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NASA NTRS1977

The velocity correlation function in cosmic-ray diffusion theory

It is shown that Earl's (1973) eigenvalue sum for the cosmic-ray spatial diffusion coefficient parallel to the mean magnetic field is precisely equivalent to the time integral of the particle-velocity correlation function parallel to the mean field. A derivation due to Kubo (1957) is applied to cosmic-ray pitch-angle scattering, and it is proven that all nine components of the cosmic-ray diffusion tensor can be expressed as integrals over the velocity correlation function. A pitch-angle correlation function is derived, and the effect of long-wavelength turbulence on the velocity correlation function and spatial diffusion coefficients is examined. Application of the velocity-correlation method to a realistic case involving both pitch-angle scattering and appreciable fluctuation in the direction of the local field indicates that long-wavelength turbulence in the local field reduces the parallel diffusion coefficient and places an upper limit on the ratio of the perpendicular to parallel diffusion coefficients.

Forman, M. A.↗

NASA NTRS1995

A FFT Method for the Quasiclassical Selection of Initial Ro-Vibrational States of Triatomic Molecules

This paper describes the use of an exact fast Fourier transform (FFT) method to prepare specified vibrational-rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating-rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational-rotational state selected. For example, in the case of the ground vibrational state of a non-rotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001 h(bar) of the specified quantization values and energies within 5 cm(sup -1) of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However for states for which the fundamental frequencies become commensurate (resonance states), there are additional complications. In these cases it is necessary to determine a new set of "fundamental" frequencies and to modify the quantization conditions. Once these adjustments are made, good results are obtained for resonance states. The major problems are in labelling the large number of Fourier coefficients and the presence of regions of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the ro-vibrational states of H2O.

Eaker, Charles W.↗

NASA NTRS1989

Numerical simulation of pressure oscillations in a ramjet combustor

Large-eddy simulations of compressible cold flow in a ramjet combustor configuration were performed. The objectives were to investigate the mechanisms for vortex-acoustic interaction in such a device and to develop a simulation method that can be extended to cases with combustion heat release to study combustion instability. From the simulation, it was found that the separated shear layer rolls up into concentrated vortices that merge to form large coherent structures. These vortices interact with the choked nozzle downstream to produce an axial acoustic dipole. The spectrum of the pressure fluctuation at the base of the backward-facing step shows that there are two types of oscillations: an acoustic resonant mode and a vortex-acoustic coupled mode. Based on the flow physics observed in the simulations, a simple one-dimensional model for the vortex-acoustic coupled mode was proposed. The eigenvalue problem based on this model was solved to obtain the frequency of the coupled mode.

Jou, Wen-Huei↗

NASA NTRS1977

A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner

Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.

Watson, W. R.↗

DOE OSTI2026

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1996

Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

Arian, Eyal↗

NASA NTRS2018

Simulation of Sound Absorption by Scattering Bodies Treated with Acoustic Liners Using a Time-Domain Boundary Element Method

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance, Z(w). Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering of geometric bodies treated with acoustic liners. This work uses an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Y(w) = 1/Z(w). An admittance boundary condition will be derived and coupled with a time domain boundary integral equation. The solution will be obtained iteratively using spatial and temporal basis functions and will allow for acoustic scattering problems to be modeled with geometries consisting of both unlined and soft surfaces. Stability will be demonstrated through eigenvalue analysis.

