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Results for “symbolic calculation”

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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29 records · Page 2

A SIMPLE TOOL TO EVALUATE COLOR FOR LEGIBILITY AND DISTINGUISHABILITY WHEN DESIGNING DIGITAL DISPLAYS

Color is important in helping users effectively process information like text and symbols when performing tasks on digital displays. Interface designers in safety- and mission-critical industries often utilize human factors design guidelines and standards to make important design decisions like the use of color for legibility and distinguishability. However, such guidance sometimes requires additional interpretation and calculation to readily apply to the design question at hand. This work describes a simple tool that can be used to evaluate the adequacy of color choices from a palette for being legible or distinguishable. The tool eliminates having to manually convert colors to a readable format while providing a specific set of colors that are acceptable from select human factors standards. This paper provides an exemplary case study applied to a digital modification at a nuclear power plant to highlight how the tool may be used in safety and mission-critical industries.

99 GENERAL AND MISCELLANEOUS↗

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES↗

Q-POP-Thermo: A general-purpose thermodynamics solver for ferroelectric materials

We report that Q-POP-Thermo is a program designed to compute thermodynamic monodomain equilibrium states and their properties for ferroelectric single crystals and thin films based on the Landau-Ginzburg-Devonshire (LGD) Theory. Utilizing symbolic manipulation with the SymPy Library, the governing equations along with appropriate boundary conditions are solved for speedy minimization of the free energy of a crystal. Utilizing the popular Differential Evolution algorithm, with appropriate hybridization, multiple phase diagrams, such as the pressure-temperature phase diagram for bulk single crystals and the common strain-temperature phase diagram for monodomain thin-film systems can be readily generated. Furthermore, a variety of material properties of stable ferroelectric phases, including dielectric, piezoelectric, and electrocaloric properties, can simultaneously be calculated. Validation studies are presented for both thin-film and single crystal systems to test the effectiveness and capability of the open-source program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synthesis, Crystal and Electronic Structure of the New Ternary Compound Ca3InAs3

Crystals of a new ternary compound in the Ca-In-As family, Ca3InAs3, have been successfully synthesized via flux growth techniques. This is only the third known compound between the respective elements. As elucidated by single-crystal X-ray diffraction measurements, Ca3InAs3 crystallizes in the orthorhombic space group Pnma (No. 62, Pearson symbol oP28) with unit cell parameters a = 12.296(2) Å, b = 4.2553(7) Å, and c = 13.735(2) Å. The smallest building motifs of the structure are InAs4 tetrahedra, which are connected to one another by shared As corners, forming infinite [InAs2As2/2] chains. The latter propagate along the crystallographic b-axis. The As-In-As bond angles within the InAs4 tetrahedra deviate from the ideal 109.5° value and range from 98.12(2)° to 116.53(2)°, attesting to a small distortion from the regular tetrahedral geometry. Electronic structure calculations indicate the opening of a bandgap, consistent with the expected (Ca2+)3(In3+)(As3–)3 formula breakdown based on conventional oxidation numbers. The calculations also show that the Ca–As interactions are an intermediate between covalent and ionic, while providing evidence of strong covalent features of the In–As interactions. Weak s-p hybridization of In states was observed, supporting the experimentally found deviation of the InAs4 moiety from the ideal tetrahedral symmetry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mean-field dynamo as a quantum-like modulational instability

Presented here is a novel formulation of the mean-field dynamo as a modulational instability of magnetohydrodynamic (MHD) turbulence. This formulation, termed mean-field wave kinetics (MFWK), is based on the Weyl symbol calculus and allows describing the interaction between the mean fields (magnetic field and fluid velocity) and turbulence without requiring scale separation that is commonly assumed in the literature. The turbulence is described by the Wigner–Moyal equation for the spectrum of the two-point correlation matrix (Wigner matrix) of magnetic-field and velocity fluctuations and depicts the turbulence as an effective plasma of quantum-like particles that interact via the mean fields. Eddy–eddy interactions, which serve as ‘collisions’ in this effective plasma, are modelled within the standard minimal tau approximation to aid comparison with existing theories. Using MFWK, the non-local electromotive force is calculated for generic turbulence from first principles, modulo the limitations of MFWK. This result is then used to study, both analytically and numerically, the modulational modes of MHD turbulence, which appear as linear instabilities of the said effective quantum-like plasma of fluctuations. The standard α 2 -dynamo and other known results are reproduced as special cases. A new dynamo effect is predicted that is driven by correlations between the turbulent flow velocity and the turbulent current.

