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Title: The four-loop $$ \mathcal{N} $$ = 4 SYM Sudakov form factor
A bstract We present the Sudakov form factor in full color $$ \mathcal{N} $$ N = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.  more » « less
Award ID(s):
2013859
PAR ID:
10339131
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
1
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  5. {"Abstract":["This dataset provides high-resolution Kikuchi diffraction patterns and\n associated orientation mapping data collected from both wrought and\n as-built additively manufactured (AM) Inconel 718 superalloys. The dataset\n includes raw electron backscatter diffraction (EBSD) patterns stored as\n .tif images and organized through .up2 metadata files, along with\n processed orientation data in .ang format. These measurements were\n acquired using a high-sensitivity EBSD detector over large scan areas,\n enabling detailed spatial resolution of microstructural features such as\n grain orientations, subgrain boundaries, and processing-induced texture.\n The dataset supports a range of applications, including machine learning\n for pattern recognition and the development of robust indexing algorithms.\n By including both wrought and AM material states, this dataset offers\n valuable insight into the influence of manufacturing route on\n crystallographic texture and cellular dislocation structure in Inconel\n 718, a critical alloy for high-temperature structural applications."],"Methods":["Materials and\n Sample Preparation: Three different nickel-based\n superalloys were used in this study: a wrought recrystallized Inconel 718\n (30 minutes at 1050°C followed by 8 hours at 720°C) with chemical\n composition of (wt.%) Ni – 0.56% Al – 17.31% Fe – 0.14% Co – 17.97% Cr –\n 5.4% Nb + Ta – 1.00% Ti – 0.023% C – 0.0062% N; a 3D-printed Inconel 718\n by DED (as-built) and a dynamically recrystallized Waspalloy\n (heat-treated) characterized by a necklace microstructure. The 3D-printed\n material was produced using a Formalloy L2 Directed Energy Deposition\n (DED) unit utilizing a 650 W Nuburu 450 nm blue laser capable of achieving\n a 400 μm laser spot size. Argon was used as the shielding and carrier gas,\n and the specimen remained in its as-built condition. The chemical\n composition is in wt.%: Ni – 0.45% Al – 18.77% Fe – 0.07% Co – 18.88% Cr –\n 5.08% Nb – 0.96% Ti – 0.036% C – 0.02% Cu - 0.04% Mn - 0.08% Si - 3.04%\n Mo. All samples were machined by EDM as flat dogbone samples of gauge\n section 1 × 3 mm2. All samples were mechanically\n polished using abrasive papers, followed by diamond suspension down to 3\n μm, and were finished using a 50 nm colloidal silica suspension.\n Electron\n BackScatter Diffraction: EBSD measurements were\n performed on a Thermo Fisher Scios 2 Dual Beam FIB-SEM with an EDAX\n OIM-Hikari detector at an accelerating voltage of 20 kV, current of 6.4\n nA, an exposure time of 8.5 ms per diffraction pattern, 12 mm of working\n distance, and a 70° tilt. In total, 3 maps of 1000 × 900 μm were collected\n with a 1 μm step size, and 4 additional maps were collected at 0.1 μm step\n size. These EBSD maps were saved to .ang files and processed using the\n MTEX toolbox1. For each of these maps, SEM signal, confidence index (CI),\n and image quality (IQ) are provided as .tif files. The orientation maps\n are transformed using the inverse pole figure MTEX coloring [2] (given as\n IPF_mtex.jpg) and provided for the X (horizontal), Y (vertical), and Z\n (normal) directions. Additionally, all Kikuchi patterns were saved with no\n binning to 16-bit images under the .up2 format. Based on the diffraction\n patterns, sharpness maps, indicating the diffuseness of Kikuchi bands [3],\n have been constructed using EMSPHINX software [4] and are provided as .tif\n files. The details on the pattern center are provided in the .ang\n file. Kikuchi\n Patterns preprocessing: The Kikuchi patterns were\n originally acquired using 1 × 1 binning at a resolution of 480 × 480\n pixels. For the purpose of data processing, two versions are provided with\n the initial 1 × 1 binning and with a 4 × 4 binning (resulting in a reduced\n resolution of 120 × 120 pixels). Additional .up2 files, referred to as\n "preprocessed", are provided in which the background was\n subtracted and pattern gray values have been rescaled to fill