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DOE OSTI2020

Quandary

Quandary numerically simulates and optimizes the time-evolution of open quantum systems. The underlying dynamics are modelled by Lindblad's master equation, a linear ordinary differential equation (ODE) describing quantum systems interacting with the environment. Quandary solves this ODE numerically by applying a time-stepping integration scheme, and utilizes a gradient-based optimization approach to determine optimal control pulses that drive the quantum system to a desired target state. Two optimization objectives are considered: (a) Unitary gate optimization that finds controls to realize a unitary gate transformation, and (b) optimal reset that aims to drive the quantum system to the ground states. Gradient-based optimization schemes utilizing Petsc's Tao optimization package are applied to generate control pulses that minimize the respective measure. To evaluate the gradient of the objective function, the discrete adjoint method is used while leveraging techniques from Algorithmic Differentiation to produce exact and consistent gradients. To mitigate excessive execution run times, the software can be build together with the XBraid software library which provides a parallelization strategy to distribute the time-evolution of the underlying dynamics onto multiple processor.

Petersson, NilsA.↗

DOE OSTI2026

Energetic Copolymers From LLM-105 and Aliphatic Isocyanates

Energetic polymers typically feature fuel-rich backbones with pendant oxidizing explosophores, which are used to modify pressure and temperature characteristics in energetic formulations. However, these pendant explosophores generally increase sensitivity and decrease the thermal stability of the polymer in the condensed phase. Direct polymerization of insensitive high explosives (IHEs) bearing polymerizable functionalities, such as amines, provides a synthetic platform for deriving tunable energetic materials. Here, this work demonstrates the first direct polymerization of the IHE 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) with aliphatic isocyanate comonomers to yield an energetic copolyurea (PUa1) and an energetic copolyurea network (PUa2). 1 H and 13 C nuclear magnetic resonance (NMR) and Fourier transform infrared spectroscopy (FTIR) confirm copolyurea synthesis. PUa1 exhibited branching reactions commonly found in polyurea syntheses, and these side reactions were suppressed in PUa2 through use of a polyfunctional isocyanate. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) demonstrate the energetic IHE based polyurea preserves the energetic decomposition of the parent monomer LLM-105 in PUa1 (1203 J g −1 ) and PUa2 (687 J g −1 ), albeit with reduced thermal stability with peak decomposition temperatures of 235°C and 233°C, respectively. This work presents a new approach for generating energetic polymers from IHE cores with tunable energetic, thermal, and structural characteristics.

Chemistry↗

DOE OSTI2021

An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.

1D2V↗

DOE OSTI2024

Photovoltaic Cable Connectors: A Comparative Assessment of the Present State of the Industry [Slides]

The consequences of failure for balance of systems (BoS) components (such as PV cable connectors) include offline module string(s); low system voltage; arc, ground, insulation, and over-temperature faults; triggered fuse(s); system shutdown; and fire. The degradation modes for connectors are studied here through an industry survey and its subsequent examination, which are compared to field-degraded specimens. 117 specimens were obtained from a variety of locations and climates or accelerated tests. A failure analysis for connectors from PV installations was developed (and applied to 54 specimens) including nondestructive examinations (photography, a custom resistance-current scan, and X-ray computed tomography) and destructive examinations (featuring milling of the external plastic, extraction of the internal convolute spring, and potting and polishing in cross-section). Surface and through-thickness composition of the metal pins and springs was quantified using scanning electron microscopy with energy-dispersive X-ray spectroscopy. Fourier-transform infrared spectroscopy was used to verify the base polymer materials and compare the chemical structure of the connector body, bushing, end nut, and o-ring. Thermogravimetric analysis and differential scanning calorimetry were used to further verify the degradation of the same polymeric components. Updated from 2023 NIST/UL Workshop on Photovoltaic Materials Durability (website: https://events.ul.com/WPMogn?rt=aAuoWsl4E0KaORLCMeOgfA) and 2024 PVRW workshop (https://pvrw.nrel.gov/past-proceedings).

