Search NASA⌕ Search

SEARCH · Search NASA

Results for “Implicit 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 73 records · Page 4

time-resolved spectroscopy fit (trspecfit) v0.01

Analyze 2D time- and energy-resolved data, such as from a pump-probe spectroscopy experiment. User can select and input different peak shapes/ functions and background types to first fit a ground state/ unperturbed spectrum. This would be similar to how standard spectroscopy data is fit. Subsequently, to describe the time domain, users can choose functions that describe the temporal dynamics of one or more spectral features, such as a peak amplitude, peak position, etc. These time dynamics functions can be added or convoluted (e.g. describing an instrument response function) with each other. Functionality to integrate implicit variables leading to distributions of certain parameters/ functions is in development. Alternatively, 2D data can be analyzed one time step at a time to get an idea of the time dynamics of the system before deploying the global 2D fit described above. Typically people write custom software for this purpose. During my PhD I've seen five internal LBL and external researchers write one-off code in different languages to analyze time- and energy-resolved spectra. While this was specifically was for a laser pump - X-ray probe spectroscopy experiment, I'm trying to write a general package for the time-resolved spectroscopy community.

Mahl, Johannes [Lawrence Berkeley National Laborat↗

BEAST DB: Grand-Canonical Database of Electrocatalyst Properties

We present BEAST DB, an open-source database comprised of ab initio electrochemical data computed using grand-canonical density functional theory in implicit solvent at consistent calculation parameters. The database contains over 20,000 surface calculations and covers a broad set of heterogeneous catalyst materials and electrochemical reactions. Calculations were performed at self-consistent fixed potential as well as constant charge to facilitate comparisons to the computational hydrogen electrode. This article presents common use cases of the database to rationalize trends in catalyst activity, screen catalyst material spaces, understand elementary mechanistic steps, analyze the electronic structure, and train machine learning models to predict higher fidelity properties. Users can interact graphically with the database by querying for individual calculations to gain a granular understanding of reaction steps or by querying for an entire reaction pathway on a given material using an interactive reaction pathway tool. BEAST DB will be periodically updated, with planned future updates to include advanced electronic structure data, surface speciation studies, and greater reaction coverage.

database↗

Rational RBF-based partition of unity method for efficiently and accurately approximating 3D objects

We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus develop an efficient local scheme via the well-known partition of unity method. The main contribution in this paper consists in constructing the local interpolants for the implicit interpolation by means of rational radial basis functions. Numerical experiments, devoted to test the accuracy of the scheme, confirm that the proposed method is particularly performing when 3D objects, or more in general implicit functions defined by scattered points, need to be approximated.

97 MATHEMATICS AND COMPUTING↗

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗

Category Theory

Functions started with an implicit definition - the dependency of some quantity on others. Functions were coined by Leibniz in 1673, were given the f(x) notation by Euler in 1734, were formalized in the language of set theory from around 1847 to 1939. Functions have since been further abstract, often capture and represent structure.

Alan Hylton↗

Investigation of solvent effects on the hydrodeoxygenation of guaiacol over Ru catalysts

The effects of a liquid phase environment on the hydrodeoxygenation of guaiacol, a prototypical lignin derived compound, have been investigated over a Ru catalyst from first principles. A microkinetic reactor model with parameters obtained from density functional theory and implicit solvation schemes was developed to study the effects of condensed phases on the reaction mechanism and kinetic parameters. Phenol was found to be the major aromatic product across all reaction environments. Our model predicts that less protic solvents such as 1-butanol, diethyl ether, and n-hexane have a positive effect on the reaction kinetics for the production of phenolics relative to vapor and aqueous reaction environments. The dominant reaction mechanism for aromatics production remains unchanged across all reaction media. Next, we investigated the possibility of cycloalkane production through hydrogenation of phenol in vapor and liquid phase environments. Our calculations indicated that the reaction pathway for cycloalkane production from phenol will most likely follow an initial dehydrogenation of the hydroxyl group. Based on the vapor phase density functional theory calculations, we proposed a probable reaction pathway and calculated the condensed phase effects along this reaction route. We observed that an aqueous phase has a more favorable effect for cycloalkane production from phenol relative to vapor phase and other less protic solvent environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theoretical Investigation of the Adsorbate and Potential–Induced Stability of Cu Facets During Electrochemical CO 2 and CO Reduction

