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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

The analysis of convolutional codes via the extended Smith algorithm

Convolutional codes have been the central part of most error-control systems in deep-space communication for many years. Almost all such applications, however, have used the restricted class of (n,1), also known as 'rate 1/n,' convolutional codes. The more general class of (n,k) convolutional codes contains many potentially useful codes, but their algebraic theory is difficult and has proved to be a stumbling block in the evolution of convolutional coding systems. In this article, the situation is improved by describing a set of practical algorithms for computing certain basic things about a convolutional code (among them the degree, the Forney indices, a minimal generator matrix, and a parity-check matrix), which are usually needed before a system using the code can be built. The approach is based on the classic Forney theory for convolutional codes, together with the extended Smith algorithm for polynomial matrices, which is introduced in this article.

Mceliece, R. J.↗
DOE OSTI2021

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Model Predictive Control of Discrete-Continuous Energy Systems via Generalized Disjunctive Programming

Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete decisions in the continuous space, and logical propositions to denote algebraic constraints in the discrete space. Compared to traditional mixed-integer programming (MIP), the inherent logic structure in GDP yields tighter relaxations that are exploited by global branch and bound algorithms to improve solution quality. In this paper, we present a general GDP model for optimal control of hybrid systems that exhibit both discrete and continuous dynamics. Specifically, we use GDP to formulate a model predictive control (MPC) model for piecewise-affine systems with implicit switching logic. As an example, the GDP-based MPC approach is used as a supervisory control to improve energy efficiency in residential buildings with binary on/off, relay-based thermostats. A simulation study is used to demonstrate the validity of the proposed approach, and the improved solution quality compared to existing MIPbased control approaches.

Bhattacharya, Arnab↗
NASA NTRS1987

Vector fields and nilpotent Lie algebras

An infinite-dimensional family of flows E is described with the property that the associated dynamical system: x(t) = E(x(t)), where x(0) is a member of the set R to the Nth power, is explicitly integrable in closed form. These flows E are of the form E = E1 + E2, where E1 and E2 are the generators of a nilpotent Lie algebra, which is either free, or satisfies some relations at a point. These flows can then be used to approximate the flows of more general types of dynamical systems.

Grayson, Matthew↗
NASA NTRS1972

Absolute stability analysis of attitude control systems for large boosters.

A method for performing absolute stability analyses of attitude control systems for large launch vehicles is presented. Absolute stability of these systems is shown in a finite region of the state space. The regions are computed by using the Lur'e-Postnikov Liapunov function. This function is chosen to provide additional information about the exponential property of absolute stability. Significant advantages of the method proposed in this paper are: it is independent of the order of the system; algebraic operations involved in the computations are relatively simple and convenient for machine implementation; and the obtained results are valid not only for a particular nonlinearity but also for an entire class of nonlinear characteristics that satisfy certain general conditions. A system model representing the Saturn V launch vehicle is used to illustrate the method.

Seltzer, S. M.↗
NASA NTRS1985

Nonlinear optimal control with tensors - Some computational issues

Some computational issues associated with the calcualtion of optimal feedback controls for nonlinear systems in a tensor setting are described. The specific issues addressed pertain to the combinatorial nature of the loading of the elements into tensors used to represent the system, cost, and feedback, and the subsequent calculations involving these elements. Particular attention is given to: the symmetric tensor algebra which is a natural setting for representing polynomials; the conversions between symmetric and nonsymmetric tensors; the general nature of the calculations required; and the solution equation for nonlinear optimal feedback control. It is concluded that nonlinear tensor feedback can improve performance both in terms of system responses and in terms of system stability region.

Osullivan, J. A.↗
NASA NTRS1982

Low-authority control synthesis for large space structures

The control of vibrations of large space structures by distributed sensors and actuators is studied. A procedure is developed for calculating the feedback loop gains required to achieve specified amounts of damping. For moderate damping (Low Authority Control) the procedure is purely algebraic, but it can be applied iteratively when larger amounts of damping are required and is generalized for arbitrary time invariant systems.

