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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
NASA NTRS1988

Rotordynamic analysis of a bearing tester

The properties of the solutions of a system of four coupled nonlinear differential equations that model the behavior of the rotating shaft of a bearing tester are studied. In particular, it is shown how the bounds for the rotations of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solution, the approach to the stability boundary can also be predicted. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots.

Zalik, Richard A.↗
NASA NTRS1991

Crystallization and properties of Sr-Ba aluminosilicate glass-ceramic matrices

Powders of roller quenched (Sr,Ba)O-Al2O3-2SiO2 glasses of various compositions were uniaxially pressed into bars and hot isostatically pressed at 1350 C for 4 hours or cold isostatically pressed and sintered at different temperatures between 800 to 1500 C for 10 or 20 hours. Densities, flexural strengths, and linear thermal expansion were measured for three compositions. The glasss transition and crystallization temperatures were determined by Differential Scanning Calorimetry (DSC). The liquidus and crystallization temperature from the melt were measured using high temperature Differential Thermal Analysis (DTA). Crystalline phases formed on heat treatment of the glasses were identified by powder x ray diffraction. In Sr containing glasses, the monoclinic celsian phase always crystallized at temperatures above 1000 C. At lower temperatures, the hexagonal analog formed. The temperature for orthorhombic to hexagonal structure transformation increased monotonically with SrO content, from 327 C for BaO-Al2O3-2SiO2 to 758 C for SrO-Al2O3-2SiO2. These glass powders can be sintered to almost full densities and monoclinic celsian phase at a relatively low temperature of 1100 C.

Bansal, Narottam P.↗
NASA NTRS1991

Crystallization and properties of Sr-Ba aluminosilicate glass-ceramic matrices

Powders of roller quenched (Sr,Ba)O-Al2O3-2SiO2 glasses of various compositions were uniaxially pressed into bars and hot isostatically pressed at 1350 C for 4 hours or cold isostatically pressed and sintered at different temperatures between 800 to 1500 C for 10 or 20 hours. Densities, flexural strengths, and linear thermal expansion were measured for three compositions. The glass transition and crystallization temperatures were determined by Differential Scanning Calorimetry (DSC). The liquidus and crystallization temperature from the melt were measured using high temperature Differential Thermal Analysis (DTA). Crystalline phases formed on heat treatment of the glasses were identified by powder X ray diffraction. In Sr containing glasses, the monoclinic celsian phase always crystallized at temperatures above 1000 C. At lower temperatures, the hexagonal analog formed. The temperature for orthorhombic to hexagonal structural transformation increased monotonically with SrO content, from 327 C for BaO-Al2O3-2SiO2 to 758 C for SrO-Al2O3-2SiO2. These glass powders can be sintered to almost full densities and monoclinic celsian phase at a relatively low temperature of 1100 C.

Bansal, Narottam P.↗
DOE OSTI2023

Thermal Polymorphism in CsCB11H12

Thermal polymorphism in the alkali-metal salts incorporating the icosohedral monocarba-hydridoborate anion, CB11H12−, results in intriguing dynamical properties leading to superionic conductivity for the lightest alkali-metal analogues, LiCB11H12 and NaCB11H12. As such, these two have been the focus of most recent CB11H12− related studies, with less attention paid to the heavier alkali-metal salts, such as CsCB11H12. Nonetheless, it is of fundamental importance to compare the nature of the structural arrangements and interactions across the entire alkali-metal series. Thermal polymorphism in CsCB11H12 was investigated using a combination of techniques: X-ray powder diffraction; differential scanning calorimetry; Raman, infrared, and neutron spectroscopies; and ab initio calculations. The unexpected temperature-dependent structural behavior of anhydrous CsCB11H12 can be potentially justified assuming the existence of two polymorphs with similar free energies at room temperature: (i) a previously reported, ordered R3 polymorph stabilized upon drying and transforming first to R3c symmetry near 313 K and then to a similarly packed but disordered I43d polymorph near 353 K and (ii) a disordered Fm3 polymorph that initially appears from the disordered I43d polymorph near 513 K along with another disordered high-temperature P63mc polymorph. Quasielastic neutron scattering results indicate that the CB11H12− anions in the disordered phase at 560 K are undergoing isotropic rotational diffusion, with a jump correlation frequency [1.19(9) × 1011 s−1] in line with those for the lighter-metal analogues.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Simulation of intense microwave pulse propagation in air breakdown environment

