Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - BOUNDARY VALUES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

First order impulsive solutions

A mathematically rigorous derivation is given of first order corrections to multi-impulse approximations to the solutions to space flight optimization problems with bang-bang control. The rocket was subjected to an inverse square gravitational force and to a thrust force with constant magnitude. The mass decreased linearly with time. An optimal impulsive solution was obtained for a problem with given initial and final conditions. The method was then used to obtain first-order corrections to the initial values of the costate variables. Indications are given on how the theory may be extended to higher order corrections. The theory was applied to intercept and rendezvous problems.

Andrus, J. F.↗
NASA NTRS1977

Response of winter and spring wheat grain yields to meteorological variation

Mathematical models which quantify the relation of wheat yield to selected weather-related variables are presented. Other sources of variation (amount of applied nitrogen, improved varieties, cultural practices) have been incorporated in the models to explain yield variation both singly and in combination with weather-related variables. Separate models were developed for fall-planted (winter) and spring-planted (spring) wheats. Meteorological variation is observed, basically, by daily measurements of minimum and maximum temperatures, precipitation, and tabled values of solar radiation at the edge of the atmosphere and daylength. Two different soil moisture budgets are suggested to compute simulated values of evapotranspiration; one uses the above-mentioned inputs, the other uses the measured temperatures and precipitation but replaces the tabled values (solar radiation and daylength) by measured solar radiation and satellite-derived multispectral scanner data to estimate leaf area index. Weather-related variables are defined by phenological stages, rather than calendar periods, to make the models more universally applicable.

Feyerherm, A. M.↗
NASA NTRS2001

Large-mutation spectra induced at hemizygous loci by low-LET radiation: evidence for intrachromosomal proximity effects

A mathematical model is used to analyze mutant spectra for large mutations induced by low-LET radiation. The model equations are based mainly on two-break misrejoining that leads to deletions or translocations. It is assumed, as a working hypothesis, that the initial damage induced by low-LET radiation is located randomly in the genome. Specifically, we analyzed data for two hemizygous loci: CD59- mutants, mainly very large-scale deletions (>3 Mbp), in human-hamster hybrid cells, and data from the literature on those HPRT- mutants which involve at least deletion of the whole gene, and often of additional flanking markers (approximately 50-kbp to approximately 4.4-Mbp deletions). For five data sets, we estimated f, the probability that two given breaks on the same chromosome will misrejoin to make a deletion, as a function of the separation between the breaks. We found that f is larger for nearby breaks than for breaks that are more widely separated; i.e., there is a "proximity effect". For acute irradiation, the values of f determined from the data are consistent with the corresponding break misrejoining parameters found previously in quantitative modeling of chromosome aberrations. The value of f was somewhat smaller for protracted irradiation than for acute irradiation at a given total dose; i.e., the mutation data show a decrease that was smaller than expected for dose protraction by fractionation or low dose rate.

Non-NASA Center↗
NASA NTRS1993

Physiologic mechanisms of circulatory and body fluid losses in weightlessness identified by mathematical modeling

Central volume expansion due to fluid shifts in weightlessness is believed to activate adaptive reflexes which ultimately result in a reduction of the total circulating blood volume. However, the flight data suggests that a central volume overdistention does not persist, in which case some other factor or factors must be responsible for body fluid losses. We used a computer simulation to test the hypothesis that factors other than central volume overdistention are involved in the loss of blood volume and other body fluid volumes observed in weightlessness and in weightless simulations. Additionally, the simulation was used to identify these factors. The results predict that atrial volumes and pressures return to their prebedrest baseline values within the first day of exposure to head down tilt (HDT) as the blood volume is reduced by an elevated urine formation. They indicate that the mechanisms for large and prolonged body fluid losses in weightlessness is red cell hemoconcentration that elevates blood viscosity and peripheral resistance, thereby lowering capillary pressure. This causes a prolonged alteration of the balance of Starling forces, depressing the extracellular fluid volume until the hematocrit is returned to normal through a reduction of the red cell mass, which also allows some restoration of the plasma volume. We conclude that the red cell mass becomes the physiologic driver for a large 'undershoot' of the body fluid volumes after the normalization of atrial volumes and pressures.

