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DOE OSTI2025

Axion Perturbations: A General Analytical Treatment

Cosmological data provides us two key constraints on dark matter (DM): it must have a particular abundance, and it must have an adiabatic spectrum of density perturbations in the early universe. Many different cosmological scenarios have been proposed that establish the abundance of axion DM in qualitatively different ways. In this paper we emphasize that, despite this variety of backgrounds, the perturbations in axion DM can be understood from universal principles. How does a feebly interacting axion field acquire perturbations proportional to those of photons? How do the isocurvature power spectrum and non-Gaussianity depend on the background evolution of the universe? We answer these questions for a completely general choice of cosmological background and temperature-dependent axion potential. We show that the most general solution to the axion field equation on super-horizon scales is entirely determined by the family of background solutions for different initial field values . This holds for both the component in the field perturbation solution contributing to the DM isocurvature perturbation (enhanced at late times by the sensitivity of the DM abundance to the initial condition, , which can be large for initial conditions near the hilltop), and the other component that contributes to the DM curvature perturbation. In particular, we explain that an unperturbed axion field in the early universe evolving into one with nontrivial adiabatic perturbations is guaranteed by Weinberg's theorem on adiabatic modes. These results have been derived before with various assumptions, such as a radiation dominated background or a quadratic potential. Our aim is to give a clear, simple derivation that is manifestly independent of those assumptions, and thus can be applied to any cosmological axion scenario.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗

NASA NTRS1976

The global reference atmospheric model, mod 2 (with two scale perturbation model)

The Global Reference Atmospheric Model was improved to produce more realistic simulations of vertical profiles of atmospheric parameters. A revised two scale random perturbation model using perturbation magnitudes which are adjusted to conform to constraints imposed by the perfect gas law and the hydrostatic condition is described. The two scale perturbation model produces appropriately correlated (horizontally and vertically) small scale and large scale perturbations. These stochastically simulated perturbations are representative of the magnitudes and wavelengths of perturbations produced by tides and planetary scale waves (large scale) and turbulence and gravity waves (small scale). Other new features of the model are: (1) a second order geostrophic wind relation for use at low latitudes which does not "blow up" at low latitudes as the ordinary geostrophic relation does; and (2) revised quasi-biennial amplitudes and phases and revised stationary perturbations, based on data through 1972.

Justus, C. G.↗

NASA NTRS1978

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

Mcclelland, J.↗

NASA NTRS1985

Changes of solar luminosity and radius following secular perturbations in the convective envelope

The effect on solar models of several types of slow, spherically symmetric perturbations, acting at various depths within the convective envelope, are calculated. Results are presented on perturbations of the efficiency of convective energy transport (alpha perturbations) and on changes in the nongas component of pressure (beta perturbations). The effects of magnetic fields concentrated near the interface between the radiative core and the convective envelope are explored. It is found that the response and relaxation diagnostics depend both on the type of perturbation and on the depth at which the perturbation is applied. In addition to the general depth dependence, model behavior is sensitive to the presence of major ionization zones near the perturbed layer. The time dependence of the solar model behavior is characterized by an initial hydrostatic reaction followed by a thermal readjustment on a time scale of about 100 years, and finally relaxation to a new thermal equilibrium on a Kelvin time scale.

Endal, A. S.↗

NASA NTRS1991

Development of a perturbation generator for vortex stability studies

Theory predicts vortex instability when subjected to certain types of disturbances. It was desired to build a device which could introduce controlled velocity perturbations into a trailing line vortex in order to study the effects on stability. A perturbation generator was designed and manufactured which can be attached to the centerbody of an airfoil type vortex generator. Details of design tests and manufacturing of the perturbation generator are presented. The device produced controlled perturbation with frequencies in excess of 250 Hz. Preliminary testing and evaluation of the perturbation generator performance was conducted in a 4 inch cylindrical pipe. Observations of vortex shedding frequencies from a centerbody were measured. Further evaluation with the perturbation generator attached to the vortex generator in a 2 x 3 foot wind tunnel were also conducted. Hot-wire anemometry was used to confirm the perturbation generator's ability to introduce controlled frequency fluctuations. Comparison of the energy levels of the disturbances in the vortex core was made between locations 42 chord lengths and 15 chord lengths downstream.

