Search NASA⌕ Search

SEARCH · Search NASA

Results for “Real Analytic Functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Interactive XCMS Online: Simplifying Advanced Metabolomic Data Processing and Subsequent Statistical Analyses

XCMS Online (xcmsonline.scripps.edu) is a cloud-based informatic platform designed to process and visualize mass-spectrometry-based, untargeted metabolomic data. Initially, the platform was developed for two-group comparisons to match the independent, “control” versus “disease” experimental design. Here, we introduce an enhanced XCMS Online interface that enables users to perform dependent (paired) two-group comparisons, meta-analysis, and multigroup comparisons, with comprehensive statistical output and interactive visualization tools. Newly incorporated statistical tests cover a wide array of univariate analyses. Multigroup comparison allows for the identification of differentially expressed metabolite features across multiple classes of data while higher order meta-analysis facilitates the identification of shared metabolic patterns across multiple two-group comparisons. Given the complexity of these data sets, we have developed an interactive platform where users can monitor the statistical output of univariate (cloud plots) and multivariate (PCA plots) data analysis in real time by adjusting the threshold and range of various parameters. On the interactive cloud plot, metabolite features can be filtered out by their significance level (p-value), fold change, mass-to-charge ratio, retention time, and intensity. The variation pattern of each feature can be visualized on both extracted-ion chromatograms and box plots. The interactive principal component analysis includes scores, loadings, and scree plots that can be adjusted depending on scaling criteria. The utility of XCMS functionalities is demonstrated through the metabolomic analysis of bacterial stress response and the comparison of lymphoblastic leukemia cell lines.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Superhydrophobic or Hydrophilic Porous Metallic/Ceramic Tubular Membranes for Continuous Separations of Biodiesel–Water W/O and O/W Emulsions

This study reports the effective surface effect of porous inorganic membranes on improving the emulsion separations (i.e., perm-selective extraction of either oil phase or aqueous phase from the emulsions). A novel tubular form of superwetting, porous, stainless steel/ceramic membranes were demonstrated for enabling continuous separations of oil–water emulsions, extracting either oil phase or aqueous phase from the flowing emulsions. The superhydrophobic membranes consist of macroporous (4 μm) stainless-steel SS434 tube with inner wall surface modified with superhydrophobicity (>150° contact angle) via perfluoro-silane grafting functionalization. The (super)hydrophilic membranes consist of 4-μm porous stainless-steel SS434 tube without/with inner wall coated with nanoporous alumina (6 nm average pore size), the surface of which was further modified with superhydrophilicity via Hydrophil-S solution deposition. With the cross-flow membrane filtration setup, the surface-engineered tubular membranes were studied for perm-selective extraction of aqueous or oil phase from oil–water emulsions (water-in-oil W/O and oil-in-water O/W) that are relevant to a real industrial biodiesel (FAME) production process. The superhydrophobic membrane (4 μm pore size) has demonstrated capability of extracting nearly 100% pure oil while rejecting water phase when either W/O or O/W emulsions were tested as feed. The superhydrophobic membrane showed distinct advantage of 2-orders-of-magnitude-higher flux extraction of oil at 100 times higher “break-through” pressures. On the other hand, the super/hydrophilic nanoporous membranes (6 nm) have shown selective water permeation (separation factor up to 35) when biodiesel-relevant W/O emulsions were tested. Finally, the membrane function is discussed from the perspective of improving industrial biodiesel processing yield by overcoming equilibrium limitations during the biodiesel formation reactions. Future work on in situ reaction–separation experiments are envisioned.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Spatially Resolved Mapping of Three-Dimensional Molecular Orientations with ~2 nm Spatial Resolution through Tip-Enhanced Raman Scattering

