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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Exact two-body expansion of the many-particle wave function

Progress toward the solution of the strongly correlated electron problem has been stymied by the exponential complexity of the wave function. Previous work established an exact two-body exponential product expansion for the ground-state wave function. By developing a reduced density-matrix analog of Dalgarno-Lewis perturbation theory, we prove here that (i) the two-body exponential product expansion is rapidly and globally convergent with each operator representing an order of a renormalized perturbation theory, (ii) the energy of the expansion converges quadratically near the solution, and (iii) the expansion is exact for both ground and excited states. The two-body expansion offers a reduced parametrization of the many-particle wave function as well as the two-particle reduced density matrix with potential applications on both conventional and quantum computers for the study of strongly correlated quantum systems. In this work, we demonstrate the result with the exact solution of the contracted Schrödinger equation for the molecular chains H 4 and H 5 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

OPE convergence in non-relativistic conformal field theories

Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NR-CFT, in particular the mapping between operators and states in a non-relativistic “radial quantization” Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2, d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1990

Polarization Aberrations

The analysis of the polarization characteristics displayed by optical systems can be divided into two categories: geometrical and physical. Geometrical analysis calculates the change in polarization of a wavefront between pupils in an optical instrument. Physical analysis propagates the polarized fields wherever the geometrical analysis is not valid, i.e., near the edges of stops, near images, in anisotropic media, etc. Polarization aberration theory provides a starting point for geometrical design and facilitates subsequent optimization. The polarization aberrations described arise from differences in the transmitted (or reflected) amplitudes and phases at interfaces. The polarization aberration matrix (PAM) is calculated for isotropic rotationally symmetric systems through fourth order and includes the interface phase, amplitude, linear diattenuation, and linear retardance aberrations. The exponential form of Jones matrices used are discussed. The PAM in Jones matrix is introduced. The exact calculation of polarization aberrations through polarization ray tracing is described. The report is divided into three sections: I. Rotationally Symmetric Optical Systems; II. Tilted and Decentered Optical Systems; and Polarization Analysis of LIDARs.

Mcguire, James P., Jr.↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
DOE OSTI2019

Properties of a potential energy matrix in oscillator basis

Matrix elements of potential energy are examined in detail. We consider a model problem — a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L{sup 2} basis (J-matrix) method for the quantum theory of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum-inspired method for solving the Vlasov-Poisson equations

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high-resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as a MPS within some tolerable error threshold. Here, in this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations for systems with one coordinate in space and one coordinate in velocity, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher-dimensional problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheres and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2004

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

observers↗
DOE OSTI2012

A preconditioning technique for Schur complement systems arising in stochastic optimization

Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based parallelization. In this paper the parallelization is obtained by using an interior-point method and a Schur complement mechanism for the interior-point linear systems. However, the direct linear solves involving the dense Schur complement matrix are expensive, and adversely affect the scalability of this approach. We address this issue by proposing a stochastic preconditioner for the Schur complement matrix and by using Krylov iterative methods for the solution of the dense linear systems. The stochastic preconditioner is built based on a subset of existing scenarios and can be assembled and factorized on a separate process before the computation of the Schur complement matrix finishes on the remaining processes. The expensive factorization of the Schur complement is removed from the parallel execution flow and the scaling of the optimization solver is considerably improved with this approach. The spectral analysis indicates an exponentially fast convergence in probability to 1 of the eigenvalues of the preconditioned matrix with the number of scenarios incorporated in the preconditioner. Numerical experiments performed on the relaxation of a unit commitment problem show good performance, in terms of both the accuracy of the solution and the execution time.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis

In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the eigenstate thermalization hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and tracing out the complementary high-energy Hilbert space, the ETH leads to an exponential suppression of trace distance between the coarse grained eigenstates. Conversely, we show that an exponential hardness of distinguishing between states implies ETH-like matrix elements. Finally, the BBBV lower bound on the query complexity of Grover search then translates directly into a complexity-theoretic statement lower bounding the hardness of distinguishing these reduced states

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Integration of EDWARD readout architecture in full-field fluorescence imaging detector

Data bandwidth, timing resolution and resource utilization in readouts of radiation detectors are a constant challenge. Event driven solutions are pushing against well-trenched framed solutions. The idea for an asynchronous readout architecture called EDWARD ( E vent- D riven W ith A ccess and R eset D ecoder) was presented at the TWEPP 2021 conference. Here we show the progress of our work which resulted in two chip prototypes. The first one, named 3FI65P1, is a full device with the analog pixel circuitry suited for full-field fluorescence imaging. It is already manufactured, and preliminary results are presented. Finally, the second chip, named EDWARD65P1, contains digital pulse generators with Poisson-exponential distribution in each pixel for extraction of the performance matrix of the EDWARD architecture alone.