The activity and product selectivity of electrocatalysts for reactions like the carbon dioxide reduction reaction (CO 2 RR) are intimately dependent on the catalyst's structure and composition. While engineering catalytic surfaces can improve performance, discovering the key sets of rational design principles remains challenging due to limitations in modeling catalyst stability under operating conditions. Herein, we perform first-principles density functional calculations adopting implicit solvation methods with potential control to study the influence of adsorbates and applied potential on the stability of different facets of model Cu electrocatalysts. Using coverage dependencies extracted from microkinetic models, we describe an approach for calculating potential and adsorbate-dependent contributions to surface energies under reaction conditions, where Wulff constructions are used to understand the morphological evolution of Cu electrocatalysts under CO 2 RR conditions. Here we identify that CO*, a key reaction intermediate, exhibits higher kinetically and thermodynamically accessible coverages on (100) relative to (111) facets, which can translate into an increased relative stabilization of the (100) facet during CO 2 RR. Our results support the known tendency for increased (111) faceting of Cu nanoparticles under more reducing conditions and that the relative increase in (100) faceting observed under CO 2 RR conditions is likely attributed to differences in CO* coverage between these facets.

30 DIRECT ENERGY CONVERSION↗

Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

This study proposes an automated calibration procedure for bond parameters in bonded discrete element modelling. By exploring the underlying physical correlations between microscopic parameters of bonds and macroscopic strength parameters of the continuum to be modelled, the microscopic shear strength and tensile strength are identified as independent variables for calibration purpose. Then a physics-informed iterative scheme is proposed to automatically approximate the bond parameters by viewing the micro-macro relation as an implicitly defined mathematical mapping function. As a result of highly non-convex features of this implicit mapping, the adaptive moment estimation (Adam), which is especially suitable for problems with noisy gradients, is adopted as the basic iterative scheme, in conjunction with other numerical techniques to approximately evaluate the partial derivatives involved. The whole procedure offers a simple and effective framework for bond parameter calibration. Finally, a numerical example of SiC ceramic is provided for validation. By compared with some existing calibration methods, the proposed method shows significant advantages in terms of calibration efficiency and accuracy.

42 ENGINEERING↗

Assembly of three-dimensional binary superlattices from multi-flavored particles

Binary superlattices constructed from nano- or micron-sized colloidal particles have a wide variety of applications, including the design of advanced materials. Self-assembly of such crystals from their constituent colloids can be achieved in practice by, among other means, the functionalization of colloid surfaces with single-stranded DNA sequences. However, when driven by DNA, this assembly is traditionally premised on the pairwise interaction between a single DNA sequence and its complement, and often relies on particle size asymmetry to entropically control the crystalline arrangement of its constituents. The recently proposed “multi-flavoring” motif for DNA functionalization, wherein multiple distinct strands of DNA are grafted in different ratios to different colloids, can be used to experimentally realize a binary mixture in which all pairwise interactions are independently controllable. Here we use various computational methods, including molecular dynamics and Wang–Landau Monte Carlo simulations, to study a multi-flavored binary system of micron-sized DNA-functionalized particles modeled implicitly by Fermi–Jagla pairwise interactions. We show how self-assembly of such systems can be controlled in a purely enthalpic manner, and by tuning only the interactions between like particles, demonstrate assembly into various morphologies. Although polymorphism is present over a wide range of pairwise interaction strengths, we show that careful selection of interactions can lead to the generation of pure compositionally ordered crystals. Additionally, we show how the crystal composition changes with the like-pair interaction strengths, and how the solution stoichiometry affects the assembled structures.

36 MATERIALS SCIENCE↗

Demonstration of resonant inelastic x-ray scattering as a probe of exciton-phonon coupling

Resonant inelastic x-ray scattering (RIXS) is a promising technique for obtaining electron-phonon coupling constants. However, the ability to extract these coupling constants throughout the Brillouin zone for crystalline materials remains limited. To address this need, we developed a Green's function formalism to capture electron-phonon contributions to core-level spectroscopies without explicitly solving the full vibronic problem. Our approach is based on the cumulant expansion of the Green's function combined with many-body theory calculated vibrational coupling constants. The methodology is applied to x-ray photoemission spectroscopy, x-ray absorption spectroscopy (XAS), and RIXS. In the case of the XAS and RIXS, we use a two-particle exciton Green's function, which accounts implicitly for particle-hole interference effects that have previously proved difficult. To demonstrate the methodology and gain a deeper understanding of the experimental technique, we apply our formalism to small molecules, for which unambiguous experimental data exist. This comparison reveals that the vibronic coupling constant probed by RIXS is in fact related to exciton-phonon coupling rather than electron-phonon coupling, challenging the conventional interpretation of the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Simulation of separated flow past a bluff body using Navier-Stokes equations

Two-dimensional flow past a bluff body is presently simulated on the basis of an analysis that employs the incompressible, unsteady Navier-Stokes equations in terms of vorticity and stream function. The fully implicit, time-marching, alternating-direction, implicit-block Gaussian elimination used is a direct method with second-order spatial accuracy; this allows it to avoid the introduction of any artificial viscosity. Attention is given to the simulation of flow past a circular cylinder with and without symmetry, requiring the use of either the half or the full cylinder, respectively.

