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At least 1,549 records · Page 86

A full-sky, high-resolution atlas of galactic 12 μm dust emission with WISE

We describe our custom processing of the entire Wide-field Infrared Survey Explorer (WISE) 12 μm imaging data set, and present a high-resolution, full-sky map of diffuse Galactic dust emission that is free of compact sources and other contaminating artifacts. The principal distinctions between our resulting co-added images and the WISE Atlas stacks are our removal of compact sources, including their associated electronic and optical artifacts, and our preservation of spatial modes larger than 1.°5. We provide access to the resulting full-sky map via a set of 430 12.°5 × 12.°5 mosaics. These stacks have been smoothed to 15'' resolution and are accompanied by corresponding coverage maps, artifact images, and bit-masks for point sources, resolved compact sources, and other defects. When combined appropriately with other mid-infrared and far-infrared data sets, we expect our WISE 12 μm co-adds to form the basis for a full-sky dust extinction map with angular resolution several times better than Schlegel et al.

79 ASTRONOMY AND ASTROPHYSICS↗

Are X-rays the key to integrated computational materials engineering?

The ultimate dream of materials science is to predict materials behavior from composition and processing history. Owing to the growing power of computers, this long-time dream has recently found expression through worldwide excitement in a number of computation-based thrusts: integrated computational materials engineering, materials by design, computational materials design, three-dimensional materials physics and mesoscale physics. However, real materials have important crystallographic structures at multiple length scales, which evolve during processing and in service. Moreover, real materials properties can depend on the extreme tails in their structural and chemical distributions. This makes it critical to map structural distributions with sufficient resolution to resolve small structures and with sufficient statistics to capture the tails of distributions. For two-dimensional materials, there are high-resolution nondestructive probes of surface and near-surface structures with atomic or near-atomic resolution that can provide detailed structural, chemical and functional distributions over important length scales. Furthermore, there are no nondestructive three-dimensional probes with atomic resolution over the multiple length scales needed to understand most materials.

36 MATERIALS SCIENCE↗

TH-CD-207B-11: Multi-Vendor Phantom Study of CT Lung Density Metrics: Is a Reproducibility of Less Than 1 HU Achievable?

Purpose: To standardize the calibration procedures of CT lung density measurements using low-density reference foams in a phantom, and to demonstrate a reproducibility of less than 1 HU for lung equivalent foam densities measured across CT vendor platforms and protocols. Methods: A phantom study was conducted on CT scanner models from 4 vendors at 100, 120, and 135/140 kVp and 1.5, 3, and 6 mGy dose settings, using a lung density phantom containing air, water, and 3 reference foams (indirectly calibrated) with discrete densities simulating a 5-cm slice of the human chest. Customized segmentation software was used to analyze the images and generate a mean HU and variance for each of the density for the 22 vendor/protocols. A 3-step calibration process was devised to remove a scanner-dependent parameter using linear regression of the HU value vs the relative electron density. The results were mapped to a single energy (80 keV) for final comparison. Results: The heterogeneity across vendor platforms for each density assessed by a random effects model was reduced by 50% after re-calibration, while the standard deviation of the mean HU values also improved by about the same amount. The 95% CI of the final HU value was within +/−1 HU for all 3 reference foam densities. For the backing lung foam in the phantom (served as an “unknown”), this CI is +/− 1.6 HU. The kVp and dose settings did not appear to have significant contributions to the variability. Conclusion: With the proposed calibration procedures, the inter-scanner reproducibility of better than 1 HU is demonstrated in the current phantom study for the reference foam densities, but not yet achieved for a test density. The sources of error are being investigated in the next round of scanning with a certified Standard Reference Material for direct calibration. Fain: research funding from GE Healthcare to develop pulmonary MRI techniques. Hoppel: employee of Toshiba Medical Research Institute USA/financial interest with GE Healthcare. M. Fuld: employee of Siemens Healthcare for medical device equipment and software. This project is supported partially by RSNA QIBA Concept Award (Fain), NIH/NIBIB, HHSN268201300071C (Y).

