on the order of 7 K, and the largest pressure difference was on the order of 0.05 MPa. The results for the hydrogen cogeneration mode did not match the design conditions nearly as well. The largest temperature difference was about 39 K and the largest pressure difference was about 0.27 MPa at the compressor outlet. The larger differences for the hydrogen cogeneration mode are attributed to the various complex components and the flow being split in the secondary loop. A transient reduction in heat removal capability of the secondary system was investigated. Reactor temperatures are anticipated to rise as a result. The core reactivity response due to this increase in temperature is investigated and is expected to add negative reactivity to the reactor. An economic dispatch model was developed for a nuclear-driven iodine-sulfur cycle system to determine hydrogen sale prices that would make such a system profitable. The study focuses on the development of the economic model and the role that input data plays on final calculated values. It was found that the input electricity prices, whether using historical data or a host of synthetic time histories, produce significantly different breakeven hydrogen sale prices. As such, great care should be used in these economic dispatch analyses to select reasonable input assumptions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Implementing a Stochastic Soot Model in a 3D Domain

In this document a highly detailed stochastic soot model limited to 0D simulations is coupled to 3D domains through the use of a Lagrangian parcel-Eulerian fluid method. Although both the stochastic soot model used and the Lagrangian parcel-Eulerian fluid method have long histories of development, their use, as described in this document, is novel and useful. Previous works significant to the model's development include documents from both the stochastic and simpler soot model genre and the fuel, aerosol, and other particle tracking and Lagrangian parcel-Eulerian fluid genres. Developing the theory behind the model is crucial to its implementation because of the unconventional Lagrangian parcel-Eulerian fluid representation. In fact, the Lagrangian parcel-Eulerian fluid coupling is only a means of simplifying the much more difficult theoretical model. Despite the accompanying assumptions, the complete model is validated from the bottom up and then again in a holistic fashion with promising results. Then the model is used in multiple case studies, showcasing capabilities not had by other models. The optical properties of soot generated in a Spray A simulation are calculated to find measured results are likely overpredicting the mass of soot along the central axis via KL extinction measurements. A thermophoresis submodel that calculates force based on the soot particles' shape is installed to find it has a high influence on the path of the heaviest soot particles. Investigations into the HACA mechanism for soot growth and the effect of syngas on soot in 3D domains are performed with much more detail than has been available before.

Strickland, Tyler↗

Modeling and Simulation of Xe-100-type Pebble Bed Gas-Cooled Reactor with SCALE

The US Department of Energy (DOE) announced the Advanced Reactor Demonstration Program (ARDP) to accelerate the deployment of advanced reactor concepts. Awardees of ARDP funds are expected to demonstrate the operation of an advanced reactor within 7 years of receiving the award. X-Energy’s advanced reactor concept, the Xe-100, was selected as one of two advanced reactor concepts to receive funding to demonstrate the operation of its high-temperature gas-cooled pebble-bed reactor before the end of this decade. As a result of this push to bring advanced reactors to maturation and commercialization, transition and deployment scenario studies are being performed under the Systems Analysis and Integration (SA&I) campaign within the DOE Office of Nuclear Energy (DOE-NE) to evaluate the transition of the current US commercial fleet of light-water reactors (LWRs) to a future fleet of advanced reactors consisting of a mix of ARDP type reactor concepts and advanced LWRs. To accurately evaluate the front- and back-end resource requirements, it is important to perform reactor physics calculations to determine the discharge burnup and isotopic content, fuel residence time, as well as other parameters. For this purpose, a summer project funded by the SA&I campaign allowed for the setup of SCALE models for full-core Xe-100 type high-temperature gas-cooled pebble-bed reactor and a Xe-100 type slice using publicly available information. The core-averaged equilibrium compositions and zone-wise equilibrium compositions for the slice and 3D models, respectively, were obtained following an iterative depletion method developed by Bostelmann et al. using SCALE’s reactor physics sequence TRITON. The slice model was used with TRITON to generate burnup-dependent cross section libraries at different temperatures which can be used with SCALE’s ORIGAMI code to rapidly determine fuel inventory and therefore to perform quick sensitivity studies on parameters such as the pebble location in the core. The SCALE/TRITON transport and depletion calculation for the Xe-100 type slice model indicates that the isotopic concentrations are in good agreement at 1,300 effective full power days (EFPD) for 235 U. An analysis of 236 U results match 239 Pu results would seem to indicate a typographical error in Mulder and Boyes wherein the reported results of 236 U and 239 Pu are reversed. In addition to SCALE/TRITON calculations, a new capability within SCALE/ORIGAMI for the simulation of pebble-bed reactors was used to study the burnup sensitivity with respect to the pebble pathway through the core. The SCALE/ORIGAMI results show that pebbles that travel closer to the reflector for the entire depletion history have a higher burnup than pebbles that travel through the middle of the core because of the higher thermal to fast flux ratio near the reflector. Consequently, a pebble’s burnup is strongly affected by the pebble’s pathway for each pass. Additional phenomena such as temperature distributions in the core and different travel times of the pebbles in the individual radial zones further affect the burnup distribution. The sensitivity of the discharge vector to the pebble pathways taken during each pass can be evaluated in the future using SCALE/ORIGAMI now that the SCALE inputs have been established.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Technical Note: Development of a 3D printed subresolution sandwich phantom for validation of brain SPECT analysis

