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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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Rational approximations to solution of second order nonlinear Ricatti equation, using linear transformations - differential equations and operational calculus
Optical implementation of the Fukunaga-Koontz transform (FKT) and the Least-Squares Linear Mapping Technique (LSLMT) is described. The FKT is a linear transformation which performs image feature extraction for a two-class image classification problem. The LSLMT performs a transform from large dimensional feature space to small dimensional decision space for separating multiple image classes by maximizing the interclass differences while minimizing the intraclass variations. The FKT and the LSLMT were optically implemented by utilizing a coded phase optical processor. The transform was used for classifying birds and fish. After the F-K basis functions were calculated, those most useful for classification were incorporated into a computer generated hologram. The output of the optical processor, consisting of the squared magnitude of the F-K coefficients, was detected by a T.V. camera, digitized, and fed into a micro-computer for classification. A simple linear classifier based on only two F-K coefficients was able to separate the images into two classes, indicating that the F-K transform had chosen good features. Two advantages of optically implementing the FKT and LSLMT are parallel and real time processing.
Linear transformation to obtain rational approximation to response of physical system described by nonlinear differential equation including Duffing equation as special case
A new characterization of the Laplace transform for Schwartz distributions is developed, using sequences of linear transformations on the space of distributions. The standard theorems on analyticity, uniqueness and invertibility of the transform are proved, using the new characterization as the definition of the Laplace transform. It is shown that this sequential definition is equivalent to Schwartz's extension of the ordinary Laplace transform to distributions which he obtained from the Fourier transform.
The measurement of the earth's radiation budget has been chosen to illustrate the technique of objective system design. The measurement process is an approximately linear transformation of the original field of radiant exitances, so that linear statistical techniques may be employed. The combination of variability, measurement strategy, and error propagation is presently made with the help of information theory, as suggested by Kondratyev et al. (1975) and Peckham (1974). Covariance matrices furnish the quantitative statement of field variability.
Rigid body rotational attitude control in three dimensions with linear transformation as output variable, noting advantages, applications and results
The pilot of a modern jet aircraft is subjected to varying workloads while being responsible for multiple, ongoing tasks. The ability to associate the pilot's responses with the task/situation, by modifying the way information is presented relative to the task, could provide a means of reducing workload. To examine the feasibility of this concept, a real time simulation study was undertaken to determine whether preprocessing of sensor data would affect pilot response. Results indicated that preprocessing could be an effective way to tailor the pilot's response to displayed data. The effects of three transformations or shaping functions were evaluated with respect to the pilot's ability to predict and detect out-of-tolerance conditions while monitoring an electronic engine display. Two nonlinear transformations, on being the inverse of the other, were compared to a linear transformation. Results indicate that a nonlinear transformation that increases the rate-or-change of output relative to input tends to advance the prediction response and improve the detection response, while a nonlinear transformation that decreases the rate-of-change of output relative to input tends to lengthen the prediction response and make detection more difficult.
Transformations of sparse linear systems by row-column permutations are considered and various algorithms are constructed to transform arbitrary symmetric positive definite sparse matrices, as well as matrices in band form, doubly bordered band form, and doubly bordered block diagonal form.
Blocked algorithms have much better properties of data locality and therefore can be much more efficient than ordinary algorithms when a memory hierarchy is involved. On the other hand, they are very difficult to write and to tune for particular machines. The reorganization is considered of nested loops through the use of known program transformations in order to create blocked algorithms automatically. The program transformations used are strip mining, loop interchange, and a variant of loop skewing in which invertible linear transformations (with integer coordinates) of the loop indices are allowed. Some problems are solved concerning the optimal application of these transformations. It is shown, in a very general setting, how to choose a nearly optimal set of transformed indices. It is then shown, in one particular but rather frequently occurring situation, how to choose an optimal set of block sizes.
A new cascade basis reduction method of computing the optimal least-squares set of basis functions steering a given function is presented. The method combines the Lie group-theoretic and the singular value decomposition approaches in such a way that their respective strengths complement each other. Since the Lie group-theoretic approach is used, the set of basis and steering functions computed can be expressed analytically. Because the singular value decomposition method is used, this set of basis and steering functions is optimal in the least-squares sense. Furthermore, the computational complexity in designing basis functions for transformation groups with large numbers of parameters is significantly reduced. The efficiency of the cascade basis reduction method is demonstrated by designing a set of basis functions that steers a Gabor function under the four-parameter linear transformation group.
The frequency transform method of Hayashi (1983a) and the asynoptic space-time transform method of Salby (1982b) for deriving space-time spectra are compared. The comparison reveals that the Galilean transformation used by Hayashi and the asynoptic coordinate transformation used by Salby produce identical spectra. The mapping between asynoptic data and the space-time Fourier spectrum is examined. The operation which maps a series of asynoptic measurements into the correct sequence of synoptic maps is described. It is observed that this linear transformation is unique and recovers the correct spectrum over wavenumber and frequency for a satellite observed field.
