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Results for “Equation discovery”

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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NASA NTRS2018

Understanding Climate-Vegetation Interactions in Global Rainforests Through a GP-Tree Analysis

The tropical rainforests are the largest reserves of terrestrial carbon and, therefore, the future of these rainforests is a question that is of immense importance in the geoscience research community. With the recent severe Amazonian droughts in 2005 and 2010 and on-going drought in the Congo region for more than two decades, there is growing concern that these forests could succumb to precipitation reduction, causing extensive carbon release and feedback to the carbon cycle. However, there is no single ecosystem model that quantifies the relationship between vegetation health in these rainforests and climatic factors. Small scale studies have used statistical correlation measure and simple linear regression to model climate-vegetation interactions, but suffer from the lack of comprehensive data representation as well as simplistic assumptions about dependency of the target on the covariates. In this paper we use genetic programming (GP) based symbolic regression for discovering equations that govern the vegetation climate dynamics in the rainforests. Expecting micro-regions within the rainforests to have unique characteristics compared to the overall general characteristics, we use a modified regression-tree based hierarchical partitioning of the space to build individual models for each partition. The discovery of these equations reveal very interesting characteristics about the Amazon and the Congo rainforests. Our method GP-tree shows that the rainforests exhibit tremendous resiliency in the face of extreme climatic events by adapting to changing conditions.

genetic programming↗

NASA NTRS1980

Structure and meteorology of the middle atmosphere of Venus Infrared remote sensing from the Pioneer orbiter

The results of the Pioneer Venus orbiter radiometric temperature-sounding experiment are presented with examples of each of the primary data products. The measured temperature field is used to model the dynamics of the middle atmosphere from 60 to 140 km, and the thermal and solar fluxes are used to calculate the planetary radiation budget. The data for the diurnal variation of temperature at a given height show fairly small amplitudes up to an altitude of about 95 km, above which the day to night contrast increases rapidly with height. At the equator the dependence of temperature in the stratosphere on solar longitude is dominated by a wave number 2 solar tide with an amplitude of about 10 K. The equator to pole gradients are larger than expected, and the stratosphere is typically 15 to 20 K warmer at the pole than at the equator. The most significant discovery concerning the cloud morphology is a dipole structure consisting of two clearings in the cloud at locations straddling the pole and rotating around it every 2.7 days.

Taylor, F. W.↗

NASA NTRS1975

Prolongation structures of nonlinear evolution equations

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Wahlquist, H. D.↗

NASA NTRS1975

Point-connected rigid bodies in a topological tree

The purpose of the present paper is to explore the applicability of several methods of analytical mechanics to the modern problem of formulating generic equations of motion of a point-connected set of rigid bodies in a topological tree, in order to compare the results of the previously published Hooker-Margulies/Hooker equations. The unexpected result of the inquiry is the discovery that with the substitution of a key kinematical identity from the Hooker and Margulies vector-dyadic equations for the multiple-rigid-body tree, identical equations emerge from each of four quite different derivation procedures.

Likins, P. W.↗

NASA NTRS2016

Documenting the NASA Armstrong Flight Research Center Oblate Earth Simulation Equations of Motion and Integration Algorithm

A desire for more complete documentation of the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC), Edwards, California legacy code used in the core simulation has led to this e ort to fully document the oblate Earth six-degree-of-freedom equations of motion and integration algorithm. The authors of this report have taken much of the earlier work of the simulation engineering group and used it as a jumping-o point for this report. The largest addition this report makes is that each element of the equations of motion is traced back to first principles and at no point is the reader forced to take an equation on faith alone. There are no discoveries of previously unknown principles contained in this report; this report is a collection and presentation of textbook principles. The value of this report is that those textbook principles are herein documented in standard nomenclature that matches the form of the computer code DERIVC. Previous handwritten notes are much of the backbone of this work, however, in almost every area, derivations are explicitly shown to assure the reader that the equations which make up the oblate Earth version of the computer routine, DERIVC, are correct.

integrators↗

NASA NTRS1994

Pseudomaster equation for the no-count process in a continuous photodetection

The detection of cavity radiation with the detector placed outside the cavity is studied. Each leaked photon has a certain probability of propagating away without being detected. It is viewed as a continuous quantum measurement in which the density matrix is continuously revised according to the readout of the detector. The concept of pseudomaster equation for the no-count process is introduced; its solution leads to the discovery of the superoperator for the same process. It has the potential to become the key equation for continuous measurement process.

