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NASA NTRS2015

The Effect of Resistance on Rocket Injector Acoustics

Combustion instability, where unsteady heat release couples with acoustic modes, has long been an area of concern in liquid rocket engines. Accurate modeling of the acoustic normal modes of the combustion chamber is important to understanding and preventing combustion instability. This study evaluates the effect of injector resistance on the mode shapes and complex eigen-frequencies of an injector/combustion chamber system by defining a high Mach-flow form of the convective wave equation (see Eq. 1) in COMSOL Multiphysics' Coefficient Form PDE Mathematics Module.

Morgan, C. J.↗

NASA NTRS1975

Analysis of nonlinear structures via mode synthesis

An effective procedure for NASTRAN was developed that permits any number of substructures of any size to be synthesized for the purpose of developing normal modes of vibration of the complete structural system. The technique is extended to permit modal transient analysis of the subdivided system. This latter procedure permits the use of NASTRAN's ability to include nonlinear forces in the problem. The five-phase process is accomplished using standard NASTRAN rigid formats with problem-independent alter packages and DMAP sequences.

Gieseke, R. K.↗

NASA NTRS1985

Oscillations of a compound drop system undergoing rotation

A compound liquid-drop system is comprised of three immiscible concentric fluids: a core fluid of density p(i) surrounded by a shell of density p(s) which is embedded in a medium of density p(o). In this analysis, the fluids are incompressible and inviscid. The effect of rotation upon the modes of oscillation of a compound drop is investigated. Rotation rate is considered as a small perturbation of the normal modes of the compound drop, thus introducing the effects of a Coriolis force and a centrifugal distortion.

Lyell, M. J.↗

NASA NTRS1996

Observational Consequences of Galactic Oscillations

The normal mode oscillations of galaxies we reported recently are large enough to produce observational consequences. The two lowest order modes were both very strong and long lived: the fundamental is a "breathing" mode in which the entire galaxy expands and contracts homologously, while the second radial mode is spherically symmetrical and has one radial node. A sheet of neutral hydrogen in an oscillating galaxy partakes of the general oscillations, and the resulting velocity fields would normally be interpreted in terms of warps or oval distortions. More interestingly, the second radial mode might be a dynamical driver for bulges in early-type spiral galaxies. If bulges result from a dynamical process within the galaxy, there might be other observable properties driven by the same dynamical process. The hole often reported in neutral hydrogen in early type spiral galaxies is one such candidate. It has sometimes been reported to be about the same size as the bulge. We will discuss evidence from velocity fields concerning the fundamental mode and from the coincidence of bulge and HI hole sizes as evidence for the second mode.

Miller, R. H.↗

NASA NTRS1990

Resonant decay of global MHD modes at 'thick' interfaces

A global surface mode can exist on a 'surface' which is not a true discontinuity, but without sufficient dissipation it is not a normal mode and it decays in time via resonance absorption. The decay rate can be calculated analytically when the 'surface' is thin. The goal of this paper is to numerically estimate the decay rate when the surface is not thin. A cold plasma in a uniform magnetic field is considered in which density varies linearly across the 'surface'. In this linearized calculation, the global surface mode is driven in steady state by an antenna located in one of the uniform regions external to the surface. The frequency is a free parameter, and resonance curves are computed numerically without approximations. The widths of the resonance curves are used to estimate the free decay times of undriven surface modes, via the uncertainty principle. When applied to the active solar corona, the decay rates are large enough to account for the coronal heating, but it should be kept in mind that the role of nonlinearity in resonance absorption is still undetermined.

Hollweg, Joseph V.↗

DOE OSTI2022

Simulation of Plasma Emission in Magnetized Plasmas

The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1977

Mathematical and computational studies of the stability of axisymmetric annular capillary free surfaces

Of principal interest is the stability of a perfectly wetting liquid in an inverted, vertical, right circular-cylindrical container having a concave spheroidal bottom. The mathematical conditions that the contained liquid be in stable static equilibrium are derived, including those for the limiting case of zero contact angle. Based on these results, a computational investigation is carried out for a particular container that is used for the storage of liquid fuels in NASA Centaur space vehicles, for which the axial ratio of the container bottom is 0.724. It is found that for perfectly wetting liquids the qualitative nature of the onset of instability changes at a critical liquid volume, which for the Centaur fuel tank corresponds to a mean fill level of approximately 0.503 times the tank's radius. Small-amplitude periodic sloshing modes for this tank were calculated; oscillation frequencies or growth rates are given for several Bond numbers and liquid volumes, for normal modes having up to six angular nodes.

Albright, N.↗

NASA NTRS1985

Computational modes and the Machenauer N.L.N.M.I. of the GLAS 4th order model

An attempt was made to use the GLAS global 4th order shallow water equations to perform a Machenhauer nonlinear normal mode initialization (NLNMI) for the external vertical mode. A new algorithm was defined for identifying and filtering out computational modes which affect the convergence of the Machenhauer iterative procedure. The computational modes and zonal waves were linearly initialized and gravitational modes were nonlinearly initialized. The Machenhauer NLNMI was insensitive to the absence of high zonal wave numbers. The effects of the Machenhauer scheme were evaluated by performing 24 hr integrations with nondissipative and dissipative explicit time integration models. The NLNMI was found to be inferior to the Rasch (1984) pseudo-secant technique for obtaining convergence when the time scales of nonlinear forcing were much smaller than the time scales expected from the natural frequency of the mode.