Pizzo, Michelle E.↗

NASA NTRS2003

Probabilistic Aeroelastic Analysis Developed for Turbomachinery Components

Aeroelastic analyses for advanced turbomachines are being developed for use at the NASA Glenn Research Center and industry. However, these analyses at present are used for turbomachinery design with uncertainties accounted for by using safety factors. This approach may lead to overly conservative designs, thereby reducing the potential of designing higher efficiency engines. An integration of the deterministic aeroelastic analysis methods with probabilistic analysis methods offers the potential to design efficient engines with fewer aeroelastic problems and to make a quantum leap toward designing safe reliable engines. In this research, probabilistic analysis is integrated with aeroelastic analysis: (1) to determine the parameters that most affect the aeroelastic characteristics (forced response and stability) of a turbomachine component such as a fan, compressor, or turbine and (2) to give the acceptable standard deviation on the design parameters for an aeroelastically stable system. The approach taken is to combine the aeroelastic analysis of the MISER (MIStuned Engine Response) code with the FPI (fast probability integration) code. The role of MISER is to provide the functional relationships that tie the structural and aerodynamic parameters (the primitive variables) to the forced response amplitudes and stability eigenvalues (the response properties). The role of FPI is to perform probabilistic analyses by utilizing the response properties generated by MISER. The results are a probability density function for the response properties. The probabilistic sensitivities of the response variables to uncertainty in primitive variables are obtained as a byproduct of the FPI technique. The combined analysis of aeroelastic and probabilistic analysis is applied to a 12-bladed cascade vibrating in bending and torsion. Out of the total 11 design parameters, 6 are considered as having probabilistic variation. The six parameters are space-to-chord ratio (SBYC), stagger angle (GAMA), elastic axis (ELAXS), Mach number (MACH), mass ratio (MASSR), and frequency ratio (WHWB). The cascade is considered to be in subsonic flow with Mach 0.7. The results of the probabilistic aeroelastic analysis are the probability density function of predicted aerodynamic damping and frequency for flutter and the response amplitudes for forced response.

Reddy, T. S. R.↗

DOE OSTI2026

Integration of Online Cross-Section Generation Capability with Depletion and Transient Solvers in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE)-based reactor multiphysics analysis application jointly developed by Argonne and Idaho National Laboratories under the DOENE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In FY25, an online crosssection generation capability based on the Self-Shielding Application Programming Interface (SSAPI) was demonstrated for TRISO-fueled reactor problems under steady-state conditions. This fiscal year, that capability was extended to support depletion and transient multiphysics calculations, enabling high-fidelity analyses that generate self-shielded cross sections on the fly from the actual evolving composition and temperature states rather than from pre-tabulated libraries. For depletion, a two-way coupling was established in which SSAPI computes compact-averaged self-shielded cross sections that the depletion solver then uses to advance the Bateman equations, with the updated compositions returned to SSAPI at each step; the depletion module was refactored to support both library-based and SSAPI-based cross sections, and additional logic was added to track daughter isotopes and to exclude minor isotopes for efficiency. For transient analysis, the SSAPI multigroup library was extended with the kinetics data required for time-dependent calculations, the Improved Quasi-Static (IQS) scheme was coupled with SSAPI, and several supporting capabilities were implemented, including a self-shielding treatment that lets control rods and drums move within a self-shielded model, which had previously been impossible and had ruled out rod- and drum-movement transients with on-the-fly cross sections altogether, a new mixing scheme for delayed-neutron precursor decay constants, a checkpoint-based restart workflow, and performance improvements such as pointwise cross-section interpolation and the bypassing of unnecessary Dancoff factor calculations. The implemented capabilities were verified against Serpent Monte Carlo solutions. For depletion, a prismatic pin-cell problem based on a Next Generation Nuclear Plant (NGNP) Very High Temperature Reactor benchmark showed excellent agreement, with eigenvalue differences within 200 pcm over the entire burnup range (up to 140 MWD/kgU) and fission-product and actinide inventories agreeing to within 0.8% and 2.5%, respectively; a heat-pipe microreactor assembly problem with a much higher fuel loading confirmed the same behavior and quantified the bias introduced when the multigroup equivalence effect is neglected. For transient analysis, a pin-cell problem with a step reactivity insertion and temperature feedback reproduced the analytically expected asymptotic power and showed close agreement between the direct and IQS solutions, and a two-dimensional microreactor core problem with control-drum rotation exercised the new moving-drum self-shielding treatment and demonstrated successful coupling of the online crosssection generation with both the direct and IQS transient methods. The capability was further exercised on a full-core pebble-bed problem, in which Griffin was coupled with the System Analysis Module (SAM) to simulate load-following operation of the gPBR with the Doppler feedback resolved at the TRISO fuel kernel temperature. These developments in Griffin provide a convenient, high-fidelity approach to cross-section generation for advanced thermal reactors with geometrically complex and highly heterogeneous configurations, including TRISO-fueled prismatic and pebble-bed systems, and support steady-state, depletion, and transient multiphysics calculations. They also enable self-shielded cross sections to be evaluated directly at the actual coupled state of the system, thereby establishing a foundation for high-fidelity, fully coupled multiphysics analysis of advanced reactors