We record local optical field images of silver nanocubes (75 nm) using tip-enhanced Raman (TER) spectral imaging. The images that we observe are consistent with several recent reports from our group, but here, we demonstrate sub-2 nm spatial resolution in local optical field nanoimaging under ambient laboratory conditions. This is achieved by scanning the substrate (nanocube on Si) relative to a 4-thiobenzonitrile (TBN)-functionalized Ag-coated TER probe. The spatial resolution that we obtain necessitates that only a few molecules govern the recorded optical response; molecular orientation becomes an important consideration in such measurements. We model the orientation through geometry optimization of a TBN molecule chemisorbed onto an Ag79 cluster (sphere with a ~1 nm diameter). Using the computed orientation of the cluster-bound molecule, we then model the optical response using formalism that accounts for the orientation of the molecule relative to vector components of the local optical fields. We find optimal agreement between experiment and theory. In effect, this work reveals the parallels between single-molecule Raman scattering and high-spatial-resolution TER spectroscopy, even when the images themselves cannot be used to visualize a single molecule in real space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Imaging the polymerization of multivalent nanoparticles in solution

Numerous mechanisms have been studied for chemical reactions to provide quantitative predictions on how atoms spatially arrange into molecules. In nanoscale colloidal systems, however, less is known about the physical rules governing their spatial organization, i.e., sel-fassembly, into functional materials. Here, we monitor real-time self-assembly dynamics at the single nanoparticle level, which reveal marked similarities to foundational principles of polymerization. Specifically, using the prototypical system of gold triangular nanoprisms, we show that colloidal self-assembly is analogous to polymerization in three aspects: ensemble growth statistics following models for step-growth polymerization, with nanoparticles as linkable “monomers”; bond angles determined by directional internanoparticle interactions; and product topology determined by the valency of monomeric units. Liquid-phase transmission electron microscopy imaging and theoretical modeling elucidate the nanometer-scale mechanisms for these polymer-like phenomena in nanoparticle systems. Furthermore, the results establish a quantitative conceptual framework for self-assembly dynamics that can aid in designing future nanoparticle-based materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Communication: Minimum in the thermal conductivity of supercooled water: A computer simulation study

We report the results of a computer simulation study of the thermodynamic properties and the thermal conductivity of supercooled water as a function of pressure and temperature using the TIP4P-2005 water model. The thermodynamic properties can be represented by a two-structure equation of state consistent with the presence of a liquid-liquid critical point in the supercooled region. Our simulations confirm the presence of a minimum in the thermal conductivity, not only at atmospheric pressure, as previously found for the TIP5P water model, but also at elevated pressures. This anomalous behavior of the thermal conductivity of supercooled water appears to be related to the maximum of the isothermal compressibility or the minimum of the speed of sound. However, the magnitudes of the simulated thermal conductivities are sensitive to the water model adopted and appear to be significantly larger than the experimental thermal conductivities of real water at low temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Application of electron beam technology to decompose persistent emerging drinking water contaminants: poly- and perfluoroalkyl substances (PFAS) and 1,4-Dioxane