14 SOLAR ENERGY↗

NASA NTRS1972

Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays the role of the thermodynamic potential for compressible, adiabatic flow in the sense that the pressure integral for stable flow is less than for all slightly different flows. This stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and the temperature, which are the arguments of the pressure function, to be generalized velocities, that is, the proper-time derivatives of scalar spare-time functions which are generalized coordinates in the canonical formalism. In a fluid context, proper-time differentiation must be expressed in terms of three independent quantities that specify the fluid velocity. This can be done in several ways, all of which lead to different variants (canonical transformations) of the same constraint-free action integral whose Euler-Lagrange equations are just the well-known equations of motion for adiabatic compressible flow.

Schmid, L. A.↗

NASA NTRS1977

A piecewise linear approximation scheme for hereditary optimal control problems

An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

Cliff, E. M.↗

NASA NTRS1995

A cryogenic scan mechanism for use in Fourier transform spectrometers

This paper describes the requirements, design, assembly and testing of the linear Scan Mechanism (SM) of the Composite Infrared Spectrometer (CIRS) Instrument. The mechanism consists of an over constrained flexible structure, an innovative moving magnet actuator, passive eddy current dampers, a Differential Eddy Current (DEC) sensor, Optical Limit Sensors (OLS), and a launch lock. Although all the components of the mechanism are discussed, the flexible structure and the magnetic components are the primary focus. Several problems encountered and solutions implemented during the development of the scan mechanism are also described.

Hakun, Claef F.↗

NASA NTRS1984

Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform

A technique for applying discrete Fourier series to infinite domains is presented. The technique uses mappings designed to minimize truncation error and can be applied to solve mixed initial boundary value problems among others. The method is alias-free and yields consistent differentiation and integration operators. The mapping-induced truncation error is explicitly expressible and small in nearly all cases of interest. The method is illustrated for three problems involving convection, diffusion, and vortex interaction.

Cain, A. B.↗

NASA NTRS1974

Morphology and types of particles of regolith sample from the Sea of Fertility

A brief description of the morphology of lunar surface material returned by Luna 16 automatic lunar station is given. Adhesiveness of the surface material and its ability to be electrified is noted. Two main genetic groups of regolith particles are differentiated: primary, represented mainly by fragments of magmatic rocks of the basalt and gabbro types, as well as mineralized grains of their constituent minerals, and secondary, particles subjected to appreciable exogenic transformation on the surface of the Moon. The second group, representing more than 70 percent of the material in coarse fractions, includes particles of breccias, sintered aggregates of complex dendritic form, and glass and vitrified particles of varied composition.

Florenskiy, K. P.↗

NASA NTRS1981

Computation of the modes and polar moment of inertial of the blades of an HAWT

The coupled differential equations of motion of the blades of a horizontal axis wind turbine are solved numerically, permitting the optimization of the design at relatively low cost. The equation of motion is transformed into a set of first order equations and solved with fourth order Runge-Kutta integrators. This technique is applied to a twisted, tapered blade of variable cross section and stiffness including discontinuities. The first six natural frequencies and mode shapes are obtained. The polar moment of inertia of the blades is obtained as a function of frequency and rotational speed.

Beaulieu, G.↗

NASA NTRS1982

Numerical computation of exponential matrices using the Cayley-Hamilton theorem

A method for computing exponential matrices, which often arise naturally in the solution of systems of linear differential equations, is developed. An exponential matrix is generated as a linear combination of a finite number (equal to the matrix order) of matrices, the coefficients of which are scalar infinite sums. The method can be generalized to apply to any formal power series of matrices. Attention is focused upon the exponential function, and the matrix exponent is assumed tri-diagonal in form. In such cases, the terms in the coefficient infinite sums can be extracted, as recursion relations, from the characteristic polynomial of the matrix exponent. Two numerical examples are presented in some detail: (1) the three dimensional infinitesimal rotation rate matrix, which is skew symmetric, and (2) an N-dimensional tri-diagonal and symmetric finite difference matrix which arises in the numerical solution of the heat conduction partial differential equation. In the second example, the known eigenvalues and eigenvectors of the finite difference matrix permit an analytical solution for the exponential matrix, through the theory of diagonalization and similarity transformations, which is used for independent verification. The convergence properties of the scalar infinite summations are investigated for finite difference matrices of various orders up to ten, and it is found that the number of terms required for convergence increases slowly with the order of the matrix.