60 APPLIED LIFE SCIENCES↗

Strategy for the Identification of an INL Comprehensive Utility Corridor

This report documents the strategy developed to identify a comprehensive utility corridor (CUC) on the Idaho National Laboratory (INL) Site. The strategy established the process for which the Campus Development Office will evaluate land management issues. It is a process that uses geographical information system geospatial technology to layer critical INL mission information in a way that thorough evaluations can be conducted and strategies developed. The objective of the CUC Project was to develop a process that could be implemented to identify potential utility corridor options for consideration. The process had to take into account all the missions occurring on the INL and other land-related issues. The process for developing a CUC strategy consists of the following four basic elements using geographical information system capabilities: 1. Development of an INL base layer map; this base layer map geospatially references all stationary geographical features on INL and sitewide information. 2. Development of current and future mission land-use need maps; this involved working with each directorate to identify current mission land use needs and future land use needs that project 30 years into the future. 3. Development of restricted and potential constraint maps; this included geospatially mapping areas such as wells, contaminated areas, firing ranges, cultural areas, ecological areas, hunting areas, easement, and grazing areas. 4. Development of state highway and power line rights of way map; this included geospatially mapping rights-of-way along existing state highways and power lines running through the INL that support INL operations. It was determined after completing and evaluating the geospatial information that the area with the least impact to INL missions was around the perimeter of the INL Site. Option 1, in this document, identifies this perimeter; however, it does not mean the entire perimeter is viable. Many places along the perimeter corridor cannot be used or are not economically viable. Specific detailed studies will need to be conducted on a case-by-case basis to clearly identify which sections along the perimeter can and cannot be used. Option 2, in this document, identifies areas along existing highways that could be a viable option. However, discussions would have to take place with the State of Idaho to use their easement as part of the corridor and mission impact would need to be evaluated if a specific request was made to the Department of Energy, Idaho Operations Office. Option 3, in this document, is a combination of Options 1 and 2. This option provides the most flexibility to minimize impacts to INL missions. As with the other two options, discussions and agreements with the State of Idaho would be needed and any specific route would need to be thoroughly evaluated for impact, implementation, and operability beyond just a strategy.

99 GENERAL AND MISCELLANEOUS↗

Hints of a rotating spiral structure in the innermost regions around IRC +10216

The Atacama Large Millimeter/submillimeter Array is allowing us to study the innermost regions of the circumstellar envelopes of evolved stars with unprecedented precision and sensitivity. Key processes in the ejection of matter and dust from these objects occur in their inner zones. In this work, we present sub-arcsecond interferometric maps of transitions of metal-bearing molecules toward the prototypical C-rich evolved star IRC +10216. While Al-bearing molecules seem to be present as a roughly spherical shell, the molecular emission from the salts NaCl and KCl presents an elongation in the inner regions with a central minimum. In order to accurately analyze the emission from the NaCl rotational lines, we present new calculations of the collisional rates for this molecule based on new spectroscopic constants. The most plausible interpretation for the spatial distribution of the salts is a spiral with a NaCl mass of 0.08 M{sub ⊙}. Alternatively, a torus of gas and dust would result in structures similar to those observed. From the torus scenario we derive a mass of ∼1.1 × 10{sup −4} M{sub ⊙}. In both cases, the spiral and the torus, the NaCl structure presents an inner minimum of 27 AU. In the case of the torus, the outer radius is 73 AU. The kinematics of both the spiral and the torus suggests that they are slowly expanding and rotating. Alternative explanations for the presence of the elongation are explored. The presence of these features only in KCl and NaCl might be a result of their comparatively high dipole moment with respect to the Al-bearing species.

79 ASTRONOMY AND ASTROPHYSICS↗

Interpreting and Accelerating Transformers for Jet Tagging

Attention-based transformers are ubiquitous in machine learning applications from natural language processing to computer vision. In high energy physics, one central application is to classify collimated particle showers in colliders based on the particle of origin, known as jet tagging. In this work, we study the interpretatbility and prospects for acceleration of Particle Transformer (ParT), a state-of-the-art model, leverages particle-level attention to improve jet-tagging performance. We analyzing ParT's attention maps and particle-pair correlations in the eta-phi plane, revealing intriguing features, such as a binary attention pattern that identifies critical substructure in jets. These insights enhance our understanding of the model's internal workings and learning process and hint at ways to improve its efficiency. Along these lines, we also explore low-rank attention, attention alternatives, and dynamic quantization to accelerate transformers for jet tagging. With quantization, we achieve a 50% reduction in model size and a 10% increase in inference speed without compromising accuracy. These combined efforts enhance both the performance and the interpretability of transformers in high-energy physics, opening avenues for more efficient and physics-driven model designs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sci-Thur PM - Colourful Interactions: Highlights 04: A Fast Quantitative MRI Acquisition and Processing Pipeline for Radiation Treatment Planning and Simulation