Purpose: To make an adaptable, head shaped radionuclide phantom to simulate molecular imaging of the brain using clinical acquisition and reconstruction protocols. This will allow the characterization and correction of scanner characteristics, and improve the accuracy of clinical image analysis, including the application of databases of normal subjects. Methods: A fused deposition modeling 3D printer was used to create a head shaped phantom made up of transaxial slabs, derived from a simulated MRI dataset. The attenuation of the printed polylactide (PLA), measured by means of the Hounsfield unit on CT scanning, was set to match that of the brain by adjusting the proportion of plastic filament and air (fill ratio). Transmission measurements were made to verify the attenuation of the printed slabs. The radionuclide distribution within the phantom was created by adding {sup 99m}Tc pertechnetate to the ink cartridge of a paper printer and printing images of gray and white matter anatomy, segmented from the same MRI data. The complete subresolution sandwich phantom was assembled from alternate 3D printed slabs and radioactive paper sheets, and then imaged on a dual headed gamma camera to simulate an HMPAO SPECT scan. Results: Reconstructions of phantom scans successfully used automated ellipse fitting to apply attenuation correction. This removed the variability inherent in manual application of attenuation correction and registration inherent in existing cylindrical phantom designs. The resulting images were assessed visually and by count profiles and found to be similar to those from an existing elliptical PMMA phantom. Conclusions: The authors have demonstrated the ability to create physically realistic HMPAO SPECT simulations using a novel head-shaped 3D printed subresolution sandwich method phantom. The phantom can be used to validate all neurological SPECT imaging applications. A simple modification of the phantom design to use thinner slabs would make it suitable for use in PET.

60 APPLIED LIFE SCIENCES↗

Flooding Capability for River-based Scenarios

This report describes the initial investigation into modeling and simulation tools for application of riverine flooding representation as part of the Risk-Informed Safety Margin Characterization (RISMC) Pathway external hazards evaluations. The report provides examples of different flooding conditions and scenarios that could impact river and watershed systems. Both 2D and 3D modeling approaches are described.

97 MATHEMATICS AND COMPUTING↗

On the explicit versus family solution of the fully diurnal photochemical equations of the stratosphere

The family approach used to solve chemical equations is examined by integrating a heirarchy of versions of a 2D model of stratospheric chemistry and transport on an isentropic surface. Errors of up to 20 percent in radical concentrations can result from the use of a small number of families; the use of more families increases the accuracy of the solutions. The minimum number of families which can be used to provide an accurate solution is discussed, and the parameterization of long-time-scale species is recommended for making the model more efficient. The most pervasive errors are found in calculations of the concentrations of radical species, a problem which can lead to errors in predicting O3 over the long run. Methods for improving the schemes are presented, emphasizing the possibility of producing an improved 3D model.