Walden, H.↗

NASA NTRS1987

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.↗

DOE OSTI2021

Detection, monitoring, and determination of location of changes in metallic structures using multimode acoustic signals

Acoustic transducers generate and receive acoustic signals at multiple locations along a surface of rigid structure, wherein longitudinal spacing between transducer locations define measurement zones. Acoustic signals with chosen amplitude-time-frequency characteristics excite multiple vibration modes in the structure within each zone. Small mechanical changes in inspection zones lead to scattering and attenuation of broadband acoustic signals, which are detectable as changes in received signal characteristics as part of a through-transmission technique. Additional use of short, narrowband pulse acoustic signals as part of a pulse-echo technique allows determination of the relative location of the mechanical change within each zone based on the differential delay profiles. For accurate acoustic modeling and simulation, the mesh size, time step, time delay, and time-window size are optimized. Frequency normalization of the Short-Time Fourier Transform of acoustic response output improves experiment-simulation cross-validation. Applications of the method to structures with arbitrarily complex geometries are also demonstrated.

Findikoglu, Alp Tugrul↗

DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗

DOE OSTI2026

Thermal Stability of LiNi x Mn y Co z O 2 Cathode Materials

Here, the thermal evolution of LiNi x Mn y Co z O 2 (NMC) lithium-ion battery electrode materials is examined at various states of charge (SOC) or lithium concentrations for a variety of Ni:Mn:Co ratios or electrode compositions. Synchrotron X-ray diffraction (XRD) combined with Rietveld analysis shows the onset decomposition temperatures of phases, decomposition products, lattice parameters, and phase fractions as a function of composition and SOC. SOC impacts the lattice parameters of the NMC phase, where a collapse of the c-axis in the NMC phases is noted due to lithium extraction. Among the compositions examined, the low-Ni NMC111 uncycled sample (NMC111 0% SOC) exhibited the highest thermal stability, with a decomposition temperature approximately 250 °C higher than that of NMC532 0% and NMC811 0%. When the SOC exceeds 50% (i.e., more than 0.4 mol of Li ions extracted), the influence of Ni content on the decomposition temperature becomes negligible, with decomposition occurring around 250−300 °C for all compositions. Ni content also affects the decomposition pathways: NMC111 tends to first form a TM 3 O 4 -type phase, where TM represents transition metals, before transforming into a TMO-type phase, whereas most of the NMC811 samples directly decompose into the TMO phase. The presence of metallic phases was confirmed by both XRD and thermogravimetric-differential scanning calorimetry (TGA-DSC) analysis, as a result of heating under inert conditions. The TGA-DSC results suggest that metallic phase formation is favored at lower SOC in samples with a higher Ni content. This work provides comprehensive insight into the thermal degradation pathways of NMC materials as a function of composition, SOC, and temperature.

Peng, Jian [Univ. of New South Wales, Sydney, NSW ↗

NASA NTRS1980

A microprocessor application to a strapdown laser gyro navigator

The replacement of analog circuit control loops for laser gyros (path length control, cross axis temperature compensation loops, dither servo and current regulators) with digital filters residing in microcomputers is addressed. In addition to the control loops, a discussion is given on applying the microprocessor hardware to compensation for coning and skulling motion where simple algorithms are processed at high speeds to compensate component output data (digital pulses) for linear and angular vibration motions. Highlights are given on the methodology and system approaches used in replacing differential equations describing the analog system in terms of the mechanized difference equations of the microprocessor. Standard one for one frequency domain techniques are employed in replacing analog transfer functions by their transform counterparts. Direct digital design techniques are also discussed along with their associated benefits. Time and memory loading analyses are also summarized, as well as signal and microprocessor architecture. Trade offs in algorithm, mechanization, time/memory loading, accuracy, and microprocessor architecture are also given.

Giardina, C.↗

NASA NTRS1984

An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics

Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.

Vijayaraghavan, A.↗

NASA NTRS1988

A novel approach to the modelling and control of flexible robot arms

A general dynamic model of a two-link Euler-Bernoulli beam flexible robot arm is presented in the form of partial-differential-integral equations. Observations are made on important properties of the dynamic model. The resulting infinite-dimensional system is then input-output decoupled and partially linearized by a diffeomorphic state transformation and nonlinear state feedback. The local stability issue is addressed for a one-link flexible robot arm.

Ding, Xuru↗