An experiment is conducted to examine the tail erosion phenomenon which occurs to an intense microwave pulse propagating in air breakdown environment. In the experiment, a 1 MW microwave pulse (1.1 microsec) is transmitted through a large plexiglas chamber filled with dry air at about 1-2 torr pressure. Two different degrees of tail erosion caused by two different mechanisms are identified. This experimental effort leads to the understanding of the fundamental behavior of tail erosion and provides a data base for validating the theoretical model. A theoretical model based on two coupled partial differential equations is established to describe the propagation on an intense microwave pulse in air breakdown environment. One is derived from the Poynting theorem, and the other one is the rate equation of electron density. A semi-empirical formula of the ionization frequency is adopted for this model. A transformation of these two equations to local time frame of reference is introduced so that they can be solved numerically with considerably reduced computation time. This model is tested by using it to perform the computer simulation of the experiment. The numerical results are shown to agree well with the experimental results.

Kuo, S. P.↗
DOE OSTI2023

Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

In this work, we present a phase-field model that captures the evolution of ionic concentrations and phase fractions during solid-state metathesis (SSM) reactions where diffusion limits the rate of transformation. The evolution of the mole fraction of each ion is obtained via governing equations that describe the reduction of a free energy, which includes an energy landscape with local minima located at compositions corresponding to stable products. We utilized two Lagrange multipliers to impose constraints of electroneutrality as well as on the sum of mole fractions, which were then eliminated to derive set of two partial differential equations that describe the dynamics of the mole fraction evolution. From these governing equations, the expressions for effective mobilities for the cations and the anions were obtained. We first study the effect of mobilities of ions on the reaction kinetics, using a simple model considering the ions with an identical absolute value of charge numbers. The simulation results show that the overall characteristic mobility, defined as the sum of the two effective ionic mobilities, provides an excellent measure of the rate at which reaction progresses and that the ratio of the effective mobilities of the anions and the cations signifies the manner by which the reaction progresses. We then generalize the model to consider ions with different charge numbers and tuned the mobility of ions based on their diffusion coefficients reported in the literature and experimental data from a thin-film experiment for the synthesis of FeS 2 to demonstrate the capability of the model to predict the phase evolution during SSM reactions. In particular, the simulation predicts nonplanar phase evolution, which is recently observed in thin-film reactions for the synthesis of FeS 2 via transmission electron microscopy. The approach can serve as a basis for models for phase transformations in other multiphase ionic mixtures, such as in all-solid-state batteries and in ionic liquids.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Galilean covariant harmonic oscillator

A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.

Horzela, Andrzej↗
NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗
NASA NTRS2019

Revolutionizing our Understanding of the Solar System via Sample Return from Mercury

Data from Mariner 10, MESSENGER, and ground-based telescopic observations have facilitated great advancements towards understanding the geochemistry, geology, internal structure, exosphere, and magnetosphere of Mercury. However, there are critical science questions that can be only addressed via examination of a sample in Earth-based laboratories, where numerous highly sensitive analytical measurements are possible. Collecting a sample from the surface of Mercury and bringing it to Earth for in-depth analysis would allow for transformative Solar System science to be conducted, examining aspects of our Solar System such as the evolution of the protoplanetary disk, space weathering on airless bodies, the geochemical behavior of elements at extreme conditions, and the origin and distribution of volatiles across the terrestrial planets. Furthermore, our knowledge of Mercury’s differentiation and geochemical processes, chronology and geologic evolution, tectonism and geomechanical properties, and past and ongoing magnetism would be greatly advanced via analysis of a sample from Mercury. Although there are ample challenges and knowledge gaps associated with sample return from Mercury in terms of both spacecraft requirements and material requirements for curatorial facilities, a sample from the planet would be an invaluable scientific resource for generations to come, enabling the most sophisticated measurements to be brought to bear for decades and helping to truly unlock the mysteries of our Solar System.