MRI-only Radiation Treatment Planning (RTP) is becoming increasingly popular because of a simplified work-flow, and less inconvenience to the patient who avoids multiple scans. The advantages of MRI-based RTP over traditional CT-based RTP lie in its superior soft-tissue contrast, and absence of ionizing radiation dose. The lack of electron-density information in MRI can be addressed by automatic tissue classification. To distinguish bone from air, which both appear dark in MRI, an ultra-short echo time (UTE) pulse sequence may be used. Quantitative MRI parametric maps can provide improved tissue segmentation/classification and better sensitivity in monitoring disease progression and treatment outcome than standard weighted images. Superior tumor contrast can be achieved on pure T{sub 1} images compared to conventional T{sub 1}-weighted images acquired in the same scan duration and voxel resolution. In this study, we have developed a robust and fast quantitative MRI acquisition and post-processing work-flow that integrates these latest advances into the MRI-based RTP of brain lesions. Using 3D multi-echo FLASH images at two different optimized flip angles (both acquired in under 9 min, and 1mm isotropic resolution), parametric maps of T{sub 1}, proton-density (M{sub 0}), and T{sub 2}{sup *} are obtained with high contrast-to-noise ratio, and negligible geometrical distortions, water-fat shifts and susceptibility effects. An additional 3D UTE MRI dataset is acquired (in under 4 min) and post-processed to classify tissues for dose simulation. The pipeline was tested on four healthy volunteers and a clinical trial on brain cancer patients is underway.

60 APPLIED LIFE SCIENCES↗

Optical wavelength conversion of quantum states with optomechanics

An optomechanical interface that converts quantum states between optical fields with distinct wavelengths is proposed. A mechanical mode couples to two optical modes via radiation pressure and mediates the quantum state mapping between the two optical modes. A sequence of optomechanical {pi}/2 pulses enables state-swapping between optical and mechanical states, as well as the cooling of the mechanical mode. Theoretical analysis shows that high-fidelity conversion can be realized for states with small photon numbers in systems with experimentally achievable parameters. The pulsed conversion process also makes it possible to maintain high conversion fidelity at elevated bath temperatures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SPATIAL VARIATIONS OF PAH PROPERTIES IN M17SW REVEALED BY SPITZER /IRS SPECTRAL MAPPING

We present Spitzer /IRS mid-infrared spectral maps of the Galactic star-forming region M17 as well as IRSF/SIRIUS Br γ and Nobeyama 45 m/FOREST {sup 13}CO ( J = 1–0) maps. The spectra show prominent features due to polycyclic aromatic hydrocarbons (PAHs) at wavelengths of 6.2, 7.7, 8.6, 11.3, 12.0, 12.7, 13.5, and 14.2 μ m. We find that the PAH emission features are bright in the region between the H ii region traced by Br γ and the molecular cloud traced by {sup 13}CO, supporting that the PAH emission originates mostly from photo-dissociation regions. Based on the spatially resolved Spitzer /IRS maps, we examine spatial variations of the PAH properties in detail. As a result, we find that the interband ratio of PAH 7.7 μ m/PAH 11.3 μ m varies locally near M17SW, but rather independently of the distance from the OB stars in M17, suggesting that the degree of PAH ionization is mainly controlled by local conditions rather than the global UV environments determined by the OB stars in M17. We also find that the interband ratios of the PAH 12.0 μ m, 12.7 μ m, 13.5 μ m, and 14.2 μ m features to the PAH 11.3 μ m feature are high near the M17 center, which suggests structural changes of PAHs through processing due to intense UV radiation, producing abundant edgy irregular PAHs near the M17 center.