Poly- and perfluoroalkyl substances (PFAS) and 1,4-dioxane are persistent emerging contaminants that are currently under consideration for federal and state-specific regulations in drinking water. Both PFAS and 1,4-dioxane are highly resistant to degradation and are not effectively removed by conventional drinking water treatment systems. Results from the Unregulated Contaminant Monitoring Rule 3 survey showed that >540 sites across the nation are contaminated with both PFAS and 1,4-dioxane. Hence, there is a need to identify technologies that can effectively remove both these contaminants. Water treatment via electron beam (e-beam) has been proven effective at treating a wide range of contaminants, including perfluorooctane sulfonate (PFOS), perfluorooctanoate (PFOA), polychlorinated biphenyls, and trichloroethylene. While the e-beam process is often considered similar to advanced oxidation processes (AOPs), e-beam technology is unique in that it produces both highly oxidizing and reducing species at the same time. The specific objectives of this study were to: (i) determine the effectiveness of 9 MeV electrons provided by the Fermilab’s Accelerator Application Development and Demonstration (A2D2) tool to decompose PFAS and 1,4-dioxane; (ii) assess the formation of byproducts during water treatment; (iii) apply the optimized treatment to field groundwater samples contaminated with PFAS and 1,4-dioxane, and (iv) assess the energy demands for the treatment of these contaminants using e-beam. Results from this study showed that e-beam is effective in treating both 1,4-dioxane and PFAS. Complete degradation of 1,4-dioxane was observed at a dose of 5 kGy for an initial concentration of up to 1 ppm without the need for any sample modification. The electrical energy per order (EEo) for treatment of 1,4-dioxane ranged from 0.46 to 0.72 kWh/m 3 /order and was comparable and even lower, in some cases, than other AOP technologies. Alkaline conditions (pH 13) and low dissolved oxygen concentration (2 mg/L) highly favored the treatment of PFAS by e-beam. Greater than 90% removal of PFOA and PFOS from an initial concentration of 100 to 500 ppb was achieved at a dose of 250 kGy and 500 kGy, respectively, under optimized conditions. The degradation efficiency was not significantly changed when treating other PFAS of fluorinated carbon chain length of 5 to 7 individually at 250 kGy with a removal ranging from 85¬–99% for different compounds. Short chain PFAS (perfluorobutanoate: PFBA and perfluorobutane sulfonate: PFBS) did not degrade under the same conditions at 250 kGy, but 70 to 99% degradation was observed at a higher dose of 1000 kGy. Short chain PFAS (perfluorohexanoate: PFHxA (C5) and perfluoroheptanoate: PFHpA (C6)) were detected after treatment of PFOA, but not after PFOS treatment. Inability to close the mass balance through targeted analysis suggests the presence of other intermediates not detectable by available analytical methods. When treating PFAS mixture containing ten compounds at equimolar concentration of 0.05 µM each, preferential degradation of polyfluorinated compound (6:2 fluorotelomer sulfonate or 6:2 FTS) followed by C8 and C7 compounds was observed as a function of increasing e-beam dose. About 30% degradation of ΣPFAS was observed at 250 kGy and no further removal was observed up to a dose of 1000 kGy. C4 to C6 PFASs showed no degradation, while C3 PFAS (PFBS) showed an increase in concentration by 34% at 1000 kGy due to formation from the breakdown of other long chain PFAS. These results suggested that (a) the reaction kinetics is likely different for different PFAS based on chain length, functional group, and the degree of fluorination of the carbon chain, and (b) there may be intermediates generated from the degradation of 6:2 FTS and C7/C8 compounds that can potentially scavenge hydrated electrons needed for reaction with the untreated PFAS molecules. Treatment of three PFAS-contaminated groundwater samples from two US states showed similar trends as observed in the treatment of equimolar PFAS mixtures. Up to 71% removal of ΣPFAS was achieved in real groundwater samples at 750 kGy and data trend suggested that higher degradation is feasible if higher doses (>1MGy) are applied to treat field samples to overcome matrix effects and competing species. Calculated EEo for PFAS ranged from as low as ~48 to 1081 kWh/m 3 /order depending on the type of PFAS treated. These values are comparable and even lower, in some cases, than other destructive technologies employed for PFAS treatment such as ultrasound, plasma, and photochemical treatment. The results from this study indicate e-beam is a promising approach under favorable conditions and should be explored further as an end-of-train treatment option for PFAS destruction.

1,4-Dioxane↗
DOE OSTI2024

Beyond the Debye–Hückel limit: Toward a general theory for concentrated electrolytes

The phenomenon of underscreening in concentrated electrolyte solutions leads to a larger decay length of the charge–charge correlation than the prediction of Debye–Hückel (DH) theory and has found a resurgence of both theoretical and experimental interest in the chemical physics community. To systematically understand and investigate this phenomenon in electrolytes requires a theory of concentrated electrolytes to describe charge–charge correlations beyond the DH theory. We review the theories of electrolytes that can transition from the DH limit to concentrations where charge correlations dominate, giving rise to underscreening and the associated Kirkwood Transitions (KTs). In this perspective, we provide a conceptual approach to a theoretical formulation of electrolyte solutions that exploits the competition between molecular-informed short-range (SR) and long-range interactions. We demonstrate that all deviations from the DH limit for real electrolyte solutions can be expressed through a single function ΣQ that can be determined both theoretically and numerically. Importantly, ΣQ can be directly related to the details of SR interactions and, therefore, can be used as a tool to understand how differences in representations of interaction can influence collective effects. The precise function form of ΣQ can be inferred through a Gaussian field theory of both the number and charge densities. The resulting formulation is validated by experiment and can accurately describe the collective phenomenon of screening in concentrated bulk electrolytes. Importantly, the Gaussian field theory predictions of the screening lengths appear to be less than ∼1 nm at concentrations above KTs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Benchmarking the GW Approximation and Bethe–Salpeter Equation for Groups IB and IIB Atoms and Monoxides

