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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Computing Hypergraph Homology in Chapel

In this paper, we discuss our experience in implementing homology computation, in particular Betti number calculation in Chapel hypergraph Library (CHGL). Given a dataset represented as a hypergraph, a Betti number for a particular dimension $k$ indicates how many $k$-dimensional `voids' are present in the dataset. Computing Betti number involves various array-centric and linear algebra operations. We demonstrate that implementing these operations in Chapel is both concise and intuitive. In addition, we show that Chapel provides language constructs for implementing parallel and distributed execution of the linear algebra kernels with minimal effort. Syntactically, Chapel provides succinctness of Python, while delivering comparable and better performance than C++-based and Julia-based packages for calculating Betti numbers respectively.

hypergraph, topological data analysis↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Unexpected topology of the temperature fluctuations in the cosmic microwave background

We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the $Λ$CDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over S 2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ 2 -test shows differences between observations and simulations, yielding p -values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3 σ sporadically at these scales. The highest observed deviation between the observations and simulations for b 0 and b 1 is approximately between 3 σ and 4 σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck ’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Topological Methods for Visualization

This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

58 GEOSCIENCES↗
DOE OSTI2017

Statistical imprints of CMB B -type polarization leakage in an incomplete sky survey analysis

One of the main goals of modern cosmology is to search for primordial gravitational waves by looking on their imprints in the B -type polarization in the cosmic microwave background radiation. However, this signal is contaminated by various sources, including cosmic weak lensing, foreground radiations, instrumental noises, as well as the E -to- B leakage caused by the partial sky surveys, which should be well understood to avoid the misinterpretation of the observed data. In this paper, we adopt the E / B decomposition method suggested by Smith in 2006, and study the imprints of E -to- B leakage residuals in the constructed B -type polarization maps, B( n-circumflex ), by employing various statistical tools. We find that the effects of E -to- B leakage are negligible for the B-mode power spectrum, as well as the skewness and kurtosis analyses of B-maps. However, if employing the morphological statistical tools, including Minkowski functionals and/or Betti numbers, we find the effect of leakage can be detected at very high confidence level, which shows that in the morphological analysis, the leakage can play a significant role as a contaminant for measuring the primordial B -mode signal and must be taken into account for a correct explanation of the data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Dark Energy Survey Year 3 results: $w$CDM cosmology from simulation-based inference with persistent homology on the sphere

We present cosmological constraints from Dark Energy Survey Year 3 (DES Y3) weak lensing data using persistent homology, a topological data analysis technique that tracks how features like clusters and voids evolve across density thresholds. For the first time, we apply spherical persistent homology to galaxy survey data through the algorithm TopoS2, which is optimized for curved-sky analyses and HEALPix compatibility. Employing a simulation-based inference framework with the Gower Street simulation suite, specifically designed to mimic DES Y3 data properties, we extract topological summary statistics from convergence maps across multiple smoothing scales and redshift bins. After neural network compression of these statistics, we estimate the likelihood function and validate our analysis against baryonic feedback effects, finding minimal biases (under $0.3σ$) in the $Ω_\mathrm{m}-S_8$ plane. Assuming the $w$CDM model, our combined Betti numbers and second moments analysis yields $S_8 = 0.821 \pm 0.018$ and $Ω_\mathrm{m} = 0.304\pm0.037$-constraints 70% tighter than those from cosmic shear two-point statistics in the same parameter plane. Our results demonstrate that topological methods provide a powerful and robust framework for extracting cosmological information, with our spherical methodology readily applicable to upcoming Stage IV wide-field galaxy surveys.

Prat, J. [Nordita; Royal Inst. Tech., Sodertalje; ↗
DOE OSTI2018

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble density increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Magnetic-field generation and its effect on ablative Rayleigh–Taylor instability in diffusive ablation fronts

The effects of self-generated magnetic fields on the ablative Rayleigh–Taylor (RT) instability are investigated in the linear regime. The main governing parameters are the Froude number (Fr), which stands for the ratio between ablative convection and acceleration of the target, and the Mach number at the ablation front (Ma), assumed to be small (isobaricity). During the development of the RT instability, magnetic fields are generated due to misalignment between pressure and density gradients (Biermann-battery effect). They accumulate at the section of the ablation front where the Nernst and the plasma velocities cancel each other. The magnetic field modifies the dynamics of the instability through the Righi–Leduc term, which acts as a heat source in the energy equation. It is found that the B fields affect perturbations with short wavelengths up to the most unstable wave in the spectrum. Here, the B field plays a destabilizing role for moderate Froude numbers and becomes stabilizing for large Froude numbers. For plastic ablators, the Fr threshold is found to be Fr = 5.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Direct-drive–ignition designs with mid-Z ablators