Park, H.↗

NASA NTRS1972

Study of modal coupling procedures for the shuttle: A matrix method for damping synthesis

The damping method was applied successfully to real structures as well as analytical models. It depends on the ability to determine an appropriate modal damping matrix for each substructure. In the past, modal damping matrices were assumed diagonal for lack of being able to determine the coupling terms which are significant in the general case of nonproportional damping. This problem was overcome by formulating the damped equations of motion as a linear perturbation of the undamped equations for light structural damping. Damped modes are defined as complex vectors derived from the complex frequency response vectors of each substructure and are obtained directly from sinusoidal vibration tests. The damped modes are used to compute first order approximations to the modal damping matrices. The perturbation approach avoids ever having to solve a complex eigenvalue problem.

Hasselman, T. K.↗

NASA NTRS1952

The excitation of unstable perturbations in a laminar friction layer

With the aid of the method of small oscillations which was used successfully in the investigation of the stability of laminar velocity distributions in the presence of two-dimensional perturbations, the excitation of the unstable perturbations for the Hartree velocity distributions occurring in plane boundary-layer flow for decreasing and increasing pressure is calculated as a supplement to a former report. The results of this investigation are to make a contribution toward calculation of the transition point on cylindrical bodies.

BOUNDARY LAYER TRANSITION - EFFECT OF SURFACE ROUG↗

NASA NTRS2003

Fast-Running Aeroelastic Code Based on Unsteady Linearized Aerodynamic Solver Developed

The NASA Glenn Research Center has been developing aeroelastic analyses for turbomachines for use by NASA and industry. An aeroelastic analysis consists of a structural dynamic model, an unsteady aerodynamic model, and a procedure to couple the two models. The structural models are well developed. Hence, most of the development for the aeroelastic analysis of turbomachines has involved adapting and using unsteady aerodynamic models. Two methods are used in developing unsteady aerodynamic analysis procedures for the flutter and forced response of turbomachines: (1) the time domain method and (2) the frequency domain method. Codes based on time domain methods require considerable computational time and, hence, cannot be used during the design process. Frequency domain methods eliminate the time dependence by assuming harmonic motion and, hence, require less computational time. Early frequency domain analyses methods neglected the important physics of steady loading on the analyses for simplicity. A fast-running unsteady aerodynamic code, LINFLUX, which includes steady loading and is based on the frequency domain method, has been modified for flutter and response calculations. LINFLUX, solves unsteady linearized Euler equations for calculating the unsteady aerodynamic forces on the blades, starting from a steady nonlinear aerodynamic solution. First, we obtained a steady aerodynamic solution for a given flow condition using the nonlinear unsteady aerodynamic code TURBO. A blade vibration analysis was done to determine the frequencies and mode shapes of the vibrating blades, and an interface code was used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor was used to interpolate the mode shapes from the structural dynamic mesh onto the computational dynamics mesh. Then, we used LINFLUX to calculate the unsteady aerodynamic forces for a given mode, frequency, and phase angle. A postprocessor read these unsteady pressures and calculated the generalized aerodynamic forces, eigenvalues, and response amplitudes. The eigenvalues determine the flutter frequency and damping. As a test case, the flutter of a helical fan was calculated with LINFLUX and compared with calculations from TURBO-AE, a nonlinear time domain code, and from ASTROP2, a code based on linear unsteady aerodynamics.