Simanonok, K. E.↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Theoretical autophotogrammetry. I - The method of the photometric potential

The present work presents preliminary efforts at a mathematical formulation of a photogrammetric method suitable for computerized processing. A theory is derived for the extraction of surface topography from stereometric pairs of photographs. The theory can be applied to either convergent or near-orthographic-projection stereo. Scene brightness is treated as a scalar function defined on a general surface embedded in ordinary three-dimensional space (the actual topography). Correspondence of points is based on adjustments leading to photometric equivalence, while the adjustments are based on the local value of the photometric gradient.

Wildey, R. L.↗
NASA NTRS1976

Structural optimization via a design space hierarchy

Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.

Vanderplaats, G. N.↗
NASA NTRS1984

Electron trapping in rad-hard RCA IC's irradiated with electrons and gamma rays

Enhanced electron trapping has been observed in n-channels of rad-hard CMOS devices due to electron and gamma-ray irradiation. Room-temperature annealing results in a positive shift in the threshold potential far beyond its initial value. The slope of the annealing curve immediately after irradiation was found to depend strongly on the gate bias applied during irradiation. Some dependence was also observed on the electron dose rate. No clear dependence on energy and shielding over a delidded device was observed. The threshold shift is probably due to electron trapping at the radiation-induced interface states and tunneling of electrons through the oxide-silicon energy barrier to fill the radiation-induced electron traps. A mathematical analysis, based on two parallel annealing kinetics, hole annealing and electron trapping, is applied to the data for various electron dose rates.

Danchenko, V.↗
NASA NTRS2017

Sensitivity Analysis of the Bone Fracture Risk Model

Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.

mathematical models↗
NASA NTRS1978

Continuum modeling of three-dimensional truss-like space structures

A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

Nayfeh, A. H.↗
NASA NTRS2002

Surface Oscillations of An Electromagnetically Levitated Droplet

Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is usually performed by electromagnetic levitation. The natural oscillation frequency a f the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to experimentally-obtained results.

Berry, S.↗
NASA NTRS1999

A More Accurate and Efficient Technique Developed for Using Computational Methods to Obtain Helical Traveling-Wave Tube Interaction Impedance

The phenomenal growth of commercial communications has created a great demand for traveling-wave tube (TWT) amplifiers. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to accurately analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. For the first time, an accurate three-dimensional helical model was developed that allows accurate prediction of TWT cold-test characteristics including operating frequency, interaction impedance, and attenuation. This computational model, which was developed at the NASA Lewis Research Center, allows TWT designers to obtain a more accurate value of interaction impedance than is possible using experimental methods. Obtaining helical slow-wave circuit interaction impedance is an important part of the design process for a TWT because it is related to the gain and efficiency of the tube. This impedance cannot be measured directly; thus, conventional methods involve perturbing a helical circuit with a cylindrical dielectric rod placed on the central axis of the circuit and obtaining the difference in resonant frequency between the perturbed and unperturbed circuits. A mathematical relationship has been derived between this frequency difference and the interaction impedance (ref. 1). However, because of the complex configuration of the helical circuit, deriving this relationship involves several approximations. In addition, this experimental procedure is time-consuming and expensive, but until recently it was widely accepted as the most accurate means of determining interaction impedance. The advent of an accurate three-dimensional helical circuit model (ref. 2) made it possible for Lewis researchers to fully investigate standard approximations made in deriving the relationship between measured perturbation data and interaction impedance. The most prominent approximations made in the analysis were addressed and fully investigated for their accuracy by using the three-dimensional electromagnetic simulation code MAFIA (Solution of Maxwell's Equations by the Finite Integration Algorithm) (refs. 3 and 4). We found that several approximations introduced significant error (ref. 5).

