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DOE OSTI2015

Investigations of Beam Dynamics Issues at Current and Future Hadron Accelerators (Final Report)

There is a synergy between the fields of Beam Dynamics (BD) in modern particle accelerators and Applied Mathematics (AMa). We have formulated significant problems in BD and have developed and applied tools within the contexts of dynamical systems, topological methods, numerical analysis and scientific computing, probability and stochastic processes, and mathematical statistics. We summarize the three main areas of our AMa work since 2011. First, we continued our study of Vlasov-Maxwell systems. Previously, we developed a state of the art algorithm and code (VM3@A) to calculate coherent synchrotron radiation in single pass systems. In this cycle we carefully analyzed the major expense, namely the integral-over-history (IOH), and developed two approaches to speed up integration. The first strategy uses a representation of the Bessel function J0 in terms of exponentials. The second relies on “local sequences” developed recently for radiation boundary conditions, which are used to reduce computational domains. Although motivated by practicality, both strategies involve interesting and rather deep analysis and approximation theory. As an alternative to VM3@A, we are integrating Maxwell’s equations by a time-stepping method, bypass- ing the IOH, using a Discontinuous Galerkin (DG) method. DG is a generalization of Finite Element and Finite Volume methods. It is spectrally convergent, unlike the commonly used Finite Difference methods, and can handle complicated vacuum chamber geometries. We have applied this in several contexts and have obtained very nice results including an explanation of an experiment at the Canadian Light Source, where the geometry is quite complex. Second, we continued our study of spin dynamics in storage rings. There is much current and proposed activity where spin polarized beams are being used in testing the Standard Model and its modifications. Our work has focused on invariant spin fields (ISFs) and amplitude dependent spin tunes (ADSTs), which are essential for estimating beam polarization. Several algorithms have been developed since the 1980s for computing the ISF, among them the Heinemann- Hoffstaetter method of stroboscopic averaging (SA) which is implemented in the code SPRINT. SA, which computes the ISF by using spin tracking data, can find the ISF to computer precision if it exists and thus can give evidence for existence of the ISF. Central to our work is resolving the ISF conjecture, which says that, off orbital resonance, an ISF exists. Thus Heinemann developed, in his 2010 PhD thesis, a new framework which unifies and generalizes the notions of ISF and ADST by using bundle theory. This lead to a long paper which was a major collaborative effort during the recent cycle. In a nutshell, our bundle approach elegantly unifies the dynamics of spin-1/2 and spin-1 particles, e.g., protons and deuterons. In fact it is well known that these two kinds of dynamics are driven by the same spin transfer matrix and in our approach one sees the deeper reason for this: the spin transfer matrix carries the natural dynamics of a principal bundle whereas the difference between the spin-1/2 and spin-1 dynamics lies in their different geometrical situation, i.e., different underlying associated bundles. Thus one arrives at new results for polarized beams, among them the Invariant Reduction Theorem (IRT) and the Cross Section Theorem (CST). The IRT gives a necessary and sufficient condition for the ISF to exist. The SA technique revealed, 20 years ago, that each ISF can be viewed as a complex agglomerate of spin tracking data. The bundle approach goes one step further by using the IRT and the CST to glue spin tracking data into agglomerates which are candidates for ISFs. We gain insight because the “good” agglomerates, in the presence of an ISF, are very different from the “bad” ones. Finally we mention that the bundle approach has analogies to the approach used in geometrical Yang-Mills theory. Third, we studied X-Ray Free Electron Lasers (FELs), which are electron accelerators producing coherent undulator radiation over a wide range of frequencies from microwaves to x-rays. The photon beams produced in FEL undulators are used to study material samples in biology, material science etc. We developed a mathematical analysis, based on the 6D Lorentz system, of energetic electrons moving through a planar undulator excited by a Maxwell traveling wave field of wavelength λ. Our Method of Averaging perturbation analysis yields non-resonant and near-to-resonant normal form approximations as a function of λ, which we present in two averaging theorems. We prove the theorems in detail, error bounds and giving a tutorial on mathematically rigorous perturbation theory in a context where proofs are easily understood. To our knowledge the planar problem has not been analyzed with the generality here nor has the standard FEL pendulum system, which appears on resonance, been derived with error bounds. In addition to the domains of validity of the normal forms we obtain new insights that require further study, including a more general low gain theory. With a firm foundation in the non-collective case above we are studying the 3D collective case from start up from noise to high gain and saturation. We have formulated the noise start up as a problem of going from the microscopic Klimontovich-Maxwell to the macroscopic Vlasov-Maxwell with a Vlasov correction term. In the 1D setting, we seek an alternative to the phenomenological Vlasov approach which models shot noise by a perturbation on an initial “smooth” density. The 1D wave equation with a Klimontovich source is often the starting point for the 1D FEL high gain theory. We have a new representation of solutions which may lead to new insights.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