79 ASTRONOMY AND ASTROPHYSICS↗

Geothermal Play-Fairway Analysis of Washington State Prospects: Final Report

The Washington State Geothermal Play-Fairway Analysis overcomes the exploration challenges posed by dense vegetation, glacial deposits, and extreme precipitation. The geothermal play-fairways we target are locations where heat, permeability, and saturated porosity are present in sufficient volume to provide adequate heat exchange at depths accessible by modern drilling technology. The three study areas lie along the Cascade Range magmatic arc and are near Mount Baker, Mount St. Helens, and the Wind River Valley. The seven-year project is divided into three phases. In Phase 1 we build on a previous statewide assessment of geothermal resources and develop an initial modeling approach. The results are a series of favorability, uncertainty, and risk maps for three targeted study areas. Based on these initial results, we collect new geologic and geophysical data to further refine our modeling and reduce exploration uncertainty in Phase 2. We improve the modeling method to handle the new data and update the favorability, uncertainty, and risk maps. We also update the conceptual geothermal resource models. In Phase 3 we validate our modeling approach by drilling two temperature-gradient holes and collecting and analyzing core, image logs, and new geochemistry. Our modeling approach improves on an earlier statewide method through a more-rigorous and detailed assessment of heat and permeability. Permeability potential is assessed through geomechanical modeling of the deformation that can generate and maintain reservoir porosity and permeability. Metrics to inform heat potential include temperature-gradient wells, which are sparse in Washington; proximity of Quaternary volcanic vents and young intrusive rock; spring temperature; and reservoir temperature inferred from geothermometry. We weight the individual components using an expert-guided approach known as the Analytical Hierarchy Process. During Phase 2 we also develop a fluid-filled fracture model, and an infrastructure model that helps to delineate areas which are more favorable for geothermal development based on proximity to transmission lines, elevation, land ownership and use restrictions, and availability of process water. New geologic and geophysical data is collected during Phase 2 in each of our three main study areas. At Mount Baker and north of Mount St. Helens we conduct 1:24,000-scale geologic mapping and lidar analysis to better constrain the location and character of surface faults; detailed mapping in the Wind River Valley was completed just prior to the start of this project. Ages of intrusive rocks are determined with 40 Ar/ 39 Ar geochronology, though all of our samples are Miocene or older. We collect ground based gravity observations (a total of 1,580 new stations) in all of our study areas and ground-based magnetic lines (a total of 93 km) at Mount Baker. These data are combined with existing gravity and aeromagnetic data and used to constrain fault locations and geometry. Two to three cross sections are constructed at each study area using the mapped surface geology and forward-modeling of the gravity and magnetic data; these cross sections form the basis for our updated conceptual models. We collect magnetotelluric surveys at Mount Baker and Mount St. Helens and these data are inverted to form a resistivity model from the surface to about 10 km depth; each model shows conductive zones that can be interpreted as upwelling geothermal fluids. At Mount St. Helens we deploy a passive seismic array and use the newly detected events to refine the location of the Saint Helens seismic zone. We also employ ambient-noise tomography to develop a detailed seismic-velocity model for the study area and use this model to help constrain our cross sections and conceptual model. Based on the new data collected during Phase 2—and our updated models—we develop a campaign of temperature-gradient holes and core analysis to validate our modeling in Phase 3. Drill hole MB76-31 is located near Little Park Creek, 11 km west-southwest of the summit of Mount Baker, and is 1,471 ft deep. About 410 ft of core from the lower portion of the hole—and image logs from ~175 ft below ground surface to the bottom—are collected and analyzed. Water samples are collected and processed for geothermometry. Drill hole MSH17-24 is located along upper Schultz Creek, 16 km north-northeast of Mount St. Helens and has core from 470 ft to the bottom at 1,053 ft. We did not collect image logs due to borehole stability concerns, but water samples are collected and analyzed for geothermometry. Repeat temperature-gradient measurements are made at both sites and thermal conductivity is measured from core samples. At MB76-31, the equilibrated temperature gradient of 64°C/km and calculated heat flow of 141–159 mW/m 2 is more than twice the regional average. Detailed mapping and analysis of the core, coupled with correlation to the image logs, indicates a history of permeability generation consistent with our predictions of high permeability. Because the site has high favorability in the Phase 2 model, we consider the results a positive validation of the modeling. At site MSH17-24, the equilibrated temperature gradient of ~15°C/km and calculated heat flow of 41–43 mW/m 2 are similar to regional. Geochemical analysis of the water samples indicates a meteoric source without any geothermal component. Detailed outcrop-based mapping of fault exposures near the drill site and analysis of image logs from nearby boreholes indicates a history of permeability generation consistent with our predictions. Because the site has low favorability in the Phase 2 model, we consider the results a positive validation of the modeling. Together, the two sites provide a reasonably positive validation of the Phase 2 modeling and should encourage future use of this modeling approach.

