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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.

Farassat, F.↗
DOE OSTI2024

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗
NASA NTRS1992

Variational derivation of equation for generalized pair correlation function

The wavefunction of a system is explicitly written down in a fully anti-symmetric way between a fermion pair and a medium, and the equations for each one of them are derived from the variation of total energy for bound systems and by forming appropriate scalar products for continuum states. High-energy particles, such as protons, electrons, and nuclei impinging upon spacecraft, produce secondary radiations. In order to protect the internal environment of spacecraft from these radiations, their intensities are determined in many instances theoretically, and an appropriate program has been developed in the High Energy Science Branch. The purpose of this research is to investigate the problem of indistinguishability of an incident projectile with one of the same in a target.

Malik, F. Bary↗
NASA NTRS1972

Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations

Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.

Miller, C. D.↗
NASA NTRS1983

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Baumeiste, K. J.↗
NASA NTRS1983

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Baumeister, K. J.↗
NASA NTRS1985

FIT: Computer Program that Interactively Determines Polynomial Equations for Data which are a Function of Two Independent Variables

A computer program for interactively developing least-squares polynomial equations to fit user-supplied data is described. The program is characterized by the ability to compute the polynomial equations of a surface fit through data that are a function of two independent variables. The program utilizes the Langley Research Center graphics packages to display polynomial equation curves and data points, facilitating a qualitative evaluation of the effectiveness of the fit. An explanation of the fundamental principles and features of the program, as well as sample input and corresponding output, are included.

Arbuckle, P. D.↗
NASA NTRS1993

Effect of design selection on response surface performance

The mathematical formulation of the engineering optimization problem is given. Evaluation of the objective function and constraint equations can be very expensive in a computational sense. Thus, it is desirable to use as few evaluations as possible in obtaining its solution. In solving the equation, one approach is to develop approximations to the objective function and/or restraint equations and then to solve the equation using the approximations in place of the original functions. These approximations are referred to as response surfaces. The desirability of using response surfaces depends upon the number of functional evaluations required to build the response surfaces compared to the number required in the direct solution of the equation without approximations. The present study is concerned with evaluating the performance of response surfaces so that a decision can be made as to their effectiveness in optimization applications. In particular, this study focuses on how the quality of approximations is effected by design selection. Polynomial approximations and neural net approximations are considered.

Carpenter, William C.↗
NASA NTRS1976

A mathematical simulation model of a 1985-era tilt-rotor passenger aircraft

A mathematical model for use in real-time piloted simulation of a 1985-era tilt rotor passenger aircraft is presented. The model comprises the basic six degrees-of-freedom equations of motion, and a large angle of attack representation of the airframe and rotor aerodynamics, together with equations and functions used to model turbine engine performance, aircraft control system and stability augmentation system. A complete derivation of the primary equations is given together with a description of the modeling techniques used. Data for the model is included in an appendix.

Mcveigh, M. A.↗
DOE OSTI2021

Multiphase tin equation of state using density functional theory

In this work, we perform density functional theory (DFT) calculations of five solid phases and the liquid phase of tin. The calculations include cold curves of the five solid phases, phonon calculations in the quasiharmonic approximation over a range of volumes for each solid phase, and DFT-based molecular dynamics (DFT-MD) simulations of the liquid phase, including those of the melt curve using the Z method. Using the DFT results, we construct a tabular multiphase sesame equation of state for tin, referred to as sesame 2162. Comparisons to experimental data are made and show a high level of agreement in isobaric data, isothermal data, shock data, and phase boundary measurements, including measurements of the melt curve. The 2162 EOS will be useful for hydrodynamics simulations and has been designed with an eye toward hydrodynamics simulations that incorporate materials strength models and allow for modeling of the kinetics of phase transitions.

3-dimensional systems↗
NASA NTRS2009

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

Johnson, W. L.↗
NASA NTRS1972

Dissipative systems.

A theory is presented that shows how the concept of dissipative systems of ordinary differential equations can be extended to include a broad class of functional and partial differential equations, such as retarded functional differential equations and parabolic partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions would not be too difficult.

Lasalle, J. P.↗
DOE OSTI2020

Liouville theory, AdS 2 string, and three-point functions

This is a write-up of the lectures given in Young Researchers Integrability School 2017. The main goal is to explain the connection between the ODE/IM correspondence and the classical integrability of strings in AdS. As a warm up, we first discuss the classical three-point function of the Liouville theory. The starting point is the well-known fact that the classical solutions to the Liouville equation can be constructed by solving a Schrodinger-like differential equation. We then convert it into a set of functional equations using a method similar to the ODE/IM correspondence. The classical three-point functions can be computed directly from these functional equations, and the result matches with the classical limit of the celebrated DOZZ formula. We then discuss the semi-classical three-point function of strings in AdS 2 and show that one can apply a similar idea by making use of the classical integrability of the string sigma model on AdS 2 . Furthermore, the result is given in terms of the "massive" generalization of Gamma functions, which show up also in string theory on pp-wave backgrounds and the twistorial generalization of topological string.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Modeling and experimental validation of a W f /W-fabrication by chemical vapor deposition and infiltration

Tungsten (W) has a unique combination of excellent thermal properties, low sputter yield, low hydrogen retention, and acceptable activation. Therefore, W is presently the main candidate for the first wall material in future fusion devices. However, its intrinsic brittleness and its further embrittlement during operation bears the risk of a sudden and catastrophic component failure. As a countermeasure, tungsten fiber-reinforced tungsten (W f /W) with extrinsic toughening is being developed. A possible synthesis route is chemical vapor deposition (CVD) using heated W fabrics as substrate. The challenge is that the growing CVD-W can isolate domains from precursor access leading to strength-reducing pores. To deepen the process understanding and to optimize the CVD parameters, models were developed with COMSOL Multiphysics and validated experimentally. W deposition rate equations as function of the temperature and the partial pressures of the precursors H 2 and WF 6 were experimentally validated in previous work. In the present article, these equations are applied to obtain partial pressures within the CVD reactor. The results are taken as input for transient simulations in the microscale, in which W coatings, growing onto multiple adjacent W fibers, were simulated via mesh deformation and remeshing. The surface-to-surface contact of the W coatings and the corresponding potential pore formation were simulated by implementing sophisticated deposition rate stop conditions. Within the measuring uncertainties of ≃ ±1%, the models are validated successfully by experimental comparison regarding the deposition rate, pore structure, and relative densities ranging from 0.6 to 0.9.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