A novel coupling of noise reduction algorithms for particle flow simulations

Proper orthogonal decomposition (POD) and its extension based on time-windows have been shown to greatly improve the effectiveness of recovering smooth ensemble solutions from noisy particle data. However, to successfully de-noise any molecular system, a large number of measurements still need to be provided. In order to achieve a better efficiency in processing time-dependent fields, we have combined POD with a well-established signal processing technique, wavelet-based thresholding. In this novel hybrid procedure, the wavelet filtering is applied within the POD domain and referred to as WAVinPOD. The algorithm exhibits promising results when applied to both synthetically generated signals and particle data. In this work, the simulations compare the performance of our new approach with standard POD or wavelet analysis in extracting smooth profiles from noisy velocity and density fields. Numerical examples include molecular dynamics and dissipative particle dynamics simulations of unsteady force- and shear-driven liquid flows, as well as phase separation phenomenon. Simulation results confirm that WAVinPOD preserves the dimensionality reduction obtained using POD, while improving its filtering properties through the sparse representation of data in wavelet basis. This paper shows that WAVinPOD outperforms the other estimators for both synthetically generated signals and particle-based measurements, achieving a higher signal-to-noise ratio from a smaller number of samples. The new filtering methodology offers significant computational savings, particularly for multi-scale applications seeking to couple continuum informations with atomistic models. It is the first time that a rigorous analysis has compared de-noising techniques for particle-based fluid simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Improved measurements of the neutrino mixing angle θ 13 with the Double Chooz detector

The Double Chooz experiment presents improved measurements of the neutrino mixing angle θ13 using the data collected in 467.90 live days from a detector positioned at an average distance of 1050 m from two reactor cores at the Chooz nuclear power plant. Several novel techniques have been developed to achieve significant reductions of the backgrounds and systematic uncertainties with respect to previous publications, whereas the efficiency of the ν¯e signal has increased. The value of θ13 is measured to be sin22θ13=0.090+0.032-0.029 from a fit to the observed energy spectrum. Deviations from the reactor ν¯e prediction observed above a prompt signal energy of 4 MeV and possible explanations are also reported. A consistent value of θ13 is obtained from a fit to the observed rate as a function of the reactor power independently of the spectrum shape and background estimation, demonstrating the robustness of the θ13 measurement despite the observed distortion.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Who is benefiting from the dramatic decline in U.S. cancer mortality? Place-based evidence of disparities in rates of improvement

After decades of increasing cancer mortality, U.S. rates declined from 1991 to 2019, a 32% decrease. we investigated rates of cancer mortality improvement across 2954 counties and selected characteristics associated with mortality improvements. Data was 21,381,009 county-level neoplasm deaths gleaned from death certificates via CDC WONDER. Analytical techniques included GIS and Moran’s I, OLS, GWR models, and trend comparisons. Counties with the greatest improvement (reduction) in cancer mortality tended to be coastal, higher-income, metropolitan locations. OLS model (R 2 = 0.65) indicated that greatest improvements were observed in counties with higher initial mortality ($\beta =.32$) closely followed by percent urban ($\beta =.31$) and median household income ($\beta =.16$). Whereas percent Black residents ($\beta =-.06$), and percent with education beyond high school ($\beta =-.10$) was less associated on outcomes. Highest income counties were the first to experience improvement in cancer mortality, the highest rates of mortality decline, and the greatest reduction in excess deaths. Even though there was significant improvement in cancer mortality nationally, there were variations in the degree of improvement linked to county location, income, and urbanisation. These results underlie the need to expand place-based initiatives designed to advance cancer health and more equitable improvements in cancer mortality outcomes.

developing world↗
DOE OSTI2014

Statistical analysis of content of Cs-137 in soils in Bansko-Razlog region

Statistical analysis of the data set consisting of the activity concentrations of {sup 137}Cs in soils in Bansko–Razlog region is carried out in order to establish the dependence of the deposition and the migration of {sup 137}Cs on the soil type. The descriptive statistics and the test of normality show that the data set have not normal distribution. Positively skewed distribution and possible outlying values of the activity of {sup 137}Cs in soils were observed. After reduction of the effects of outliers, the data set is divided into two parts, depending on the soil type. Test of normality of the two new data sets shows that they have a normal distribution. Ordinary kriging technique is used to characterize the spatial distribution of the activity of {sup 137}Cs over an area covering 40 km{sup 2} (whole Razlog valley). The result (a map of the spatial distribution of the activity concentration of {sup 137}Cs) can be used as a reference point for future studies on the assessment of radiological risk to the population and the erosion of soils in the study area.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Comparative Study of Data-Driven Area Inertia Estimation Approaches on WECC Power Systems

