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Results for “Analytic linearization”

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 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Linear and nonlinear propagation of water wave groups

Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.

Pierson, W. J., Jr.↗
NASA NTRS1976

The motion and stability of spin stabilized spacecraft with hinged appendages

The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to massless booms of fixed length whose orientation relative to the main part can change. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis. Analytic stability criteria indicate that hinge damping must be present and that for limiting cases, where the spin axis is an axis of symmetry, certain conditions relating the hinge point offset coordinates to the moment of inertia ratio and end masses must be satisfied. The hinge damping is always required for the nominal deployment of hinge members.

Sellappan, R.↗
NASA NTRS1982

Analytical solution for the drift behavior of Dynamics Explorer-B

The Dynamics Explorer (DE) mission was designed to explore the earth's magnetosphere, ionosphere, and plasmasphere. The DE mission employs two spacecraft, including DE-A and DE-B. The spacecraft were launched from the Western Test Range on Aug. 3, 1981, onboard the same Delta launch vehicle. The two spacecraft were placed in a coplanar polar orbit, with DE-A in a high altitude orbit (perigee = 570 km and apogee = 23174 km) and DE-B in a low altitude orbit (perigee = 309 km and apogee = 1013 km). In the present investigation, an attempt has been made to validate the flight data for DE-B with analytic and simulation results. The external torques acting on the spacecraft are represented in terms of tractable mathematical functions. A piecewise linear model of the superrotation of the upper atmosphere is assumed. The effect of individual torques on the long-term pitch axis motion is investigated using analytic and simulation methods. The results are found to be in very good agreement with the available flight data.

Sellappan, R. G.↗
NASA NTRS1991

Mixed convective/dynamic roll vortices and their effects on initial wind and temperature profiles

The onset and development of both dynamically and convectively forced boundary layer rolls are studied with linear and nonlinear analyses of a truncated spectral model of shallow Boussinesq flow. Emphasis is given here on the energetics of the dominant roll modes, on the magnitudes of the roll-induced modifications of the initial basic state wind and temperature profiles, and on the sensitivity of the linear stability results to the use of modified profiles as basic states. It is demonstrated that the roll circulations can produce substantial changes to the cross-roll component of the initial wind profile and that significant changes in orientation angle estimates can result from use of a roll-modified profile in the stability analysis. These results demonstrate that roll contributions must be removed from observed background wind profiles before using them to investigate the mechanisms underlying actual secondary flows in the boundary layer. The model is developed quite generally to accept arbitrary basic state wind profiles as dynamic forcing. An Ekman profile is chosen here merely to provide a means for easy comparison with other theoretical boundary layer studies; the ultimate application of the model is to study observed boundary layer profiles. Results of the analytic stability analysis are validated by comparing them with results from a larger linear model. For an appropriate Ekman depth, a complete set of transition curves is given in forcing parameter space for roll modes driven both thermally and dynamically. Preferred orientation angles, horizontal wavelengths and propagation frequencies, as well as energetics and wind profile modifications, are all shown to agree rather well with results from studies on Ekman layers as well as with studies on near-neutral and convective atmospheric boundary layers.

Haack, Tracy↗
DOE OSTI2016

Analytical and numerical treatment of resistive drift instability in a plasma slab

An analytic approach combining the effect of equilibrium diamagnetic flows and the finite ionsound gyroradius associated with electron−ion decoupling and kinetic Alfvén wave dispersion is derived to study resistive drift instabilities in a plasma slab. Linear numerical computations using the NIMROD code are performed with cold ions and hot electrons in a plasma slab with a doubly periodic box bounded by two perfectly conducting walls. A linearly unstable resistive drift mode is observed in computations with a growth rate that is consistent with the analytic dispersion relation. The resistive drift mode is expected to be suppressed by magnetic shear in unbounded domains, but the mode is observed in numerical computations with and without magnetic shear. In the slab model, the finite slab thickness and the perfectly conducting boundary conditions are likely to account for the lack of suppression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Finite-difference multiple fluid solution for source-driven rotation in highly magnetized linear plasma device