Reddy, T. S. R.↗

NASA NTRS1987

A general method for dynamic analysis of structures overview

The presented research deals with the development of a dynamic analysis method for structural systems. The modeling approach is essentially a finite element method in the sense that the structure is divided into n elements. An element is defined as any structural unit whose degree of freedom (dofs) can be categorized as either interface or non-interface dofs. An element could be a fundamental unit such as a rod, a beam, a plate etc., or it could be an entire structural component. Furthermore, the parameters for the element could be distributed or lumped. The choice of elements is totally arbitrary and is a matter of user convenience. In particular, issues of accuracy and convergence do not enter on the level of example that bookkeeping is reduced to a minimum. Each element is modeled using a set of interface constraint modes (ICM) combined with a set of interface restrained normal models (IRNM). The next step is the solution of the system eigenvalue problem. The procedure calls for the sequential solution of a number of small eigenvalue problems based on a truncation principle for IRNM. In addition, the form of these eigenvalue problems is very simple such that an escalator type of eigenvalue problem solver can be used which is extremely cost-effective and fast.

Engels, Remi C.↗

NASA NTRS1992

Hybrid suboptimal control of multi-rate multi-loop sampled-data systems

A hybrid state-space controller is developed for suboptimal digital control of multirate multiloop multivariable continuous-time systems. First, an LQR is designed for a continuous-time subsystem which has a large bandwidth and is connnected in the inner loop of the overall system. The designed LQR would optimally place the eigenvalues of a closed-loop subsystem in the common region of an open sector bounded by sector angles + or - pi/2k for k = 2 or 3 from the negative real axis and the left-hand side of a vertical line on the negative real axis in the s-plane. Then, the developed continuous-time state-feedback gain is converted into an equivalent fast-rate discrete-time state-feedback gain via a digital redesign technique (Tsai et al. 1989, Shieh et al. 1990) reviewed here. A real state reconstructor is redeveloped utilizing the fast-rate input-output data of the system of interest. The design procedure of multiloop multivariable systems using multirate samplers is shown, and a terminal homing missile system example is used to demonstrate the effectiveness of the proposed method.

Shieh, Leang S.↗

NASA NTRS1977

Application of system identification to analytic rotor modeling from simulated and wind tunnel dynamic test data, part 2

An introduction to aircraft state and parameter identification methods is presented. A simplified form of the maximum likelihood method is selected to extract analytical aeroelastic rotor models from simulated and dynamic wind tunnel test results for accelerated cyclic pitch stirring excitation. The dynamic inflow characteristics for forward flight conditions from the blade flapping responses without direct inflow measurements were examined. The rotor blades are essentially rigid for inplane bending and for torsion within the frequency range of study, but flexible in out-of-plane bending. Reverse flow effects are considered for high rotor advance ratios. Two inflow models are studied; the first is based on an equivalent blade Lock number, the second is based on a time delayed momentum inflow. In addition to the inflow parameters, basic rotor parameters like the blade natural frequency and the actual blade Lock number are identified together with measurement bias values. The effect of the theoretical dynamic inflow on the rotor eigenvalues is evaluated.

Hohenemser, K. H.↗

NASA NTRS1986

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Warming, Robert F.↗

NASA NTRS2001

Cross-Axis Proportional Gains Used to Control Gyroscopic Effects in a Magnetic- Bearing-Supported Flywheel