With the increasing integration of inverter-based resources into the power grid, there has been a notable reduction in system inertia, potentially compromising frequency stability. To assess the suitability of existing area inertia estimation techniques for real-world power systems, this paper presents a rigorous comparative analysis of system identification, measurement reconstruction, and electromechanical oscillation-based area inertia estimation methodologies, specifically applied to the large-scale and multi-area WECC 240-bus power system. Comprehensive results show that the system identification-based approach exhibits superior robustness and accuracy relative to its counterparts.

area inertia estimation↗
DOE OSTI2012

ISABELA for effective in situ compression of scientific data: ISABELA FOR EFFECTIVE IN-SITU REDUCTION OF SPATIO-TEMPORAL DATA

Exploding dataset sizes from extreme-scale scientific simulations necessitates efficient data management and reduction schemes to mitigate I/O costs. With the discrepancy between I/O bandwidth and computational power, scientists are forced to capture data infrequently, thereby making data collection an inherently lossy process. Although data compression can be an effective solution, the random nature of real-valued scientific datasets renders lossless compression routines ineffective. These techniques also impose significant overhead during decompression, making them unsuitable for data analysis and visualization, which require repeated data access. To address this problem, we propose an effective method for In situ Sort-And-B-spline Error-bounded Lossy Abatement (ISABELA) of scientific data that is widely regarded as effectively incompressible. With ISABELA, we apply a pre-conditioner to seemingly random and noisy data along spatial resolution to achieve an accurate fitting model that guarantees a ≥0.99 correlation with the original data. We further take advantage of temporal patterns in scientific data to compress data b ≈ 85%, while introducing only a negligible overhead on simulations in terms of runtime. ISABELA significantly outperforms existing lossy compression methods, such as wavelet compression, in terms of data reduction and accuracy. We extend upon our previous paper by additionally building a communication-free, scalable parallel storage framework on top of ISABELA-compressed data that is ideally suited for extreme-scale analytical processing. The basis for our storage framework is an inherently local decompression method (it need not decode the entire data), which allows for random access decompression and low-overhead task division that can be exploited over heterogeneous architectures. Furthermore, analytical operations such as correlation and query processing run quickly and accurately over data in the compressed space. Copyright © 2012 John Wiley & Sons, Ltd.

Computer Science↗
DOE OSTI2017

aCORN: An experiment to measure the electron-antineutrino correlation coefficient in free neutron decay

Here, we describe an apparatus used to measure the electron-antineutrino angular correlation coefficient in free neutron decay. This apparatus employs a novel measurement technique in which the angular correlation is converted into a proton time-of-flight asymmetry that is counted directly, avoiding the need for proton spectroscopy. We present details of the method, apparatus, detectors, data acquisition, and data reduction scheme, along with a discussion of the important systematic effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A High-Quality Workflow for Multi-Resolution Scientific Data Reduction and Visualization

Multi-resolution methods such as Adaptive Mesh Refinement (AMR) can enhance storage efficiency for HPC applications generating vast volumes of data. However, their applicability is limited and cannot be universally deployed across all applications. Furthermore, integrating lossy compression with multi-resolution techniques to further boost storage efficiency encounters significant barriers. To this end, we introduce an innovative workflow that facilitates high-quality multi-resolution data compression for both uniform and AMR simulations. Initially, to extend the usability of multi-resolution techniques, our workflow employs a compression-oriented Region of Interest (ROI) extraction method, transforming uniform data into a multi-resolution format. Subsequently, to bridge the gap between multi-resolution techniques and lossy compressors, we optimize three distinct compressors, ensuring their optimal performance on multi-resolution data. These optimizations can improve the compression ratio of SOTA approaches by up to 3.3× under the same data quality loss. Lastly, we incorporate an advanced uncertainty visualization method into our workflow to understand the potential impacts of lossy compression. Experimental evaluation demonstrates that our workflow achieves significant compression quality improvements.