The rotation profile of a magnetized plasma cylinder composed of multiple fluids is investigated analytically, expanding on previous results. The analytic steady-state solution is used as a benchmark for a time-dependent multiple-fluid finite-difference code, MITNS: Multiple-Ion Transport Numerical Solver. Magnetic field evolution is taken into account, both analytically and numerically. Its details are shown to be of importance when particles are allowed out of the domain. MITNS reproduces the asymptotic expansion results for a small parameter $δ<<<1$. For $\sqrt{m_elm_i} ~ δ << 1$ , a slightly different regime, dominated by viscosity-induced transport of ions, is found numerically and analytically. Finally, this verification supports the use of this code for more complex time-dependent calculations in the future. Additionally, we derive the angular velocity profile of each species due to radial particle and charge fluxes of various strengths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2005

Theoretical and Experimental Unsteady Aerodynamics Compared for a Linear Oscillating Cascade With a Supersonic Leading-Edge Locus

Experimental data were obtained to help validate analytical and computational fluid dynamics (CFD) codes used to compute unsteady cascade aerodynamics in a supersonicaxial- flow regime. Results from two analytical codes and one CFD code were compared with experimental data. One analytical code did not account for airfoil thickness or camber; another, using piston theory (piston code), accounted for thickness and camber upstream of the first shockwave/airfoil impingement locations. The Euler CFD code accounted fully for airfoil shape.

Ramsey, John K.↗
NASA NTRS1979

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

Mitchell, C. E.↗
NASA NTRS1985

An experimental and analytical investigation of isolated rotor flap-lag stability in forward flight

For flap-lag stability of isolated rotors, experimental and analytical investigations are conducted in hover and forward flight on the adequacy of a linear quasisteady aerodynamics theory with dynamic inflow. Forward flight effects on lag regressing mode are emphasized. A soft inplane hingeless rotor with three blades is tested at advance ratios as high as 0.55 and at shaft angles as high as 20 degrees. In combination with lag natural frequencies, collective pitch settings and flap-lag coupling parameters, the data base comprises nearly 1200 test points (damping and frequency) in forward flight and 200 test points in hover. By computerized symbolic manipulations, an analytic model is developed in substall to predict stability margins with mode identification. It also predicts substall and stall regions to help explain the correlation between theory and data.

Gaonkar, G. H.↗
DOE OSTI2016

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the POTFIT approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

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

Multifrontal Non-negative Matrix Factorization

Non-negative matrix factorization (Nmf) is an important tool in high-performance large scale data analytics with applications ranging from community detection, recommender system, feature detection and linear and non-linear unmixing. While traditional Nmf works well when the data set is relatively dense, however, it may not extract sufficient structure when the data is extremely sparse. Specifically, traditional Nmf fails to exploit the structured sparsity of the large and sparse data sets resulting in dense factors. We propose a new algorithm for performing Nmf on sparse data that we call multifrontal Nmf (Mf-Nmf) since it borrows several ideas from the multifrontal method for unconstrained factorization (e.g. LU and QR). We also present an efficient shared memory parallel implementation of Mf-Nmf and discuss its performance and scalability. We conduct several experiments on synthetic and realworld datasets and demonstrate the usefulness of the algorithm by comparing it against standard baselines. We obtain a speedup of 1.2x to 19.5x on 24 cores with an average speed up of 10.3x across all the real world datasets.

Sao, Piyush↗
DOE OSTI2015

Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES(k) method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm , which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers Re≈1–1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case specific. Here, in this work, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate Re. In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier–Stokes equations in the small-amplitude limit to obtain a system of linear partial differential equations. Using a combination of numerical (finite element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere–sphere interactions, between one sphere's motion and (1) the oscillating background flow induced by the other's motion, and (2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counterintuitive and rich motility is in the parameter space of finite inertia of particles and fluid.

