Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “wave equation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,009 records · Page 56

A Survey of Small-Scale Waves and Wave-Like Phenomena in Jupiter’s Atmosphere Detected by JunoCam

In the first 20 orbits of the Juno spacecraft around Jupiter, we have identified a variety of wave‐like features in images made by its public‐outreach camera, JunoCam. Because of Juno's unprecedented and repeated proximity to Jupiter's cloud tops during its close approaches, JunoCam has detected more wave structures than any previous surveys. Most of the waves appear in long wave packets, oriented east‐west and populated by narrow wave crests. Spacing between crests were measured as small as ~30 km, shorter than any previously measured. Some waves are associated with atmospheric features, but others are not ostensibly associated with any visible cloud phenomena and thus may be generated by dynamical forcing below the visible cloud tops. Some waves also appear to be converging, and others appear to be overlapping, possibly at different atmospheric levels. Another type of wave has a series of fronts that appear to be radiating outward from the center of a cyclone. Most of these waves appear within 5° of latitude from the equator, but we have detected waves covering planetocentric latitudes between 20°S and 45°N. The great majority of the waves appear in regions associated with prograde motions of the mean zonal flow. Juno was unable to measure the velocity of wave features to diagnose the wave types due to its close and rapid flybys. However, both by our own upper limits on wave motions and by analogy with previous measurements, we expect that the waves JunoCam detected near the equator are inertia‐gravity waves.

Lunar and Planetary Science and Exploration↗

On the Symmetry of Blast Waves

This paper presents a brief historical review of G. I. Taylor’s solution of the point blast wave problem which was applied to the Trinity test of the first atomic bomb. Lie group symmetry techniques (also referred to throughout this paper as geometric techniques) are used to derive Taylor’s famous two-fifths law that relates the position of a blast wave to the time after the explosion and the total energy released. The theory of exterior differential systems is combined with the method of characteristics to demonstrate that the solution of the blast wave problem is directly related to the basic relationships that exist between the symmetry (or geometry) and the physics of wave propagation through the equations of motion. The point blast wave model is cast in terms of two exterior differential systems, and both systems are shown to be integrable with local solutions for the velocity, pressure, and density along curves in space and time behind the blast wave. This work is dedicated to the memory of Professor Roy Axford, who introduced many of his students to the topic of symmetry analysis of differential equations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Kinetic-j : A computational kernel for solving the linearized Vlasov equation applied to calculations of the kinetic, configuration space plasma current for time harmonic wave electric fields

We present the Kinetic-j code, a computational kernel for evaluating the linearized Vlasov equation withapplication to calculating the kinetic plasma response (current) to an applied time harmonic wave electricfield. This code addresses the need for a configuration space evaluation of the plasma current to enablekinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourierspectral methods. We benchmark the kernel via comparison with the standard k-space forms of the hotplasma conductivity tensor.

Green, David L.↗

Analysis of the dependence of surfatron acceleration of electrons by an electromagnetic wave in space plasma on the particle momentum along the wave front

Based on the numerical solution of the nonlinear nonstationary second-order equation for the wave phase on the particle trajectory, the dynamics of surfatron acceleration of electrons by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed as a function of the electron momentum along the wave front. Numerical calculations show that, for strongly relativistic initial values of the electron momentum component along the wave front g{sub y}(0) (the other parameters of the problem being the same), electrons are trapped into the regime of ultrarelativistic surfatron acceleration within a certain interval of the initial wave phase Ψ(0) on the particle trajectory. It is assumed in the calculations that vertical bar Ψ(0) vertical bar ≤ π. For strongly relativistic values of g{sub y}(0), electrons are immediately trapped by the wave for 19% of the initial values of the phase Ψ(0) (favorable phases). For the rest of the values of Ψ(0), trapping does not occur even at long times. This circumstance substantially simplifies estimations of the wave damping due to particle acceleration in subsequent calculations. The dynamics of the relativistic factor and the components of the electron velocity and momentum under surfatron acceleration is also analyzed. The obtained results are of interest for the development of modern concepts of possible mechanisms of generation of ultrarelativistic particle fluxes in relatively calm space plasma, as well as for correct interpretation of observational data on the fluxes of such particles and explanation of possible reasons for the deviation of ultrarelativistic particle spectra detected in the heliosphere from the standard power-law scalings and the relation of these variations to space weather and large-scale atmospheric processes similar to tropical cyclones.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

