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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Particle-number fluctuations near the critical point of nuclear matter

Equation of state with the quantum statistics corrections is used for particle-number fluctuations ω of the isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. Here, the fluctuations, ω ∝ 1/K, are analytically derived through the isothermal incompressibility K at first order over a small quantum-statistics parameter. Our approximate analytical results appear to be in good agreement with the results of accurate numerical calculations. These results are also close to those obtained by using more accurate Tolman and Rowlinson expansions of the incompressibility K near the critical point. More general formula for fluctuations ω, improved at the critical point, was obtained for a finite particle-number average $\langle$N$\rangle$ by neglecting, for simplicity, small quantum statistics effects. It is shown that for a large dimensionless parameter, α ∝ K 2 $\langle$N$\rangle$/K", where K" is the second derivative of the incompressibility K as function of the average particle density n, far from the critical point (α >> 1), one finds the traditional asymptote, ω ∝ 1/K, for the fluctuations ω. For a small parameter, α << 1, near the critical point, where K = 0 and α = 0, one obtains another asymptote of ω. These fluctuations, having a maximum near the critical point as function of the average density n, for finite values of $\langle$N$\rangle$ are finite and relatively small, in contrast to the results of the traditional calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Field moment expansion method for interacting bosonic systems

In this work, we introduce a numerical method and python package, https://github.com/andillio/CHiMES, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum breaktime of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting Bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and that the growth of the higher order moments be hierarchical.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗
DOE OSTI2020

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical gate synthesis for quantum heuristics on bosonic quantum processors

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ( > 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Vlasov equation eigenvalues and eigenvectors for Fourier-Hermite dispersion matrices of order greater than 1,000

The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).

Grant, F. C.↗
NASA NTRS1973

Turbulent jet mixing at high supersonic speeds.

The results of three related studies of turbulent jet mixing are presented and discussed. The major effort was the collection of mean-flow data at a much higher free stream Mach number than was previously available. The effects of initial swirl in the injectant were found to be minimal. Numerical predictions of the non-swirling experimental case obtained using an eddy viscosity approximation are found to be in reasonable agreement with the data. Lastly, an approximate analysis of the decay of the swirling velocity is developed. This analysis is based upon an eddy viscosity model for transport in the circumferential direction adapted from wing-tip vortex work.

Schetz, J. A.↗
NASA NTRS1975

Research study on stabilization and control: Modern sampled-data control theory. Design of the large space telescope system

Conditions of self-sustained oscillations in a two-axis model of the nonlinear LST system are studied. The describing function of the CMG frictional nonlinearity of the LST system is used for the analysis, as well as continuous-data and discrete-data models of the simplified LST control system. A numerical-iterative method is described for the analysis of the two-axis system. Approximation methods and the direct plotting of the stability equation are implemented in the study. It is shown that although the dynamics of the two axes are identical, the amplitudes of self-sustained oscillations in the two axes may in principle be different. Analysis shows that the LST systems are of equal amplitudes but with 180-degree phase shift.

Kuo, B. C.↗
NASA NTRS1975

Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation

The semiclassical approximation (quantum oscillator, classical path) is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1975

Shear-flexible finite-element models of laminated composite plates and shells

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Noor, A. K.↗
NASA NTRS1976

One-dimensional numerical study of charged particle trajectories in turbulent electrostatic wave fields

The paper describes a numerical simulation of electron trajectories in weak random electric fields under conditions that are approximately true for Langmuir waves whose wavelength is much longer than the Debye length. Two types of trajectory calculations were made: (1) the initial particle velocity was made equal to the mean phase velocity of the waves, or (2) it was equal to 0.7419 times the mean velocity of the waves, so that the initial velocity differed substantially from all phase velocities of the wave spectrum. When the autocorrelation time is much greater than the trapping time, the particle motion can change virtually instantaneously from one of three states - high-velocity, low-velocity, or trapped state - to another. The probability of instantaneous transition from a high- or low-velocity state becomes small when the difference between the particle velocity and the mean phase velocity of the waves becomes high in comparison to the trapping velocity. Diffusive motion becomes negligible under these conditions also.

Graham, K. N.↗
NASA NTRS1977

Effects of stream-associated fluctuations upon the radial variation of average solar wind parameters

A numerical MHD model in both spherically symmetric time-dependent and corotating equatorial flow approximations is used to compute the effects of nonlinear fluctuations due to solar wind streams upon radial gradients of average solar wind parameters. Significant effects of correlations between fluctuations on the gradients of azimuthal magnetic field, radial velocity, density, and azimuthal velocity are found. It is found that nonlinear fluctuations are a significant effect in determining the radial gradients of the solar wind at distances as small as 0.2 AU; at distances greater than 1 AU, nonlinear fluctuations dominate the behavior of the radial gradients.

Goldstein, B. E.↗
NASA NTRS1977

Meteorite impact ejecta - Dependence of mass and energy lost on planetary escape velocity

The amounts of material and energy which escape a planet in a meteorite impact event is calculated as functions of impact and escape velocities. Results are obtained from the computed flow induced by the impact of iron and gabbroic anorthosite spheres onto a half-space of anorthosite at impact velocities of 5 to 45 km/sec. The impact-induced flows were determined by a numerical method using the mass, momentum, and energy conservation relations in finite-difference approximation, within an Eulerian computational grid. The impact velocities at which ejecta losses equal meteorite mass gains are found to be approximately 20, 35, and 45 km/sec for anorthosite objects and approximately 25, 35, and 40 km/sec for iron objects striking anorthosite surfaces for the gravity fields of the moon, Mercury and Mars.

Okeefe, J. D.↗
NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