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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2024

Efficient simulations of charge density waves in the transition metal Dichalcogenide TiSe 2

Charge density waves (CDWs) in transition metal dichalcogenides are the subject of growing scientific interest due to their rich interplay with exotic phases of matter and their potential technological applications. Here, using density functional theory with advanced meta-generalized gradient approximations (meta-GGAs) and linear response time-dependent density functional theory (TDDFT) with state-of-the-art exchange-correlation kernels, we investigate the electronic, vibrational, and optical properties in 1T-TiSe 2 with and without CDW. In both bulk and monolayer TiSe 2 , the electronic bands and phonon dispersions in either normal or CDW (semiconducting) phase are described well via meta-GGAs, which separate the valence and conduction bands just as HSE06 does but with significantly more computational feasibility. The experimentally observed humps of electron energy loss spectroscopy are successfully reproduced in TDDFT. Our work opens the door to simulating these complexities in CDW compounds from first principles by revealing meta-GGAs as an accurate low-cost alternative to HSE06.

Electronic properties and materials↗
DOE OSTI2024

Density functional theory of material design: fundamentals and applications—II

Abstract This is the second and the final part of the review on density functional theory (DFT), referred to as DFT-II. In the first review, DFT-I, we have discussed wavefunction-based methods, their complexity, and basics of density functional theory. In DFT-II, we focus on fundamentals of DFT and their implications for the betterment of the theory. We start our presentation with the exact DFT results followed by the concept of exchange-correlation (xc) or Fermi-Coulomb hole and its relationship with xc energy functional. We also provide the exact conditions for the xc-hole, xc-energy and xc-potential along with their physical interpretation. Next, we describe the extension of DFT for non-integer number of electrons, the piecewise linearity of total energy and discontinuity of chemical potential at integer particle numbers, and derivative discontinuity of the xc potential, which has consequences on fundamental gap of solids. After that, we present how one obtains more accurate xc energy functionals by going beyond the LDA. We discuss the gradient expansion approximation (GEA), generalized gradient approximation (GGA), and hybrid functional approaches to designing better xc energy functionals that give accurate total energies. However, these functionals fail to predict properties like the ionization potential and the band gap. Thus, we next describe different methods of modelling these potentials and results of their application for calculation of the band gaps of different solids to highlight accuracy of different xc potentials. Finally, we conclude with a glimpse on orbital-free density functional theory and the machine learning approach.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Systems and methods for producing metal clusters; functionalized surfaces; and droplets including solvated metal ions

The invention generally relates to systems and methods for producing metal clusters; functionalized surfaces; and droplets including solvated metal ions. In certain aspects, the invention provides methods that involve providing a metal and a solvent. The methods additionally involve applying voltage to the solvated metal to thereby produce solvent droplets including ions of the metal containing compound, and directing the solvent droplets including the metal ions to a target. In certain embodiments, once at the target, the metal ions can react directly or catalyze reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Generalized parton distributions through universal moment parameterization: zero skewness case

We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions (PDFs) from phenomenology and generalized form factors from lattice calculations, and show that the parameterization is flexible enough to accommodate these constraints. In addition, we can also fit direct lattice calculations of GPDs from large-momentum effective theory. In this work we focus on the analysis of t-dependent PDFs which correspond to GPDs in the ξ → 0 limit. The strategy also applies to the ξ ≠ 0 region with extra parameters, and therefore can be fitted to experimental observables in the future. With a demonstrative example of fitted GPDs, we exhibit the quark transverse angular momentum densities of the proton as well as the impact parameter space distributions of quarks in both unpolarized and transversely polarized protons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

Overview of the fatigue/fracture/life working group program at the Lewis Research Center

Constitutive and life prediction models are developed and verified for materials typically used in hot gas path components of reusable space propulsion systems over the range of relevant operating environments. The efforts were centered on the development of crack initiation life prediction methods, while the efforts of a counterpart group were centered on the development of cyclic crack propagation life prediction methods. The complexion of the active tasks are presented. A significant new task started this year will incorporate the various material constitutive and life prediction models developed in this program into a comprehensive creep-fatigue damage analysis and life assessment computer code. The program will function as a postprocessor to general structural analysis programs (such as finite element or boundary element codes) using the output of such analyses (stress, strain, and temperature fields as functions of time) as the input to the damage analysis and life assessment code. The code will be designed to execute on engineering/scientific workstations and will feature a windowing, mouse-driven user interface. Current plans call for the code to be finished and made available for use in mid 1991.

Mcgaw, Michael A.↗
DOE OSTI2023

Exact and Model Exchange-Correlation Potentials for Open-Shell Systems

The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn–Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. Here, we present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn–Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems–four atoms (Li, C, N, and O) and two molecules (CN and CH 2 )–using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of $O$(10 –3 to 10 –2 ), the relative errors in the model XC potentials remain substantially large–$O$(10 –1 to 10 0 ).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Tal-Ezer, Hillel↗
DOE OSTI2023

Delayed leaf greening involves a major shift in the expression of cytosolic and mitochondrial ribosomes to plastid ribosomes in the highly phosphorus-use-efficient Hakea prostrata (Proteaceae)

