A stochastic description of pH within nanoscopic water pools
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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SEARCH · Engineering Papers
Results for “distributed analytics”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Imaging plant metabolism in situ
Abstract Mass spectrometry imaging (MSI) has emerged as an invaluable analytical technique for investigating the spatial distribution of molecules within biological systems. In the realm of plant science, MSI is increasingly employed to explore metabolic processes across a wide array of plant tissues, including those in leaves, fruits, stems, roots, and seeds, spanning various plant systems such as model species, staple and energy crops, and medicinal plants. By generating spatial maps of metabolites, MSI has elucidated the distribution patterns of diverse metabolites and phytochemicals, encompassing lipids, carbohydrates, amino acids, organic acids, phenolics, terpenes, alkaloids, vitamins, pigments, and others, thereby providing insights into their metabolic pathways and functional roles. In this review, we present recent MSI studies that demonstrate the advances made in visualizing the plant spatial metabolome. Moreover, we emphasize the technical progress that enhances the identification and interpretation of spatial metabolite maps. Within a mere decade since the inception of plant MSI studies, this robust technology is poised to continue as a vital tool for tackling complex challenges in plant metabolism.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Generalized master equation for particle transport in binary random media with renewal statistics
Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.
Fluctuations & noise↗
Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach
Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. In this work, facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Ion Trapping Studies and Mitigation Strategies for the EIC ERL-Based Strong Hadron Cooler
An Energy Recovery Linac based strong hadron cooler was previously considered for the Electron-Ion Collider. The required electron beam parameters for variable-energy strong hadron cooling place significant constraints on ion trapping and collective effects. This paper presents initial studies of these constraints through a combination of analytical modelling and numerical simulations of ion production, trapping behaviour, and mitigation strategies. A multi-bunch tracking framework based on ELEGANT with the ionEffects module is used to simulate machine operation over millisecond time scales, corresponding to more than 3 × 10^5 electron bunches. The simulations include modelling of ionisation processes together with transverse electron–ion dynamics, allowing the evolution and accumulation of ions to be investigated. Analytical expressions based on Gaussian beam distributions are used to estimate ion trapping conditions and benchmark the simulation results. A bi-periodic bunch spacing scheme is also investigated as a possible mitigation method by detuning the ion oscillation frequency. These studies provide an initial assessment of ion trapping in the strong hadron cooler and demonstrate possible approaches for reducing beam–ion effects.
Bi, R. [Lancaster University, Cockcroft Institute]↗
STREAM: A Scalable Federated HPC Telemetry Platform
Obtaining and analyzing high performance computing (HPC) telemetry in real time is a complex task that can impact algo- rithmic performance, operating costs, and ultimately scientific outcomes. If your organization operates multiple HPC systems, filesystems, and clusters, telemetry streams can be synthesized in order to ease operational and analytics burden. In order to collect this telemetry, the Oak Ridge Leadership Computing Facility (OLCF) has deployed STREAM (Streaming Telemetry for Resource Events, Analytics, and Monitoring), which is a distributed and high-performance message bus based on Apache Kafka. STREAM collects center-wide performance information and must interface with many sources, including five HPE deployed supercomputers, each with their own Kafka cluster which is managed by HPCM. OLCF Supercomputers and their attached scratch filesystems currently send more than 300 million messages to over 200 topics producing around 1.3 Terabytes per day of telemetry data to STREAM. This paper describes the architectural principles that enable STREAM to be both resilient and highly performant while supporting multiple upstream Kafka clusters and other data sources. It also discusses the design challenges and decisions faced in adapting our existing system- monitoring infrastructure to support the first Exascale computing platform.
Adamson, Ryan↗
Physics-Based Machine Learning Methods for U-235 Forensics Signatures
Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collectedunder structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore,their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distanceto the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensembleof trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fittingobserved in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inversephysical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of thesource strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations ofunderlying regression methods.
Rao, Nageswara↗
Physics-Based Machine Learning Methods for U-235 Forensics Signatures
Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.