Navon, I. M.↗

NASA NTRS2012

Nonlinear Reduced-Order Simulation Using An Experimentally Guided Modal Basis

A procedure is developed for using nonlinear experimental response data to guide the modal basis selection in a nonlinear reduced-order simulation. The procedure entails using nonlinear acceleration response data to first identify proper orthogonal modes. Special consideration is given to cases in which some of the desired response data is unavailable. Bases consisting of linear normal modes are then selected to best represent the experimentally determined transverse proper orthogonal modes and either experimentally determined inplane proper orthogonal modes or the special case of numerically computed in-plane companions. The bases are subsequently used in nonlinear modal reduction and dynamic response simulations. The experimental data used in this work is simulated to allow some practical considerations, such as the availability of in-plane response data and non-idealized test conditions, to be explored. Comparisons of the nonlinear reduced-order simulations are made with the surrogate experimental data to demonstrate the effectiveness of the approach.

Rizzi, Stephen A.↗

DOE OSTI2019

First-principles electronic structure in second-moment calculation of mode frequencies: Failure of quasiharmonic approximation in silicon

Using first-principles electronic structure calculations (local density approximation), we present second-moment calculations of the temperature dependence of the vibrational normal mode frequencies in Si up to 1500 K . The method is based on simple ensemble averages of displacements and forces and is easy to implement. These efficient calculations incorporate all interactions nonperturbatively, implicitly including all high order force constants, in contrast to typical perturbative approaches. Also in this work, we propose and apply to our classical calculations an estimated quantum correction that could be used for classical approaches other than the moments method. We compare our results to available experiments, including recent inelastic neutron scattering data and conclude that the second-moment gives the frequency shift to within a factor of 2 in contrast to quasiharmonic approaches that fail by an order of magnitude to predict the anharmonic shift. Noting the relative simplicity and speed of the calculations, we conclude that the second-moment approximation reasonably accounts for anharmonicity in a system that has been very closely studied experimentally and may reliably be applied in an exploratory way to more complex systems. Finally, we suggest that further improvement on the results could be obtained by incorporating the fourth moment, which can be implemented with little additional cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Low-frequency Raman active modes of twisted bilayer MoS 2

Abstract We study the low-frequency Raman active modes of twisted bilayer MoS 2 for several twist angles using a force-field approach and a parametrized bond polarizability model. We show that twist angles near high-symmetry stacking configurations exhibit stacking frustration that leads to significant buckling of the moiré superlattice. We find that atomic relaxation due to the twist is of prime importance. The periodic displacement of the Mo atoms shows the realization of a soliton network, and in turn, leads to the emergence of a number of frequency modes not seen in the high-symmetry stacking systems. Some of the modes are only seen in the XZ Raman polarization setup while others are seen in the XY setup. The symmetry of the normal modes, and how this affects the Raman tensors is examined in detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Quantum-to-classical crossover in generalized spin systems: Temperature-dependent spin dynamics of FeI 2

Simulating quantum spin systems at finite temperatures is an open challenge in many-body physics. This work studies the temperature-dependent spin dynamics of a pivotal compound, FeI 2 , to determine if universal quantum effects can be accounted for by a phenomenological renormalization of the dynamical spin structure factor $S$(q, $ω$) measured by inelastic neutron scattering. Renormalization schemes based on the quantum-to-classical correspondence principle are commonly applied at low temperatures to the harmonic oscillators describing normal modes. However, it is not clear how to extend this renormalization to arbitrarily high temperatures. Here we introduce a temperature-dependent normalization of the classical moments, whose magnitude is determined by imposing the quantum sum rule, e.g., $∫$ $dωd$q$S$ ($q, ω$) = $N$ $S$ $S$ ($S$ + 1)for $N$ $S$ dipolar magnetic moments. We show that this simple renormalization scheme significantly improves the agreement between the calculated and measured $S$(q, $ω$) for FeI 2 at all temperatures. In conclusion, due to the coupled dynamics of dipolar and quadrupolar moments in that material, this renormalization procedure is extended to classical theories based on SU(3) coherent states, and by extension, to any SU($N$) coherent state representation of local multipolar moments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1980

Theoretical studies of solar oscillations

Possible sources for the excitation of the solar 5 minute oscillations were investigated and a linear non-adiabatic stability code was applied to a preliminary study of the solar g-modes with periods near 160 minutes. Although no definitive conclusions concerning the excitation of these modes were reached, the excitation of the 5 minute oscillations by turbulent stresses in the convection zone remains a viable possibility. Theoretical calculations do not offer much support for the identification of the 160 minute global solar oscillation (reported by several independent observers) as a solar g-mode. A significant advance was made in attempting to reconcile mixing-length theory with the results of the calculations of linearly unstable normal modes. Calculations show that in a convective envelope prepared according to mixing length theory, the only linearly unstable modes are those which correspond to the turbulent eddies which are the basic element of the heuristic mixing length theory.

