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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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At least 19 records

Annotation of DOM metabolomes with an ultrahigh resolution mass spectrometry molecular formula library

Current approaches to analyzing metabolomic data often rely on matching MS/MS fragmentation data to sparse libraries or databases. This approach results in limited identification of features, often with less than 10% of the dataset being annotated. A complementary approach is to assign molecular formula to features based on accurate mass measurements, but the platforms commonly used for metabolomics do not have the needed accuracy or resolving power to do this robustly, particularly for larger molecules. Using our newly modified analysis tool, CoreMS, we generated a library of molecular formula from pooled samples analyzed with LC-21T FT-ICR MS. This library successfully annotated approximately 53.2% of features identified from the exometabolome of marine diatom Phaeodactylum tricornutum – a nearly ten-fold increase over the 5.9% annotation rate achieved using a conventional MS/MS library matching approach. Using this FT-ICR MS library approach, we were able to differentiate differences in the exometabolome of P. tricornutum in iron replete and iron limited conditions, with 668 metabolites being differentially expressed (p < 0.05, 2 x intensity difference) under these conditions. The traditional MS/MS fragmentation-based annotation approach only annotated 61 of these metabolites, while our novel pipeline annotated 450 metabolites and revealed 12 metabolites that were significantly more abundant under low iron conditions. Our results demonstrate the utility of ultrahigh resolution mass spectrometry for generating more comprehensive and confident molecular annotations.

21T-FTICR-MS, CoreMS↗

Generalized Lapse Rate Formulas for Use in Entraining CAPE Calculations

Abstract Common assumptions in temperature lapse rate formulas for lifted air parcels include neglecting mixing, hydrostatic balance, the removal of all condensate once it forms (pseudoadiabatic), and/or the retention of all condensate within the parcel (adiabatic). These formulas are commonly derived from the conservation of entropy, which leads to errors when nonequilibrium mixed-phase condensate is present. To evaluate these assumptions, a new general lapse rate formula is derived from an expression for energy conservation, rather than entropy conservation. This new formula incorporates mixing of the parcel with its surroundings, relaxes the hydrostatic assumption, allows for nonequilibrium mixed-phase condensate, and can be formulated for pseudoadiabatic or adiabatic ascent. The new formula is shown to exactly conserve entropy for reversible ascent. Predictions by the new formula are compared to that of older and less general formulas. The errors in previous formulas arise from the assumption of hydrostatic balance, which results in considerable warm biases due to the neglect of the energy sink from buoyancy. Predictions of ascent with entrainment using the new formula are then compared to parcel properties along trajectories in large eddy simulations. Simulated parcel properties are better predicted by the formula using a diluted analogy to adiabatic ascent, wherein condensate is diluted at the same rate as other parcel properties, than by the diluted analogy to pseudoadiabatic ascent, wherein all condensate is removed. These results suggest that CAPE should be computed with adiabatic, rather than pseudoadiabatic, parcel ascent.

54 ENVIRONMENTAL SCIENCES↗

Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n -points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Chapter Six - Derivation, cross-validation, and comparison of analytic formulas for electrostatic deflector aberrations

Here, we derived first and second order analytic aberration formulas in the horizontal transverse plane for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation was performed using an iterative order-by-order perturbation method in a Frenet–Serret beamline coordinate system. We produced a C program edabrt for calculation of the first and second order aberrations using the formulas that we derived. The electrostatic deflector aberration formulas from Wollnik (1965) disagree with COSY INFINITY and the aberration formulas that we derived here, and they also deviate from the first and second order symplecticity conditions. The reason for this discrepancy is that the aberration formulas from Wollnik (1965) consider only motion in the main field of the deflector and do not properly account for fringe field effects, in particular the necessarily occurring change of kinetic energy due to the change in potential. The code GIOS uses electrostatic aberration formulas from Wollnik (1965) and exhibits the same discrepancy. We performed a comparison of first and second order electrostatic deflector aberrations for (1) the analytic formulas derived in this work, (2) differential-algebraic (DA) numerical integration of the equations of motion using the code COSY INFINITY, (3) the aberration formulas from Wollnik (1965), (4) aberrations computed using the code GIOS, and (5) the aberration formulas from Wollnik (1965) adjusted to account for the occurring change in potential. An electrostatic spherical deflector and an electrostatic cylindrical deflector were used as test cases for this comparison. There is excellent agreement between methods (1), (2), and (5), and these three methods satisfy the first and second order symplecticity conditions.