Rao, Nageswara↗
Precise measurements of W - and Z -boson transverse momentum spectra with the ATLAS detector using pp collisions at $\sqrt{s} = 5.02$ TeV and 13 TeV
This paper describes measurements of the transverse momentum spectra of W and Z bosons produced in proton–proton collisions at centre-of-mass energies of $\sqrt{s}$ = 5.02 TeV and $\sqrt{s}$ = 13 TeV with the ATLAS experiment at the Large Hadron Collider. Measurements are performed in the electron and muon channels, W → $\ell$$v$ and Z → $\ell$$\ell$ ($\ell$ = e or μ), and for W events further separated by charge. The data were collected in 2017 and 2018, in dedicated runs with reduced instantaneous luminosity, and correspond to 255 and 338 pb -1 at $\sqrt{s}$ = 5.02 TeV and 13 TeV, respectively. These conditions optimise the reconstruction of the W-boson transverse momentum. The distributions observed in the electron and muon channels are unfolded, combined, and compared to QCD calculations based on parton shower Monte Carlo event generators and analytical resummation. The description of the transverse momentum distributions by Monte Carlo event generators is imperfect and shows significant differences largely common to W - , W + and Z production. The agreement is better at $\sqrt{s}$ = 5.02 TeV, especially for predictions that were tuned to Z production data at $\sqrt{s}$ = 7 TeV. Higher-order, resummed predictions based on DYTurbo generally match the data best across the spectra. Distribution ratios are also presented and test the understanding of differences between the production processes.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates
Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework that couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas, and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m s -1 standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.
54 ENVIRONMENTAL SCIENCES↗
Improving the Physical Basis for Updraft Dynamics in Deep Convection Parameterizations
This article presents a new deep convective parameterization that determines cloud characteristics based on a specified cloud size distribution. The vertical profiles of cloud properties are determined by analytic equations, which formulate entrainment with an inverse relationship to cloud width. In line with recent studies of large eddy simulations (LES), cloud widths are assumed to be constant with height and vertical mass flux (M) characteristics of the clouds are therefore regulated by the vertical velocity profile. The parameterization is configured to work with existing cloud base M closure formulations, with the closure predicting the total cloud area rather than the cloud base M directly. Analytic formula are also used to connect the vertical wind shear magnitude to the cloud size distribution, wherein larger shear magnitudes result in more numerous large updrafts than weaker shear magnitudes, which is in line with recent research results. The parameterization is compared against 10 deep convective LES with varying thermodynamic and vertical wind shear profiles. Results show dramatic improvements in the prediction of normalized M, detrainment, and the properties of detrained air over the existing Zhang and McFarlane (1995) scheme. In particular, the new model is able to correctly portray the transition from a bottom-heavy M profile in weakly sheared environments, to a top-heavy M profile in strongly sheared environments.
54 ENVIRONMENTAL SCIENCES↗
Validation of Hadron Mass Correction Schemes in Deep Inelastic Scattering at Low Energy Transfer
One method of describing the quark-gluon of the structure proton relies on factorizing its cross-section into a process-dependent short distance element and an independent long distance element that quantifies the quark and gluon momentum distributions within the proton. This research focuses on validating the kinematic range at which factorization theorems still accurately describe the cross-section, in particular for events that simulate scattering on large momentum quarks, that are sensitive to the details of the color mechanism. In this regime, effects which otherwise scale away at large energies, become non-negligible at low energies. The goal of this research is to assess the viability of an extended version of ?collinear factorization? recently proposed by J. Guerrero and A. Accardi, which includes kinematic corrections at quark level, known as ?hadron mass corrections?, to account for the masses of the quarks and the target. To accomplish this, deep inelastic scattering events are simulated using a realistic model of deep inelastic scattering, in which one may analytically calculate both the structure functions and the quark distribution functions. These simulated experiments are then used to test the viability of the proposed factorization theorem by fitting the quark distributions and comparing these to the analytically calculable ones. It is found that the viability of hadron mass corrections in low energy scattering experiments, such as those at Jefferson Lab, extends beyond the kinematic range suggested by analytic calculations alone, provided that residual higher twist corrections are simultaneously fitted to the data.
