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NASA NTRS1987

Extension of Kirchhoff's formula to radiation from moving surfaces

Kirchhoff's formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoff's formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applies to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. In addition, Morgans' result is further extended by showing that edge line integrals appear in the formula when applied to a surface that is piecewise smooth. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

Farassat, F.↗

NASA NTRS1988

Extension of Kirchhoff's formula to radiation from moving surfaces

Farassat, F.↗

NASA NTRS2004

Model of Mixing Layer With Multicomponent Evaporating Drops

A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The study is motivated by the fact that typical real petroleum fuels contain hundreds of chemical species. Previously, for the sake of computational efficiency, spray studies were performed using either models based on a single representative species or models based on surrogate fuels of at most 15 species. The present multicomponent model makes it possible to perform more realistic simulations by accounting for hundreds of chemical species in a computationally efficient manner. The model is used to perform Direct Numerical Simulations in continuing studies directed toward understanding the behavior of liquid petroleum fuel sprays. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and the drops, respectively. This representation is consistent with the expected volumetrically small loading of the drops in gas (of the order of 10 3), although the mass loading can be substantial because of the high ratio (of the order of 103) between the densities of liquid and gas. The drops are treated as point sources of mass, momentum, and energy; this representation is consistent with the drop size being smaller than the Kolmogorov scale. Unsteady drag, added-mass effects, Basset history forces, and collisions between the drops are neglected, and the gas is assumed calorically perfect. The model incorporates the concept of continuous thermodynamics, according to which the chemical composition of a fuel is described probabilistically, by use of a distribution function. Distribution functions generally depend on many parameters. However, for mixtures of homologous species, the distribution can be approximated with acceptable accuracy as a sole function of the molecular weight. The mixing layer is initially laden with drops in its lower stream, and the drops are colder than the gas. Drop evaporation leads to a change in the gas-phase composition, which, like the composition of the drops, is described in a probabilistic manner

Bellan, Josette↗

NASA NTRS1983

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.↗

DOE OSTI2023

Real-space Green's function approach for intrinsic losses in x-ray spectra

Intrinsic inelastic losses in x-ray spectra originate from excitations in an interacting electron system due to a suddenly created core-hole. These losses characterize the features observed in x-ray photoemission spectra (XPS), as well as many-body effects such as satellites and edge-singularities in x-ray absorption spectra (XAS). However, they are usually neglected in practical calculations. As shown by Langreth these losses can be treated within linear response in terms of a cumulant Green's function in momentum space. Here we present a complementary ab initio real-space Green's function generalization of the Langreth cumulant in terms of the dynamically screened core-hole interaction W c (ω) and the independent particle response function. Here we find that the cumulant kernel β⁡(ω) is analogous to XAS, but with the transition operator replaced by the core-hole potential with monopole selection rules. The behavior reflects the analytic structure of the loss function, with peaks near the zeros of the dielectric function, consistent with delocalized quasiboson excitations. The approach simplifies when W c (ω) is localized and spherically symmetric. In conclusion, illustrative results and comparisons are presented for the electron gas, sodium, and some early transition metal compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1974

An evaluation of Skylab habitability hardware

For effective mission performance, participants in space missions lasting 30-60 days or longer must be provided with hardware to accommodate their personal needs. Such habitability hardware was provided on Skylab. Equipment defined as habitability hardware was that equipment composing the food system, water system, sleep system, waste management system, personal hygiene system, trash management system, and entertainment equipment. Equipment not specifically defined as habitability hardware but which served that function were the Wardroom window, the exercise equipment, and the intercom system, which was occasionally used for private communications. All Skylab habitability hardware generally functioned as intended for the three missions, and most items could be considered as adequate concepts for future flights of similar duration. Specific components were criticized for their shortcomings.