43 PARTICLE ACCELERATORS↗

An Analytic Formula for Entraining CAPE in Midlatitude Storm Environments

Abstract This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from an environmental sounding, rather than prescribed by the formula user. Entrainment is connected to the background environment using an eddy diffusivity approximation for lateral mixing, updraft geometry assumptions, and mass continuity. These approximations result in a direct correspondence between the storm-relative flow and the updraft radius and an inverse scaling between the updraft radius squared and entrainment rate. The aforementioned concepts, combined with the assumption of adiabatic conservation of moist static energy, yield an explicit analytic equation for ECAPE that depends entirely on state variables in an atmospheric profile and a few constant parameters with values that are established in past literature. Using a simplified Bernoulli-like equation, the ECAPE formula is modified to account for updraft enhancement via kinetic energy extracted from the cloud’s background environment. CAPE and ECAPE can be viewed as predictors of the maximum vertical velocity w max in an updraft. Hence, these formulas are evaluated using w max from past numerical modeling studies. Both of the new formulas improve predictions of w max substantially over commonly used diagnostic parameters, including undiluted CAPE and ECAPE with a constant prescribed entrainment rate. The formula that incorporates environmental kinetic energy contribution to the updraft correctly predicts instances of exceedance of by w max , and provides a conceptual explanation for why such exceedance is rare among past simulations. These formulas are potentially useful in nowcasting and forecasting thunderstorms and as thunderstorm proxies in climate change studies. Significance Statement Substantial mixing occurs between the upward-moving air currents in thunderstorms (updrafts) and the surrounding comparatively dry environmental air, through a process called entrainment. Entrainment controls thunderstorm intensity via its diluting effect on the buoyancy of air within updrafts. A challenge to representing entrainment in forecasting and predictions of the intensity of updrafts in future climates is to determine how much entrainment will occur in a given thunderstorm environment without a computationally expensive high-resolution simulation. To address this gap, this article derives a new formula that computes entrainment from the properties of a single environmental profile. This formula is shown to predict updraft vertical velocity more accurately than past diagnostics, and can be used in forecasting and climate prediction to improve predictions of thunderstorm behavior and impacts.

54 ENVIRONMENTAL SCIENCES↗

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

Suzuki type estimates for exponentiated sums and generalized Lie-Trotter formulas in JB-algebras

Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with such formulas are investigated in the JB-algebraic setting. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. In conclusion, we also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements.

97 MATHEMATICS AND COMPUTING↗

Analysis and fringe field scaling of a legacy set of electrostatic deflector aberration formulas [Chapter Seven]

In this work we performed an analysis of the derivation of first and second order analytic aberration formulas by Wollnik (1965) for the case of electrostatic deflectors in the horizontal plane. We found that these aberration formulas are valid for the main field of the deflector; however, they do not account for any fringe field effects. To address this issue, we modified the aberration formulas from Wollnik (1965) for a hard edge fringe field by scaling the particle inclinations at the entrance and exit edges of the deflector. These modified aberration formulas fully agree with electrostatic aberration formulas derived by Valetov and Berz (2020), as well as with differential-algebraic (DA) calculations of electrostatic deflector aberrations using the code COSY INFINITY.

43 PARTICLE ACCELERATORS↗

A Formula for the Maximum Vertical Velocity in Supercell Updrafts

In supercell environments, previous authors have shown strong connections between the vertical wind shear magnitude, updraft width, and entrainment. Based on these results, it is hypothesized that the influences of entrainment-driven dilution on buoyancy and maximum updraft vertical velocity w in supercell environments are a predictable function of the vertical wind shear profile. It is also hypothesized that the influences of pressure perturbation forces on maximum updraft w are small because of a nearly complete offset between upward dynamic pressure forces and downward buoyant pressure forces. To address these hypotheses, we derive a formula for the maximum updraft w that incorporates the effects of entrainment-driven dilution on buoyancy but neglects pressure gradient forces. Solutions to this formula are compared with output from previous numerical simulations. This formula substantially improves predictions of maximum updraft w over past CAPE-derived formulas for maximum updraft w, which supports the first hypothesis. Furthermore, integrated vertical accelerations along trajectories show substantial offsets between dynamic and buoyant pressure forces, supporting the second hypothesis. It is argued that the new formula should be used in addition to CAPE-derived measures for w in forecast and research applications when accurate diagnosis of updraft speed is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inferring the Contribution of Microbial Taxa and Organic Matter Molecular Formulas to Ecological Assembly

