SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.
Interpretation of multi-angle spectro-polarimetric data in remote sensing of atmospheric aerosols require fast and accurate methods of solving the vector radiative transfer equation (VRTE). The single and double scattering approximations could provide an analytical framework for the inversion algorithms and are relatively fast, however accuracy assessments of these approximations for the aerosol atmospheres in the atmospheric window channels have been missing. This paper provides such analysis for a vertically homogeneous aerosol atmosphere with weak and strong asymmetry of scattering. In both cases, the double scattering approximation gives a high accuracy result (relative error approximately 0.2%) only for the low optical path - 10(sup -2) As the error rapidly grows with optical thickness, a full VRTE solution is required for the practical remote sensing analysis. It is shown that the scattering anisotropy is not important at low optical thicknesses neither for reflected nor for transmitted polarization components of radiation.
Abstract A self‐potential (SP) data‐inversion algorithm was developed and tested on an analytical model of electrical‐potential profile data attributed to single and multiple polarized electrical sources. The developed algorithm was then validated by an application to SP‐monitoring field data measured on the floodplain of East Fork Poplar Creek, Oak Ridge, Tennessee, to image electrical sources in areas conducive to preferential flow into the flood plain from the bedrock‐lined riverbed. The algorithm combined stochastic source‐localization by particle‐swarm‐optimization (PSO) of electrical sources characterized by simplified geometries with source tomography by regularized weighted least‐squares minimization of a quadratic objective function. Prior information was incorporated by preconditioning the tomography algorithm by PSO results. Variable percentages of random noise were added to analytical‐model data to evaluate the algorithm performance. Results indicated that true parameters of single‐source models were inverted and approximated with small residual error, whereas inversion of analytical‐model data representing multiple electrical sources accurately approximated the locations of the sources but miscalculated some parameters because of the non‐uniqueness of the inverse‐model solution. Source tomography applied to analytical model data during testing produced a spatially continuous parameter field that identified the locations of point‐scale synthetic dipole sources of electrical current flow with varying degrees of accuracy depending on the prior information incorporated into the tomography. When applied to SP‐monitoring field data, the algorithm imaged electrical sources within a known fault that intersects the bedrock riverbed and flood plain of East Fork Poplar Creek and depicted dynamic electrical conditions attributed to hyporheic exchange.
This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods, generalizing the iterative alternating scheme to nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a hierarchical Bayesian model characterized by a conditionally Gaussian prior and generalized gamma hyperpriors. Suitable choices of hyperparameters yield sparsity-promoting regularization. We propose an iterative algorithm for MAP estimation, which alternates between updating the unknown with an ensemble Kalman method and updating the hyperparameters in the regularization to promote sparsity. Here, the effectiveness of our methodology is demonstrated in several computed examples, including compressed sensing and subsurface flow inverse problems.
Abstract We use first-principles simulation and alchemical mixing approximation to reveal the unique double band inversion and topological phase transition in Ge Sn alloys. Wave function parity, spatial charge distribution and surface state spectrum analyses suggest that the band inversion in Ge Sn is relayed by its first valence band. As the system evolves from Ge to -Sn, its conduction band moves down, and inverts with the first and the second valence bands consecutively. The first band inversion makes the system nontrivial, while the second one does not change the topological invariant of the system. Both of the band inversions yield surface modes spanning the individual inverted gaps, but only the surface mode in the upper gap associates with the nontrivial nature of tensile-strained -Sn.
Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.
Second normal stress difference measurement by annular flows, giving approximate method for experimental data inversion
Possible evolutionary paths of the spin axis of Mercury are studied theoretically in terms of generalized Cassini's laws using the Hamiltonian approach. Three stable positions (Cassini states) of the spin axis are discerned. The Cassini states in which the spin axis remains fixed in the frame rotating with the orbit precession are extremes in the tide-free Hamiltonian under the condition of constant angular momentum. The stability of the 3/2 spin resonance for Mercury as a function of obliquity is discussed, and it is shown how control of the resonance is passed from one to another term in the averaged potential as the obliquity is increased with a corresponding loss of stability at each transfer. A sampling technique is used to infer the evolution due to tidal interaction. Two tidal models are used - one with a constant value of the specific dissipation function Q and the other with Q inversely proportional to frequency. An approximate analytic solution for precession trajectories very close to a Cassini state is developed.