Ghia, K. N.↗

Arctic Shrub Expansion, Plant Functional Trait Variation, and Effects on Belowground Carbon Cycling (Final Technical Report)

Terrestrial ecosystems are undergoing dramatic changes in response to climate warming, and these changes are expected to feedback to the atmosphere, potentially altering the trajectory of future climate change. Feedbacks from Arctic ecosystems are a major concern because the Arctic is projected to warm significantly in the 21 st century and because >50% of global belowground organic carbon is stored in permafrost and overlying soils. Warming-driven release of this carbon could drastically increase atmospheric greenhouse gas concentrations and accelerate climate warming. Plant communities are also responding to warming, as evidenced by the widely documented increase in woody-shrub growth and “greening” across much of the Arctic tundra biome. This vegetation shift may offset or amplify warming by altering carbon cycling. The direction and magnitude of shrub effects remain highly uncertain, however, due to limited understanding of the consequences of shrub expansion for belowground carbon cycling and simplification of these relationships in models. The major shrubs expanding in the Arctic (Betula, Salix, and Alnus) vary widely with respect to aboveground and belowground traits (e.g., tissue production and chemistry, rooting depth, microbial symbionts), and may also exhibit substantial intraspecific variation in these traits in response to environmental conditions. Such variation is likely to have profound implications for soil carbon cycling. The overarching goal of this project was to improve process-based understanding of the influence of shrub expansion on carbon cycling to enable improved representation of carbon dynamics in ecosystem and Earth system models. We investigated how plant functional traits vary among shrub genera, respond to environmental conditions, and affect belowground carbon and nutrient cycling by quantifying relationships among functional traits and biogeochemical cycling along edaphic gradients nested within a climate gradient in the Alaskan tundra. We found consistent differences in leaf and root traits among shrub genera and between shrubs and a widespread sedge species, indicating diverse nutrient acquisition strategies and belowground impacts among different arctic shrubs. We also found striking differences in trait values among individuals within the same species or genera within sites. Soil parameters were more important than climate parameters for predicting size and leaf trait variation, and root trait responses were less dependent on climate overall. For all but one root trait, including parameters representing aboveground traits improved the predictive ability of models. These results demonstrate that tundra shrub traits vary considerably at local scales and soil factors drive this variation, especially belowground. Furthermore, leveraging information about aboveground traits and soil conditions can improve predictions of how belowground traits will respond to climate change. Despite these differences, soil carbon and nitrogen pools in the active layer did not vary among plots dominated by different shrub or sedge genera. Instead, pool sizes generally decreased from warmer to colder sites, consistent with a productivity gradient. Patterns of isotopic N composition indicate that shrubs tighten nitrogen cycling via nitrogen resorption or immobilization of shrub litter. Overall, these results suggest that further identifying the specific shrub genera in the tundra landscape will ultimately provide better predictions of belowground dynamics across the changing arctic. We also performed simulation experiments with the Terrestrial Ecosystem Model (TEM) incorporated in the Predictive Ecosystem Analyzer (PEcAn) framework, treats model parameters as probability distributions, estimates parameters based on a synthesis of available field data, and then quantifies both model sensitivity and uncertainty to a given parameter or suite of parameters. We performed simulations across different types of tundra, including shrub tundra. One key finding was that both model sensitivity and uncertainty to a given parameter could vary within the same type of tundra, but in a different geographical location, such as over the climate gradient of shrub tundra described above. We organized a special session at the annual meeting of the Ecological Society of America in August 2019 to disseminate our results, refine recommendations for model improvement, and initiate collaborations to implement these recommendations in existing models of tundra carbon dynamics at ecosystem to Earth system scales. Our results support DOE near-term priorities by providing mechanistic insights into the role of vegetation change in the terrestrial carbon cycle in a region that is inadequately represented in Earth system models. Current models reduce the complexity of Arctic vegetation to a small number of plant functional types (PFTs). This approach implicitly assumes that each PFT represents the average ecological function of its constituent species, thus ignoring the effects of trait variation on biogeochemical cycling and potentially leading to large uncertainty in the sign and magnitude of ecosystem feedbacks to climate. By quantifying variation of plant functional traits across broad gradients of climatic and edaphic conditions and elucidating the linkages of such variation with carbon and nutrient cycling, our results illustrate the need and create a foundation for further developing trait-based modeling approaches that allow the traits of PFTs to vary as a function of environmental conditions. These approaches should improve the capacity of simulation models to offer insights into ecosystem carbon dynamics associated with novel plant communities in a rapidly changing Arctic.