Energies from the GW approximation and the Bethe–Salpeter equation (BSE) are benchmarked against the excitation energies of transition-metal (Cu, Zn, Ag, and Cd) single atoms and monoxide anions. We demonstrate that best estimates of GW quasiparticle energies at the complete basis set limit should be obtained via extrapolation or closure relations, while numerically converged GW -BSE eigenvalues can be obtained on a finite basis set. Calculations using real-space wave functions and pseudopotentials are shown to give best-estimate GW energies that agree (up to the extrapolation error) with calculations using all-electron Gaussian basis sets. We benchmark the effects of a vertex approximation (ΓLDA) and the mean-field starting point in GW and the BSE, performing computations using a real-space, transition-space basis and scalar-relativistic pseudopotentials. Here, while no variant of GW improves on perturbative G 0 W 0 at predicting ionization energies, G 0 W 0 Γ LDA -BSE computations give excellent agreement with experimental absorption spectra as long as off-diagonal self-energy terms are included. We also present G 0 W 0 quasiparticle energies for the CuO – , ZnO – , AgO – , and CdO – anions, in comparison to available anion photoelectron spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

How far do electrons delocalize?

Electron delocalization is central to chemical bonding, but it is also a fundamentally nonclassical and nonintuitive quantum mechanical phenomenon. Tools to quantify and visualize electron delocalization help to understand, teach, and predict chemical reactivity. We develop a new approach to quantify and visualize electron delocalization in real space. Our electron delocalization range function EDR(r{sup -vector};u) quantifies the degree to which electrons at point r{sup -vector} in a calculated wavefunction delocalize over length scale u. Its predictions are physically reasonable. For example, EDR(r{sup -vector};u=0.25 bohr) is close to one at points r{sup -vector} in the cores of first-row atoms, consistent with the localization of core electrons to ∼0.25 bohr. EDR(r{sup -vector};u=1 bohr) is close to one at points r{sup -vector} in typical covalent bonds, consistent with electrons delocalizing over the length of the bond. Our approach provides a rich representation of atomic shell structure; covalent and ionic bonding; the delocalization of excited states, defects, and solvated electrons; metallic and insulating systems; and bond stretching and strong correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The scalar chemical potential in cosmological collider physics

Non-analyticity in co-moving momenta within the non-Gaussian bispectrum is a distinctive sign of on-shell particle production during inflation, presenting a unique opportunity for the “direct detection” of particles with masses as large as the inflationary Hubble scale ( H ). However, the strength of such non-analyticity ordinarily drops exponentially by a Boltzmann-like factor as masses exceed H . In this paper, we study an exception provided by a dimension-5 derivative coupling of the inflaton to heavy-particle currents, applying it specifically to the case of two real scalars. The operator has a “chemical potential” form, which harnesses the large kinetic energy scale of the inflaton, \( {\overset{\cdot }{\phi}}_0^{1/2}\approx 60H \) , to act as an efficient source of scalar particle production. Derivative couplings of inflaton ensure radiative stability of the slow-roll potential, which in turn maintains (approximate) scale-invariance of the inflationary correlations. We show that a signal not suffering Boltzmann suppression can be obtained in the bispectrum with strength f NL ~ \( \mathcal{O} \) (0 . 01–10) for an extended range of scalar masses \( \lesssim {\overset{\cdot }{\phi}}_0^{1/2} \) , potentially as high as 10 15 GeV, within the sensitivity of upcoming LSS and more futuristic 21-cm experiments. The mechanism does not invoke any particular fine-tuning of parameters or breakdown of perturbation-theoretic control. The leading contribution appears at tree-level , which makes the calculation analytically tractable and removes the loop-suppression as compared to earlier chemical potential studies of non-zero spins. The steady particle production allows us to infer the effective mass of the heavy particles and the chemical potential from the variation in bispectrum oscillations as a function of co-moving momenta. Our analysis sets the stage for generalization to heavy bosons with non-zero spin.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Imaging Supramolecular Morphogenesis with Confocal Laser Scanning Microscopy at Elevated Temperatures