A particle size spectrometer having a fixed field of view within the forward light scattering cone at an angle theta sub s between approximately 100 and 200 minutes of arc (preferably at 150 minutes), a spectral range extending approximately from 0.2 to 4.0 inverse micrometers, and a spectral resolution between about 0.1 and 0.2 inverse micrometers (preferably toward the lower end of this range of spectral resolution), is employed to determine the distribution of particle sizes, independently of the chemical composition of the particles, from measurements of incident light, at each frequency, sigma (=1/lambda), and scattered light, I(sigma).
Several methods for computing many eigenvalues and eigenfunctions of a single anharmonic oscillator Schroedinger operator whose potential may have one or two minima are described. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. Rigorous bounds are given, and it is proved that the approximations converge faster than any inverse power of the size of the matrices needed to compute them. The results of computations for the g:phi(4):1 theory are presented. These results indicate that the methods actually converge exponentially fast.
A method for predicting the strong interaction between the viscous and inviscid flows which occurs in flow separation is reviewed. An inverse boundary-layer procedure approximately accounts for normal pressure gradients that may be important in strongly interacting flows. Transformed boundary-layer equations are written in which the pressure gradient is set equal to the inviscid pressure gradient. As the boundary-layer edge is approached and the viscous shear and heat conduction terms vanish, the viscous flow solution is required to asymptotically approach the inviscid solution over the generalized displacement body. Attention is then focused on viscous-inviscid interacting flows with a first-order viscous formulation and constant pressure across the boundary layer. Results obtained with this procedure are presented for: (1) transitional separation bubbles near an airfoil leading edge, (2) subsonic boattail separated turbulent flow, and (3) transonic turbulent shock wave boundary-layer interaction on an axisymmetric bump configuration.
Semi-discrete Galerkin approximation schemes in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems are considered. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given.
A set of preliminary reference atmosphere models of significant trace species which play important roles in controlling the chemistry, radiation budget, and circulation patterns of the atmosphere were produced. These models of trace species distributions are considered to be reference models rather than standard models; thus, it was not crucial that they be correct in an absolute sense. These reference models can serve as a means of comparison between individual observations, as a first guess in inversion algorithms, and as an approximate representation of observations for comparison to theoretical calculations.
Solar p-mode frequency splittings, parameterized by the coefficients through order N = 12 of a Legendre polynomial expansion of the mode frequencies as a function of m/L, were obtained from an analysis of helioseismology data taken at Big Bear Solar Observatory during the 4 years 1986 and 1988-1990 (approximately solar minimum to maximum). Inversion of the even-index splitting coefficients confirms that there is a significant contribution to the frequency splittings originating near the solar poles. The strength of the polar contribution is anti correlated with the overall level or solar activity in the active latitudes, suggesting a relation to polar faculae. From an analysis of the odd-index splitting coefficients we infer an uppor limit to changes in the solar equatorial near-surface rotatinal velocity of less than 1.9 m/s (3 sigma limit) between solar minimum and maximum.
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of waypoints through which the aircraft trajectory must pass. The waypoints typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory that satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multidimensional, multiaxis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions are required to be smooth. The proposed guidance algorithm is based on the inversion of the pure feedback approximation, followed by correction for the effects of zero dynamics. The paper describes the structure and major modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
We suggest a new approach to cloud retrieval, using a normalized difference of nadir reflectivities (NDNR) constructed from a non-absorbing and absorbing (with respect to liquid water) wavelength. Using Monte Carlo simulations we show that this quantity has the potential of removing first order scattering effects caused by cloud side illumination and shadowing at oblique Sun angles. Application of the technique to TM (Thematic Mapper) radiance observations from Landsat-5 over the Southern Great Plains site of the ARM (Atmospheric Radiation Measurement) program gives very similar regional statistics and histograms, but significant differences at the pixel level. NDNR can be also combined with the inverse NIPA (Nonlocal Independent Pixel Approximation) of Marshak (1998) which is applied for the first time on overcast Landsat scene subscenes. We demonstrate the sensitivity of the NIPA-retrieved cloud fields on the parameters of the method and discuss practical issues related to the optimal choice of these parameters.
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.