Lee, Ching-Tsung↗

NASA NTRS2005

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Thompson, David E.↗

NASA NTRS2002

The Statistical Mechanics of Ideal Homogeneous Turbulence

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Shebalin, John V.↗

NASA NTRS2004

Future Probes of the Neutron Star Equation of State Using X-ray Bursts

Observations with NASA s Rossi X-ray Timing Explorer (RXTE) have resulted in the discovery of fast (200 - 600 Hz), coherent X-ray intensity oscillations (hereafter, %urstoscillations ) during thermonuclear X-ray bursts from 12 low mass X-ray binaries (LMXBs). Although many of their detailed properties remain to be fully understood, it is now beyond doubt that these oscillations result from spin modulation of the thermonuclear burst flux from the neutron star surface. Among the new timing phenomena revealed by RXTE the burst oscillations are perhaps the best understood, in the sense that many of their properties can be explained in the framework of this relatively simple model. Because of this, detailed modelling of burst oscillations can be an extremely powerful probe of neutron star structure, and thus the equation of state (EOS) of supra-nuclear density matter. Both the compactness parameter beta = GM/c(sup 2)R, and the surface velocity, nu(sub rot) = Omega(sub spin)R, are encoded in the energy-dependent amplitude and shape of the modulation pulses. The new discoveries have spurred much new theoretical work on thermonuclear burning and propagation on neutron stars, so that in the near future it is not unreasonable to think that detailed physical models of the time dependent flux from burning neutron stars will be available for comparison with the observed pulse profiles from a future, large collecting area X-ray timing observatory. In addition, recent high resolution burst spectroscopy with XMM/Newton suggests the presence of redshifted absorption lines from the neutron star surface during bursts. This leads to the possibility of using large area, high spectral resolution measurements of X-ray bursts as a precise probe of neutron star structure. In this work I will explore the precision with which constraints on neutron star structure, and hence the dense matter EOS, can be made with the implementation of such programs.

Strohmayer, Tod E.↗

NASA NTRS1989

Universal features of the equation of state of solids

A study of the energetics of solids leads to the conclusion that the equation of state for all classes of solids in compression can be expressed in terms of a universal function. The form of this universal function is determined by scaling experimental compression data for measured isotherms of a wide variety of solids. The equation of state is thus known (in the absence of phase transitions), if zero-pressure volume and isothermal compression and its pressure derivative are known. The discovery described in this paper has two immediate consequences: first, despite the well known differences in the microscopic energetics of the various classes of solids, there is a single equation of state for all classes in compression; and second, a new method is provided for analyzing measured isotherms and extrapolating high-pressure data from low-pressure (e.g. acoustic) data.

Vinet, Pascal↗

NASA NTRS1973

Which electromagnetic equations apply in rotating coordinates

It was discovered some years ago by Schiff that two equations for fields in vacuum do not carry over without change from an inertial frame to a frame with rotating axes of space coordinates, even for a region with all velocities much lower than the speed of light. However, the belief that all four of the field equations are invariant under such conditions is still prevalent and causes misconceptions in physical applications, including astrophysical and geophysical ones. The purpose of the present paper is therefore to call attention to Schiff's discovery, discussing its basis and its extension to fields in material media, and to interpret the additional terms that must be added to the equations in order to obtain valid transformations to rotating axes of coordinates.

Webster, D. L.↗

NASA NTRS2003

Hydrostatic Stress Effects Incorporated Into the Analysis of the High-Strain-Rate Deformation of Polymer Matrix Composites

Procedures for modeling the effect of high strain rate on composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and strain rate dependence of the composite response is primarily due to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. An experimental program has been carried out through a university grant with the Ohio State University to obtain tensile and shear deformation data for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used at the NASA Glenn Research Center to develop, characterize, and correlate a material model in which the strain rate dependence and nonlinearity (including hydrostatic stress effects) of the polymer are correctly analyzed. To obtain the material data, Glenn s researchers designed and fabricated test specimens of a representative toughened epoxy resin. Quasi-static tests at low strain rates and split Hopkinson bar tests at high strain rates were then conducted at the Ohio State University. The experimental data confirmed the strong effects of strain rate on both the tensile and shear deformation of the polymer. For the analytical model, Glenn researchers modified state variable constitutive equations previously used for the viscoplastic analysis of metals to allow for the analysis of the nonlinear, strain-rate-dependent polymer deformation. Specifically, we accounted for the effects of hydrostatic stresses. An important discovery in the course of this work was that the hydrostatic stress effects varied during the loading process, which needed to be accounted for within the constitutive equations. The model is characterized primarily by shear data, with tensile data used to characterize the hydrostatic stress effects.