X-ray third-order nonlinear dynamical diffraction in a crystal

The dynamic diffraction of an X-ray wave in a crystal with a third-order nonlinear response to external field strength has been theoretically investigated. General equations for the wave propagation in crystal and nonlinear Takagi equations for both ideal and deformed crystals are derived. Integrals of motion are determined for the nonlinear problem of dynamic diffraction. The results of the numerical calculations of reflectivity in the symmetric Laue geometry for an incident plane wave and the intensity distributions on the output crystal surface for a point source are reported as an example.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Direct inference of nuclear equation-of-state parameters from gravitational-wave observations

The observation of neutron star mergers with gravitational waves (GWs) has provided a new method to constrain the dense-matter equation of state (EOS) and to better understand its nuclear physics. However, inferring nuclear microphysics from GW observations necessitates the sampling of EOS model parameters that serve as input for each EOS used during the GW data analysis. The sampling of the EOS parameters requires solving the Tolman–Oppenheimer–Volkoff (TOV) equations a large number of times—a process that slows down each likelihood evaluation in the analysis on the order of a few seconds. Here, we employ emulators for the TOV equations built using multilayer perceptron neural networks to enable direct inference of nuclear EOS parameters from GW strain data. Our emulators allow us to rapidly solve the TOV equations, taking in EOS parameters and outputting the associated tidal deformability of a neutron star in only a few tens of milliseconds. We implement these emulators in PyCBC to directly infer the EOS parameters using the event GW170817, providing posteriors on these parameters informed solely by GWs. We benchmark these runs against analyses performed using the full TOV solver and find that the emulators achieve speed ups of nearly two orders of magnitude, with negligible differences in the recovered posteriors. Additionally, we constrain the slope and curvature of the symmetry energy at the 90% upper credible interval to be $L$ sym ≲ 106 MeV and $K$ sym ≲ 26 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

On a theory of surface waves in a smoothly inhomogeneous plasma in an external magnetic field

A theory of surface waves in a magnetoactive plasma with smooth boundaries has been developed. A dispersion equation for surface waves has been derived for a linear law of density change at the plasma boundary. The frequencies of surface waves and their collisionless damping rates have been determined. A generalization to an arbitrary density profile at the plasma boundary is given. The collisions have been taken into account, and the application of the Landau rule in the theory of surface wave damping in a spatially inhomogeneous magnetoactive collisional plasma has been clarified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multiple soliton production and the Korteweg-de Vries equation.

Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.

Hershkowitz, N.↗

Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case—in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear dynamics near the stability margin in rotating pipe flow

