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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Generalized trigonometric Fourier-series method with automatic time step control for non-linear point kinetics equations

The trigonometric Fourier-series method (TFS) is generalized to provide approximate solutions for non-linear point kinetics equations with feedback using varying step sizes. This method can provide a very stable solution against the size of the discrete time step allowing much larger step sizes to be used. Systems of the point kinetics equations are solved using Fourier-series expansion over a partition of the total time interval. The approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high-order derivatives of the solution vector at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. This system is similar to the Vandermonde system. Two successive orders of the partial sums are used to estimate the local truncation error. This error and some other constrains are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The process of calculating suitable step sizes should be automatic and inexpensive. Convergence and stability of the proposed method are discussed and a new formula is introduced to maintain stability. The proposed method solves the general linear and non-linear kinetics problems. The method has been applied to five different types of reactivities including step/ramp insertions with temperature feedback. The method is seemed to be valid for larger time intervals than those used in the conventional numerical integration, and is thus useful in reducing computing time. Computational results are found to be consistent with the analysis, they demonstrate that the convergence of the iteration scheme can be accelerated and the resulting computing times can be greatly reduced while maintain computational accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Characterizing phonon dynamics using stochastic sampling

Predicting phonon relaxation time from molecular dynamics (MD) requires a long simulation time to compute the mode energy auto-correlation function. Here, we present an alternative approach to infer the phonon life-time from an approximate form of the energy auto-correlation function. The method requires as an input a set of sampled equilibrium configurations. A stochastic sampling method is used to generate the equilibrium configurations. We consider a truncated Taylor series expansion of the phonon energy auto-correlation function. The different terms in the truncated correlation function are obtained using the stochastic sampling approach. The expansion terms, thus, obtained are in good agreement with the corresponding values obtained using MD. We then use the approximate function to compute the phonon relaxation time. The relaxation time computed using this method is compared with that obtained from the exact correlation function. The two values are in agreement with each other.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1966

Optical interferometry of inhomogeneous gases.

One-dimensional refractive index distribution using power series expansions for refractive index and ray traces obtained from relation of inhomogeneities and interference pattern of Mach- Zehnder interferometer

MACH-ZEHNDER INTERFEROMETER↗
NASA NTRS1975

Series solution for the planar asymmetric blunt-body problem

Accurate semianalytic solutions to the inverse blunt-body problem have been obtained using a method of series expansion. Rational fractions are employed for series summation and analytic continuation. Angles of incidence up to 30 deg and Mach numbers as low as 2 have been considered. The maximum-entropy streamline will not wet the body surface in asymmetric flow. It may pass either above or below the stagnation streamline. Limit lines appear in the supersonic portion of the flow field, both in the shock layer and in its upstream analytic continuation.

Schwartz, L. W.↗
DOE OSTI2020

Calculating the divided differences of the exponential function by addition and removal of inputs

We introduce a method for calculating the divided differences of the exponential function by means of addition and removal of items from the input list to the function. Our technique exploits a new identity related to divided differences recently derived by F. Zivcovich. We show that upon adding an item to or removing an item from the input list of an already evaluated exponential, the re-evaluation of the divided differences can be done with only O(sn) floating point operations and O(sn) bytes of memory, where [z 0 ,...,z n ] are the inputs and s ∝ max i,j |z i – z j |. We demonstrate our algorithm’s ability to deal with input lists that are orders-of-magnitude longer than the maximal capacities of the current state-of-the-art. Here, we discuss in detail one practical application of our method: the efficient calculation of weights in the off-diagonal series expansion quantum Monte Carlo algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Transmutation of a trans-series: the Gross-Witten-Wadia phase transition

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g 2 and a gauge index N , as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N , in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms ‘condense’ at the transition point to match with the double-scaling limit trans-series. Furthermore, we also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.

1/N Expansion↗
DOE OSTI2018

Sufficient Condition for Consistency of Infinite Systems

Based on the theory of double series, we obtain a sufficient condition for the existence of strictly partial solutions to infinite systems of linear algebraic equations. We prove series expansion theorems for infinite determinants of Gaussian infinite matrices. Examples of application of the proposed condition are given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Note: Precise radial distribution of charged particles in a magnetic guiding field

Current high precision beta decay experiments of polarized neutrons, employing magnetic guiding fields in combination with position sensitive and energy dispersive detectors, resulted in a detailed study of the mono-energetic point spread function (PSF) for a homogeneous magnetic field. A PSF describes the radial probability distribution of mono-energetic electrons at the detector plane emitted from a point-like source. With regard to accuracy considerations, unwanted singularities occur as a function of the radial detector coordinate which have recently been investigated by subdividing the radial coordinate into small bins or employing analytical approximations. In this note, a series expansion of the PSF is presented which can numerically be evaluated with arbitrary precision.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