astrophysical plasmas↗

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Symbolic pregression: Discovering physical laws from distorted video

In this work, we present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled synthetic video (or, more generally, for discovering and modeling predictable features in time-series data). We first train an autoencoder that maps each video frame into a low-dimensional latent space where the laws of motion are as simple as possible, by minimizing a combination of nonlinearity, acceleration, and prediction error. Differential equations describing the motion are then discovered using Pareto-optimal symbolic regression. We find that our pre-regression (“pregression”) step is able to rediscover Cartesian coordinates of unlabeled moving objects even when the video is distorted by a generalized lens. Using intuition from multidimensional knot theory, we find that the pregression step is facilitated by first adding extra latent space dimensions to avoid topological problems during training and then removing these extra dimensions via principal component analysis. An inertial frame is autodiscovered by minimizing the combined equation complexity for multiple experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the New Oxyarsenides Eu 5 Zn 2 As 5 O and Eu 5 Cd 2 As 5 O

The new quaternary phases Eu5Zn2As5O and Eu5Cd2As5O have been synthesized by metal flux reactions and their structures have been established through single-crystal X-ray diffraction. Both compounds crystallize in the centrosymmetric space group Cmcm (No. 63, Z = 4; Pearson symbol oC52), with unit cell parameters a = 4.3457(11) Å, b = 20.897(5) Å, c = 13.571(3) Å; and a = 4.4597(9) Å, b = 21.112(4) Å, c = 13.848(3) Å, for Eu5Zn2As5O and Eu5Cd2As5O, respectively. The crystal structures include one-dimensional double-strands of corner-shared MAs4 tetrahedra (M = Zn, Cd) and As–As bonds that connect the tetrahedra to form pentagonal channels. Four of the five Eu atoms fill the space between the pentagonal channels and one Eu atom is contained within the channels. An isolated oxide anion O2– is located in a tetrahedral hole formed by four Eu cations. Applying the valence rules and the Zintl concept to rationalize the chemical bonding in Eu5M2As5O (M = Zn, Cd) reveals that the valence electrons can be counted as follows: 5 × [Eu2+] + 2 × [M2+] + 3 × [As3–] + 2 × [As2–] + O2–, which suggests an electron-deficient configuration. The presumed h+ hole is confirmed by electronic band structure calculations, where a fully optimized bonding will be attained if an additional valence electron is added to move the Fermi level up to a narrow band gap (Eu5Zn2As5O) or pseudo-gap (Eu5Cd2As5O). In order to achieve such a formal charge balance, and hence, narrow-gap semiconducting behavior in Eu5M2As5O (M = Zn, Cd), europium is theorized to be in a mixed-valent Eu2+/ Eu3+ state.

36 MATERIALS SCIENCE↗

Moments of the Boltzmann collision operator for Coulomb interactions

Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A diagrammatic approach for automatically deriving analytical gradients of tensor hyper-contracted electronic structure methods

In this work, we introduce a diagrammatic approach to facilitate the automatic derivation of analytical nuclear gradients for tensor hyper-contraction (THC) based electronic structure methods. The automatically derived gradients are guaranteed to have the same scaling in terms of both operation count and memory footprint as the underlying energy calculations, and the computation of a gradient is roughly three times as costly as the underlying energy. The new diagrammatic approach enables the first cubic scaling implementation of nuclear derivatives for THC tensors fitted in molecular orbital basis (MO-THC). Furthermore, application of this new approach to THC-MP2 analytical gradients leads to an implementation, which is at least four times faster than the previously reported, manually derived implementation. Finally, we apply the new approach to the 14 tensor contraction patterns appearing in the supporting subspace formulation of multireference perturbation theory, laying the foundation for developments of analytical nuclear gradients and nonadiabatic coupling vectors for multi-state CASPT2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