Propagation of Cross-Section Uncertainties in Criticality Calculations in the Framework of UAM-Phase I Using MCNPX-2.7e and SCALE-6.1

In the framework of the OECD/NEA project on Benchmark for Uncertainty Analysis in Modeling (UAM) for Design, Operation, and Safety Analysis of LWRs, several approaches and codes are being used to deal with the exercises proposed in Phase I, “Specifications and Support Data for Neutronics Cases.” At UPM, our research group treats these exercises with sensitivity calculations and the “sandwich formula” to propagate cross-section uncertainties. Two different codes are employed to calculate the sensitivity coefficients of to cross sections in criticality calculations: MCNPX-2.7e and SCALE-6.1. The former uses the Differential Operator Technique and the latter uses the Adjoint-Weighted Technique. In this paper, the main results for exercise I-2 “Lattice Physics” are presented for the criticality calculations of PWR. These criticality calculations are done for a TMI fuel assembly at four different states: HZP-Unrodded, HZP-Rodded, HFP-Unrodded, and HFP-Rodded. The results of the two different codes above are presented and compared. The comparison proves a good agreement between SCALE-6.1 and MCNPX-2.7e in uncertainty that comes from the sensitivity coefficients calculated by both codes. Differences are found when the sensitivity profiles are analysed, but they do not lead to differences in the uncertainty.

Transvaal & Orange Free State Regions, South Africa, ca. 1899 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Bacon's large-print map of the Transvaal and Orange Free State. It was published by G.W. Bacon & Co. ca. 1899. Scale [ca. 1:1,900,000]. Covers also Swaziland, Lesotho, and portions of Botswana, Zimbabwe, and Mozambique.The image inside the map neatline is georeferenced to the surface of the earth and fit to the Africa Sinusoidal projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial and administrative boundaries, roads, railroads, shoreline features, and more. Relief shown by shading and spot heights. Includes also insets: "Map showing the routes from England and India to South Africa", "Environs of Cape Town", "Lorenço Marquez [and vicinity]", 'South Africa" and "Durban and Port Natal".This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Jamaica, 1763 (Image 1 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: This map of the island of Jamaica; laid down from the papers and under the direction of Henry Moore, Esqr.; His Majesty's Lieutenant Governor and Commander in Chief of that island, in the years 1756, 57, 58, 59, 60 & 61; & from a great number of actual surveys performed by the publishers is humbly inscribed by his lordship's most obedient & most humble servants, Thos. Craskell, engineer, Jas. Simpson, surveyor. It was published by D. Fournier in 1763. Scale [ca 1:200,000]. This layer is image 1 of 4 total images of the four sheet map, representing the southwest portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the Jamaica Grid projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as towns, villages, and other human settlements, roads, drainage, selected buildings, ground cover, shoreline features, and more. Relief shown pictorially. Includes also illustrations.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

County of Cornwall, Jamaica, 1763 (Image 1 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: This map of the county of Cornwall, in the island of Jamaica; laid down from the papers, under the direction of, Henry Moore, Esqr., His Majesty's Lieutenant Governor, and Commander in Chief of that island, in the years 1756, 57, 58, 59, 60 & 61, & from a great number of actual surveys performed by the publishers is humbly inscribed by his lordship's most obedient & humble servants, Thos. Craskell, engineer, Jas. Simpson, surveyor. It was published by D. Fournier in 1763. Scale [ca. 1:95,000]. This layer is image 1 of 4 total images of the four sheet source map, representing the southwest portion of the map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Jamaica Grid projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as towns, villages, and other human settlements, roads, parish boundaries, drainage, selected buildings and names of landowners, ground cover, shoreline features, shoals, channels, anchorage points, and more.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

