Analysis of the Apollo heat shield performance. Volume 1 - Analytical methods
Analysis of Apollo heat shield using mathematical models
Del Casal, E. P.↗
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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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Mathematical circulatory system model
A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.
Lakin, William D.↗
The method of complex characteristics for transonic airfoil design, with an application to compressors
The use of mathematical models to study physical problems of current interest to aeronautical engineers has been made possible by the development of numerical techniques to compute solutions of the differential equations of transonic aerodynamics. These advances have encouraged the improvement of supercritical wing technology. A method to determined steady, shockless flow of an inviscid, compressible fluid past a cascade of airfoils in the (x,y)-plane is considered, taking into account also the case of an isolated airfoil. The method of complex characteristics solves the equations in the hodograph plane by extending all variables into the complex domain, where the notion of type is no longer significant. Attention is given to the mathematical background, the method of complex characteristics, and numerical calculations.
Bledsoe, M.↗
Determining the Products of Inertia for Small Scale UAVs
Moments of inertia and products of inertia often need to be determined for aircraft. As complex bodies, their mass properties need to be determined experimentally for best accuracy. While several moment of inertia experimental techniques have been developed, there are few to determine the products of inertia. Products of inertia can be easily determined mathematically if the angle between the aircraft x body axis and principal x axis is known. This method finds the principal inclination angle by mathematically correlating the measured moments of inertia about a range of axes of the aircraft. This correlation uses a least squares error minimization of a mathematical model that describes the ellipse of inertia in the aircraft's x-z axes plane. Results from a test conducted on a small scale UAV (Unmanned Aerial Vehicle) at NASA Armstrong Flight Research Center is also presented, which is an example of the intended application of this technique.
mass properties↗
buhito
buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.
Pimonova, Yulia↗
Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications
This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.
97 MATHEMATICS AND COMPUTING↗
Analytical Methods in Vibrations.
Book on analytical methods in vibrations covering general mathematical formulations of common features of various vibrating systems
STATISTICAL ANALYSIS↗
Study of the modulatory effects of the solar wind on galactic cosmic rays
Mathematical model using Monte Carlo method for modulation of galactic protons by solar wind
Moss, T. A.↗
The modulation of galactic protons by the solar wind - A Monte Carlo approach
Solar wind modulation effects on galactic protons and cosmic rays, using radial magnetic field mathematical model and Monte Carlo method
Giuli, R. T.↗
A real time spectrum to dose conversion system
A system has been developed which permits the determination of dose in real time or near real time directly from the pulse-height output of a radiation spectrometer. The technique involves the use of the resolution matrix of a spectrometer, the radiation energy-to-dose conversion function, and the geometrical factors, although the order of matrix operations is reversed. The new technique yields a result which is mathematically identical to the standard method while requiring no matrix manipulations or resolution matrix storage in the remote computer. It utilizes only a single function for each type dose required and each geometric factor involved.
Farmer, B. J.↗
Numerical study of supersonic turbulent flow over small protuberances
Supersonic turbulent boundary layers over two-dimensional protuberances are investigated, using the numerical finite difference alternating direction implicit (ADI) method. The turbulence is modeled mathematically. The turbulence is represented here by the eddy viscosity approach. The turbulent boundary layer structure as well as an interest in thick boundary layers and much larger protuberance heights than in the laminar case lead to new difficulties. The problems encountered and the means to remove them are discussed.
Polak, A.↗
Theoretical determination of the minimum drag of airfoils at supersonic speeds
A method is reported for determining mathematically the combined disturbance field, and in certain cases the minimum drag, of wings at supersonic speeds. The simplest analytic example is provided by the wing of elliptic planform, which achieves its minimum drag when the lift is distributed uniformly over the surface. With a symmetrical distribution of thickness, the requirement of minimum drag for a given total volume is found to lead to profiles of constant curvature.
Jones, R. T.↗
A network of automatic atmospherics analyzer
The design and function of an atmospheric analyzer which uses a computer are discussed. Mathematical models which show the method of measurement are presented. The data analysis and recording procedures of the analyzer are discussed.
Schaefer, J.↗
Handling Qualities of Large Flexible Aircraft
The effects on handling qualities of elastic modes interaction with the rigid body dynamics of a large flexible aircraft are studied by a mathematical computer simulation. An analytical method to predict the pilot ratings when there is a severe modes interactions is developed. This is done by extending the optimal control model of the human pilot response to include the mode decomposition mechanism into the model. The handling qualities are determined for a longitudinal tracking task using a large flexible aircraft with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction.
Poopaka, S.↗
Optimality criteria solution strategies in multiple constraint design optimization
Procedures and solution strategies are described to solve the conventional structural optimization problem using the Lagrange multiplier technique. The multipliers, obtained through solution of an auxiliary nonlinear optimization problem, lead to optimality criteria to determine the design variables. It is shown that this procedure is essentially equivalent to an alternative formulation using a dual method Lagrangian function objective. Although mathematical formulations are straight-forward, successful applications and computational efficiency depend upon execution procedure strategies. Strategies examined, with application examples, include selection of active constraints, move limits, line search procedures, and side constraint boundaries.
Levy, R.↗
Transonic aerodynamics; Transonic Perspective Symposium, Moffett Field, CA, February 18-20, 1981, Technical Papers
After an historical account of the development of transonic aerodynamics before 1940 and in the period 1945-1975, attention is given to the design for cruise performance efficiency of commercial transport aircraft, with emphasis on transonic wing design, the practical aerodynamic problems of military aircraft, with emphasis on store carriage and separation, experimental testing in transonic wind tunnels capable of Reynolds number simulation and aerodynamic flow visualization, and such mathematical techniques as potential equation methods for flow prediction and Reynolds-averaged Navier-Stokes computations of transonic flows. Also considered are transonic design using computational aerodynamics, the application of computation methods to transonic wing design, computational experience with advanced tactical aircraft, the evaluation of full potential flow methods, and the application of a shock-turbulent boundary layer interaction theory to transonic flowfield analysis.
Nixon, D.↗
Simulation and evaluation of the Sh-2F helicopter in a shipboard environment using the interchangeable cab system
The operation of the SH-2F helicopter from the decks of small ships in adverse weather was simulated using a large amplitude vertical motion simulator, a wide angle computer generated imagery visual system, and an interchangeable cab (ICAB). The simulation facility, the mathematical programs, and the validation method used to ensure simulation fidelity are described. The results show the simulator to be a useful tool in simulating the ship-landing problem. Characteristics of the ICAB system and ways in which the simulation can be improved are presented.
Paulk, C. H., Jr.↗
On the connection between multigrid and cyclic reduction
A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.
Merriam, M. L.↗