Kory, Carol L.↗
NASA NTRS2006

Extended Aging Theories for Predictions of Safe Operational Life of Critical Airborne Structural Components

The previously developed Ko closed-form aging theory has been reformulated into a more compact mathematical form for easier application. A new equivalent loading theory and empirical loading theories have also been developed and incorporated into the revised Ko aging theory for the prediction of a safe operational life of airborne failure-critical structural components. The new set of aging and loading theories were applied to predict the safe number of flights for the B-52B aircraft to carry a launch vehicle, the structural life of critical components consumed by load excursion to proof load value, and the ground-sitting life of B-52B pylon failure-critical structural components. A special life prediction method was developed for the preflight predictions of operational life of failure-critical structural components of the B-52H pylon system, for which no flight data are available.

Ko, William L.↗
DOE OSTI2024

Parameterization of vacancy production rate in phase-field models of fission gas bubble evolution in nuclear fuel

Phase-field modeling has increasingly been used to study microstructural evolution in fission gas bubbles in nuclear fuel to improve understanding of fission gas release. To improve computational efficiency, often only vacancies and gas atoms are included as defect species. In this case, the net effects of vacancy and interstitial production, recombination, and biased sink absorption are included as a net vacancy source, or net vacancy source combined with an effective sink. However, there has been a lack of clarity on what parameter values should be used for these approaches to best match the more complete physical picture that includes interstitials and vacancies. Here, we compare a phase-field model of void growth to analytical models for the source-only and source plus sink approach to gain insight into how the phase-field models can be parameterized effectively. The source-only approach provides greater flexibility to match growth rates determined from the full vacancy-interstitial picture. A strategy was developed for determining the value of the net vacancy source term by comparing to an analytical model that includes vacancy and interstitial production, recombination, and biased sink absorption. Finally, this strategy can be used to parameterize phase-field models of fission gas bubble growth.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2010

Radiation Beamline Testbeds for the Simulation of Planetary and Spacecraft Environments for Human and Robotic Mission Risk Assessment

The Center for Radiation Engineering and Science for Space Exploration (CRESSE) at Prairie View A&M University, Prairie View, Texas, USA, is establishing an integrated, multi-disciplinary research program on the scientific and engineering challenges faced by NASA and the international space community caused by space radiation. CRESSE focuses on space radiation research directly applicable to astronaut health and safety during future long term, deep space missions, including Martian, lunar, and other planetary body missions beyond low earth orbit. The research approach will consist of experimental and theoretical radiation modeling studies utilizing particle accelerator facilities including: 1. NASA Space Radiation Laboratory (NSRL) at Brookhaven National Laboratory; 2. Proton Synchrotron at Loma Linda University Medical Center; and 3. Los Alamos Neutron Science Center (LANSCE) at Los Alamos National Laboratory. Specifically, CRESSE investigators are designing, developing, and building experimental test beds that simulate the lunar and Martian radiation environments for experiments focused on risk assessment for astronauts and instrumentation. The testbeds have been designated the Bioastronautics Experimental Research Testbeds for Environmental Radiation Nostrum Investigations and Education (BERT and ERNIE). The designs of BERT and ERNIE will allow for a high degree of flexibility and adaptability to modify experimental configurations to simulate planetary surface environments, planetary habitats, and spacecraft interiors. In the nominal configuration, BERT and ERIE will consist of a set of experimental zones that will simulate the planetary atmosphere (Solid CO2 in the case of the Martian surface.), the planetary surface, and sub-surface regions. These experimental zones can be used for dosimetry, shielding, biological, and electronic effects radiation studies in support of space exploration missions. BERT and ERNIE are designed to be compatible with the experimental areas associated with the above facilities. CRESSE has broad expertise in space radiation in the areas of space radiation environment modeling, Monte-Carlo radiation transport modeling, space radiation instrumentation and dosimetry, radiation effects on electronics, and multi-functional composite shielding materials. The BERT and ERNIE testbeds will be utilized in individual and collaborative research incorporating this expertise. The research goal is to maximize the technical readiness level (TRL) of radiation instrumentation for human and robotic missions, optimizing the return value of CRESSE for NASA exploration and international co-operative missions. Outcomes and knowledge from research utilizing BERT and ERNIE will be applied to a variety of scientific and engineering disciplines vital for safe and reliable execution of future space exploration missions, which can be negatively impacted by the space radiation environment. The testbeds will be central to a variety of university educational activities and educational goals of NASA. Specifically, BERT and ERNIE will enhance educational opportunities in science, technology, engineering and mathematics (STEM) disciplines for engineering and science students at PVAMU, a historically black college/university. Preliminary data on prototype testbed configurations, including simulated lunar regolith (JSC-1A stimulant based on Apollo 11 samples), regolith/polyethylene composites, and dry ice, will be presented to demonstrate the usefulness of BERT and ERNIE in radiation beam line experiments.

