Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematical methods”

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 649 records · Page 36

Singlet Fission Rate: Optimized Packing of a Molecular Pair. Ethylene as a Model

Here, a procedure is described for unbiased identification of all π-electron chromophore pair geometry choices that locally maximize the rate of conversion of a singlet exciton into a singlet biexciton (triplet pair), using a simplified version of the diabatic frontier orbital model of singlet fission (SF).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology-Informed Design Rules for Deconstructable Thermoset Copolymer Networks

Existing models of thermoset deconstruction facilitated by incorporating cleavable comonomers rely on a mean-field reverse gel point paradigm, which predicts network dissolution once cleavable bonds reach a critical stoichiometric threshold, but does not account for where those bonds reside within the network architecture. Using reactive coarse-grained molecular dynamics simulations coupled with graph-theoretic analysis, we extend this stoichiometric picture to show that deconstructability is governed by the curing-imprinted network topology rather than stoichiometry alone. This topological organization is hierarchical: at the local scale, the elastic effectiveness of cross-link junctions determines which cross-links constitute the load-bearing scaffold; at the mesoscale, the cross-linking rate kinetically templates that scaffold into topologically modular communities─densely cross-linked clusters connected by sparse bridging strands that sustain network connectivity. Using betweenness centrality to identify nodes that disproportionately lie on intercommunity shortest paths, we demonstrate that effective deconstruction of the network into macromolecular fragments requires cleavable comonomers to intercept these high-centrality bridging strands. We further find that under uniform, disassortative comonomer incorporation, this topological requirement provides a mechanistic basis for extending the reverse gel point to incorporate network topology. We also show that modularity imposes a fundamental limit on fragment uniformity that persists even when the centrality requirement is met. Finally, we demonstrate that chain stiffness provides a nearly independent lever to suppress mechanically redundant cross-links and raise the glass transition temperature without significantly altering the deconstruction outcome. Together, these findings reframe the thermoset design space around network topology and provide actionable guidelines for engineering thermoset copolymers with predictable deconstructability and targeted thermomechanical performance.

coarse-grained molecular dynamics↗

Neutral Loss Mass Spectral Data Enhances Molecular Similarity Analysis in $\mathrm{METLIN}$

We report Neutral loss (NL) spectral data presents a mirror of MS 2 data and is a valuable yet largely untapped resource for molecular discovery and similarity analysis. Tandem mass spectrometry (MS 2 ) data is effective for the identification of known molecules and the putative identification of novel, previously uncharacterized molecules (unknowns). Yet, MS 2 data alone is limited in characterizing structurally related molecules. To facilitate unknown identification and complement the METLIN-MS 2 fragment ion database for characterizing structurally related molecules, we have created a MS 2 to NL converter as a part of the METLIN platform. The converter has been used to transform METLIN’s MS 2 data into a neutral loss database (METLIN-NL) on over 860 000 individual molecular standards. The platform includes both the MS 2 to NL converter and a graphical user interface enabling comparative analyses between MS 2 and NL data. Examples of NL spectral data are shown with oxylipin analogues and two structurally related statin molecules to demonstrate NL spectra and their ability to help characterize structural similarity. Mirroring MS 2 data to generate NL spectral data offers a unique dimension for chemical and metabolite structure characterization.

59 BASIC BIOLOGICAL SCIENCES↗

“Did you eat a MOLEcule today?” An Interactive Demonstration of Molecular Weight with Real-Time Breath Analysis Using Mass Spectrometry for All Ages

Although mass spectrometry is a widely used analytical tool, age-appropriate, interactive outreach activities for laboratory visitors, especially children, are lacking. Furthermore, the presented interactive demonstration, “Did you eat a MOLEcule today?”, introduces all ages to molecular weight concepts and mass spectrometry in a research laboratory, while connecting the concepts to real-world applications. Through real-time breath analysis, participants explore the concepts of molecular weight, electrostatic field manipulation of charged molecules, and analyte identification by mass analysis. This module is rapid and highly adaptable for outreach activities but also includes age- or classroom-appropriate variations to decrease or increase difficulty levels. The presented interactive demonstration has repeatedly been implemented, with over 2300 participants during six annual “Take Our Daughters & Sons to Work Day” and two corporate “Family Day” outreach activities, successfully engaging, exciting, and educating both kids and parents.