Vander Kaaden, Kathleen E.↗
NASA NTRS1984

Multigrid applications to three-dimensional elliptic coordinate generation

The multigrid algorithm was applied to solve the coupled set of elliptic quasilinear partial differential equations associated with three-dimensional coordinate generation. The results indicate that the multigrid scheme is more than twice as fast as conventional relaxation schemes on moderate-size grids. Convergence factors of order 0.90 per work unit were achieved on 36,000-point grids. The paper covers the form of transformation, develops the set of generation equations, and gives details on the multigrid approach used. Included are a development of the full-approximation storage scheme, details of the smoothing-rate analysis, and a section devoted to rational programming techniques applicable to the multigrid algorithm.

Thames, F. C.↗
NASA NTRS2011

Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics: Basic Concepts and Operations - Part 1

This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.

Farassat, Fereidoun↗
NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗
DOE OSTI2020

Managing time-substitutable electricity usage using dynamic controls

A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Ghosh, Soumyadip↗
NASA NTRS1985

New eutectic alloys and their heats of transformation

Eutectic compositions and congruently melting intermetallic compounds in binary and multicomponent systems among common elements such as Al, Ca, Cu, Mg, P, Si, and Zn may be useful for high temperature heat storage. In this work, heats of fusion of new multicomponent eutectics and intermetallic phases are reported, some of which are competitive with molten salts in heat storage density at high temperatures. The method used to determine unknown eutectic compositions combined results of differential thermal analysis, metallography, and microprobe analysis. The method allows determination of eutectic compositions in no more than three steps. The heats of fusion of the alloys were measured using commercial calorimeters, a differential thermal analyzer, and a differential scanning calorimeter.

Farkas, D.↗
DOE OSTI2022

Enhanced Catalytic Performance of a Ce/V Oxo Cluster through Confinement in Mesoporous SBA-15

To increase catalytic efficiency, mesoporous supports have been widely applied to immobilize well-defined metal oxide clusters due to their ability to stabilize highly dispersed clusters. Here, for this study, a redox-active heterometallic Ce 12 V 6 -oxo cluster (CeV) was first presynthesized and then incorporated into mesoporous silica, SBA-15, via a straightforward impregnation method. Scanning transmission electron microscopy (STEM) and Fourier transform infrared spectroscopy (FTIR), in concert with scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM-EDS), verified the successful introduction of the CeV cluster inside the pore of SBA-15. The 51 V magic angle spinning solid-state nuclear magnetic resonance ( 51 V MAS NMR) spectroscopy and differential pair distribution function (dPDF) analysis confirmed the structural integrity of the CeV cluster inside the SBA-15. The composite was then benchmarked for liquid-phase oxidation of 2-chloroethyl ethyl sulfide (CEES) under mild conditions and gas-phase oxidative dehydrogenation (ODH) of propane under high temperatures (up to 550 °C). The catalytic reactivity results demonstrated 8- and 14-fold increase in turnover frequency (TOF) values of the composite (CeV@10SBA-2) than the bulk CeV cluster under the same conditions for CEES oxidation and ODH, respectively. These results highlight the improved reactivity of the catalytically active CeV cluster as attributed to the higher dispersion of the discrete cluster upon immobilization within the SBA-15 support.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

An assessment of Landsat MSS and TM data for urban and near-urban land-cover digital classification

The information content of Landsat TM and MSS data was examined to assess the ability to digitally differentiate urban and near-urban land covers around Miami, FL. This examination included comparisons of unsupervised signature extractions for various cover types, training site statistics for intraclass and interclass separability, and band and band combination selection from an 11-band multisensor data set. The principal analytical tool used in this study was transformed divergence calculations. The TM digital data are typically more useful than the MSS data in the homogeneous near-urban land-covers and less useful in the heterogeneous urban areas.

Haack, Barry↗
NASA NTRS2015

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Goldman, Benjamin D.↗