Krause, Andrew↗
PipeSight: A High-Performance Computing Platform for Pipeline Integrity Management
The Phase I feasibility study completed as part of this project has led to a number of innovative technologies being developed and has laid the foundation for a successful Phase II effort to commercialize a platform for managing the integrity of pipelines for the damage mechanisms of the new, hybrid-energy based economy. To ground the development efforts and direction of the project, an extensive market research and customer discovery effort was undertaken early in Phase I. Through this effort, a number of pipeline owners and operators were interviewed, and the following key findings were discovered about the pipeline industry: • Small pipeline operators do not have the central engineering groups necessary to perform their own independent analysis of inspection data, but instead rely on summarized tally sheets provided to them by inspection service providers. • The time it takes to go from an inspection to a completed engineering assessment, even for small segments of pipeline, can take anywhere from 30-120 days. During this delay, critical threats can (and have been known to) cause failures. • Uncertainty is often not accounted for in the assessment of pipeline integrity. The tally sheets provided by third-party service providers are almost always deterministic in nature, identifying threats that present a concern only to the current (not the future) integrity of the pipeline. • It is uncommon to apply the latest technologies to perform advanced assessments of damaged pipelines. There is a desire to use more advanced analysis capabilities to assess threats. Many pipeline operators indicated that they would often excavate a pipeline to perform an inspection and find that the damage was not as bad as they anticipated, thus using limited resources unnecessarily. Companies are not consistent in their use of inspection data to determine corrosion rates, and those that do only calculate deterministic corrosion rates. • The industry has prominently relied on time-based inspections but has recently started to transition to risk-based inspections. However, there appears to be no uniform guidance on how to do so while properly accounting for all sources of uncertainty. • Companies are not storing inspection data in a manner that allows for the ready determination of temporal trends. • Predictive maintenance principles and practices are beginning to be used by early adopters • Some pipelines are being re-purposed to transport different process fluids than they were designed for, e.g., H 2 and CO 2 rich process streams to serve the new hybrid-energy based economy, which are presenting new integrity concerns for the existing pipeline network that crisscrosses the United States. As a result of these discoveries, we were able to target the development efforts in Phase I to best serve the needs of the industry. In Phase I, we developed a way to correlate multiple large-scale scans of the pipeline to determine a probabilistic corrosion rate that accounts for all sources of error and uncertainty in the inspection process. This probabilistic corrosion rate can be used to predict the future thickness distribution of the pipe wall. We demonstrate how this analysis may be performed in an analytical fashion and has been implemented in such a manner that it can be readily distributed using GPU computing through integration of the Kokkos programming model. We also make a very novel extension of the analytical corrosion rate model to Bayesian Networks (an explainable AI technique) that can account for non-parametric distributions of corrosion rates. With the predictions made above for the probabilistic corrosion rate and corresponding future distribution of the pipe wall thickness, we can assess the integrity of the pipeline through the use of a probabilistic engineering assessment. We developed a novel screening data analysis approach that can rapidly identify ‘hotspots’ (local thin areas) where the integrity of the pipeline is a concern. Once more, we implemented this screening approach in C++ to leverage GPU computing via the Kokkos programming model. After the critical hotspots are identified, we developed a program that can automatically generate an advanced finite element model of the damaged regions. Since the number of damaged regions that require advanced analysis can number in the thousands, we integrated an open-source container-native workflow engine for orchestrating parallel jobs on the cloud. Initially, these advanced numerical models were only designed to account for loading due to internal pressure. However, in a slight pivot from the initial Phase I proposal, we developed a complete pipe stress analysis program (called Simflex) which can simulate the complete pipeline and its response to thermal expansion, pressure, thermal bowing, weight, wind, earthquake, support displacement, support friction and external forces. This pipe stress analysis program was written generically, to handle any piping system, but contains the features needed to model long pipelines (i.e., it incorporates a model for soil mechanics and can account for the nonlinear boundary conditions necessary to simulate long underground pipelines). This pipe stress analysis