County of Middlesex, Jamaica, 1763 (Image 1 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: This map of the county of Middlesex in the island of Jamaica; laid down from the papers, and under the direction of Henry Moore, Esqr., His Majesty's Lieutenant Governor and Commander in Chief of that island, in the years 1756, 57, 58, 60, & 61 and from a great number of actual surveys performed by the publishers is humbly inscribed by his lordship's most obedient & most humble servants, Thos. Craskell, engineer, Jas. Simpson, surveyor. It was published by D. Fournier in 1763. Scale [ca. 1:95,000]. The layer is image 1 of 4 total images of the four sheet map, representing the southeast portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the Jamaica Grid projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as towns, villages, and other human settlements, roads, parish boundaries, drainage, selected buildings and names of landowners, ground cover, shoreline features, shoals, channels, anchorage points, and more.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

County of Surrey, Jamaica, 1763 (Sheet 3 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: This map of the county of Surry in the island of Jamaica; laid down from the papers and under the direction of Henry Moore, Esqr., His Majesty's Lieutenant Governor and Commander in Chief of that island, in the years 1756, 57, 58, 59, 60 & 61, & from a great number of actual surveys performed by the publishers is humbly inscribed, by his most obedient and humble servants, Thos. Craskell, engineer, Jas. Simpson, surveyor. It was published by D. Fournier in 1763. The layer is image 3 of 4 total images of the four sheet map, representing the southwest portion of the map. Scale ca. 1:100,000. Covers County of Surrey, Jamaica. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Jamaica Grid projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, cities and other human settlements, parish boundaries, shoreline features, plantations, and more. Includes also illustrations.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

County of Surrey, Jamaica, 1763 (Sheet 4 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: This map of the county of Surry in the island of Jamaica; laid down from the papers and under the direction of Henry Moore, Esqr., His Majesty's Lieutenant Governor and Commander in Chief of that island, in the years 1756, 57, 58, 59, 60 & 61, & from a great number of actual surveys performed by the publishers is humbly inscribed, by his most obedient and humble servants, Thos. Craskell, engineer, Jas. Simpson, surveyor. It was published by D. Fournier in 1763. The layer is image 4 of 4 total images of the four sheet map, representing the northwest portion of the map. Scale ca. 1:100,000. Covers County of Surrey, Jamaica. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Jamaica Grid projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, cities and other human settlements, parish boundaries, shoreline features, plantations, and more. Includes also illustrations.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Coast, North Africa, Tunisia and Algeria, 1829 (Image 2 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte comparée des régences d'Alger et de Tunis, dressée par le Chev. Lapie, Géographe du Roi ; les noms anciens ont été revus par ... Hase ; les noms arabes par ... Taubert ; gravé par Flahaut ; écrit par Lallemand. It was published by Chez Ch. Picquet, Quai Conti, no. 17 in 1829. Scale [ca. 1:1,632,653], 16 km=9.8 cm. This layer is image 2 of 2 total images of the two sheet source map, representing the eastern portion of the map. Covers the coast of North Africa including Tunisia, Algeria and portions of Morocco and Libya. Map in French. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Europe Lambert Conformal Conic coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, roads, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 3 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 3 of 9 total images of the nine sheet source map, representing the southeast portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 4 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 4 of 9 total images of the nine sheet source map, representing the central north portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 5 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 5 of 9 total images of the nine sheet source map, representing the central portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 6 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 6 of 9 total images of the nine sheet source map, representing the central south portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 7 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 7 of 9 total images of the nine sheet source map, representing the northwest portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 8 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 8 of 9 total images of the nine sheet source map, representing the central west portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Florence, Italy, ca. 1690 (Image 9 of 9) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Nova pvlcherrimaae civitatis Florentiaae topographia accuratissime delineata. It was published by Gio. Iacomo de Rossi ca. 1690. Scale ca. 1:24,000. This layer is image 9 of 9 total images of the nine sheet source map, representing the southwest portion of the map. Map in Latin.The image inside the map neatline is georeferenced to the surface of the earth and fit to the European Datum 1950, Universal Transverse Mercator (UTM) Zone 32N projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, built-up areas and selected buildings, fortifications, ground cover, and more. Relief and selected features shown pictorially.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.