Abstract Background and aims Hakea prostrata (Proteaceae) is a highly phosphorus-use-efficient plant native to southwest Australia. It maintains a high photosynthetic rate at low leaf phosphorus (P) and exhibits delayed leaf greening, a convergent adaptation that increases nutrient-use efficiency. This study aimed to provide broad physiological and gene expression profiles across leaf development, uncovering pathways leading from young leaves as nutrient sinks to mature leaves as low-nutrient, energy-transducing sources. Methods To explore gene expression underlying delayed greening, we analysed a de novo transcriptome for H. prostrata across five stages of leaf development. Photosynthesis and respiration rates, and foliar pigment, P and nitrogen (N) concentrations were determined, including the division of P into five biochemical fractions. Key results Transcripts encoding functions associated with leaf structure generally decreased in abundance across leaf development, concomitant with decreases in foliar concentrations of 85% for anthocyanins, 90% for P and 70% for N. The expression of genes associated with photosynthetic function increased during or after leaf expansion, in parallel with increases in photosynthetic pigments and activity, much later in leaf development than in species that do not have delayed greening. As leaves developed, transcript abundance for cytosolic and mitochondrial ribosomal proteins generally declined, whilst transcripts for chloroplast ribosomal proteins increased. Conclusions There was a much longer temporal separation of leaf cell growth from chloroplast development in H. prostrata than is found in species that lack delayed greening. Transcriptome-guided analysis of leaf development in H. prostrata provided insight into delayed greening as a nutrient-saving strategy in severely phosphorus-impoverished landscapes.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1974

Operations on power series and higher derivatives of functions

Equations are derived for the general terms of the series obtained when certain operations are carried out on one or several given series. Explicit and recurrence relations are given for the literal groups which are common to the given series. A general method is shown to obtain the multipliers which depend on the operation being performed, and the method is illustrated for several examples.

Chang, F.-C.↗
DOE OSTI2023

Shock-induced metallization of polystyrene along the principal Hugoniot investigated by advanced thermal density functionals

To date, none of the ab-initio molecular dynamics simulations of polystyrene, often used as an ablator material in inertial confinement fusion targets, with the standard ground-state exchange-correlation (XC) functional in density-functional theory can satisfactorily agree with experiments in terms of reflectivity measurements. Here, we use recently developed thermal strongly constrained and appropriately normed Laplacian dependent meta-generalized gradient approximation XC density functional (T-SCAN-L) and thermal hybrid XC density functional (KDT0) to show that the inclusion of thermal and inhomogeneity effects is crucial for accurate prediction of structural evolution and corresponding insulator-metal transition (IMT) during shock compression. Optical reflectivity calculated as an indicator of IMT is in perfect accord with experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1976

Thermodynamics of two-dimensional plasmas or discrete line vortex fluids

The equilibrium properties of a two-dimensional plasma are examined theoretically within the framework of the random-phase approximation. The guiding-center case is of most interest because of the formal equivalence to two-dimensional discrete-line vortex fluids and because of the formal admissibility of negative temperatures. Using a judicious treatment of the periodic boundary conditions, extensive thermodynamics for nonnegative temperatures and a new value for the energy at which the temperature becomes negative are found. An explicit form for the structure function is derived and compared with the result of a Monte Carlo calculation. Good agreement is found for the negative-temperature-threshold prediction and for the general shape of the structure function. An equilibrium energy spectrum is calculated, which for positive temperatures, is the Debye-Hueckel result; for negative temperatures, it predicts an enhanced excitation of the lowest mode, corresponding to macroscopic charge separation.

Seyler, C. E., Jr.↗
NASA NTRS1978

Stochastic inverse problem in the radiation of noise

The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.

Chow, P. L.↗
DOE OSTI2024

Tagged DVCS on neutron with the CLAS12 Experiment and the detector BONuS12 at Jefferson Lab (USA)

Hadronic physics studies the properties of the proton and neutron. The theory of Quantum Chromodynamics (QCD) governs the structure of hadrons. Non-perturbative structure functions are used to describe the hadrons? structure. Generalized Parton Distributions (GPDs) are a set of structure functions providing access to a 3D view of the nucleon. GPDs contain information about the longitudinal momentum and transverse position of quarks and their correlation. They are related to the spin structure and play a role in solving the proton spin puzzle. They provide access to the quarks? orbital angular momentum, a crucial puzzle piece. For this, measurements on the proton, already present, and neutron are necessary. This thesis aims to explore Compton scattering on the neutron with a deuterium target by measuring the spectator proton with the CLAS12 detector and the BONuS12 RTPC at Jefferson Lab. This work first describes the implementation, which I carried out, of a Kalman filter to reconstruct spectator protons in the BONuS12 detector. The second part of the manuscript is dedicated to the work on the analysis of DVCS on the neutron with the subtraction of background noises. Two different methods for the subtraction of ?0 will be detailed. Finally, the obtained results are presented and discussed

Ouillon, Mathieu↗
NASA NTRS1988

On a useful functional representation of control system structure

An alternative structure for control systems is proposed. The structure is represented by a three-element block diagram and three functional definitions. It is argued that the three functional elements form a canonical set. The set includes the functions description, estimation and control. General overlay of the structure on parallel state and nested-state control systems is discussed. Breakdown of two real nested-state control systems into the proposed functional format is displayed. Application of the process to the mapping of complex control systems R and D efforts is explained with the Mars Rover Sample and Return mission as an example. A previous application of this basic functional structure to Space Station performance requirements organization is discussed.

Malchow, Harvey L.↗