program can simulate any segment of the pipeline (simple or complex) under any set of conditions and loads, to determine the supplemental loads (axial forces and bending moments) at the location of damage. This enables the most accurate state of stress to be accounted for in the pipeline, which can prove critical when evaluating the integrity of a damaged region. In the process of developing the technologies to perform the integrity assessment of the pipeline, we also extended one of the industry standard approaches for performing the assessment of local thin areas that extend more in the circumferential direction than the longitudinal direction of the pipeline. This approach was presented to the API 579-1/AS ME FFS-1 steering committee in November 2021 for consideration in the next edition of the industry standard for Fitness-For-Service (expected to be released in 2023). To help pipeline operators make decisions with the results on any integrity assessment, we developed a new approach to the life-cycle management of pipelines which uses a Bayesian Decision Network. The network is designed to help pipeline operators plan and prioritize inspection activities and ultimately make smarter, more cost-effective decisions. The Bayesian approach accounts for all sources of uncertainty and carries them through to the final optimal decisions, providing a probabilistic framework for optimizing inspection intervals. The proof-of-concept networks developed in the feasibility study are complete, verified, and are focused on a subset of the pipeline. To expand this novel approach to the scale necessary for an entire network of pipelines in Phase II, we will leverage the DOE-funded Bengi solver for industrial-scale decision making with Bayesian Networks [22]. Once implemented, we will be able to provide the pipeline industry with a much-needed tool for optimal inspection planning using truly explainable artificial intelligence (XAI). To handle all of these advanced capabilities into a cloud-based platform, the architecture of the Equity Engineering Cloud (EEC) was extended to include Argo Workflows, a framework capable of distributing and managing a massive number of jobs that consume their own resources, such that thousands of serial finite element simulations can be run in parallel. As part of this substantial undertaking, we also integrated Argo Continuous Delivery (CD) into the EEC, to aid with the rapid prototyping and iterations that will be imperative to the success of the PipeSight platform’s Agile development process in Phase II. As part of the pipe stress analysis program, we also developed a custom visualizer that leverages the DOE-funded VTK visualization library. We added custom contouring capabilities and a means for interacting visually with both the inputs and outputs of the pipe stress analysis program. We also developed routines for automating the post-processing of the finite element simulations to determine if any failure criteria are met and to visualize the deformations, stresses and strains in ParaView using the exodus II file format (a subset of netCDF).
24 POWER TRANSMISSION AND DISTRIBUTION↗
Stress due to electric charge density distribution in a dielectric slab
The spatial distribution of electric field due to an imposed electric charge density profile in an infinite slab of dielectric material is derived analytically by integrating Gauss’s law. Various charge density distributions are considered, including exponential and power-law forms. Here, the Maxwell stress tensor is used to compute a notional static stress in the material due to the charge density and its electric field. Characteristics of the electric field and stress distributions are computed for example cases in polyethylene, showing that field magnitudes exceeding the dielectric strength would be required in order to achieve a stress exceeding the ultimate tensile strength.
42 ENGINEERING↗
Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm
In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.
Physics↗
(U) A Theoretical Study of Asay Foil Trajectories (V.02)
We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.
42 ENGINEERING↗
A two-and-a-half dimensional symplectic space-charge solver
The nonlinear space-charge effect plays a significant role in high-intensity accelerators and has been extensively studied using multi-particle tracking methods. In this paper, we present a novel 2.5- dimensional symplectic space-charge solver specifically designed for long beam bunches. We begin by detailing its application to a transverse Gaussian density distribution under open boundary conditions in a straight system, where a semi-analytical expression is derived. We then demonstrate the solver’s adaptation to arbitrary distributions in open space, as well as within rectangular and round conducting pipes. Finally, we discuss the extension of this solver to circular accelerator systems. This study shows that the fast 2.5-dimensional solver can be a good approximation to the fully three-dimensional solver for long bunches in large circular accelerators.
Beam code development & simulation techniques↗
Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm
In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.
Data Analysis, Statistics and Probability (physics↗