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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Towards the development of micromechanics equations for ceramic matrix composites via fiber substructuring

A generic unit cell model which includes a unique fiber substructuring concept is proposed for the development of micromechanics equations for continuous fiber reinforcement ceramic composites. The unit cell consists of three constituents: fiber, matrix, and an interphase. In the present approach, the unit cell is further subdivided into several slices and the equations of micromechanics are derived for each slice. These are subsequently integrated to obtain ply level properties. A stand alone computer code containing the micromechanics model as a module is currently being developed specifically for the analysis of ceramic matrix composites. Towards this development, equivalent ply property results for a SiC/Ti-15-3 composite with 0.5 fiber volume ratio are presented and compared with those obtained from customary micromechanics models to illustrate the concept. Also, comparisons with limited experimental data for the ceramic matrix composite, SiC/RBSN (Reaction Bonded Silicon Nitride) with a 0.3 fiber volume ratio are given to validate the concepts.

Murthy, P. L. N.↗
NASA NTRS1966

Matrix methods

Partial differential equations and matrix method for obtaining equations of motion in orbit

MOTION EQUATION↗
NASA NTRS1977

Inverse solution of the pseudoscalar transfer equation through nonlinear matrix inversion

Nonlinear matrix inversion operators have been developed which, applied to observed radiances, infer maximal information regarding atmospheric scattering parameters and vertical distribution of radiant sources and sinks. The algorithm has the attractive feature of noise discrimination, attributing instrumental errors to extra-atmospheric sources.

King, J. I. F.↗
NASA NTRS1976

Computation and sensitivity considerations of the Ricatti equation in spacecraft CMG steering laws

The steady-state matrix Ricatti equation is studied with respect to sensitivity and computational burden for a linear regulator controller in spacecraft. The class of systems studied use control moment gyros (CMGs) as the torque driver, assuming that the CMGs are free of gimbal stops. Different solution techniques are evaluated relative to computation time and accuracy to determine which solution method is most acceptable with respect to the prescribed requirements. It is shown that it is not feasible to eliminate off-diagonal Ricatti equation terms in the relevent updata equation due to their high sensitivity, that Potter's algebraic technique requires the least computation time of the methods studied, and that the simple Euler method yields the best results when accuracy and computation time are equally weighted. If an optimal linear regulator formulation is employed, a full Ricatti equation solution of n(n + 1)2 elements of the symmetric positive definite gain matrix which is the solution to the matrix Ricatti equation must be computed at each update cycle.

Colburn, B. K.↗
NASA NTRS1977

Lie theoretic aspects of the Riccati equation

Various features of the application of Lie theory to matrix Riccati equations, of basic importance in control and system theories, are discussed. Particular consideration is given to centralizer foliation, the Cartan decomposition, matrix Riccati equations as Lie systems on Grassmanians, local analysis near a zero point of a vector field, linearization in homogeneous space, the tangent bundle in terms of partitioned matrices, and stability properties of fixed points of Riccati vector fields.

Hermann, R.↗
NASA NTRS1973

Some optimal considerations in attitude control systems

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

Boland, J. S., III↗
NASA NTRS1985

A unique set of micromechanics equations for high temperature metal matrix composites

A unique set of micromechanic equations is presented for high temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Hopkins, D. A.↗
NASA NTRS1989

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Danabasoglu, G.↗
DOE OSTI2022

Matrix Approach to Land Carbon Cycle Modeling

Land ecosystems contribute to climate change mitigation by taking up approximately 30% of anthropogenically emitted carbon. However, estimates of the amount and distribution of carbon uptake across the world's ecosystems or biomes display great uncertainty. The latter hinders a full understanding of the mechanisms and drivers of land carbon uptake, and predictions of the future fate of the land carbon sink. The latter is needed as evidence to inform climate mitigation strategies such as afforestation schemes. To advance land carbon cycle modeling, we have developed a matrix approach. Land carbon cycle models use carbon balance equations to represent carbon exchanges among pools. Our approach organizes this set of equations into a single matrix equation without altering any processes of the original model. The matrix equation enables the development of a theoretical framework for understanding the general, transient behavior of the land carbon cycle. While carbon input and residence time are used to quantify carbon storage capacity at steady state, a third quantity, carbon storage potential, integrates fluxes with time to define dynamic disequilibrium of the carbon cycle under global change. The matrix approach can help address critical contemporary issues in modeling, including pinpointing sources of model uncertainty and accelerating spin-up of land carbon cycle models by tens of times. The accelerated spin-up liberates models from the computational burden that hinders comprehensive parameter sensitivity analysis and assimilation of observational data to improve model accuracy. Such computational efficiency offered by the matrix approach enables substantial improvement of model predictions using ever-increasing data availability. Overall, the matrix approach offers a step change forward for understanding and modeling the land carbon cycle.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1980

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Chakravarthy, S. R.↗
NASA NTRS1990

A Chebyshev matrix method for the spatial modes of the Orr-Sommerfeld equation

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blasius boundary layer. The problems is linearized by the companion matrix technique for semiinfinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Danabasoglu, Gokhan↗
DOE OSTI2021

Spin-dependent Seebeck and Nernst effects in an ideal skyrmion gas

In this work, we theoretically and numerically study spin-dependent Seebeck and Nernst effects in 2D ferromagnetic materials with the topological spin texture (skyrmion and vortex) ideal gas. From the numerical solution of the matrix Boltzmann equation for a nonequilibrium distribution function and the Lippmann–Schwinger equation for a T-matrix we find the strong nonlinear behaviors in the thermoelectric coefficients depending on skyrmion/vortex diameters and electron concentrations. In particular, the dramatic dependences in the Seebeck and Nernst coefficients take place at larger magnetic texture sizes where the abrupt sign flip in the vortex Seebeck and Nernst coefficients occurs in the narrow region of electron concentrations. In this case the normalized Nernst coefficient changes from +5 to -7. The spin-dependent thermoelectric coefficients are proportional to T at low temperatures for all skyrmion/vortex sizes.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Computational complexities and storage requirements of some Riccati equation solvers

The linear optimal control problem of an nth-order time-invariant dynamic system with a quadratic performance functional is usually solved by the Hamilton-Jacobi approach. This leads to the solution of the differential matrix Riccati equation with a terminal condition. The bulk of the computation for the optimal control problem is related to the solution of this equation. There are various algorithms in the literature for solving the matrix Riccati equation. However, computational complexities and storage requirements as a function of numbers of state variables, control variables, and sensors are not available for all these algorithms. In this work, the computational complexities and storage requirements for some of these algorithms are given. These expressions show the immensity of the computational requirements of the algorithms in solving the Riccati equation for large-order systems such as the control of highly flexible space structures. The expressions are also needed to compute the speedup and efficiency of any implementation of these algorithms on concurrent machines.

Utku, Senol↗