42 ENGINEERING↗
DOE OSTI2025

Mean-field dynamo as a quantum-like modulational instability

Presented here is a novel formulation of the mean-field dynamo as a modulational instability of magnetohydrodynamic (MHD) turbulence. This formulation, termed mean-field wave kinetics (MFWK), is based on the Weyl symbol calculus and allows describing the interaction between the mean fields (magnetic field and fluid velocity) and turbulence without requiring scale separation that is commonly assumed in the literature. The turbulence is described by the Wigner–Moyal equation for the spectrum of the two-point correlation matrix (Wigner matrix) of magnetic-field and velocity fluctuations and depicts the turbulence as an effective plasma of quantum-like particles that interact via the mean fields. Eddy–eddy interactions, which serve as ‘collisions’ in this effective plasma, are modelled within the standard minimal tau approximation to aid comparison with existing theories. Using MFWK, the non-local electromotive force is calculated for generic turbulence from first principles, modulo the limitations of MFWK. This result is then used to study, both analytically and numerically, the modulational modes of MHD turbulence, which appear as linear instabilities of the said effective quantum-like plasma of fluctuations. The standard α 2 -dynamo and other known results are reproduced as special cases. A new dynamo effect is predicted that is driven by correlations between the turbulent flow velocity and the turbulent current.

astrophysical plasmas↗
DOE OSTI2016

Collisional effects on interaction potential in complex plasma in presence of magnetic field

Interaction potential in complex plasma with streaming ions is derived analytically in presence of ion-neutral collision and magnetic field. The linear dielectric response function obtained describes the behavior of charged micron sized dust particles in strong collisional limit. A new type of repulsive potential is found to be operative among the dust grains apart from the normal Debye–Hückel potential. The amplitude and shielding length involved in the potential are substantially affected by the parameters describing ion cyclotron frequency, collision frequency among ions and neutrals, and ion streaming. It is also observed that the usual mechanism of ion focusing surrounding the grain is inhibited due to collision. As a result, the attractive wake potential structure is destroyed in the ion flow direction. The horizontal interaction involves only Debye–Hückel potential.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Deep learning surrogate model for kinetic Landau-fluid closure with collision

In this work, the kinetic Landau-fluid (LF) closure with collision and periodic boundary condition is used in the development of the deep learning (DL) surrogate model. A classical neural network, namely, feedforward neural network or sometimes termed multilayer perceptron, is constructed and trained to learn the kinetic LF closure in the static limit and arbitrary mean free path in configuration space. The preliminary relation between best hyperparameters and critical parameters for data generation is found. Compared with the numerical approach (non-Fourier method) of the LF closure, the deep learning surrogate model shows an order of magnitude of improvement in terms of accuracy. Perhaps most importantly, the surrogate model closure has been integrated for the first time with fluid simulations. Our DL-enabled fluid simulations, for the first time, give the correct Landau damping rate for a wide range of wave vectors, while the Hammett–Perkins closure cannot produce the correct damping rate. We correctly connect the collisionless Hammett–Perkins closure and collisional Braginskii closure to reproduce the intrinsic nonlocal feature of the heat flux with DL techniques. We address the most concerning error accumulation problem and find that simulations with the deep learning surrogate model are as good as, if not better than, simulations with the analytic closure in terms of long-term numerical stability in the linear Landau damping test.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Dynamics of electrified liquid metal surface using shallow water model

A shallow water model that incorporates surface tension and electric field effects is developed to investigate the dynamics of an electrified liquid surface. The computational model is verified against the Zakharov–Kuznetsov equation and is applied to study the growth and damping of the electrified liquid surface. A linear wave analysis is performed under a shallow water theory assuming an analytic solution of the electric field, similar to the Tonks–Frenkel instability. The electrified liquid surface grows or dampens based on the balance of the electric field, surface tension, and gravitational forces. As a result, the numerical results obtained from the electrified shallow water solver are in good agreement with the theoretical analysis.

Computational models↗