Riester, J. E.↗

NASA NTRS1993

Transient development of perturbations in stratified shear flow

Transient development of perturbations in inviscid stratified shear flow is investigated. Use is made of closed form analytic solutions that allow concise identification of optimally growing plane-wave solutions for the case of an unbounded flow with constant shear and stratification. For the case of channel flow, variational techniques are employed to determine the optimally growing disturbances. The maximum energy growth attained over a specific time interval decreases continuously with increasing stratification, and no special significance attaches to Ri = 0.25. Indeed, transient growth can be substantial even for Ri = O(1). A general lower bound on the energy growth attained by an optimal perturbation in a stratified flow over a given time interval is the square root of the growth attained by the corresponding perturbation in unstratified flow. Enhanced perturbation persistence is found for mean-flow stratification lying in the range Ri between 0.1 and 0.3. Small but finite perturbations in mean flow with Ri less than 0.4 produce regions with locally negative total density gradient, which are expected to overturn. Although the perturbations are of wave form, buoyancy fluxes mediate transfer between perturbation kinetic and potential energy during transient development, thus implying that buoyancy flux is not a determinative diagnostic for distinguishing between waves and turbulence in stratified flows.

Farrell, Brian F.↗

NASA NTRS2004

Kinematid Parameters of Corrective Postural Responses Differ between Upper and Lower Body Perturbations

Balance control is disrupted following prolonged microgravity exposure, and to better understand this, both upper and lower body perturbations have been used to study postural control in space flight crewmembers. However, differences between several postural response indicators observed using the two techniques suggest that different sensory systems may be involved in organizing responses to these different perturbation approaches. The present study sought to compare differences in parameters of corrective postural responses between upper body perturbations (pushes to the chest) and forward translations of the support surface. Nine subjects participated in this study. Forward translations were performed using a NeuroCom EquiTest(TM) CDP system, which was synchronized with a Northern Digital OptoTrak motion tracking system (3 subjects). Chest pushes were applied using a hand-held force transducer device and were performed using a stabilometric system (6 subjects). Analysis of EMG has shown that: i) the earliest response of the leg muscles was registered significantly later during forward translation of the support surface than during chest pushes, and ii) there was a tendency for the different order of leg muscles activation during the translation tests. Analysis of the kinematic data showed a significant difference in the subject's body segments inclinations during corrective postural responses to upper and lower body perturbations. It appears that upper body perturbations likely engage the vestibular system more rapidly, while lower body perturbations likely engage somatosensory systems more rapidly. These differences must be taken into account when choosing the type of perturbation for testing postural function.

Sayenko, G.↗

NASA NTRS2008

Changes in Head Stability Control in Response to a Lateral Perturbation while Walking in Older Adults

Falling is a main contributor of injury in older adults. The decline in sensory systems associated with aging limits information needed to successfully compensate for unexpected perturbations. Therefore, sensory changes result in older adults having problems maintaining balance stability when experiencing an unexpected lateral perturbation (e.g. slip) in the environment. The goal of this study was to determine head stability movement strategies used by older adults when experiencing an unexpected lateral perturbation during walking. A total of 16 healthy adults, aged 66-81 years, walked across a foam pathway 6 times. One piece of the foam pathway covered a movable platform that translated to the left when the subject stepped on the foam. Three trials were randomized in which the platform shifted. Angular rate sensors were placed on the center of mass for the head and trunk segments to collect head and trunk movement in all three planes of motion. The predominant movement strategies for maintaining head stability were determined from the results of the cross-correlation analyses between the head and trunk segments. The Chi square test of independence was used to evaluate the movement pattern distributions of head-trunk coordination during perturbed and non-perturbed walking. When perturbed, head stabilization was significantly challenged in the yaw and roll planes of motion. Subjects demonstrated a movement pattern of the head leading the trunk in an effort to stabilize the head. The older adult subjects used this head stabilization movement pattern to compensate for sensory changes when experiencing the unexpected lateral perturbation.