Stokes, J.↗

NASA NTRS1994

Coordinated scheduling for dynamic real-time systems

In this project, we addressed issues in coordinated scheduling for dynamic real-time systems. In particular, we concentrated on design and implementation of a new distributed real-time system called R-Shell. The design objective of R-Shell is to provide computing support for space programs that have large, complex, fault-tolerant distributed real-time applications. In R-shell, the approach is based on the concept of scheduling agents, which reside in the application run-time environment, and are customized to provide just those resource management functions which are needed by the specific application. With this approach, we avoid the need for a sophisticated OS which provides a variety of generalized functionality, while still not burdening application programmers with heavy responsibility for resource management. In this report, we discuss the R-Shell approach, summarize the achievement of the project, and describe a preliminary prototype of R-Shell system.

Natarajan, Swaminathan↗

NASA NTRSDate not supplied

Standard Measures During Spaceflight

The key goal of the Spaceflight Standard Measures project is to ensure that a set of measures, representing the Human Research Program’s key risks and acquired with minimal impact on time and resources, is consistently captured from crewmembers through the end of the International Space Station (ISS) Program. Data collected under the Spaceflight Standard Measures project include assessments of sleep/wake cycles, cognition, immune status and function, general blood and urine chemistry (urine is collected only before flight and after landing), microbiome composition (gastrointestinal tract, saliva, and body surface), cardiovascular structure and function (carotid intima-media thickness, orthostatic responses), sensorimotor function, and team processes. Data is collected once or twice before the flight (180 and 90 days before launch), twice during the 6-month missions (fight day 30 and 30 days before return to Earth) with the exception of actigraphy, which is recorded continuously during the mission, and during two-week periods before and after the mission. In this presentation, we will review the data collected to date on twelve ISS crew members. These data are placed in the NASA Life Sciences Data Archive and are available for occupational surveillance (using non-identifiable data) Institutional Review Board-approved data sharing requests, and retrospective data requests. This data repository enables high-level monitoring of the effectiveness of countermeasures and meaningful interpretation of health and performance outcomes for various mission durations. The knowledge gained from this project informs and supports future hypothesis-driven research that will enable the success of planetary missions.

G R Clement↗

NASA NTRSDate not supplied

Standard Measures During Spaceflight

The goal of the Spaceflight Standard Measures project is to ensure that a set of measures, representing the Human Research Program’s key risks and acquired with minimal impact on time and resources, is consistently captured from crewmembers through the end of the International Space Station (ISS) Program. Data collected under the Spaceflight Standard Measures project include assessments of sleep/wake cycles, cognition, immune status and function, general blood and urine chemistry (urine is collected only before flight and after landing), microbiome composition (gastrointestinal tract, saliva, and body surface), cardiovascular structure and function (carotid intima-media thickness, orthostatic responses), sensorimotor function, sleep quality, and team processes. Data is collected once or twice before the flight (180 and 90 days before launch), twice during the 6-month missions (flight day 30 and 30 days before return to Earth) with the exception of actigraphy, which is recorded during two-week periods before, during, and after the mission. In this presentation, we will review the data collected to date on 31 ISS crewmembers. These data are placed in the NASA Life Sciences Portal (NLSP) and are available for occupational surveillance (using non-identifiable data), Institutional Review Board-approved data sharing requests, and retrospective data requests. This data repository enables high-level monitoring of the effectiveness of countermeasures and meaningful interpretation of health and performance outcomes for various mission durations. The knowledge gained from this project informs and supports future hypothesis-driven research that will enable the success of planetary missions.

G R Clement↗

NASA NTRS2023

Distorted-Toroidal Flux Rope Model

The 3D characterization of magnetic flux ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitations on inferring the 3D global topology and physical properties from the 1D time series from any spacecraft. To advance our understanding of magnetic flux ropes whose configuration departs from the typical stiff geometries, here we present an analytical solution for a 3D flux rope model with an arbitrary cross section and a toroidal global shape. This constitutes the next level of complexity following the elliptic-cylindrical (EC) geometry. The mathematical framework was established by Nieves-Chinchilla et al. with the EC flux rope model, which describes a magnetic topology with an elliptical cross section as a first approach to changes in the cross section. In the distorted-toroidal flux rope model, the cross section is described by a general function. The model is completely described by a nonorthogonal geometry and the Maxwell equations can be consistently solved to obtain the magnetic field and relevant physical quantities. As a proof of concept, this model is generalized in terms of the radial dependence of current density components. The last part of this paper is dedicated to a specific function, F (φ) = δ (1 - λ cosφ), to illustrate possibilities of the model. This model paves the way toward the investigation of complex distortions of magnetic structures in the solar wind. Future investigations will explore these distortions in depth by analyzing specific events; studying implications for physical quantities, such as magnetic fluxes, helicity, or energy; and evaluating the force balance with the ambient solar wind that allows such distortions.