Wang, Daoce↗
DOE OSTI2013

Search for the Rare Decay $B_s^0 \to \mu^+\mu^-$ at D0

Results of the search for the rare decay B 0 s → μ + μ - using data collected by the D0 detector at the Fermilab Tevatron collider are presented. This analysis covers the full Run II data set, corresponding to approximately 10.4 fb -1 of integrated luminosity in p¯p collisions at a center of mass energy of 1.96 TeV. The analysis used new variables and a multivariate technique to improve the background reduction. After seeing fewer events than expected from background, a new Tevatron best observed limit was set on the branching fraction of the decay at B(B 0 s → μ + μ - ) < 15 x 10 -9 (12 x 10 -9 ) at the 95% (90%) C.L.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

AUTOMATIC LIMIT SURFACE SEARCH FOR PWR TRANSIENTS BY RELAP5-3D/RAVEN CODES

Deterministic safety analysis of nuclear power plants can be improved by applying modern algorithms and codes exploiting machine learning and parallel computing. In this paper we show the application of some of these advanced methodologies for the determination of limit surfaces. A limit surface is an n-dimensional surface describing the plant status, e.g. identifying, as function of selected plant parameters, the boundaries between failed and safe conditions for the core fuel. Using the RELAP5-3D system thermal-hydraulic code coupled to the RAVEN statistical-analysis code, we show how to apply machine-learning algorithms (near-neighbor, support-vector machine, etc.) for determining relevant limit surfaces for PWR station-blackout and loss of offsite power. As a first step, a set of training simulations is run to sample the nuclear power plant responses. Those calculations are used to train a Reduced-Order-Model (ROM), which RAVEN then uses for determining an approximated limit surface. Verification of the guessed limit surface is then automatically performed and calculation is terminated depending by the chosen convergence criteria. The combination of High Performance Computing (HPC) and ROMs allow a remarkable reduction of the time required for the surface determination. RAVEN performs also the automatic data collection of the output of the numerous runs, thus easing the workload of the safety analyst. Finally, using RAVEN “Ensamble Forward” sampling technique, we show how to inform the limit surface calculations with some of the code and input uncertainties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Explainable AI for Multivariate Time Series Pattern Exploration: Latent Space Visual Analytics With Temporal Fusion Transformer and Variational Autoencoders in Power Grid Event Diagnosis

Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and interconnected nature of complex patterns, which hinder the understanding of their underlying physical processes. Existing AI methods often face limitations in interpretability, computational efficiency, and scalability, reducing their applicability in real-world scenarios. This paper proposes a novel visual analytics framework that integrates two generative AI models, Temporal Fusion Transformer (TFT) and Variational Autoencoders (VAEs), to reduce complex patterns into lower-dimensional latent spaces and visualize them in 2D using dimensionality reduction techniques such as PCA, t-SNE, and UMAP with DBSCAN. These visualizations, presented through coordinated and interactive views and tailored glyphs, enable intuitive exploration of complex multivariate temporal patterns, identifying patterns’ similarities and uncover their potential correlations for a better interpretability of the AI outputs. The framework is demonstrated through a case study on power grid signal data, where it identifies multi-label grid event signatures, including faults and anomalies with diverse root causes. Additionally, novel metrics and visualizations are introduced to validate the models and assess the performance, efficiency, and consistency of latent maps generated by VAE, which have been utilized in prior studies for latent space cartography and used as a benchmark in this study, and the emerging TFT architecture under various configurations. These analyses provide actionable insights for model parameter tuning and reliability improvements. Comparative results highlight that TFT achieves shorter run times and superior scalability to diverse time-series data shapes compared to VAE. This work advances fault diagnosis in multivariate time series, fostering explainable AI to support critical system operations.

Explainable AI↗
DOE OSTI2026

Toward memory-efficient melt pool monitoring: a classification framework using event-based imaging and sparse sensing technique

Vision sensors like CMOS and CCD cameras are often used for in-process monitoring of melt pools in laser-based additive and welding processes, but they require transferring large amounts of data and computational processing resources. Event-based neuromorphic imagery, on the other hand, detects only the change in pixel intensity, thus potentially reducing the data amount and latency. With an event imager, this study develops a framework for melt pool condition classification, including image construction, time scale selection, optimal pixel selection, and sparse classification, to achieve a highly memory-efficient scheme. These are based on sparse sensing techniques with singular value decomposition (SVD) and QR pivoting, the two fundamental matrix transformations for linear dimensionality reduction. The framework is then validated by classifying a controlled experiment by exciting various mode shapes of liquid gallium pools of varying depths (3, 6, and 8 mm). At 200 pixels, the classifier can reach overall accuracy of 75%, while at 2000 pixels (0.013% of the total possible pixels), the accuracy is nearly 90% (89.86%). At the same number of pixels, random selection can only achieve 46% and 67%, respectively. The memory savings of the sparsely sampled event data compared to a conventional imager is about 500 times. In addition to performance, implementation and limitations of the framework are also discussed.