the complete\n 16-bit range (between 0 and 65535). Due to the large size of the raw,\n unbinned data, they are not hosted on Dryad but can be made available upon\n request to the authors. Files\n Provided: The nomenclature of the provided files is\n described below, and a detailed explanation is available in the\n accompanying ReadMe.txt file, formatted according to DRYAD\n recommendations. The labels 718RX, AM718, and Waspalloy correspond to the\n wrought recrystallized Inconel 718, the as-built additively manufactured\n Inconel 718 (produced by DED), and a partially recrystallized Waspalloy,\n respectively. The term 1um refers to maps collected with a spatial\n resolution of 1 um, while 0.1um_1 and 0.1um_2 denote two separate maps\n acquired at 0.1 um resolution. The file labeled sharpness contains\n sharpness maps, as defined in [3], and computed using the EMSPHINX\n software [4]. Files labeled CI, IQ, and SEM represent the Confidence\n Index, Image Quality, and associated SEM maps obtained using MTEX1 and are\n provided as .tif files. Similarly, IPF_X, IPF_Y, and IPF_Z refer to\n inverse pole figure maps along the X (horizontal), Y (vertical), and Z\n (normal) directions and are provided as .jpg files. The file IPF_mtex\n gives the associated inverse pole figure MTEX coloring [1, 2]. 480x480 and\n 120x120 indicate the diffraction pattern resolutions, with the initial\n binning and with the 4 x 4 binning operation, respectively. All the images\n are stored as .up2 files. Files denoted as 120×120_preprocessed include\n the corresponding preprocessed patterns at the 120 x 120 resolution. The\n preprocessing procedure is detailed in the section "Kikuchi Patterns\n preprocessing." File\n format: The .up2 file is a proprietary data format\n used by EDAX/TSL systems to store Kikuchi pattern images and associated\n metadata from electron backscatter diffraction (EBSD) experiments. Each\n .up2 file contains high-resolution diffraction patterns acquired at each\n scan point, typically stored in a compressed or indexed form for efficient\n access. These files are commonly used when raw Kikuchi patterns are\n required for post-processing, including pattern remapping, machine\n learning applications, or simulation-based indexing. In addition to image\n data, .up2 files also include key acquisition parameters such as beam\n voltage, working distance, detector settings, image resolution, and stage\n coordinates, enabling full traceability of each pattern to its spatial\n location in the sample. The .ang file is a widely used text-based format\n for storing processed electron backscatter diffraction (EBSD) data.\n Generated by EDAX/TSL OIM software, it contains orientation mapping\n results after successful indexing of Kikuchi patterns. Each row in an .ang\n file corresponds to a single scan point and includes key information such\n as spatial coordinates (X, Y), Euler angles (Phi1, PHI, Phi2) defining\n crystallographic orientation, image quality (IQ), confidence index (CI),\n phase ID, and other optional metrics (e.g., grain ID or local\n misorientation). The file begins with a header that describes metadata,\n including step size, scan grid type (square or hexagonal), phase\n information, and scanning parameters. .ang files are commonly used for\n downstream analyses such as grain reconstruction, texture analysis, and\n misorientation mapping, and are often imported into visualization tools\n like MTEX toolbox1 or Dream.3D for further processing. The .tif (Tagged\n Image File Format) is a high-fidelity raster image format widely used in\n scientific imaging due to its ability to store uncompressed or losslessly\n compressed image data. In the context of EBSD datasets, .tif files\n typically store individual Kikuchi diffraction patterns collected during a\n scan. When used within a .up2 dataset, each pattern is saved as a separate\n .tif file, preserving the original grayscale intensity distribution\n necessary for accurate post-processing tasks such as reindexing, pattern\n matching, or machine learning-based classification. These images often\n have high bit-depth (e.g., 12-bit or 16-bit grayscale) to retain subtle\n contrast variations in the diffraction bands, which are critical for\n crystallographic orientation determination. The file naming and\n organization are indexed and referenced by the accompanying .up2 metadata\n file to maintain spatial correlation with the scan grid. The .jpg (or\n .jpeg), standing for Joint Photographic Experts Group, file format is a\n commonly used compressed image format designed to store photographic and\n continuous-tone images efficiently. .jpg uses lossy compression, meaning\n some image detail is discarded to significantly reduce file size. This\n makes it suitable for visual display and documentation purposes, but less\n ideal for quantitative image analysis, where preserving original pixel\n intensity values is critical. References:\n Bachmann, F., Hielscher, R. & Schaeben, H.