Understanding the mechanisms underlying the assembly of communities has long been the goal of many ecological studies. While several studies have evaluated community wide ecological assembly, fewer have focused on investigating the impacts of individual members within a community or assemblage on ecological assembly. Here, we adapted a previous null model β-nearest taxon index (βNTI) to measure the contribution of individual features within an ecological community to overall assembly. This new metric, called feature-level βNTI (βNTI feat ), enables researchers to determine whether ecological features (e.g., individual microbial taxa) contribute to divergence, convergence, or have insignificant impacts across spatiotemporally resolved metacommunities or meta-assemblages. Using βNTI feat , we revealed that unclassified microbial lineages often contributed to community divergence while diverse groups (e.g., Crenarchaeota, Alphaproteobacteria, and Gammaproteobacteria) contributed to convergence. We also demonstrate that βNTI feat can be extended to other ecological assemblages such as organic molecules comprising organic matter (OM) pools. OM had more inconsistent trends compared to the microbial community though CHO-containing molecular formulas often contributed to convergence, while nitrogen and phosphorus-containing formulas contributed to both convergence and divergence. A network analysis was used to relate βNTI feat values from the putatively active microbial community and the OM assemblage and examine potentially common contributions to ecological assembly across different communities/assemblages. This analysis revealed that P-containing formulas often contributed to convergence/divergence separately from other ecological features and N-containing formulas often contributed to assembly in coordination with microorganisms. Additionally, members of Family Geobacteraceae were often observed to contribute to convergence/divergence in conjunction with both N- and P-containing formulas, suggesting a coordinated ecological role for family members and the nitrogen/phosphorus cycle. Overall, we show that βNTI feat offers opportunities to investigate the community or assemblage members, which shape the phylogenetic or functional landscape, and demonstrate the potential to evaluate potential points of coordination across various community types.

59 BASIC BIOLOGICAL SCIENCES↗

Leveraging 13C-Labeling to Assign Molecular Formulas to Unknown Yeast Metabolites

Mass spectrometry analyses have identified tens of thousands of unknown small molecule-associated peaks in different biological specimens. Notably, even the simplest and best studied organisms like Escherichia coli and Saccharomyces cerevisiae yield thousands of unknown peaks. A key question is how many of these reflect actual novel endogenous metabolites. To explore this, Mahieu and Patti used complete 13 C -labeling in E. coli to credential peaks as biological. This reduced the number of unknowns by more than 90%. Here, we carry out similar uniform 13 C-labeling in the Baker’s yeast S. cerevisiae and two less-studied bioenergy-relevant yeasts Rhodotorula toruloides (lipid producer) and Issatchenkia orientalis (organic acid producer). Identification of unknown metabolite peaks and their molecular formulas is facilitated through software tailored for 13 C labeling data and resulting knowledge of carbon atom count. A classification model evaluates the plausibility of each candidate formula, with peaks lacking plausible candidate formulas unlikely to reflect metabolite molecular ions. This approach prioritizes about one hundred candidate abundant unknown metabolites with logical molecular formulas. Most of these are species-specific rather than conserved across yeasts, and more are found in the nonmodel yeasts than S. cerevisiae. Thus, 13 C-labeling data on unknown metabolites highlights the potential for discovering new metabolites and pathways in nonmodel yeasts.