15 GEOTHERMAL ENERGY↗

Inspection design using 2D phased array, TFM and cueMAP software

A simulation suite, cueMAP, has been developed to facilitate the design of inspection processes and sparse 2D array configurations. At the core of cueMAP is a Total Focusing Method (TFM) imaging algorithm that enables computer assisted design of ultrasonic inspection scenarios, including the design of bespoke array configurations to match the inspection criteria. This in-house developed TFM code allows for interactive evaluation of image quality indicators of ultrasonic imaging performance when utilizing a 2D phased array working in FMC/TFM mode. The cueMAP software uses a series of TFM images to build a map of resolution, contrast and sensitivity of imaging performance of a simulated reflector, swept across the inspection volume. The software takes into account probe properties, wedge or water standoff, and effects of specimen curvature. In the validation process of this new software package, two 2D arrays have been evaluated on 304n stainless steel samples, typical of the primary circuit in nuclear plants. Thick section samples have been inspected using a 1MHz 2D matrix array. Due to the processing efficiency of the software, the data collected from these array configurations has been used to investigate the influence sub-aperture operation on inspection performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum states for quantum processes: A toy model for ammonia inversion spectra

Chemical transformations are viewed here as quantum processes modulated by external fields, that is, as shifts in reactant to product amplitudes within a quantum state represented by a linear (coherent) superposition of electronuclear basis functions; their electronic quantum numbers identify the ''chemical species.'' This basis set can be mapped from attractors built from a unique electronic configurational space that is invariant with respect to the nuclear geometry. In turn, the quantum numbers that label these basis functions and the semiclassical potentials for the electronic attractors may be used to derive reaction coordinates to monitor progress as a function of the applied field. A generalization of Feynman's three-state model for the ammonia inversion process illustrates the scheme; to enforce symmetry for the entire inversion process model and ensure invariance with respect to nuclear configurations, the three attractors and their basis functions are computed with a grid of fixed floating Gaussian functions. The external-field modulation of the effective inversion barrier is discussed within this conceptual approach. This analysis brings the descriptions of chemical processes near modern technologies that employ molecules to encode information by means of confinement and external fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

GPU-based Scalable Volumetric Reconstruction for Multi-view Stereo

We present a new scalable volumetric reconstruction algorithm for multi-view stereo using a graphics processing unit (GPU). It is an effectively parallelized GPU algorithm that simultaneously uses a large number of GPU threads, each of which performs voxel carving, in order to integrate depth maps with images from multiple views. Each depth map, triangulated from pair-wise semi-dense correspondences, represents a view-dependent surface of the scene. This algorithm also provides scalability for large-scale scene reconstruction in a high resolution voxel grid by utilizing streaming and parallel computation. The output is a photo-realistic 3D scene model in a volumetric or point-based representation. We demonstrate the effectiveness and the speed of our algorithm with a synthetic scene and real urban/outdoor scenes. Our method can also be integrated with existing multi-view stereo algorithms such as PMVS2 to fill holes or gaps in textureless regions.

97 MATHEMATICS AND COMPUTING↗

Snowmass 2021 cross frontier report: Dark matter complementarity

The fundamental nature of Dark Matter is a central theme of the Snowmass 2021 process, extending across all frontiers. In the last decade, advances in detector technology, analysis techniques and theoretical modeling have enabled a new generation of experiments and searches while broadening the types of candidates we can pursue. Over the next decade, there is great potential for discoveries that would transform our understanding of dark matter. In the following, we outline a road map for discovery developed in collaboration among the frontiers. A strong portfolio of experiments that delves deep, searches wide, and harnesses the complementarity between techniques is key to tackling this complicated problem, requiring expertise, results, and planning from all Frontiers of the Snowmass 2021 process.

Boveia, Antonio [The Ohio State Univ., Columbus, O↗

Dark Matter Complementarity (Snowmass 2021 Cross Frontier Report: Extended Version)

The fundamental nature of Dark Matter is a central theme of the Snowmass 2021 process, extending across all frontiers. In the last decade, advances in detector technology, analysis techniques and theoretical modeling have enabled a new generation of experiments and searches while broadening the types of candidates we can pursue. Over the next decade, there is great potential for discoveries that would transform our understanding of dark matter. In the following, we outline a road map for discovery developed in collaboration among the frontiers. A strong portfolio of experiments that delves deep, searches wide, and harnesses the complementarity between techniques is key to tackling this complicated problem, requiring expertise, results, and planning from all Frontiers of the Snowmass 2021 process.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Machine Learning Algorithms for Matching Theories, Simulations, and Observations in Cosmology (Final Project)