\n Texture analysis with mtex–free and open source software toolbox.\n Solid state phenomena 160, 63–68 (2010).\n Nolze, G. & Hielscher, R. Orientations–perfectly\n colored. Appl. Crystallogr. 49, 1786–1802\n (2016). Wang, F. et al. Dislocation cells in\n additively manufactured metallic alloys characterized by electron\n backscatter diffraction pattern sharpness. Mater.\n Charact. 197, 112673 (2023). EMsoft-org.\n EMSphInx: Spherical indexing software for diffraction patterns. Public\n beta release; GPL-2.0 license. \n Acknowledgments: M.C., H.W., K.V., and J.C.S.\n are grateful for financial support from the Defense Advanced Research\n Projects Agency (DARPA - HR001124C0394). C.B., D.A., and J.C.S.\n acknowledge the NSF (award #2338346) for financial support. This work was\n carried out in the Materials Research Laboratory Central Research\n Facilities, University of Illinois. Carpenter Technology is acknowledged\n for providing the 718 and Waspalloy material. Tresa Pollock, McLean\n Echlin, and James Lamb are acknowledged for their support on the EBSD\n sharpness calculations."],"TechnicalInfo":["# Kikuchi pattern dataset from wrought and as-built additively\n manufactured superalloys Dataset DOI:\n [10.5061/dryad.zcrjdfnr9](10.5061/dryad.zcrjdfnr9) ## Description of the\n data and file structure #### Files Provided: See the Methods section for a\n description of file naming patterns and meaning. #### Folder architecture:\n 718RX: * 1um * 718RX_1um.ang * 718RX_1um_sharpness.tif * 718RX_1um_CI.tif\n * 718RX_1um_IQ.tif * 718RX_1um_SEM.tif * IPF_mtex.jpg *\n 718RX_1um_IPF_X.jpg * 718RX_1um_IPF_Y.jpg * 718RX_1um_IPF_Z.jpg *\n 718RX_1um_480x480.up2 * 718RX_1um_120x120.up2 *\n 718RX_1um_120x120_preprocessed.up2 * 0.1um_1 * 718RX_0.1um_1.ang *\n 718RX_0.1um_1_sharpness.tif * 718RX_0.1um_1_CI.tif * 718RX_0.1um_1_IQ.tif\n * 718RX_0.1um_1_SEM.tif * IPF_mtex.jpg * 718RX_0.1um_1_IPF_X.jpg *\n 718RX_0.1um_1_IPF_Y.jpg * 718RX_0.1um_1_IPF_Z.jpg *\n 718RX_0.1um_1_480x480.up2 * 718RX_0.1um_1_120x120.up2 *\n 718RX_0.1um_1_120x120_preprocessed.up2 * 0.1um_2 * 718RX_0.1um_2.ang *\n 718RX_0.1um_2_sharpness.tif * 718RX_0.1um_2_CI.tif * 718RX_0.1um_2_IQ.tif\n * 718RX_0.1um_2_SEM.tif * IPF_mtex.jpg * 718RX_0.1um_2_IPF_X.jpg *\n 718RX_0.1um_2_IPF_Y.jpg * 718RX_0.1um_2_IPF_Z.jpg *\n 718RX_0.1um_2_480x480.up2 * 718RX_0.1um_2_120x120.up2 *\n 718RX_0.1um_2_120x120_preprocessed.up2 AM718: * 1um * AM718_1um.ang *\n AM718_1um_sharpness.tif * AM718_1um_CI.tif * AM718_1um_IQ.tif *\n AM718_1um_SEM.tif * IPF_mtex.jpg * AM718_1um_IPF_X.jpg *\n AM718_1um_IPF_Y.jpg * AM718_1um_IPF_Z.jpg * AM718_1um_480x480.up2 *\n AM718_1um_120x120.up2 * AM718_1um_120x120_preprocessed.up2 * 0.1um_1 *\n AM718_0.1um_1.ang * AM718_0.1um_1_sharpness.tif * AM718_0.1um_1_CI.tif *\n AM718_0.1um_1_IQ.tif * AM718_0.1um_1_SEM.tif * IPF_mtex.jpg *\n AM718_0.1um_1_IPF_X.jpg * AM718_0.1um_1_IPF_Y.jpg *\n AM718_0.1um_1_IPF_Z.jpg * AM718_0.1um_1_480x480.up2 *\n AM718_0.1um_1_120x120.up2 * AM718_0.1um_1_120x120_preprocessed.up2 *\n 0.1um_2 * AM718_0.1um_2.ang * AM718_0.1um_2_sharpness.tif *\n AM718_0.1um_2_CI.tif * AM718_0.1um_2_IQ.tif * AM718_0.1um_2_SEM.tif *\n IPF_mtex.jpg * AM718_0.1um_2_IPF_X.jpg * AM718_0.1um_2_IPF_Y.jpg *\n AM718_0.1um_2_IPF_Z.jpg * AM718_0.1um_2_480x480.up2 *\n AM718_0.1um_2_120x120.up2 * AM718_0.1um_2_120x120_preprocessed.up2\n Waspalloy: * 1um * Waspalloy_1um.ang * Waspalloy_1um_sharpness.tif *\n Waspalloy_1um_CI.tif * Waspalloy_1um_IQ.tif * Waspalloy_1um_SEM.tif *\n IPF_mtex.jpg * Waspalloy_1um_IPF_X.jpg * Waspalloy_1um_IPF_Y.jpg *\n Waspalloy_1um_IPF_Z.jpg * Waspalloy_1um_480x480.up2 *\n Waspalloy_1um_120x120.up2 * Waspalloy_1um_120x120_preprocessed.up2 ##\n Code/software See Methods for recommendations on how to open files."]} 
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