36 MATERIALS SCIENCE↗

Deep Learning on Multimodal Chemical and Whole Slide Imaging Data for Predicting Prostate Cancer Directly from Tissue Images

Prostate cancer is one of the most common cancers globally and is the second most common cancer in the male population in the US. Here we develop a study based on correlating the hematoxylin and eosin (H&E)-stained biopsy data with MALDI mass-spectrometric imaging data of the corresponding tissue to determine the cancerous regions and their unique chemical signatures and variations of the predicted regions with original pathological annotations. We obtain features from high-resolution optical micrographs of whole slide H&E stained data through deep learning and spatially register them with mass spectrometry imaging (MSI) data to correlate the chemical signature with the tissue anatomy of the data. We then use the learned correlation to predict prostate cancer from observed H&E images using trained coregistered MSI data. This multimodal approach can predict cancerous regions with ~80% accuracy, which indicates a correlation between optical H&E features and chemical information found in MSI. Further, we show that such paired multimodal data can be used for training feature extraction networks on H&E data which bypasses the need to acquire expensive MSI data and eliminates the need for manual annotation saving valuable time. Two chemical biomarkers were also found to be predicting the ground truth cancerous regions. This study shows promise in generating improved patient treatment trajectories by predicting prostate cancer directly from readily available H&E-stained biopsy images aided by coregistered MSI data.

60 APPLIED LIFE SCIENCES↗

A physical zero-knowledge object-comparison system for nuclear warhead verification

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Construction of ground-state preserving sparse lattice models for predictive materials simulations

First-principles based cluster expansion models are the dominant approach in ab initio thermodynamics of crystalline mixtures enabling the prediction of phase diagrams and novel ground states. However, despite recent advances, the construction of accurate models still requires a careful and time-consuming manual parameter tuning process for ground-state preservation, since this property is not guaranteed by default. In this paper, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of their reference data. The method builds on the recently introduced compressive sensing paradigm for cluster expansion and employs quadratic programming to impose constraints on the model parameters. The robustness of our methodology is illustrated for two lithium transition metal oxides with relevance for Li-ion battery cathodes, i.e., Li 2x Fe 2(1-x) O 2 and Li 2x Ti 2(1-x) O 2 , for which the construction of cluster expansion models with compressive sensing alone has proven to be challenging. We demonstrate that our method not only guarantees ground-state preservation on the set of reference structures used for the model construction, but also show that out-of-sample ground-state preservation up to relatively large supercell size is achievable through a rapidly converging iterative refinement. This method provides a general tool for building robust, compressed and constrained physical models with predictive power.

36 MATERIALS SCIENCE↗

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Landau ghost pole problem in quantum field theory: From 50th of last century to the present day

In this paper we present our results of the investigation of asymptotical behavior of amplitude at short distances in four-dimensional scalar field theory with ϕ{sup 4} interaction. To formulate of our calculating model – two-particle approximation of the mean-field expansion we have used an Rochev’s iteration scheme of solution of the Schwinger-Dyson equations with the fermion bilocal source. We have considered the nonlinear integral equations in deep-inelastic region of momenta. As result we have a non-trivial behavior of amplitude at large momenta.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fast methods for multisite charge transfer. Processes II. Analytic nuclear gradients and nonadiabatic dynamics for cCASSCF(1,n) and cCASSCF(2n-1,n) wavefunctions

In this work we derive and implement analytic nuclear gradients and derivative couplings for a constrained complete active space self-consistent field with a small active space designed to model electron or hole transfer. Using a Lagrangian formalism, we are able to differentiate both the CASSCF energy and the constraint (which is required for smooth surfaces over a wide range of parameter space), and the resulting efficient algorithm can be immediately applied to nonadiabatic dynamics simulations of charge transfer processes. Here, we run initial surface-hopping simulations of a proton coupled electron transfer event for a phenoxyl–phenol system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