The morphogenesis of supramolecular assemblies is a highly dynamic process that has only recently been recognized, and our understanding of this phenomenon will require imaging techniques capable of crossing scales. Shape transformations depend both on the complex energy landscapes of supramolecular systems and the kinetically controlled pathways that define their structures and functions. We report here the use of confocal laser scanning microscopy coupled with a custom-designed variable-temperature sample stage that enables in situ observation of such shape changes. The submicrometer resolution of this technique allows for real-time observation of the nanostructures in the native liquid environments in which they transform with thermal energy. We use this technique to study the temperature-dependent morphogenic behavior of peptide amphiphile nanofibers and photocatalytic chromophore amphiphile nanoribbons. Furthermore, the variable-temperature confocal microscopy technique demonstrated in this work can sample a large volume and provides real-time information on thermally induced morphological changes in the solution.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A digital twin platform for building performance monitoring and optimization: Performance simulation and case studies

Advancements in sensor technology, data analytics, affordable compute, and communication infrastructure have paved the way for Digital Twin technology in optimizing building operations and controls. This study presents the development of an open and interoperable web-based Digital Twin platform for integrating diverse data streams and facilitating effective user interactions. The platform utilizes modern technologies for the web framework and time-series data management, ensuring scalability and responsiveness. The backend supports seamless integration of diverse data sources and emulators, incorporating data from building sensors and meters, external weather Application Programming Interfaces, and advanced EnergyPlus simulation models of the building and its energy systems including the Distributed Energy Resources that are formulated in Functional Mockup Units. A simulation case study was conducted with FlexLab, a test facility on Lawrence Berkeley National Laboratory campus. The case study includes normal operations, Distributed Energy Resource integration, and power outage scenarios, to illustrate the Digital Twin’s ability to provide critical insights into energy performance and thermal resilience. The results demonstrated the platform’s potential as a decision-support tool for optimizing building energy performance and enhancing resilience against extreme weather events. Future work will focus on deploying the Digital Twin platform to a real building for field validation, extending its capabilities to cover more scenarios such as bidirectional Electric Vehicle interactions, and enhancing user engagement.

EnergyPlus↗
DOE OSTI2020

Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations

In this article, we report a scheme to analyze and visualize the energy density fluctuations during the real-time time-dependent density functional theory (RT-TDDFT) simulations. Using Ag 4 –N 2 complexes as examples, here we show that the grid-based Kohn–Sham energy density can be computed at each time step using a procedure from Nakai and coworkers. Then the instantaneous energy of each molecular fragment (such as Ag 4 and N 2 ) can be obtained by partitioning the Kohn–Sham energy densities using Becke or fragment-based Hirshfeld (FBH) scheme. A strong orientation-dependence is observed for the energy flow between the Ag 4 cluster and a nearby N 2 molecule in the RT-TDDFT simulations. Future applications of such an energy density analysis in electron dynamics simulations are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Anharmonic densities of states: A general dynamics-based solution

Density of states is a fundamental physical characteristic that lies at the foundation of statistical mechanics and theoretical constructs that derive from them (e.g., kinetic rate theories, phase diagrams, and others). Even though most real physical systems are anharmonic, the vibrational density of states is customarily treated within the harmonic approximation, or with some partial, often limited, account for anharmonicity. The reason for this is that the problem of anharmonic densities of states stubbornly resisted a general and exact, yet convenient and straightforward in applications, solution. Here we formulate such a solution within both classical and quantum mechanics. It is based on actual dynamical behavior of systems as a function of energy and as observed, or monitored, on a chosen time scale, short or long. As a consequence, the resulting anharmonic densities of states are fully dynamically informed and, in general, time-dependent. As such, they lay the ground for formulation of new statistical mechanical frameworks that incorporate time and are ergodic, by construction, with respect to actual dynamical behavior of systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Interrogation of bimetallic particle oxidation in three dimensions at the nanoscale