54 ENVIRONMENTAL SCIENCES↗

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗

Derivation of the fundamental equation of sound generated by moving aerodynamic surfaces

Ffowcs Williams and Hawkings (1969) based their derivation of the fundamental equation of the sound generated by arbitrarily moving aerodynamic surfaces on the study of mass and momentum balance of a control volume imbedding a mathematical surface(s) exactly corresponding to real surface(s). These investigators also sketched an alternative method, employing generalized functions, for its derivation. This latter method, which was later developed by Farassat (1975), is purely mathematical and formal. Goldstein (1976) used the free-space Green function to produce an implicit derivation of the Ffowcs Williams and Hawkings equation. In the study presented here, Lowson's (1965) concept of moving point singularities is generalized to moving surface singularities, and a new derivation is given of the fundamental equation. The derivation is based on topological considerations of the underlying space, the fluid medium, and the integral properties of the Dirac delta function.

Aggarwal, H. R.↗

Implicit renormalization approach to the problem of Cooper instability

In the vast majority of cases, superconducting transition takes place at exponentially low temperature T c out of the Fermi liquid regime. We discuss the problem of determining T c from known system properties at temperatures T >> T c , and stress that this cannot be done reliably by following the standard protocol of solving for the largest eigenvalue of the original gap-function equation. However, within the implicit renormalization approach, the gap-function equation can be used to formulate an alternative eigenvalue problem, where solving leads to an accurate prediction for both T c and the gap function immediately below T c . Furthermore, with diagrammatic Monte Carlo techniques, this eigenvalue problem can be solved without invoking the matrix inversion or even explicitly calculating the four-point vertex function.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reaction Energetics and 13 C Fractionation of Alanine Transamination in the Aqueous and Gas Phases

The alanine transaminase enzyme catalyzes the transfer of an amino group from alanine to α-ketoglutarate to produce pyruvate and glutamate. Isotope fractionation factors (IFFs) for the reaction +H 3 NCH(CH 3 )COO – + – OOCCH 2 CH 2 C(O)COO – ↔ CH 3 C(O)COO – + + H 3 NCH(CH 2 CH 2 COO – )COO – (zwitterionic neutral alanine + doubly deprotonated α-ketoglutarate ↔ pyruvate + zwitterionic glutamate anion) were calculated from the partition functions of explicitly and implicitly solvated molecules at 298 K. Calculations were done for alanine (noncharge separated, zwitterion, deprotonated), pyruvic acid (neutral, deprotonated), glutamic acid (noncharge separated, zwitterion, deprotonated, doubly deprotonated), and α-ketoglutaric acid (neutral, deprotonated, doubly deprotonated). The computational results, calculated from gas phase- and aqueous-optimized clusters with explicit H 2 O molecules at the MP2/aug-cc-pVDZ and MP2/aug-cc-pVDZ/COSMO levels, respectively, predict that substitution of 13 C at the C2 position of alanine and pyruvic acid and their various forms leads to the C2 position of pyruvic acid/pyruvate being enriched in 13 C/ 12 C ratio by 9‰. Simpler approaches that estimate the IFFs based solely on changes in the zero-point energies (ZPEs) are consistent with the higher-level model. ZPE-based IFFs calculated for simple analogues formaldehyde and methylamine (analogous to the C2 positions of pyruvate and alanine, respectively) predict a 13 C enrichment in formaldehyde of 7–8‰ at the MP2/aug-cc-pVDZ and aug-cc-pVTZ levels. A simple predictive model using canonical functional group frequencies and reduced masses for 13 C exchange between R 2 C=O and R 2 CH–NH 2 predicted enrichment in R 2 C=O that is too large by a factor of two but is qualitatively accurate compared with the more sophisticated models. Our models are all in agreement with the expectation that pyruvate and formaldehyde will be preferentially enriched in 13 C because of the strength of their >C=O bond relative to that of ≡C–NH 2 in alanine and methylamine. 13 C/ 12 C substitution is also modeled at the methyl and carboxylic acid sites of alanine and pyruvic acid, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