Carbon↗

Proving the 6d Cardy formula and matching global gravitational anomalies

A Cardy formula for 6d superconformal field theories (SCFTs) conjectured by Di Pietro and Komargodski in [1] governs the universal behavior of the supersymmetric partition function on S^1_\beta \times S^5 S β 1 × S 5 in the limit of small \beta β and fixed squashing of the S^5 S 5 . For a general 6d SCFT, we study its 5d effective action, which is dominated by the supersymmetric completions of perturbatively gauge-invariant Chern-Simons terms in the small \beta β limit. Explicitly evaluating these supersymmetric completions gives the precise squashing dependence in the Cardy formula. For SCFTs with a pure Higgs branch (also known as very Higgsable SCFTs), we determine the Chern-Simons levels by explicitly going onto the Higgs branch and integrating out the Kaluza-Klein modes of the 6d fields on S^1_\beta S β 1 . We then discuss tensor branch flows, where an apparent mismatch between the formula in [1] and the free field answer requires an additional contribution from BPS strings. This ``missing contribution’’ is further sharpened by the relation between the fractional part of the Chern-Simons levels and the (mixed) global gravitational anomalies of the 6d SCFT. We also comment on the Cardy formula for 4d \mathcal{N}=2 𝒩 = 2 SCFTs in relation to Higgs branch and Coulomb branch flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

"Spectrally gapped" random walks on networks: a Mean First Passage Time formula

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices H=\langle H\rangle +\delta H H = ⟨ H ⟩ + δ H , with \langle H\rangle ⟨ H ⟩ rank- 1 1 and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement.

97 MATHEMATICS AND COMPUTING↗

Geometry of conformal manifolds and the inversion formula

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Euclidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in 2d examples. In particular, for 2d (2,2) superconformal field theories we derive a lower bound on the scalar curvature, which is saturated by free theories when the central charge is a multiple of three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Data Set Analysis to Reduce Uncertainty in Formula Assignments of Ultrahigh Resolution Mass Spectra

Environmental samples contain a vast array of organic compounds with diverse elemental compositions and heteroatom content. Molecular formula assignments of ultrahigh resolution mass spectra (HRMS) hold promise for elucidating the molecular composition of these compounds. However, the need to account for an assortment of heteroatoms increases the uncertainty associated with individual assignments – and ultimately the ecological, biological, and biogeochemical insights gleaned from the assignments. To address this challenge, we introduce a formula assignment strategy that leverages HRMS data sets to improve assignment confidence, filter false assignments, and mitigate bias in assignment routines. The strategy, implemented using CoreMS, first identifies the highest confidence assignment for a recurring ion in a data set by assessing the mass accuracy and isotopologue similarity of all assignments to the ion across the data set. The second component of the strategy examines the consistency of mass errors for an assigned ion throughout a data set and flags formulas with statistically unlikely deviations in mass error. Here, we illustrate the application and utility of the strategy by comparing its results against documented misassignment patterns within a set of oceanographic samples that were measured with 21 T Fourier Transform Ion Cyclotron Resonance Mass Spectrometry. Because the efficacy of our strategy improves with data set size, it is particularly useful for enhancing assignment confidence in large HRMS data sets common in studies of environmental systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Water Dielectric Function at Finite Wavelength and the Convergence of Its Large Wavelength Limit (Static Dielectric) by Fluctuation Formulas

Here we provide a general analysis of the longitudinal dielectric function ε l (k) via fluctuation formulas at finite wavelength k, including the static dielectric constant ε w = ε l (k → 0), and analyze the different sources of errors, deriving explicit formulas. Simulations with the SPC/E water model show that the convergence of fluctuation formulas to compute the static dielectric constant is slow and requires long simulations. The analysis of ε l (k) allows us to identify the long- and short-wavelength limits and provide a precise determination of the location of the poles as well as the zeros in the complex plane, which determine the short-distance form of the electrostatic (Coulomb) interaction among charged particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Formula for the ionisation rate of an atom or ion in a strong electromagnetic field for numerical simulation

A formula is proposed for calculating the rate of field ionisation of an atom or ion, taking into account both tunnel ionisation and barrier suppression ionisation. Compared with the previous formula proposed in 2018, it more accurately describes the transition region between both ionisations and is determined mainly by two parameters: the ionisation potential of an atom or ion and the amplitude of an external electric field. This makes the presented formula suitable for use in numerical packages simulating the interaction of high-power laser radiation with matter by the particle-in-cell (PIC) method. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