42 ENGINEERING↗
DOE OSTI2018

Evidence for an Electronic State at the Interface between the SnO 2 Core and the TiO 2 Shell in Mesoporous SnO 2 /TiO 2 Thin Films

A comparative spectroelectrochemical study of micron thick mesoporous thin films composed of TiO 2 and SnO 2 nanocrystallites was undertaken to identify the location and identity of electronic state(s) in core/shell SnO 2 /TiO 2 films that have emerging applications in energy science. The mesoporous TiO 2 and SnO 2 films were synthesized by sol–gel techniques, and the core/shell material was created by atomic layer deposition of a TiO 2 shell on a SnO 2 core. Electrochemical reduction of these materials in aqueous electrolytes resulted in a blue shift of the fundamental VB → CB absorbance as well as a broad absorbance across the visible region. For SnO 2 , three unique spectra were required to model the potential dependent data while only one unique spectrum was needed to model the corresponding data for SnO 2 /TiO 2 and TiO 2 . Significantly, standard addition of the spectra measured for SnO 2 and TiO 2 did not model that for SnO 2 /TiO 2 . In other words, upon reduction of SnO 2 /TiO 2 there was no spectroscopic evidence for electrons residing in the SnO 2 core or in the TiO 2 shell. Instead, the appearance of a single potential-independent absorption spectrum was observed and attributed to electrons present within an interfacial region between the core and the shell. The charge extraction technique was used to determine that the density of SnO 2 /TiO 2 states was more similar to that of TiO 2 than SnO 2 . The potential onset followed the trend SnO 2 /TiO 2 > SnO 2 > TiO 2 , with TiO 2 closest to the vacuum level and SnO 2 /TiO 2 the furthest away. The implications of these results for solar energy conversion are discussed.

14 SOLAR ENERGY↗
DOE OSTI2018

Active Subspaces for Wind Plant Surrogate Modeling

Understanding the uncertainty in wind plant performance is crucial to their cost-effective design and operation. However, conventional approaches to uncertainty quantification (UQ), such as Monte Carlo techniques or surrogate modeling, are often computationally intractable for utility-scale wind plants because of poor congergence rates or the curse of dimensionality. In this paper we demonstrate that wind plant power uncertainty can be well represented with a low-dimensional active subspace, thereby achieving a significant reduction in the dimension of the surrogate modeling problem. We apply the active sub-spaces technique to UQ of plant power output with respect to uncertainty in turbine axial induction factors, and find a single active subspace direction dominates the sensitivity in power output. When this single active subspace direction is used to construct a quadratic surrogate model, the number of model unknowns can be reduced by up to 3 orders of magnitude without compromising performance on unseen test data. We conclude that the dimension reduction achieved with active subspaces makes surrogate-based UQ approaches tractable for utility-scale wind plants.

17 WIND ENERGY↗
DOE OSTI2013

Categorical Dimensions of Human Odor Descriptor Space Revealed by Non-Negative Matrix Factorization

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain unclear. Here, we use nonnegative matrix factorization (NMF) – a dimensionality reduction technique – to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor dimensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain un- clear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor di- mensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.

Chennubhotla, Chakra↗
DOE OSTI2025

Systematic characterization of unknown compounds via dimensionality reduction of time series

Analysis of ambient aerosols provides valuable insight into particle sources and formation chemistry. However, due to the complexity of atmospheric data and the dynamic nature of aerosol composition, a substantial fraction of data often become discarded by conventional analysis methods. Furthermore, a large fraction of chemical species within those data are unidentifiable due to a lack of matching spectral information, resulting in suboptimal characterization of chemical composition. Previous work has demonstrated techniques for cataloging analytes in a chromatographic dataset by deconvolution of mass spectra, but integration of these analytes throughout a large dataset remains time consuming. Here, we present a method to automatically identify an ion for quantitation for single-ion chromatogram based peak fitting and integration, enabling comprehensive integration of analytes with minimal user interaction. The resulting time series are clustered with a machine-learning based dimensionality reduction technique to systematically investigate the underlying characteristics of the categorized analytes and gain new insights into the chemical composition and physicochemical properties of the unidentifiable analytes. We apply these methods to existing atmospheric datasets collected in Manacapuru, Brazil during the GoAmazon2014/5 campaign to identify new analytes and interpret their variability and transformations in the atmosphere. The analysis results generate 408 time series from cataloged analytes of interest, and the clustering of those time series with spherical k-means results in 8 distinct clusters. We find the analytes form clusters based on their distinct physicochemical properties, demonstrating the method’s ability to systematically identify and selectively filter contaminants and instrumental analytes and characterize the unidentifiable analytes.

54 ENVIRONMENTAL SCIENCES↗