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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Elastic Properties of Plasma-Exposed Tungsten Predicted by Molecular-Dynamics Simulations

We report results of systematic molecular-dynamics computations of the elastic properties of single-crystalline tungsten containing structural defects, voids and overpressurized He nanobubbles, related to plasma exposure of tungsten serving as a plasma- facing component (PFC) in nuclear fusion devices. Our computations reveal that the empty voids are centers of dilatation resulting in development of tensile stress in the tungsten matrix, whereas He-filled voids (nanobubbles) introduce compressive stress in the plasma-exposed tungsten. We find that the dependence of the elastic moduli of plasma-exposed tungsten, namely, the bulk, Young, and shear modulus, on its void fraction follows a universal exponential scaling relation. We also find that the elastic moduli of plasma-exposed tungsten soften substantially as a function of He content in the tungsten matrix, following an exponential scaling relation; this He-induced exponential softening is in addition to the softening caused in the matrix with increasing temperature. A systematic characterization of the dependence of the elastic moduli on the He bubble size reveals that He bubble growth affects significantly both the bulk modulus and the Poisson ratio of plasma-exposed tungsten, while its effect on the Young and shear moduli of the plasma-exposed material is weak. Our findings contribute directly to the development of a structure-properties database that is required for the predictive modeling of the dynamical response of PFCs in nuclear fusion devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

King, Andrew D. [D-Wave Quantum Inc., Burnaby, BC ↗
DOE OSTI2012

Exotic states and rare B {sub s }-decays in the covariant quark model

The consequences of treating X(3872) meson as a tetraquark bound state are explored. The covariant quark model that effectively includes infrared confinement is employed as a dynamical framework. The strong decay widths of observed channels X → J/Ψ + 2π(3π) and X → + D-bar {sup 0} + D{sup 0} + π{sup 0} are calculated via the intermediate off-shell states X → J/Ψ + ρ(ω) and X → D + D*. For reasonable values of the size parameter Λ{sub X }of X(3872) meson the results are found to be consistent with the available experimental data. The possible impact of X(3872) on the behavior of the total cross section of J/Ψ dissociation by light particles within the framework of the s-channel dominance description is also discussed. The single-photon decay X → γ + J/Ψ is then analyzed. To introduce electromagnetic interactions, a nonlocal effective Lagrangian, which describes an interaction of X(3872) meson with its four constituent quarks, is gauged by using the P-exponential path-independent formalism. The matrix element of the transition X → γ + J/Ψ is evaluated and its gauge invariance is proved. The decay width of X → γ + J/Ψ and longitudinal/transverse composition of J/Ψ in this decay are calculated. For a reasonable value of the size parameter Λ{sub X }of X(3872) meson, the results are found to be consistent with the available experimental data. The helicity and multipole amplitudes of the process are computed as well, and the procedure of obtaining them from the covariant transition amplitude by using the covariant projection is described. Considering the surge of great interest to the problem of CP violation recently observed in a B {sub s }−{ie749-2} system, decays of B {sub s }to D-{ie749-3} and color suppressed decay B {sub s }→ J/Ψ ϕ attracted the attention of both theorists and experimentalists. We find new values for the covariant quark model parameters (with built-in infrared confinement) in the meson sector by fitting the leptonic decay constants and a number of electromagnetic decays, and then evaluate in a parameter-free way the form factors of B(B {sub s }) → P(V) transitions within an entire kinematic range of the momentum transfer. Our results are applied to calculating the widths of nonleptonic B {sub s }decays to D{sup −}{sub s }D{sup +}{sub s }, {ie749-4}, and {ie749-5}. The largest contribution to Δγ for B {sub s }-{ie749-6} system comes from these modes. The nonleptonic decay B {sub s }→ J/Ψϕ is also considered. Though this decay mode is color suppressed it has important implications in the search for possible CP-violating novel physics effects in B {sub s }-{ie749-7} mixing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗
NASA NTRS1985

Multiprocessor sparse L/U decomposition with controlled fill-in

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Alaghband, G.↗
DOE OSTI2020

The impact of nanoparticle softness on its tracer diffusion coefficient in all polymer nanocomposites

The diffusion of nanoparticles in a polymer matrix is an area of current interest. However, a complete understanding is still limited as it is often difficult to quantify the much slower motion of nanoparticles in a polymer matrix. To combat this problem, we have developed a protocol to measure the diffusion coefficient of soft nanoparticles in a linear polymer matrix. Recently developed synthetic control over soft nanoparticle structures combined with this protocol provides a pathway to separately elucidate the effects of the molecular weight and nanoparticle softness on its diffusive behavior. These results indicate that the nanoparticle softness and deformability dictate its motion. Increasing the cross-linking density of the nanoparticle for all molecular weights increases its hardness and suppresses its motion in the linear matrix. Additionally, the nanoparticle molecular weight dependence deviates from the exponential dependence for star polymers suggesting that these nanoparticles benefit from the cooperative motion of the matrix to open pathways for the nanoparticle. Finally, comparison of these experimentally determined values to the Stokes–Einstein theory demonstrates that the nanoparticles diffuse much slower than a hard sphere. This is interpreted to indicate that there exist additional interactions between the nanoparticle and polymer matrix that are not captured by Stokes–Einstein, including threading or entanglement of the linear chain with the nanoparticle.