The problem is considered of classifying into one of m distinct n-variate classes an arbitrary n-channel multispectral measurement vector x. The classification procedure used is the maximum likelihood procedure. Information loss in compressing the n-channel data to k channels is taken to be the difference in the average interclass divergences (or probability of misclassification) in n-space and in k-space. Data compression is accomplished by kxn linear transformation i.e., multiplication of the spectral n-vector by a kxn matrix of rank k.
This article describes a large deformation solid mechanics solver implemented as part of the freely available and open source MOOSE finite element simulation framework. The article documents the choices made in developing the solid mechanics framework and describes novel formulations for the gradient operator and constitutive modeling framework made to simplify implementations of different coordinate systems, stabilized gradient operators, and different constitutive model inputs and outputs. In the process, the article describes a new formulation that casts objective integration of the Cauchy stress as a linear transformation of the small stress rate. Finally, the article presents key implementation details and examines the parallel efficiency of the solid mechanics solver implemented in MOOSE. The implementation retains a good weak scaling efficiency beyond 1,000 parallel processes. The article includes a discussion of the factors limiting the parallel efficiency of implicit, large deformation solid mechanics codes on current high-performance computers, with the main current limitation being the scalability of the algebraic multigrid methods used to solve the linearized equilibrium equations.
Several theorems related to the Householder transformation and separability criteria are proven. Orthogonal transformations, topology, divergence, mathematical matrices, and group theory are discussed.
Nonlinear encoding of optical information can be achieved using various forms of data representation. Here, we analyze the performances of different nonlinear information encoding strategies that can be employed in diffractive optical processors based on linear materials and shed light on their utility and performance gaps compared to the state-of-the-art digital deep neural networks. For a comprehensive evaluation, we used different datasets to compare the statistical inference performance of simpler-to-implement nonlinear encoding strategies that involve, e.g., phase encoding, against data repetition-based nonlinear encoding strategies. We show that data repetition within a diffractive volume (e.g., through an optical cavity or cascaded introduction of the input data) causes the loss of the universal linear transformation capability of a diffractive optical processor. Therefore, data repetition-based diffractive blocks cannot provide optical analogs to fully connected or convolutional layers commonly employed in digital neural networks. However, they can still be effectively trained for specific inference tasks and achieve enhanced accuracy, benefiting from the nonlinear encoding of the input information. Our results also reveal that phase encoding of input information without data repetition provides a simpler nonlinear encoding strategy with comparable statistical inference accuracy to data repetition-based diffractive processors. Our analyses and conclusions would be of broad interest to explore the push-pull relationship between linear material-based diffractive optical systems and nonlinear encoding strategies in visual information processors.
There is a wide agreement on the urgency of transforming linear management of plastics towards a circular economy model. However, no clear pathways exist as to required recycling technologies involved and system-wide environmental impacts. This study explores such pathways in the U.S. for the most commonly used packaging plastics through a combination of mechanical and emerging advanced recycling technologies. A system optimization model aimed at minimizing environmental impacts was developed to determine optimal end-of-life (EOL) management and locations of existing and emerging U.S. recycling infrastructures. Our study includes material flows from virgin resin production through semi-manufacturing processes to existing EOL disposal and recycling processes. An optimized circular plastics packaging system achieved greenhouse gas (GHG) emission savings of up to 28% and cumulative energy demand (CED) savings of up to 46%, compared to the linear economy. Moreover, these savings of GHG emissions and CED impacts represent a reduction of 0.16% and 0.49% compared to annual U.S. GHG emissions and energy consumption in 2022, respectively. The optimal recycling rates and systems-level circularity ranged from 78–99% and 57–75%, respectively. Increased energy savings led to increased GHG emissions showing a potential trade-off between GHG emissions and energy. Analysis of 40 scenarios showed the importance of material collection distances, blend limit of mechanically recycled resins, process yields, and mandated recycling rates for achieving a sustainable circular economy of plastics.
Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024
This project focused on using pulsed-power-driven techniques to study the coupling of high-energy-density (HED) magnetic fields to HED matter in the laboratory. Specifically, we studied a phenomenon known as "micro-pinching" to obtain HED conditions on a modest, university-scale pulsed-power driver: the 1-MA, 100-ns MAIZE linear transformer driver (LTD) facility at the University of Michigan. We used the "X-pinch" platform as a means of generating micro-pinch HED plasmas. An X-pinch is formed when two or more wires are crossed into the shape of an 'X' and a large electrical current is driven through the wires. This creates an intense electrical current density at the crossing point of the wires. Associated with this current density is an intense magnetic field and an intense magnetic field pressure. The magnetic field pressure compresses and heats the wire material into the HEDP regime. The use of an X-pinch platform ensures that the micro-pinch HED plasma will form in a well-controlled location, which helps with diagnostics alignment. This platform allowed us to explore the extreme plasma conditions and magnetic field pressures that can be generated with compact pulsed-power technology and intensely focused discharge currents. Understanding the limits of intensely focused discharge currents could have an enormous impact on HED science, especially when one considers the scaling of these platforms to the 30-MA Z facility at Sandia National Laboratories, where pressures well in excess of 1 Gbar could be achieved.