47 OTHER INSTRUMENTATION↗
NASA NTRS2012

Large-Strain Transparent Magnetoactive Polymer Nanocomposites

A document discusses polymer nano - composite superparamagnetic actuators that were prepared by the addition of organically modified superparamagnetic nanoparticles to the polymer matrix. The nanocomposite films exhibited large deformations under a magnetostatic field with a low loading level of 0.1 wt% in a thermoplastic polyurethane elastomer (TPU) matrix. The maximum actuation deformation of the nanocomposite films increased exponentially with increasing nanoparticle concentration. The cyclic deformation actuation of a high-loading magnetic nanocomposite film was examined in a low magnetic field, and it exhibited excellent reproducibility and controllability. Low-loading TPU nanocomposite films (0.1-2 wt%) were transparent to semitransparent in the visible wavelength range, owing to good dispersion of the magnetic nanoparticles. Magnetoactuation phenomena were also demonstrated in a high-modulus, high-temperature polyimide resin with less mechanical deformation.

Meador, Michael A.↗
DOE OSTI2014

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground {sup 4}S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite-basis limit

Here In this paper we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density-matrix renormalization-group method by computing the core-valence entanglement in the C 2 ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Investigating the age distribution of fracture discharge using multiple environmental tracers, Bedrichov Tunnel, Czech Republic

We investigated the transit time distribution (TTD) of discharge collected from fractures in the Bedrichov Tunnel, Czech Republic, using lumped parameter models and multiple environmental tracers. We then utilize time series of δ 18 O, δ 2 H and 3 H along with CFC measurements from individual fractures in the Bedrichov Tunnel of the Czech Republic to investigate the TTD, and the uncertainty in estimated mean travel time in several fracture networks of varying length and discharge. We also compare several TTDs, including the dispersion distribution, the exponential distribution, and a developed TTD which includes the effects of matrix diffusion. The effect of seasonal recharge is explored by comparing several seasonal weighting functions to derive the historical recharge concentration. We identify best fit mean ages for each TTD by minimizing the error-weighted, multi-tracer χ2 residual for each seasonal weighting function. We use this methodology to test the ability of each TTD and seasonal input function to fit the observed tracer concentrations, and the effect of choosing different TTD and seasonal recharge functions on the mean age estimation. We find that the estimated mean transit time is a function of both the assumed TTD and seasonal weighting function. Best fits as measured by the χ2 value were achieved for the dispersion model using the seasonal input function developed here for two of the three modeled sites, while at the third site, equally good fits were achieved with the exponential model and the dispersion model and our seasonal input function. The average mean transit time for all TTDs and seasonal input functions converged to similar values at each location. The sensitivity of the estimated mean transit time to the seasonal weighting function was equal to that of the TTD. These results indicated that understanding seasonality of recharge is at least as important as the uncertainty in the flow path distribution in fracture networks and that unique identification of the TTD and mean transit time is difficult given the uncertainty in the recharge function. But, the mean transit time appears to be relatively robust to the structural model uncertainty. The results presented here should be applicable to other studies using environmental tracers to constrain flow and transport properties in fractured rock systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

A note on large gauge transformations in double field theory

Here, we give a detailed proof of the conjecture by Hohm and Zwiebach in double field theory. Our result implies that their proposal for large gauge transformations in terms of the Jacobian matrix for coordinate transformations is, as required, equivalent to the standard exponential map associated with the generalized Lie derivative along a suitable parameter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Chaos in inhomogeneous neutrino fast flavor instability

In dense neutrino gases, the neutrino-neutrino coherent forward scattering gives rise to a complex flavor oscillation phenomenon not fully incorporated in simulations of neutron star mergers (NSM) and core collapse supernovae (CCSNe). Moreover, it has been proposed to be chaotic, potentially limiting our ability to predict neutrino flavor transformations in simulations. To address this issue, we explore how small flavor perturbations evolve in the nonlinear regime of the neutrino quantum kinetic equation within a narrow centimeter-scale region inside a NSM and a toy neutrino distribution. Our findings reveal that paths in the flavor state space of solutions with similar initial conditions diverge exponentially, exhibiting chaos. This inherent chaos makes the microscopic scales of neutrino flavor transformations unpredictable. However, the domain-averaged neutrino density matrix remains relatively stable, with chaos minimally affecting it. This particular property suggests that domain-averaged quantities remain reliable despite the exponential amplification of errors. Published by the American Physical Society 2024

Astronomy & Astrophysics↗