Buccello, Regina R.↗

NASA NTRS2009

Characterization of the Head Stabilization Response to a Lateral Perturbation During Walking in Older Adults

A main contributor of fractures in older adults is from a lateral fall. The decline in sensory systems results in difficulty maintaining balance stability. Head stabilization contributes to postural control by serving as a stable platform for the sensory systems. The purpose of this study was to characterize the head stabilization response to a lateral perturbation while walking. A total of 16 healthy older adults, aged 66-81 years, walked across a foam pathway 6 times. One piece of the foam pathway covered a movable platform that translated to the left when the subject stepped on the foam. Three trials were randomized in which the platform shifted. Angular rate sensors placed on the center of mass of the head and trunk collected head and trunk movement in all three planes of motion. The roll plane was analyzed to examine motion in the plane of the perturbation. Subjects stepped onto the platform with the right foot. Recovery step time and distance were recorded. The first trial was analyzed to capture the novelty of the perturbation. Results indicate a significant difference in footfall distance t=0.004, p<0.05, as well as the speed of foot recovery t=0.001, p<0.05, between natural and perturbed walking. Results indicate that the head t=0.005, p<0.05, and trunk t=0.0001, p<0.05, velocities increase during perturbed compared to natural walking. Older adults place their recovery foot down faster when perturbed to re-establish their base of support. Head and trunk segments are less stable and move with greater velocities to reestablish stability when perturbed.

Buccello-Stout, Regina R.↗

NASA NTRS2015

Boundary Layer Instabilities Generated by Freestream Laser Perturbations

A controlled, laser-generated, freestream perturbation was created in the freestream of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT). The freestream perturbation convected downstream in the Mach-6 wind tunnel to interact with a flared cone model. The geometry of the flared cone is a body of revolution bounded by a circular arc with a 3-meter radius. Fourteen PCB 132A31 pressure transducers were used to measure a wave packet generated in the cone boundary layer by the freestream perturbation. This wave packet grew large and became nonlinear before experiencing natural transition in quiet flow. Breakdown of this wave packet occurred when the amplitude of the pressure fluctuations was approximately 10% of the surface pressure for a nominally sharp nosetip. The initial amplitude of the second mode instability on the blunt flared cone is estimated to be on the order of 10 −6 times the freestream static pressure. The freestream laser-generated perturbation was positioned upstream of the model in three different configurations: on the centerline, offset from the centerline by 1.5 mm, and offset from the centerline by 3.0 mm. When the perturbation was offset from the centerline of a blunt flared cone, a larger wave packet was generated on the side toward which the perturbation was offset. The offset perturbation did not show as much of an effect on the wave packet on a sharp flared cone as it did on a blunt flared cone.

Chou, Amanda↗

NASA NTRS2018

Azimuthal Variation of Instabilities Generated on a Flared Cone by Laser Perturbations

To study the azimuthal development of boundary-layer instabilities, a controlled, laser-generated perturbation was created in the freestream of the Boeing/U.S. Air Force Office of Scientific Research Mach 6 Quiet Tunnel. The freestream perturbation convected downstream in the wind tunnel to interact with a flared-cone model. The flared cone is a body of revolution bounded by a circular arc with a 3 m radius. Pressure transducers were used to measure a wave packet generated in the cone boundary layer by the freestream perturbation. Nine of these sensors formed three stations of azimuthal arrays and were used to determine the azimuthal variation of the wave packets in the boundary layer. The freestream laser-generated perturbation was positioned upstream of the model in three different configurations: along the centerline axis, offset from the centerline axis by 1.5 mm, and offset from the centerline axis by 3.0 mm. When the freestream perturbation was offset from the centerline of a flared cone with a 1.0 mm nose radius, a larger wave packet was generated on the side toward which the perturbation was offset. As a result, transition occurred earlier on that side. The offset perturbation did not have as large of an effect on the boundary layer of a nominally sharp flared cone.

