A trace method for directly synthesizing Liapunov functions of aperiodic systems
Liapunov functions synthesis for aperiodic linear systems by inspecting traces of state matrix and products
Chen, C. F.↗
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Multivariable system synthesis with step disturbance rejection
The primary objective of this paper is to present a constructive procedure for the synthesis of linear multivariable systems whose entire internal state and output are corrupted by unknown step disturbances. It is assumed that the dynamical behavior of the system is expressed in any one of three equivalent ways - i.e., the state space representation, the controllable and observable differential operator representation, and the transfer matrix representation. In terms of the transfer matrix representation, T(s), the synthesis procedure is shown to be capable of producing any stable, desired closed loop transfer matrix, Td(s), which can be expressed as the product of T(s) and any proper rational matrix, Tc(s), while simultaneously eliminating the steady-state effect of step disturbances at the output of the system. Furthermore, the synthesis scheme outlined employes only the known, directly measurable input and output signals.
Wolovich, W. A.↗
Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow
The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
Miles, J. H.↗
Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow
The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one-dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
Miles, J. H.↗
Adaptive Filtering for Large Space Structures: A Closed-Form Solution
In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system.
Rauch, H. E.↗
The capacity of the Hopfield associative memory
Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory stores n-tuple of + or - 1s. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products of m fundamental memories, it may be possible to recover a certain one of the m memories by using an initial n-tuple probe vector less than a Hamming distance n/2 away from the fundamental memory. If m fundamental memories are chosen at random, the maximum asymptotic value of m in order that most of the m original memories are exactly recoverable is n/(2 log n). With the added restriction that every one of the m fundamental memories be recoverable exactly, m can be no more than n/(4 log n) asymptotically as n approaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory-capacity problem is closely related to the capacity of the quantized Gaussian channel.
Mceliece, Robert J.↗
Development of an image converter of radical design
A long term investigation of thin film sensors, monolithic photo-field effect transistors, and epitaxially diffused phototransistors and photodiodes to meet requirements to produce acceptable all solid state, electronically scanned imaging system, led to the production of an advanced engineering model camera which employs a 200,000 element phototransistor array (organized in a matrix of 400 rows by 500 columns) to secure resolution comparable to commercial television. The full investigation is described for the period July 1962 through July 1972, and covers the following broad topics in detail: (1) sensor monoliths; (2) fabrication technology; (3) functional theory; (4) system methodology; and (5) deployment profile. A summary of the work and conclusions are given, along with extensive schematic diagrams of the final solid state imaging system product.
Irwin, E. L.↗
Derivation of the chemical-equilibrium rate coefficient using scattering theory
Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.
Mickens, R. E.↗
An intrinsically n-dimensional generalized flux vector splitting implicit finite element Euler algorithm
A generalized flux-vector splitting implicit Galerkin finite-element algorithm for the Euler equations in curvilinear coordinates for ideal and reacting gases is derived. For an arbitrary equation of state, the curvilinear-coordinate flux vector is split in kinematic and kinetic components, and the associated jacobian matrix eigenvalues explicitly depend on the metric data. After directional semidiscretization, the terminal ordinary differential-equation system is solved via a nonlinearly stable implicit Runge-Kutta scheme in concert with an accurate tensor matrix product factorization. The results for selected two-dimensional supersonic and axisymmetric hypersonic flows validate the algorithm and verify its robustness for curvilinear-coordinate computations. The evolution towards a steady state is achieved for large Courant numbers without indication of numerical instabilities.
Iannelli, G. S.↗
Effect of fiber orientation on the fracture toughness of brittle matrix composites
The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. The orientation distribution of the fibers is likely to be biased, and not in an ideal random or aligned state. A micromechanical model is formulated for the postcracking behavior using the force-displacement relation for an arbitrary fiber bridging a crack, the fiber orientation density function, and the fiber location density function. This model is then used to determine an effective traction law for the bridging fibers, as well as the steady state bridging toughness increment. In most cases, the results may be placed in the form of a product of the aligned fiber results times a modifying integrated orientation factor. The frictional shear stress on fiber pull-out is allowed to vary during pull-out, modeling the effects of matrix breakdown, fiber surface smoothing or wear debris accumulation. Results are presented for a variety of representative planar and three-dimensional fiber orientation states.