Austin, John↗

Next Generation Flight Displays Using HTML5

The Human Integrated Vehicles and Environments (HIVE) lab at Johnson Space Center (JSC) is focused on bringing together inter-disciplinary talent to design and integrate innovative human interface technologies for next generation manned spacecraft. As part of this objective, my summer internship project centered on an ongoing investigation in to building flight displays using the HTML5 standard. Specifically, the goals of my project were to build and demo "flight-like" crew and wearable displays as well as create a webserver for live systems being developed by the Advanced Exploration Systems (AES) program. In parallel to my project, a LabVIEW application, called a display server, was created by the HIVE that uses an XTCE (XML (Extensible Markup Language) Telemetry and Command Exchange) parser and CCSDS (Consultative Committee for Space Data System) space packet decoder to translate telemetry items sent by the CFS (Core Flight Software) over User Datagram Protocol (UDP). It was the webserver's job to receive these UDP messages and send them to the displays. To accomplish this functionality, I utilized Node.js and the accompanying Express framework. On the display side, I was responsible for creating the power system (AMPS) displays. I did this by using HTML5, CSS and JavaScript to create web pages that could update and change dynamically based on the data they received from the webserver. At this point, I have not started on the commanding, being able to send back to the CFS, portion of the displays but hope to have this functionality working by the completion of my internship. I also created a way to test the webserver's functionality without the display server by making a JavaScript application that read in a comma-separate values (CSV) file and converted it to XML which was then sent over UDP. One of the major requirements of my project was to build everything using as little preexisting code as possible, which I accomplished by only using a handful of JavaScript libraries. As a side project, I created a model of the HIVE lab and Building 29 using SketchUp. I obtained the floorplans of the building from the JSC Geographic Information Systems (GIS), which were computer-aided design (CAD) files, and imported them into SketchUp. I then took those floorplans and created a 3D model of the building from them. Working in conjunction with the Hybrid Reality lab in Building 32, the SketchUp model was imported into Unreal Engine for use with the HTC Vive. Using the Vive, I was able to interact with the model I created in virtual reality (VR). The purpose of this side project was to be able to visualize potential lab layouts and mockup designs as they are in development in order to finalize design decisions. Pending approval, the model that I created will be used in the Build-As-You-Test: Can Hybrid Reality Improve the SE/HSI Design Process project in the fall. Getting the opportunity to work at NASA has been one of the most memorable experiences of my life. Over the course of my internship, I improved my programming and web development abilities substantially. I will take all the skills and experiences I have had while at NASA back to school with me in the fall and hope to pursue a career in the aerospace industry after graduating in the spring.

Greenwood, Brian↗

3D Crustal Tomography Model of Utah

The ability to accurately locate seismic events is necessary for treaty monitoring. When using techniques that rely on the comparison of observed and predicted travel times to obtain these locations, it is important that the estimated travel times and their estimated uncertainties are also accurate. The methodology of Ballard et al. (2016a) has been used in the past to generate an accurate 3D tomographic global model of compressional wave slowness (the SAndia LoS Alamos 3D tomography model, i.e. SALSA3D). To re-establish functionality and to broaden the capabilities of the method to local distances, we have applied the methodology of Ballard et al. (2016a) to local data in Utah. This report details the results of the initial model generated, including relocations performed using analyst picked mining events at West Ridge Mine and three ground-truth events at Bingham Mine. We were successfully able to generate a feasible tomography model that resulted in reasonable relocations of the mining events.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DAVIS: A direct algorithm for velocity-map imaging system

Here, we report a direct (non-iterative) algorithm to reconstruct the three-dimensional (3D) momentum-space picture of any charged particles collected with a velocity-map imaging system from the two-dimensional (2D) projected image captured by a position-sensitive detector. The technique consists of fitting the measured image with the 2D projection of a model 3D velocity distribution defined by the physics of the light-matter interaction. The meaningful angle-correlated information is first extracted from the raw data by expanding the image with a complete set of Legendre polynomials. Both the particle’s angular and energy distributions are then directly retrieved from the expansion coefficients. The algorithm is simple, easy to implement, fast, and explicitly takes into account the pixelization effect in the measurement.

74 ATOMIC AND MOLECULAR PHYSICS↗