Chou, Amanda↗

DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1978

Perturbations of non-resonant satellite orbits due to a rotating earth

The dominant perturbations of the motion of a satellite near the earth are due to atmospheric drag and the non-symmetrical gravitational field. Atmospheric drag perturbation continually pulls the satellite in and out of the different long period resonant frequencies. The result is that the resonances never become apparent and may be neglected. The tesseral harmonics have no true secular perturbation but the periodicities in the mean motion induce a secular perturbation in the mean anomaly. This secular perturbation may be determined by simply using the average mean motion instead of the osculating mean motion. The Von Ziepel method is used to determine tesseral perturbations. The solution is found first in the singular DS phi elements and then rewritten in the PS phi elements to remove singularities. The notation used in the development is described in the appendix.

Mueller, A.↗

NASA NTRS1983

Effects of core perturbations on the structure of the sun

The effects of perturbing the inner part of the solar core where the hydrogen abundance has been partially depleted by nuclear burning are investigated. Small regions are mixed within the core and the evolution of the resulting luminosity and radius perturbations is followed. The sensitivity of the solar luminosity and radius to mixing events of different sizes and at different locations in the core is determined and several relationships between the luminosity and radius perturbations are examined to see if the value of one of these perturbations can be inferred from a measurement of the other. It is found that any core perturbation which alters the hydrostatic structures will immediately affect the solar luminosity and radius. The behavior of these perturbations depends on the location of the mixing event within the core. Mixing events cannot produce the decrease in the solar radius without leading to a homogeneous evolution of the solar core and/or to a prohibitively large change in the solar luminosity.

Sweigart, A. V.↗

NASA NTRS1985

Perturbations of the Richardson number field by gravity waves

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

Wurtele, M. G.↗

NASA NTRS1989

Computing induced velocity perturbations due to a helicopter fuselage in a free stream

The velocity field of a representative helicopter fuselage in a free stream is computed. Perturbation velocities due to the fuselage are computed in a plan above the location of the helicopter rotor (rotor removed). The velocity perturbations computed by a source-panel model of the fuselage are compared with experimental measurements taken with a laser velocimeter. Three paneled fuselage models are studied: fuselage shape, fuselage shape with hub shape, and a body of revolution. The velocity perturbations computed for both fuselage shape models agree well with the measured velocity field except in the close vicinity of the rotor hub. In the hub region, without knowing the extent of separation, modeling of the effective source shape is difficult. The effects of the fuselage perturbations are not well-predicted with a simplified ellipsoid fuselage. The velocity perturbations due to the fuselage at the plane of the measurements have magnitudes of less than 8 percent of free-stream velocity. The velocity perturbations computed by the panel method are tabulated for the same locations at which previously reported rotor-inflow velocity measurements were made.

Berry, John D.↗

NASA NTRS1990

A hybrid perturbation-Galerkin technique for partial differential equations

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Geer, James F.↗

NASA NTRS1991

Measurement of cavity perturbation to determine the microwave absorption of a sphere in a single mode resonator

Experiments have been conducted on materials in a single mode microwave resonator to test predictions of a new theory of microwave absorption by a lossy dielectric sphere. An analysis of cavity perturbation for verifying the new absorption model revealed a limitation of a standard form of cavity perturbation theory and led to a modification which generalized its application. The cavity perturbations of a nylon sphere were used to calculate the complex permittivity using the standard perturbation theory and the modified form. These permittivity values were compared to that determined from cavity perturbation using a thin nylon rod where the standard and modified forms agree. The results show that the modification is necessary to correctly apply perturbation theory to spherical samples. A second experiment confirmed the theoretical prediction that under certain sample conditions the power absorbed by a sphere in a resonant cavity can be maximum at a location in the cavity where the empty cavity electric field intensity is a minimum.

Watkins, J. L.↗