Goldreich, P.↗

NASA NTRS1994

Growing 'Alfvenic' modes in the upstream region of Saturn

Recent studies of low-frequency electromagnetic waves upstream of the Saturn bow shock have shown that these waves, in contrast to those at Earth, are observed not in one, but in at least two, distinct frequency bands. The results of wave mode identification based on the Hall-magnetohydrodynamic (MHD) model of plasma and observed wave polarization suggested that these waves propagate in the high beta intermediate mode. However, the underlying instability was not unambiguously determined. In the present paper we use the full electromagnetic dispersion relation derived from linear Vlasov theory in order to examine which of the plasma modes, with observed properties, are unstable in an isotropic Maxwellian plasma in the presence of backstreaming proton beams consistent with Voyager 2 observations at Saturn. As a result we find that the unstable 'Alfvenic' beam mode, as well as resonant and non-resonant fast magnetosonic modes have properties consistent with the data. Moreover, we find that in contrast to the Earth's upstream waves, at Saturn no 'kinetic' normal mode can account for the observed magnetic polarization.

Orlowski, D. S.↗

NASA NTRS1988

Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula

The axisymmetric perturbations of a thin, differentially rotating gas disk in which the vertical temperature stratification is superadiabatic are analyzed. The growth rate of adiabatic convective normal modes is calculated, departures from simple polytropic disk models are briefly discussed, and the detailed vertical structure of the eigenfunctions is analyzed. The stabilizing effect of radiative diffusion on convective modes is considered. It is found that rotation and compressibility tend to reduce the rate of growth of the disturbances, and that the growth rate increases without limit and is proportional to the square root of the radial wavenumber in polytropic equilibria. The maximum radial size of convective eddies scales like the square root of the degree of superadiabaticity times the size of the convective zone. There is significant convective penetration into radiatively stable layers only for the fundamental and low-order harmonic modes, whose vertical wavelength is comparable to the size of the convective layer.

Ruden, Steven P.↗

NASA NTRS2022

Structural and chemical complexity of minerals: An update

The complexities of chemical composition and crystal structure are fundamental characteristics of minerals that have high relevance to the understanding of their stability, occurrence and evolution. This review summarises recent developments in the field of mineral complexity and outlines possible directions for its future elaboration. The database of structural and chemical complexity parameters of minerals is updated by H-correction of structures with unknown H positions and the inclusion of new data. The revised average complexity values (arithmetic means) for all minerals are 3.54(2) bits/atom and 345(10) bits/cell (based upon 4443 structure reports). The distributions of atomic information amounts, chemIG and strIG, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities, chemIG,total and strIG,total, along with numbers of atoms per formula and per unit cell are log normal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterised within the last five years. The most important complexity-generating mechanisms in minerals are: (1) the presence of isolated large clusters; (2) the presence of large clusters linked together to form three-dimensional frameworks; (3) formation of complex three-dimensional modular frameworks; (4) formation of complex modular layers; (5) high hydration state in salts with complex heteropolyhedral units; and (6) formation of ordered superstructures of relatively simple structure types. The relations between symmetry and complexity are considered. The analysis of temporal dynamics of mineralogical discoveries since 1875 with the step of 25 years show the increasing chemical and structural complexities of human knowledge of the mineral kingdom in the history of mineralogy. In the Earth’s history, both diversity and complexity of minerals experience dramatic increases associated with the formation of Earth’s continental crust, initiation of plate tectonics and the Great Oxidation event.

complexity↗

NASA NTRS1974

Spacecraft control/flexible structures interaction study

An initial study to begin development of a flight experiment to measure spacecraft control/flexible structure interactions was completed. The approach consisted of developing the equations of motion for a vehicle possessing a flexible solar array, then linearizing about some nominal motion of the craft. A set of solutions is assumed for array deflection using a continuous normal mode method and important parameters are identified. Interrelationships between these parameters, measurement techniques, and input requirements are discussed which assure minimization of special vehicle maneuvers and optimization of data to be obtained during the normal flight sequence. Limited consideration is given to flight data retrieval and processing techniques as correlated with the requirements imposed by the measurement system. Results indicate that inflight measurement of the bending and torsional mode shapes and respective frequencies, and damping ratios, is necessary. Other parameters may be measured from design data.

Kaplan, M. H.↗

DOE OSTI2022

Radiative properties of an artificial atom coupled to a Josephson-junction array

We study the radiative properties—the Lamb shift, Purcell decay rate, and spontaneous emission dynamics—of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to a nonperturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson-junction array. As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are nontrivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode nonperturbative regime. This modal framework generalizes the normal-mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high-impedance Josephson-junction arrays.

42 ENGINEERING↗