Solar wind↗

NASA NTRS1974

Stability properties of functional difference equations

Hale and Cruz (1970) have defined the concept of a stable difference operator, and have found that this class of operators is sometimes 'super sensitive' to perturbations. In the present paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations. Also, the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions, and essentially bounded functions.

Melvin, W. R.↗

NASA NTRS2017

Linear Actuator System for the NASA Docking System

The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS, which implements the Soft Impact Mating and Attenuation Concept (SIMAC). This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.

Dick, Brandon↗

NASA NTRS1992

Detection of x ray sources in PROS

The problem of detecting discrete sources in x-ray images has much in common with the problem of automatic source detection at other wavelengths. In all cases, one searches for positive brightness enhancements exceeding a certain threshold, which appear consistent with what one expects for a point source, in the presence of a (possibly) spatially variable background. Multidimensional point spread functions (e.g., dependent on detector position and photon energy) are also common. At the same time, the problem in x-ray astronomy has some unique aspects. For example, for typical x-ray exposures in current or recent observatories, the number of available pixels far exceeds the number of actual x-ray events, so Poisson, rather than Gaussian statistics apply. Further, extended cosmic x-ray sources are common, and one often desires to detect point sources in the vicinity or even within bright, diffuse x-ray emission. Finally, support structures in x-ray detectors often cast sharp shadows in x-ray images making it necessary to detect sources in a region of rapidly varying exposure. We have developed a source detection package within the IRAF/PROS environment which attempts to deal with some of the problems of x-ray source detection. We have patterned our package after the successful Einstein Observatory x-ray source detection programs. However, we have attempted to improve the flexibility and accessibility of the functions and to provide a graphical front-end for the user. Our philosophy has been to use standard IRAF tasks whenever possible for image manipulation and to separate general functions from mission-specific ones. We will report on the current status of the package and discuss future developments, including simulation tasks, to allow the user to assess detection efficiency and source significance, tasks to determine source intensity, and alternative detection algorithms.

Deponte, J.↗

NASA NTRS2006

XBoard: A Framework for Integrating and Enhancing Collaborative Work Practices

Teams typically collaborate in different modes including face-to-face meetings, meetings that are synchronous (i. e. require parties to participate at the same time) but distributed geographically, and meetings involving asynchronously working on common tasks at different times. The XBoard platform was designed to create an integrated environment for creating applications that enhance collaborative work practices. Specifically, it takes large, touch-screen enabled displays as the starting point for enhancing face-to-face meetings by providing common facilities such as whiteboarding/electronic flipcharts, laptop projection, web access, screen capture and content distribution. These capabilities are built upon by making these functions inherently distributed by allowing these sessions to be easily connected between two or more systems at different locations. Finally, an information repository is integrated into the functionality to provide facilities for work practices that involve work being done at different times, such as reports that span different shifts. The Board is designed to be extendible allowing customization of both the general functionality and by adding new functionality to the core facilities by means of a plugin architecture. This, in essence, makes it a collaborative framework for extending or integrating work practices for different mission scenarios. XBoard relies heavily on standards such as Web Services and SVG, and is built using predominately Java and well-known open-source products such as Apache and Postgres. Increasingly, organizations are geographically dispersed, and rely on "virtual teams" that are assembled from a pool of various partner organizations. These organizations often have different infrastructures of applications and workflows. The XBoard has been designed to be a good partner in these situations, providing the flexibility to integrate with typical legacy applications while providing a standards-based infrastructure that is readily accepted by most organizations. The XBoard has been used on the Mars Exploration Rovers mission at JPL, and is currently being used or considered for use in pilot projects at Johnson Space Center (JSC) Mission Control, the University of Arizona Lunar and Planetav Laboratory (Phoenix Mars Lander), and MBART (Monterey Bay Aquarium Research Institute).