The search for simple and elegant equations to explain and predict observable natural phenomena has been a driving force in scientific theory for several centuries. The great successes of Newton's laws, Maxwell's equations, the Schrodinger equation, and the theory of General Relativity have encouraged this perspective, and perhaps a beautiful equation comprising a “theory of everything” remains to be discovered. But now scientists are grappling with systems of ever-increasing complexity, fraught with nonlinearity, and with the quantities of interest often only indirectly observed. Nature may resist a simple description, and the most important discoveries of the next century may be complex theories with countless variables and parameters. The era of big data opens up a promising new approach to scientific discovery in this setting. The predictions of modern theories, even if complex or nonlinear, can be examined through detailed and computationally-intensive simulations that take days or weeks to run and fill petabytes of disk space. The upcoming generation of scientific instruments will provide petabytes of observations at unprecedented resolution and depth. The challenge is to compare data to simulations so as to test theories and identify those that best match the observations. The data are numerous and rich but are subject to noise and various systematic biases. The simulations are large and detailed but are so costly that the effective sample size is small. Moreover, the mapping from data to simulation to the parameters of interest is typically complicated and ill-conditioned. Although these challenges, and the solutions we propose, apply across the sciences, we will ground our efforts by focusing on cosmology. Here, we are truly entering the era of big data in several senses. Ever larger experiments survey larger and larger cosmological volumes, resulting in enormous amounts of pixel data to process and extract the information of cosmological interest. These include large imaging surveys, which collect all the light in broad wavelength ranges over significant fractions of the sky, and spectroscopic surveys, which measure the light as a function of wavelength to map out 3D distances. These experiments are designed to shed light on the big unanswered questions in cosmology. Distilling the petabytes of data into observed quantities for comparison with theory is a daunting task. But these large experiments do not only result in large amounts of data to analyze: if we wish to compare to theories of physics, then we need increasingly extensive predictions for the observed quantities as well, which requires ever-larger cosmological simulations that take substantial -- and at times prohibitive -- computational resources to produce. Our goal is to develop statistical and machine learning methods for using observed and simulated data to advance machine learning with applications cosmology. In particular, we focus our research efforts on the following tasks: The challenge for automated science is that it is computationally impossible and statistically dangerous to consider every possible model in order to find the best one. We will develop Bayesian Optimization based active-learning methods that accelerate both the execution of the simulations and the search for best-fitting parameters. The key idea is to make the simulations adaptive -- across resolutions, time, and parameters -- using the data to search as the simulation runs; Most ML methods operate on simple finite dimensional feature vectors. However, many cosmology and other science applications require ML methods that can operate on more complex objects as inputs or outputs such as functions, distributions, or sets and point clouds. Our goal is to develop efficient ML methods for this problem and demonstrate their applicability in Cosmology, Astrophysics, and other science problems.

79 ASTRONOMY AND ASTROPHYSICS↗

Nondestructive Measurement of Residual Strain in Connecting Rods Using Neutrons

Increasing the strength of materials is effective in reducing weight and boosting structural part performance, but there are cases where the residual strain generated during the process of manufacturing of high-strength materials results in a decline of durability. It is therefore important to understand how the residual strain in a manufactured component changes due to processing conditions. In the case of a connecting rod, because the strain load on the connecting rod rib sections is high, it is necessary to clearly understand the distribution of strain in the ribs. However, because residual strain is generally measured by using X-ray diffractometers or strain gauges, measurements are limited to the surface layer of the parts. Neutron beams, however, have a higher penetration depth than X-rays, allowing for strain measurement in the bulk material. The research discussed within this article consists of nondestructive residual strain measurements in the interior of connecting rods using the Second Generation Neutron Residual Stress Mapping Facility (NRSF2) at Oak Ridge National Laboratory (ORNL), measuring the Fe (211) diffraction peak position of the ferrite phase. The interior strain distribution of the connecting rod, which was prepared under different manufacturing processes, was revealed. By the visualization of interior strains, clear understandings of differences in various processing conditions were obtained. In addition, it is known that the peak width, which is also obtained during measurement, is suggestive of the size of crystallites in the structure; however, the peak width can additionally be caused by microstresses and material dislocations.

36 MATERIALS SCIENCE↗

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