79 ASTRONOMY AND ASTROPHYSICS↗

The Mira–Titan Universe – IV. High-precision power spectrum emulation

Modern cosmological surveys are delivering data sets characterized by unprecedented quality and statistical completeness; this trend is expected to continue in the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the non-linear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. We have recently introduced the Mira–Titan Universe simulation suite designed to construct emulators for a range of cosmological probes. This gravity-only set of simulations covers the standard six cosmological parameters {ω m , ω b , σ 8 , $h, n_s, w_0$} and, in addition, includes massive neutrinos and a dynamical dark energy equation of state {ω ν , $w_a$}. In this paper, we present the final emulator for the matter power spectrum based on 111 cosmological simulations, each covering a (2.1 Gpc) 3 volume and evolving 3200 3 particles. In this work, an additional set of 1776 lower resolution simulations and TimeRG perturbation theory results for the power spectrum are used to cover scales straddling the linear to mildly non-linear regimes (maximum wavenumber $\textit{k}$ = 5 Mpc –1 ). The emulator provides predictions at the 2–3 percent level of accuracy over a wide range of cosmological parameters and is publicly released as part of this paper.

79 ASTRONOMY AND ASTROPHYSICS↗

Resurgence and Lefschetz thimble in three-dimensional $\mathcal{N}=2$ supersymmetric Chern–Simons matter theories

We study a certain class of supersymmetric (SUSY) observables in three-dimensional N=2 SUSY Chern–Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have non-trivial resurgent structures by expressing the exact results as a full transseries consisting of perturbative and non-perturbative parts. As real mass parameters are varied, we encounter Stokes phenomena at an infinite number of points, where the perturbative series becomes non-Borel-summable due to singularities on the positive real axis of the Borel plane. We also investigate the Stokes phenomena when the phase of the coupling constant is varied. For these cases, we find that the Borel ambiguities in the perturbative sector are canceled by those in non-perturbative sectors and end up with an unambiguous result which agrees with the exact result even on the Stokes lines. We also decompose the Coulomb branch localization formula, which is an integral representation for the exact results, into Lefschetz thimble contributions and study how they are related to the resurgent transseries. We interpret the non-perturbative effects appearing in the transseries as contributions of complexified SUSY solutions which formally satisfy the SUSY conditions but are not on the original path integral contour.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synchronization of Lienard-Type Oscillators in Uniform Electrical Networks

This paper presents a condition for global asymptotic synchronization of Lienard-type nonlinear oscillators in uniform LTI electrical networks with series R-L circuits modeling interconnections. By uniform electrical networks, we mean that the per-unit-length impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation of a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series R-L circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov- and passivity-based arguments that strong coupling is required to ensure synchronization.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Measuring Bus Frequency During Transients: Some Fundamentals

The success of digital instruments seems sometimes to founder when it comes to frequency measurement. Measurement science has developed certain broad principles over the centuries. They are so deep-rooted they are sometimes overlooked. The paper defines measurement largely by elucidating some of these broad principles, and defines frequency, a word subject to much interpretation, as a mathematical entity. Methods of measuring frequency are discussed. An example of the behavior of frequency during a fault, measured in accordance with all the basic principles, is given. The results are not particularly useful. Methods of improving the usefulness are discussed, but may violate some of the basic principles. In essence, “frequency” may not be the best measurand for a signal obtained during a fault.

Frequency, measurement, model, representational, o↗

Propagation Pattern for Moment Representation of the Lattice Boltzmann Method

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This article extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

42 ENGINEERING↗

Simulation of the ohmic loss in photovoltaic laser-power converters for wavelengths of 809 and 1064 nm

The method of mathematical simulation is used to examine the influence exerted by the characteristics of the epitaxial structure and contact grid of photovoltaic laser-power converters on their ohmic loss. The maximum attainable photoconverter efficiency at a Gaussian distribution of the laser-beam intensity on the surface of a photovoltaic converter and at dark-current densities of p–n junctions typical of structures grown by the metal-organic vapor-phase epitaxy (MOVPE) technique are determined. An approach to finding the optimal parameters of GaAs and In{sub 0.24}Ga{sub 0.76}As/GaAs photovoltaic converters in relation to the optical power being converted is suggested, and the structural parameters for incident-power values of 5, 20, and 50 W at wavelengths of 809 and 1064 nm are determined. It is found that, at laser-light intensities of up to 5 W, >60% efficiency can be achieved in laser-light conversion at a wavelength of 809 nm and >55% efficiency, at a wavelength of 1064 nm.

36 MATERIALS SCIENCE↗