Shab, Ted↗

NASA NTRS1974

An extension of the Laplace transform to Schwartz distributions

A characterization of the Laplace transform is developed which extends the transform to the Schwartz distributions. The class of distributions includes the impulse functions and other singular functions which occur as solutions to ordinary and partial differential equations. The standard theorems on analyticity, uniqueness, and invertibility of the transform are proved by using the characterization as the definition of the Laplace transform. The definition uses sequences of linear transformations on the space of distributions which extends the Laplace transform to another class of generalized functions, the Mikusinski operators. It is shown that the sequential definition of the transform is equivalent to Schwartz' extension of the ordinary Laplace transform to distributions but, in contrast to Schwartz' definition, does not use the distributional Fourier transform. Several theorems concerning the particular linear transformations used to define the Laplace transforms are proved. All the results proved in one dimension are extended to the n-dimensional case, but proofs are presented only for those situations that require methods different from their one-dimensional analogs.

Price, D. R.↗

NASA NTRS2021

Functional Autonomy Challenges in Sampling for an Europa Lander Mission

We present a baseline approach to Functional Autonomyfor the purpose of conducting excavation and samplingbehaviors in a proposed Europa Lander mission. Aspects ofthe problems of site selection, excavation progress tracking,and fault identification are related; with particular emphasison parameters peculiar to an icy moon environment. Firstpass approaches to addressing these challenges are presentedin isolation, while motivating the current development goal ofproducing a general Functional Autonomy architecture thatallows state estimation, fault diagnosis, isolation, & recovery(FDIR), and adaptive behaviors to be formulated in concert.

Backes, Paul↗

DOE OSTI2025

Time-domain theory of transient heat conduction in the local limit

Ultrafast and nanoscale heat conduction demands a unified theoretical framework that rigorously bridges macroscopic transport equations with microscopic material properties derived from statistical physics. Existing empirical generalizations of Fourier's law often lack a solid microscopic foundation, failing to connect observed non-Fourier behavior with underlying atomic-scale mechanisms. In this work, we present a time-domain theory of transient heat conduction rooted in Zwanzig's statistical theory of irreversible processes. Central to this framework is the time-domain transport function $\overleftrightarrow{𝑍}$⁡(𝑡) defined through equilibrium time-correlation functions of heat fluxes. This function generalizes the conventional concept of steady-state thermal conductivity, governing the transition of conduction dynamics from onset second sound type wave propagation at finite speeds to diffusion-dominated behavior across broad temporal and spatial scales. Unlike phonon hydrodynamic models that rely on mesoscopic constructs such as phonon drift velocity, our approach provides a quantitative and microscopic description of intrinsic memory effects in transient heat fluxes and applies universally to bulk materials at any temperature or length scale. By integrating atomistic-scale first-principles calculations with continuum-level macroscopic equations, this framework offers a robust foundation for numerical simulations of transient temperature fields. Furthermore, it facilitates the interpretation and design of transient thermal grating experiments using nanometer-scale heat sources and ultrafast laser systems in the extreme ultraviolet and x-ray wavelength ranges, advancing our understanding of heat dissipation dynamics.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1962

Periodic Motions in Banach Space and Applications to Functional-Differential Equations

In establishing the existence of periodic solutions for nonautonomous differential equations of the form x = g(x, t), where g is periodic in t of period ω for fixed x, it is often convenient to consider the translation operator T(x(t)) = x(t + ω). If corresponding to each initial vector chosen in an appropriate region there corresponds a unique solution of our equation, then periodicity may be established by proving the existence of a fixed point under T. This same technique is also useful for more general functional equations and can be extended in a number of interesting ways. In this paper we shall consider a variable type of translation operator which is useful in investigating periodicity for autonomous differential and functional equations where the period involved is less obvious.

Jones, G. Stephen↗