Rostom, Sahar↗
DOE OSTI2020

Dual-cone variational calculation of the two-electron reduced density matrix

The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher $\textit{N}$-representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. Further, we apply the method to computing the energies and properties of strongly correlated electrons—including atomic charges, electron densities, dipole moments, and orbital occupations—in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Pauli transfer matrix direct reconstruction: channel characterization without full process tomography

Abstract We present a tomographic protocol for the characterization of multiqubit quantum channels. We discuss a specific class of input states, for which the set of Pauli measurements at the output of the channel directly relates to its Pauli transfer matrix components. We compare our results to those of standard quantum process tomography, showing an exponential reduction in the number of different experimental configurations required by a single matrix element extraction, while keeping the same number of shots. This paves the way for more efficient experimental implementations, whenever a selective knowledge of the Pauli transfer matrix is needed. We provide several examples and simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Landau-Zener transition between two levels coupled to continuum

We report for a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, i, to survive the transition and to remain in the first level, depends exponentially on the square of the tunnel matrix element between the two levels. This result remains valid when the second level, f, is broadened due to e.g. coupling to continuum (Akulin and Schleich (1992) [26]). If the level, i, is also coupled to continuum, albeit much weaker than the level f, a particle, upon surviving the transition, will eventually escape. However, for shorter times, the probability to find the particle in the level i after crossing f is enhanced due to the coupling to continuum. This, as shown in the present paper, is the result of a second-order process, which is an additional coupling between the levels. The underlying mechanism of this additional coupling is virtual tunneling from i into continuum followed by tunneling back into f.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Time-reversal symmetric resolution of unity without background integrals in open quantum systems

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green’s function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schrödinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly, the exponential decays due to the resonance poles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Online Optimization as a Feedback Controller: Stability and Tracking

This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1999

Optimal Frequency-Domain System Realization with Weighting

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation uses a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. Three different approaches are introduced to fine-tune the model using nonlinear programming methods to minimize the desired cost function. The first method uses an eigenvalue assignment technique to reassign a subset of system poles to improve the identified model. The second method deals with the model in the real Schur or modal form, reassigns a subset of system poles, and adjusts the columns (rows) of the input (output) influence matrix using a nonlinear optimizer. The third method also optimizes a subset of poles, but the input and output influence matrices are refined at every optimization step through least-squares procedures.

Juang, Jer-Nan↗
NASA NTRS1999

Optimal System Realization in Frequency Domain

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation begins with a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. An approach is introduced to fine-tune the model using non-linear programming methods to minimize the desired cost function. The method deals with the model in the real Schur or modal form and reassigns a subset of system poles using a nonlinear optimizer. At every optimization step, the input and output influence matrices are refined through least-squares procedures. The proposed approaches are used to identify an analytical model for a NASA testbed from experimental data.

Juang, Jer-Nan↗
DOE OSTI2018

H{sub ∞} memory feedback control for uncertain singular Markov jump systems with time-varying delay and input saturation

This paper concerns with the H{sub ∞} robust exponential stability and memory state feedback stabilization of singular Markov jump systems with time-delay and input saturation. Linear matrix inequality conditions are given to guarantee regularity, impulse-freeness and exponential stability for the singular Markov jump system. Moreover, sufficient conditions are presented to ensure the H{sub ∞} disturbance attenuation level, and the design method of memory feedback controller is developed by solving linear matrix inequalities optimization problem without any decompositions of system matrices and equivalent transformation. Furthermore, the function in the proof procedure belongs to multiple Lyapunov-like functions whose advantage lies in their flexibility. Finally, numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

High-order commutator-free exponential time-propagation of driven quantum systems

We discuss the numerical solution of the Schroedinger equation with a time-dependent Hamilton operator using commutator-free time-propagators. These propagators are constructed as products of exponentials of simple weighted sums of the Hamilton operator. Owing to their exponential form they strictly preserve the unitarity of time-propagation. The absence of commutators or other computationally involved operations allows for straightforward implementation and application also to large scale and sparse matrix problems. We explain the derivation of commutator-free exponential time-propagators in the context of the Magnus expansion, and provide optimized propagators up to order eight. An extensive theoretical error analysis is presented together with practical efficiency tests for different problems. Issues of practical implementation, in particular the use of the Krylov technique for the calculation of exponentials, are discussed. We demonstrate for two advanced examples, the hydrogen atom in an electric field and pumped systems of multiple interacting two-level systems or spins that this approach enables fast and accurate computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Gradient-based stochastic estimation of the density matrix

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H) ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. Here, we introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S -(d+2)/2d , where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum Joule expansion of one-dimensional systems

Here, we investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. A barrier initially confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time t = 0. We investigate the properties of the time-evolved density matrix, the diagonal ensemble density matrix, and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation using exact diagonalization. The weights for the diagonal ensemble and the canonical ensemble match well for high initial temperatures that correspond to negative effective final temperatures after the expansion. At long times after the barrier is removed, the time-evolved Rényi entropy of subsystems bigger than half can equilibrate to the thermal entropy with exponentially small fluctuations. The time-evolved reduced density matrix at long times can be approximated by a thermal density matrix for small subsystems. Few-body observables, like the momentum distribution function, can be approximated by a thermal expectation of the canonical ensemble with strongly suppressed fluctuations. The negative effective temperatures for finite systems go to non-negative temperatures in the thermodynamic limit for bosons, but there is a true thermodynamic effect for fermions, which is confirmed by finite-temperature density matrix renormalization group calculations. We propose the Joule expansion as a way to dynamically create negative temperature states for fermion systems with repulsive interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