Aubrun, J. N.↗
NASA NTRS1967

Analytical Methods in Vibrations.

Book on analytical methods in vibrations covering general mathematical formulations of common features of various vibrating systems

STATISTICAL ANALYSIS↗
NASA NTRS1972

Elimination on sparse symmetric systems of a special structure.

Consideration of the problem of finding a permutation of rows and columns and an algorithm for solving ordered systems of linear algebraic equations with sparse matrices having a certain regular structure. Two approaches to the solution of this problem, in which the sparsity is used to some extent, are outlined. One of them is a very general approach where optimal (or nearly optimal) ordering is sought and the algorithm for solving the ordered system treats the matrix element by element to perform only necessary operations. The other approach involves the use of band matrices. After comparing these two approaches, a third approach is then suggested which involves the use of pipe matrices, and a means of ordering the rows and columns to obtain this type of matrix is presented. Examples of matrices reordered by the proposed procedure are cited.

Segethova, J.↗
DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Explicit Equations for Exterior Square of the General Linear Group

Several explicit systems of equations defining the exterior square of the general linear group ⋀{sup 2} GL{sub n} as affine group scheme are presented. Algebraic ingredients of the equations, so called exterior numbers, are translated to the language of weight diagrams corresponding to a Lie group of type A{sub n−1} in the representation with the highest weight ϖ{sub 2}.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

NOSS altimeter algorithm specifications

A description of all algorithms required for altimeter processing is given. Each description includes title, description, inputs/outputs, general algebraic sequences and data volume. All required input/output data files are described and the computer resources required for the entire altimeter processing system were estimated. The majority of the data processing requirements for any radar altimeter of the Seasat-1 type are scoped. Additions and deletions could be made for the specific altimeter products required by other projects.

Hancock, D. W.↗
NASA NTRS1985

Optical linear algebra processors - Noise and error-source modeling

The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

Casasent, D.↗
NASA NTRS2001

Automatic Overset Grid Generation with Heuristic Feedback Control

An advancing front grid generation system for structured Overset grids is presented which automatically modifies Overset structured surface grids and control lines until user-specified grid qualities are achieved. The system is demonstrated on two examples: the first refines a space shuttle fuselage control line until global truncation error is achieved; the second advances, from control lines, the space shuttle orbiter fuselage top and fuselage side surface grids until proper overlap is achieved. Surface grids are generated in minutes for complex geometries. The system is implemented as a heuristic feedback control (HFC) expert system which iteratively modifies the input specifications for Overset control line and surface grids. It is developed as an extension of modern control theory, production rules systems and subsumption architectures. The methodology provides benefits over the full knowledge lifecycle of an expert system for knowledge acquisition, knowledge representation, and knowledge execution. The vector/matrix framework of modern control theory systematically acquires and represents expert system knowledge. Missing matrix elements imply missing expert knowledge. The execution of the expert system knowledge is performed through symbolic execution of the matrix algebra equations of modern control theory. The dot product operation of matrix algebra is generalized for heuristic symbolic terms. Constant time execution is guaranteed.

Robinson, Peter I.↗
DOE OSTI2020

Landau quantization of multilayer graphene on a Haldane sphere

Here, we consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary nonrelativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current toolkits of the numerical studies on fractional quantum Hall effects in systems of graphite multilayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1972

Control systems on Lie groups.

The controllability properties of systems which are described by an evolution equation in a Lie group are studied. The revelant Lie algebras induced by a right invariant system are singled out, and the basic properties of attainable sets are derived. The homogeneous case and the general case are studied, and results are interpreted in terms of controllability. Five examples are given.

Jurdjevic, V.↗
NASA NTRS1973

A new approach to the design of time-varying control systems with application to the Space Shuttle Boost

A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.

Ramanth, R. V.↗