Jain, L. K.↗
Hydrothermal Alteration on Basaltic Mauna Kea Volcano as a Template for Identification of Hydrothermal Alteration on Basaltic Mars
Certain samples of palagonitic tephra from Mauna Kea Volcano (Hawaii) are spectral analogues for bright martian surface materials at visible and near-IR wavelengths because both are characterized by a ferric absorption edge extending from about 400 to 750 nm and relatively constant reflectivity extending from about 750 nm to beyond 2000 nm. Palagonite is a yellow or orange isotropic mineraloid formed by hydration and devitrification of basaltic glass. For Mars-analogue palagonite, the pigment is nanometersized ferric oxide particles (np-Ox) dispersed throughout an allophane-like hydrated basaltic glass matrix. Crystalline phyllosilicates are not generally detected, and the hydration state of the is not known. The poorly crystalline nature of glass alteration products implies relatively low temperature formation pathways. We report here x-ray diffraction, major element, Mossbauer, and VNIR data for 9 basaltic tephras. Thermal emission spectra are reported in a separate abstract. Our multidisciplinary approach both tightly constrains mineralogical interpretations and maximizes overlap with datasets available for the martian surface available now and in the future.
Morris, R. V.↗
Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests
This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.
Pressure-Sensitive Paint↗
Diagrammatic technique for calculating matrix elements of collective operators in superradiance
Adopting the so-called genealogical construction, one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicity the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes.
Lee, C. T.↗
Quantum Cohesion Oscillation of Electron Ground State in Low Temperature Laser Plasma
The development of radically new technological and economically efficient methods for obtaining chemical products and for producing new materials with specific properties requires the study of physical and chemical processes proceeding at temperature of 10(exp 3) to 10(exp 4) K, temperature range of low temperature plasma. In our paper, by means of Wigner matrix of quantum statistical theory, a formula is derived for the energy of quantum coherent oscillation of electron ground state in laser plasma at low temperature. The collective behavior would be important in ion and ion-molecule reactions.
Zhao, Qingxun↗
eddy Users Manual
eddy is a collection of tools - nonlinear solvers, meshing, post-processing, visualization, optimization, etc. - for performing scale-resolving simulations of multi-physics applications. The framework is designed to enable advanced R&D on a variety of topics by leveraging a mature capability for scale resolving simulations, and simultaneously be an appropriate tool for application analysis and support. Currently, eddy is at a relatively low technical readiness level (TRL), and users and developers should maintain appropriate expectations. The technical details behind eddy are outlined in several publications which can be consulted for more information [1–10]. The solvers are built around an unstructured high-order capability, and heavily utilize the tensor product sum-factorization approach for efficiency. The unsteady formulation utilizes a fully implicit space-time approach with a matrix-free Newton- Krylov method. A primitive steady-state solver is available for testing purposes, but is not expected to converge for all but simple verification cases. The Navier-Stokes fluid solvers do not support either RANS or hybrid-RANS capability, only LES and wall-modeled LES approaches. All of the solvers within eddy support three modes of operation: a primal solve of the full nonlinear problem, and two linearization approaches of the primal solve - the ad joint and the tangent solution. Details on how to select and use these three modes are outlined in Sec. 3.
Murman, Scott M.↗
The Frequency Detuning Correction and the Asymmetry of Line Shapes: The Far Wings of H2O-H2O
A far-wing line shape theory which satisfies the detailed balance principle is applied to the H2O-H2O system. Within this formalism, two line shapes are introduced, corresponding to band-averages over the positive and negative resonance lines, respectively. Using the coordinate representation, the two line shapes can be obtained by evaluating 11-dimensional integrations whose integrands are a product of two factors. One depends on the interaction between the two molecules and is easy to evaluate. The other contains the density matrix of the system and is expressed as a product of two 3-dimensional distributions associated with the density matrices of the absorber and the perturber molecule, respectively. If most of the populated states are included in the averaging process, to obtain these distributions requires extensive computer CPU time, but only have to be computed once for a given temperature. The 11-dimensional integrations are evaluated using the Monte Carlo method, and in order to reduce the variance, the integration variables are chosen such that the sensitivity of the integrands on them is clearly distinguished.
Ma, Q.↗
Quantum Search in Hilbert Space
A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.
Zak, Michail↗
Parity-violating electric-dipole transitions in helium
The paper examines parity-violating electric-dipole transitions in He in order to gain insight into the reliability of approximate calculations which are carried out for transitions in many-electron atoms. The contributions of the nearest-lying states are computed with a variety of wave functions, including very simple product wave functions, Hartree-Fock functions and Hylleraas-type wave functions with up to 84 parameters. It is found that values of the matrix elements of the parity-violating interaction can differ considerably from the values obtained from the good wave functions, even when these simple wave functions give accurate values for the matrix elements in question
Hiller, J.↗