Goldberg, Robert K.↗

NASA NTRS1997

STS-82 Mission Highlight Presentation

The STS-82 is the second in a series of planned service missions to the Hubble Space Telescope (HST). The flight crew of STS-82, Cmdr. Kenneth D. Bowersox, Pilot Scott J. Horowitz, Mission specialists, Mark C. Lee, Steven A. Hawley, Gregory J. Harbaugh, Steven L. Smith, and Joseph R. Tanner can be seen performing pre-launch activities preparing for the night launch. The crew meets the press for pre-launch photos before being transported to the launch pad. Several views can be seen of the final inspection team on the O level and the crew being readied in the 'white room'. Launch activities such as the oxygen vent hood retraction, liftoff, SRB separation, and personnel activities in the Houston Integrated Mission Control room are viewed. Subsequent footage is provided of the crew's activities during the HST rendezvous and docking, Extravehicular Activities (EVA's) preparation and EVA numbers 1, 3 and 5. During the first EVA the earth can be seen clearly in a reflection off of HST's offshroud during its 60th orbit crossing the equator. The HST deployment and views of the Hale-Bopp comet are clearly seen before Discovery's reentry and landing. After reentry a beautiful view of Discovery moving at 10,400 mph can be seen looking east from Mission Control. The ususal twin sonic boom precedes Discovery's touchdown on runway 15 at Kennedy Space Center. This second HST service mission orbited Earth 150 times and traveled 1.4 million miles.

Source record↗

NASA NTRS2011

CIRS-lite, a Fourier Transform Spectrometer for Low-Cost Planetary Missions

Passive spectroscopic remote sensing of planetary atmospheres and surfaces in the thermal infrared is a powerful tool for obtaining information about surface and atmospheric temperatures, composition, and dynamics (via the thermal wind equation). Due to its broad spectral coverage, the Fourier transform spectrometer (FTS) is particularly suited to the exploration and discovery of molecular species. NASA's Goddard Space Flight Center (GSFC) developed the CIRS (Composite Infrared Spectrometer) FTS for the NASA/ESA Cassini mission to the Saturnian system. CIRS observes Saturn, Titan, icy moons such as Enceladus, and the rings in thermal self-emission over the spectral range of 7 to 1000 ell11. CIRS has given us important new insights into stratospheric composition and jets on Jupiter and Saturn, the cryo-geyser and thermal stripes on Enceladus, and the winter polar vortex on Titan. CIRS has a mass of 43 kg, contrasted with the earlier GSFC FTS, pre-Voyager IRIS (14 kg). Future low-cost planetary missions will have very tight constraints on science payload mass, thus we must endeavor to return to IRIS-level mass while maintaining CIRS-level science capabilities ("do more with less"). CIRS-lite achieves this by pursuing: a) more sensitive infrared detectors (high Tc superconductor) to enable smaller optics. b) changed long wavelength limit from 1000 to 300 microns to reduce diffraction by smaller optics. c) CVD (chemical vapor deposition) diamond beam-splitter for broad spectral coverage. d) single FTS architecture instead of a dual FTS architecture. e) novel materials, such as single crystal silicon for the input telescope primary.

Brasunas, J.↗

NASA NTRS2012

CIRS and CIRS-Lite as Designed for the Outer Planets: TSSM, EJSM, JUICE

Brasunas, J.↗

NASA NTRS1978

New trends in cosmology

A review of big-bang cosmology is presented, emphasizing the big-bang model, hypotheses on the origin of galaxies, observational tests of the big-bang model that may be possible with the Large Space Telescope, and the scale-covariant theory of gravitation. Detailed attention is given to the equations of general relativity, the redshift-distance relation for extragalactic objects, expansion of the universe, the initial singularity, the discovery of the 3-K blackbody radiation, and measurements of the amount of deuterium in the universe. The curvature of the expanding universe is examined along with the magnitude-redshift relation for quasars and galaxies. Several models for the origin of galaxies are evaluated, and it is suggested that a model of galaxy formation via the formation of black holes is consistent with the model of an expanding universe. Scale covariance is discussed, a scale-covariant theory is developed which contains invariance under scale transformation, and it is shown that Dirac's (1937) large-numbers hypothesis finds a natural role in this theory by relating the atomic and Einstein units.

Canuto, V. M.↗

NASA NTRS2003

Coherent interannual and decadal variations inthe atmosphere-ocean system

We investigate the source of poleward propagating atmospheric zonal wind anomalies, originating at the equator and penetrating to high latitudes in both hemispheres in conjunction with ENSO [Dickey et al.,1992], and report the discovery of similar variability on decadal and longer timescales. Since atmospheric dissipation times are generally on the order of a month or less, we examine the ocean as a 'memory' source for these globally coherent anomalies. This hypothesis is substantiated by the observation of complementaryoscillation in the sea surface temperature (SST) field; further, we detect a robust decadal variability (~1012 yrs)in both the SST and contemporaneous atmospheric angular momentum (AAM) series. Analyzing GISST SST data beginning in 1902, we confirm this decadal mode and find signatures of longer (multidecadal) SST variability centered in the equatorial and North Pacific.

coherent decadal meridional↗

NASA NTRS2021

A Study into Validating a Coupled Method of Characteristics and Direct Simulation Monte Carlo Method Against Empirical Data

The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.

Direct Simulation Monte Carlo Analysis Code↗