Achieving thermonuclear ignition using direct laser illumination relies on the capability to accelerate spherical shells to high implosion velocities while maintaining shell integrity. Ablator materials of moderate atomic number Z reduce the detrimental effects of laser–plasma instabilities in direct-drive implosions. To validate the physics of moderate-Z ablator materials for ignition target designs on the National Ignition Facility (NIF), hydro-equivalent targets are designed using pure plastic (CH), high-density carbon, and glass (SiO{sub 2}) ablators. The hydrodynamic stability of these targets is investigated through two-dimensional (2D) single-mode and multimode simulations. The overall stability of these targets to laser-imprint perturbations and low-mode asymmetries makes it possible to design high-gain targets. Designs using polar-drive illumination are developed within the NIF laser system specifications. Mid-Z ablator targets are an attractive candidate for direct-drive ignition since they present better overall performance than plastic ablator targets through reduced laser–plasma instabilities and a similar hydrodynamic stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Betti multiplets, flows across dimensions and c-extremization

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2d , similarly to the 4d picture, where the exact R-current maximizes the central charge a 4d . There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS 5 to AdS 3 vacua in the supergravity picture. We verify the existence of the flow to AdS 3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Betty Perkins: A giant in nuclear weapons research Reports amassed after testing ban are vital to today’s work

Today’s nuclear weapons research builds upon the work of the past, often on the shoulders of the giants of nuclear document preservation in the absence of testing. One of these giants is weapons historian Betty Perkins. Before her retirement in 2016, Perkins held numerous roles at LANL, but she is best known for her pioneering work in the Weapons Program where she generated classified reports on nuclear weapons design and development. Over many years, she meticulously researched and recorded the histories of a number of critical efforts in Los Alamos’s nuclear weapons program, culminating in 13 reports comprising more than 7,200 pages.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2023

Arctic warming by abundant fine sea salt aerosols from blowing snow

Abstract The Arctic warms nearly four times faster than the global average, and aerosols play an increasingly important role in Arctic climate change. In the Arctic, sea salt is a major aerosol component in terms of mass concentration during winter and spring. However, the mechanisms of sea salt aerosol production remain unclear. Sea salt aerosols are typically thought to be relatively large in size but low in number concentration, implying that their influence on cloud condensation nuclei population and cloud properties is generally minor. Here we present observational evidence of abundant sea salt aerosol production from blowing snow in the central Arctic. Blowing snow was observed more than 20% of the time from November to April. The sublimation of blowing snow generates high concentrations of fine-mode sea salt aerosol (diameter below 300 nm), enhancing cloud condensation nuclei concentrations up to tenfold above background levels. Using a global chemical transport model, we estimate that from November to April north of 70° N, sea salt aerosol produced from blowing snow accounts for about 27.6% of the total particle number, and the sea salt aerosol increases the longwave emissivity of clouds, leading to a calculated surface warming of +2.30 W m −2 under cloudy sky conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Visualizing fast electron energy transport into laser-compressed high-density fast-ignition targets

Understanding of fast electron generation inside the cone and their subsequent transport into hot dense plasmas is crucial to the success of the cone guided fast ignition (FI) scheme of inertial confinement fusion. In our prior work, we developed a new platform that measured, for the first time, the spatial map of fast electron transport in the vicinity of the core of an imploded shell in joint OMEGA and OMEGA EP experiments. In this University of California San Diego-led NLUF project we are using the same platform to investigate several methods of improving coupling efficiency into an imploded CH/CD shell attached to a re-entrant gold cone targets. The shell has an outer diameter of 870 µm consisting of a 15 µm thick outer CH ablator and a 23 µm thick inner CD layer. A Cu dopant (at ~ 1% atomic number density of CD) is added to the CD layer of the shell, which allows characterization of fast electrons transport via their induced Cu K-shell fluorescence radiation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Effects of residual kinetic energy on yield degradation and ion temperature asymmetries in inertial confinement fusion implosions

The study of Rayleigh–Taylor instability in the deceleration phase of inertial confinement fusion implosions is carried out using the three-dimensional (3-D) radiation-hydrodynamic Eulerian parallel code DEC3D. In this paper, we show that the yield-over-clean is a strong function of the residual kinetic energy (RKE) for low modes. Our analytical models indicate that the behavior of larger hot-spot volumes observed in low modes and the consequential pressure degradation can be explained in terms of increasing the RKE. These results are derived using a simple adiabatic implosion model of the deceleration phase as well as through an extensive set of 3-D single-mode simulations using the code DEC3D. The effect of the bulk velocity broadening on ion temperature asymmetries is analyzed for different mode numbers ℓ = 1 -12. The jet observed in low mode ℓ = 1 is shown to cause the largest ion temperature variation in the mode spectrum. Finally, the vortices of high modes within the cold bubbles are shown to cause lower ion temperature variations than low modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Contribution of expanded marine sulfur chemistry to the seasonal variability of dimethyl sulfide oxidation products and size-resolved sulfate aerosol