Wilkins, Richard↗
NASA NTRS2006

The Spatial Standard Observer

The spatial standard observer is a computational model that provides a measure of the visibility of a target in a uniform background image or of the visual discriminability of two images. Standard observers have long been used in science and industry to quantify the discriminability of colors. Color standard observers address the spectral characteristics of visual stimuli, while the spatial standard observer (SSO), as its name indicates, addresses spatial characteristics. The SSO is based on a model of human vision. The SSO was developed in a process that included evaluation of a number of earlier mathematical models that address optical, physiological, and psychophysical aspects of spatial characteristics of human visual perception. Elements of the prior models are incorporated into the SSO, which is formulated as a compromise between accuracy and simplicity. The SSO operates on a digitized monochrome still image or on a pair of such images. The SSO consists of three submodels that operate sequentially on the input image(s): 1. A contrast model, which converts an input monochrome image to a luminance contrast image, wherein luminance values are expressed as excursions from, and normalized to, a mean; 2. A contrast-sensitivity-filter model that includes an oblique-effect filter (which accounts for the decline in contrast sensitivity at oblique viewing angles); and 3. A spatial summation model, in which responses are spatially pooled by raising each pixel to the power beta, adding the results, and raising the sum to the 1/b power. In this model, b=2.9 was found to be a suitable value. The net effect of the SSO is to compute a numerical measure of the perceptual strength of the single image, or of the visible difference (denoted the perceptual distance) between two images. The unit of a measure used in the SSO is the just noticeable difference (JND), which is a standard measure of perceptual discriminability. A target that is just visible has a measure of 1 JND.

Watson, Andrew B.↗
NASA NTRS1989

The Fault Tree Compiler (FTC): Program and mathematics

The Fault Tree Compiler Program is a new reliability tool used to predict the top-event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, AND m OF n gates. The high-level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precisely (within the limits of double precision floating point arithmetic) within a user specified number of digits accuracy. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Equipment Corporation (DEC) VAX computer with the VMS operation system.

Butler, Ricky W.↗
NASA NTRS1982

Mathematical modeling of ice accretion on airfoils

The progress toward development of a computer model suitable for predicting icing behavior on airfoils over a wide range of environmental conditions and airfoils shapes is reported. The LEWICE program was formulated to solve a set of equations which describe the physical processes which occur during accretion of ice on an airfoil, including heat transfer in a time dependent mode, with the restriction that the flow must be describable by a two-dimensional flow code. Input data comprises the cloud liquid water content, mean droplet diameter, ambient air temperature, air velocity, and relative humidity. A potential flowfield around the airfoil is calculated, along with the droplet trajectories within the flowfield, followed by local values of water droplet collection efficiency at the impact points. Both glaze and rime ice conditions are reproduced, and comparisons with test results on icing of circular cylinders showed good agreement with the physical situation.

Macarthur, C. D.↗