For magnetic-bearing-supported high-speed machines with significant gyroscopic effects, it is necessary to stabilize both forward and backward tilt whirling modes. Instability or the low damping of these modes can prevent the attainment of desired shaft speeds. Previous work elsewhere showed that cross-axis derivative gain in the magnetic bearing control law can improve the stability of the forward whirl mode, but it is commonly recognized that derivative gains amplify high-frequency noise and increase the required control effort. At the NASA Glenn Research Center, it has been shown previously that a simple cross-axis proportional gain can add stability (without adding noise) to either forward whirl or backward whirl, depending on the sign of the gain, but that such a gain destabilizes the other mode. It has been predicted by Glenn analysis that both modes can be stabilized by cross-axis proportional gains by utilizing the large-frequency separation of the two modes at speeds where the gyroscopic effects are significant. We use a modal controller that decouples the tilt and center-of-mass-translation modes. Only the tilt modes exhibit speed-dependent gyroscopic effects. The key to controlling them by the present method is to stabilize the backward whirl tilt mode with the appropriate sign of cross-axis proportional gain in the control law, but to include a low-pass filter on that gain term to restrict its effect only to the low-frequency backward-whirl mode. A second cross-axis term with the opposite sign and a high-pass filter stabilizes the forward whirl, which can have a frequency one or two orders of magnitude higher than the backward whirl, permitting very independent action of the two terms. Because the physical gyroscopic torques are proportional to the spinning speed of the shaft, it is convenient to gain-schedule the cross-axis control terms by making them proportional to shaft speed. This has the added benefit of avoiding a somewhat awkward zero-speed splitting of the tilt-mode eigenvalues.

Brown, Gerald V.↗

DOE OSTI2024

Quantum-enhanced photoprotection in neuroprotein architectures emerges from collective light-matter interactions

Background Superradiance is the phenomenon of many identical quantum systems absorbing and/or emitting photons collectively at a higher rate than any one system can individually. This phenomenon has been studied analytically in idealized distributions of electronic two-level systems (TLSs), each with a ground and excited state, as well as numerically in realistic photosynthetic nanotubes and cytoskeletal architectures. Methods Superradiant effects are studied here in idealized toy model systems and realistic biological mega-networks of tryptophan (Trp) molecules, which are strongly fluorescent amino acids found in many proteins. Each Trp molecule acts as a chromophore absorbing in the ultraviolet spectrum and can be treated approximately as a TLS, with its 1 L a excited singlet state; thus, organized Trp networks can exhibit superradiance. Such networks are found, for example, in microtubules, actin filaments, and amyloid fibrils. Microtubules and actin filaments are spiral-cylindrical protein polymers that play significant biological roles as primary constituents of the eukaryotic cytoskeleton, while amyloid fibrils have been targeted in a variety of neurodegenerative diseases. We treat these proteinaceous Trp networks as open quantum systems, using a non-Hermitian Hamiltonian to describe interactions of the chromophore network with the electromagnetic field. We numerically diagonalize the Hamiltonian to obtain its complex eigenvalues, where the real part is the energy and the imaginary part is its associated enhancement rate. We also consider multiple realizations of increasing static disorder in either the site energies or the decay rates. Results We obtained the energies and enhancement rates for realistic microtubules, actin filament bundles, and amyloid fibrils of differing lengths, and we use these values to calculate the quantum yield, which is the ratio of the number of photons emitted to the number of photons absorbed. We find that all three of these structures exhibit highly superradiant states near the low-energy portion of the spectrum, which enhances the magnitude and robustness of the quantum yield to static disorder and thermal noise. Conclusion The high quantum yield and stable superradiant states in these biological architectures may play a photoprotective rolein vivo, downconverting energetic ultraviolet photons—absorbed from those emitted by reactive free radical species—to longer, safer wavelengths and thereby mitigating biochemical stress and photophysical damage. Contrary to conventional assumptions that quantum effects cannot survive in large biosystems at high temperatures, our results suggest that macropolymeric collectives of TLSs in microtubules, actin filaments, and amyloid fibrils exhibit increasingly observable and robust effects with increasing length, up to the micron scale, due to quantum coherent interactions in the single-photon limit. Superradiant enhancement and high quantum yield exhibited in neuroprotein polymers could thus play a crucial role in information processing in the brain, the development of neurodegenerative diseases such as Alzheimer’s and related dementias, and a wide array of other pathologies characterized by anomalous protein aggregates.

Physics↗