Marine emissions of dimethyl sulfide (DMS) and the subsequent formation of its oxidation products methanesulfonic acid (MSA) and sulfuric acid (H 2 SO 4 ) are well-known natural precursors of atmospheric aerosols, contributing to particle mass and cloud formation over ocean and coastal regions. Despite a long recognized and well-studied role in the marine troposphere, DMS oxidation chemistry remains a work in progress within many current air quality and climate models, with recent advances exploring heterogeneous chemistry and uncovering previously unknown intermediate species. With the identification of additional DMS oxidation path ways and intermediate species that influence the eventual fate of DMS, it is important to understand the impact of these pathways on the overall sulfate aerosol budget and aerosol size distribution. In this work, we update and evaluate the DMS oxidation mechanism of the chemical transport model GEOS-Chem by implementing expanded DMS oxidation pathways in the model. These updates include gas- and aqueous-phase reactions, the formation of the intermediates dimethyl sulfoxide (DMSO) and methanesulfinic acid (MSIA), and cloud loss and aerosol uptake of the recently quantified intermediate hydroperoxymethyl thioformate (HPMTF). We find that this updated mechanism collectively decreases the global mean surface-layer gas-phase sulfur dioxide (SO 2 ) mixing ratio by 40 % and enhances the sulfate aerosol ($SO^{2-}_{4}$) mixing ratio by 17 %. We further perform sensitivity analyses exploring the contribution of cloud loss and aerosol uptake of HPMTF to the overall sulfur budget. Comparing modeled concentrations to available observations, we find improved biases relative to previous studies. To quantify the impacts of these chemistry updates on global particle size distributions and the mass concentration, we use the TwO-Moment Aerosol Sectional (TOMAS) aerosol microphysics module coupled to GEOS-Chem and find that changes in particle formation and growth affect the size distribution of aerosol. With this new DMS-oxidation scheme, the global annual mean surface-layer number concentration of particles with diameters smaller than 80 nm decreases by 16.8 %, with cloud loss processes related to HPMTF being mostly responsible for this reduction. However, the global annual mean number of particles larger than 80 nm (corresponding to particles capable of acting as cloud condensation nuclei, CCN) increases by 3.8 %, suggesting that the new scheme promotes seasonal particle growth to these sizes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Analysis of limited coverage effects on areal density measurements in inertial confinement fusion implosions

Accurate diagnosis of areal density ($\textit{ρR}$) is critical for the inference of performance metrics in inertial confinement fusion implosions. One potential source of error in this diagnosis is the existence of low mode perturbations in the imploding target, which lead to asymmetries in the inference of the $\textit{ρR}$ from different lines of sight. Here, the error accrued as a result of limited coverage of the sphere due to a finite number of detectors is quantified, and the development of a forward scatter measurement from the OMEGA neutron time-of-flight detectors is motivated. In this work, a method by which the 1D-equivalent 4 π-averaged $\langleρR\rangle$ can be reconstructed, if accurate mode information can be diagnosed by other means, is validated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Going Off Grid: A Comparative Study of the Lagrangian and Eulerian Perspectives of New Particle Formation Events

New particle formation and growth (NPF&G) is the process by which ultrafine particles are formed from gas-phase precursors. NPF&G is the dominant source of global aerosol number with important influences on climate. Most observations of NPF&G events are conducted at stationary sites; however, NPF&G observed from stationary sites is influenced by gradual or rapid changes in the air masses passing over the site, complicating NPF&G analysis. In this work, we use observations and a 3D aerosol model to compare aerosol size distributions at a stationary site (Southern Great Plains [SGP] observatory, Oklahoma, USA) and along Lagrangian trajectories crossing the site. The model simulates the NPF&G events reasonably well at SGP. Using the model to compare the Lagrangian and stationary perspectives, we can explain previously unanalyzable days with some evidence of NPF&G as either non-event or analyzable NPF&G days. We find most of the unanalyzable NPF&G days are due to isolated and inhomogeneous NPF&G occurring upwind of the stationary site, often in the outflow of urban regions. Finally, we compare formation rates of 3 nm particles, growth rates, and the survival probability of 3 nm particles growing to 25 nm between the stationary and Lagrangian perspectives. Because of the much larger number of analyzable days along the Lagrangian trajectories, this perspective potentially provides more robust statistics and better characterization of NPF&G event extremes. Our method for extracting chemical/physical properties along Lagrangian trajectories from 3D models can be applied to a wide range of science questions.

O’Donnell, Samuel E. [Colorado State Univ., Fort C↗
DOE OSTI2021

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