An understanding of bimetallic alloy oxidation is key to the design of hollow-structured binary oxides and the optimization of their catalytic performance. However, one roadblock encountered in studying these binary oxide systems is the difficulty in describing the heterogeneities that occur in both structure and chemistry as a function of reaction coordinate. This is due to the complexity of the three-dimensional mosaic patterns that occur in these heterogeneous binary systems. By combining real-time imaging and chemical-sensitive electron tomography, we show that it is possible to characterize these systems with simultaneous nanoscale and chemical detail. We find that there is oxidation-induced chemical segregation occurring on both external and internal surfaces. Additionally, there is another layer of complexity that occurs during the oxidation, namely that the morphology of the initial oxide surface can change the oxidation modality. As a result, this work characterizes the pathways that can control the morphology in binary oxide materials.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Understanding the formation and growth of Ag nanoparticles on silver chromate induced by electron irradiation in electron microscope: A combined experimental and theoretical study

Ag{sub 2}CrO{sub 4} microcrystals were synthesized using the co-precipitation method. These microcrystals were characterized through X-ray diffraction (XRD) with Rietveld analysis, field-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM) with energy-dispersive spectroscopy (EDS), micro-Raman (MR). XRD patterns and Rietveld refinement data showed that the material exhibits an orthorhombic structure without any deleterious phases. FE-SEM and TEM micrographs revealed the morphology and the growth of Ag nanoparticles on Ag{sub 2}CrO{sub 4} microcrystals during electron beam irradiation. These events were directly monitored in real-time. Their optical properties were investigated using ultraviolet-visible (UV–vis) diffuse reflectance spectroscopy that allowed the calculation of the optical band gap energy. Theoretical analyses based on the density functional theory level indicate that the incorporation of electrons is responsible for structural modifications and formation of defects on the [AgO{sub 6}] and [AgO{sub 4}] clusters, generating ideal conditions for the growth of Ag nanoparticles. - Graphical abstract: Theoretical representation of the Ag{sub 2}CrO{sub 4} orthorhombic structure. Display Omitted - Highlights: • The Ag{sub 2}CrO{sub 4} microcrystals indicate an orthorhombic structure. • The formation of Ag{sup 0} promotes Ag-nanoparticle growth on the surface of the Ag{sub 2}CrO{sub 4}. • Electron irradiation of the material induces the formation of Ag vacancies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

What is the best method to fit time-resolved data? A comparison of the residual minimization and the maximum likelihood techniques as applied to experimental time-correlated, single-photon counting data

The need for measuring fluorescence lifetimes of species in subdiffraction-limited volumes in, for example, stimulated emission depletion (STED) microscopy, entails the dual challenge of probing a small number of fluorophores and fitting the concomitant sparse data set to the appropriate excited-state decay function. This need has stimulated a further investigation into the relative merits of two fitting techniques commonly referred to as “residual minimization” (RM) and “maximum likelihood” (ML). Fluorescence decays of the well-characterized standard, rose bengal in methanol at room temperature (530 ± 10 ps), were acquired in a set of five experiments in which the total number of “photon counts” was approximately 20, 200, 1000, 3000, and 6000 and there were about 2–200 counts at the maxima of the respective decays. Each set of experiments was repeated 50 times to generate the appropriate statistics. Each of the 250 data sets was analyzed by ML and two different RM methods (differing in the weighting of residuals) using in-house routines and compared with a frequently used commercial RM routine. Convolution with a real instrument response function was always included in the fitting. While RM using Pearson’s weighting of residuals can recover the correct mean result with a total number of counts of 1000 or more, ML distinguishes itself by yielding, in all cases, the same mean lifetime within 2% of the accepted value. For 200 total counts and greater, ML always provides a standard deviation of <10% of the mean lifetime, and even at 20 total counts there is only 20% error in the mean lifetime. Here, the robustness of ML advocates its use for sparse data sets such as those acquired in some subdiffraction-limited microscopies, such as STED, and, more importantly, provides greater motivation for exploiting the time-resolved capacities of this technique to acquire and analyze fluorescence lifetime data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Real-space formulation of the stress tensor for O (N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O (N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O (N) methods. We then describe its evaluation within the O (N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 10 6 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