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Yang, Z.↗

Superboom Caustic Analysis and Measurement Program (SCAMP) Final Report

The objectives of the Superboom Caustic Analysis and Measurement (SCAMP) Program were to develop and validate, via flight-test measurements, analytical models for sonic boom signatures in and around focal zones as they are expected to occur during commercial aircraft transition from subsonic to supersonic flight, and to apply these models to focus boom prediction of low-boom aircraft designs. The SCAMP program has successfully investigated sonic boom focusing both analytically and experimentally, while gathering a comprehensive empirical flight test and acoustic dataset, and developing a suite of focused sonic boom prediction tools. An experimental flight and acoustic measurement test was designed during the initial year of the SCAMP program, with execution of the SCAMP flight test occurring in May 2011. The current SCAMP team, led by Wyle, includes partners from the Boeing Company, Pennsylvania State University, Gulfstream Aerospace, Eagle Aeronautics, and Central Washington University. Numerous collaborators have also participated by supporting the experiment with human and equipment resources at their own expense. The experiment involved precision flight of a McDonnell Douglas (now Boeing) F-18B executing different maneuvers that created focused sonic booms. The maneuvers were designed to center on the flight regime expected for commercial supersonic aircraft transonic transition, and also span a range of caustic curvatures in order to provide a variety of conditions for code validations. The SCAMP experiment was designed to capture concurrent F-18B on-board flight instrumentation data, high-fidelity ground-based and airborne acoustic data, and surface and upper air meteorological data. Close coordination with NASA Dryden resulted in the development of new experimental instrumentation and techniques to facilitate the SCAMP flight-test execution, including the development of an F-18B Mach rate cockpit display, TG-14 powered glider in-flight sonic boom measurement instrumentation and "Where's the Focus?" (WTF) software for near-real time way-point computation accounting for local atmospherics. In May 2011, 13 F-18B flights were conducted during 5 flying days over a 2 week period. A densely populated 10,000 ft-long ground acoustic array with 125-ft microphone spacing was designed to capture pre-, focus, and post-focus regions. The ground-based acoustic array was placed in a nominally east-west orientation in the remote Cuddeback lakebed region, north of Edwards AFB. This area was carefully selected to avoid placing focused booms on populated areas or solar power facilities. For the SCAMP measurement campaign, approvals were obtained to temporarily extend the Black Mountain supersonic corridor northward by three miles. The SCAMP flight tests successfully captured 70 boom events, with 61 focus passes, and 9 calibration passes. Seventeen of the focus passes and three of the calibration passes were laterally offset; with the others being centerline flights. Airborne incoming sonic boom wave measurements were measured by the TG-14 for 10 of the F-18B flight passes including one maximum focus signature, several N-u combinations, several overlapped N-u signatures, and several evanescent waves. During the 27-month program, the SCAMP team developed a suite of integrated computer codes with sonic boom focusing predictive capabilities: PCBoom, Lossy Nonlinear Tricomi Equation Method (LNTE) and the Nonlinear Progressive wave Equation (NPE) method. PCBoom propagates the rays through the atmosphere and, in addition to legacy focus signature prediction based on the Gill-Seebass method, provides input source characteristics and propagation parameters to LNTE and NPE. LNTE, a Tricomi solver that incorporates atmospheric losses, computes the focus signature at the focus, and computes the focus signature in the vicinity of the focal zone, including the evanescent and post-focus zones. LNTE signature auralization from low-boom vehicle designs has been demonstrated in the NASA Langley Interior Effects Room (IER). The NPE has also been validated for use in prediction of focused ground boom signatures in sonic boom focal zones. The NPE formulation has the capability to incorporate atmospheric turbulence in the predictions. This has been applied to sonic boom propagation in the past. Prediction of turbulence effects on focal zone signatures was not, however, explored during the SCAMP program.

Page, Juliet↗

Plasma wave interactions with energetic ions near the magnetic equator

An intense band of electromagnetic noise is frequently observed near the magnetic equatorial plane at radial distance from about 2 to 5 Re. Recent wideband wave-form measurements with the IMP-6 and Hawkeye-1 satellites have shown that the equatorial noise consists of a complex superposition of many harmonically spaced lines. Several distinctly different frequency spacings are often evident in the same spectrum. The frequency spacing typically ranges from a few Hz to a few tens of Hz. It is suggested that these waves are interacting with energetic protons, alpha particles, and other heavy ions trapped near the magnetic equator. The possible role these waves play in controlling the distribution of the energetic ions is considered.

Gurnett, D. A.↗

Numerical modelling of nonlinear full-wave acoustic propagation

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Abstract In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β -derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β -derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Engineering↗

Prediction of the Wave Normal Angle of Proton‐Band EMIC Waves Near Geosynchronous Orbit

We investigate how the wave normal angle (WNA) and polarization of proton-band electromagnetic ion cyclotron (EMIC) waves change as they travel from their source to Earth. This paper marks a significant milestone as the first full-wave simulation of proton-band EMIC waves reflecting from the ionosphere. Our findings show that the WNA can change rapidly during propagation, primarily due to plasma inhomogeneities, such as variations in the Alfvén speed. The wave polarization is strongly related to the WNA, consistent with theory. Newly generated EMIC waves near the equator propagate with a WNA of 0° , then the WNA gradually shifts to 90° as they move toward Earth. In contrast, reflecting waves having 90° of WNA at Earth maintain a relatively larger WNA even near the magnetic equator. As a result, only the newly generated waves close to the source, where the magnetic latitude is less than approximately 20° , show left-handed polarization, while linear polarization remains dominant throughout the rest of the propagation.

EMIC wave↗

A procedure for computing surface wave trajectories on an inhomogeneous surface

Equations are derived for computing surface waves on smooth surfaces, including surfaces with a nonuniform wave speed. The prior literature dealt primarily with the theoretical development with little consideration given to computational methods, and examples were limited to waves on surfaces of simple analytic description, such as cones, spheres, and cylinders. The computational procedure presented is a relatively general method. Sample calculations illustrate the procedure for a class of practical shapes of the type that include aerodynamic and hydrodynamic surfaces. Equations are also included for computing the spreading of rays into a surrounding medium that will support waves.

Barger, Raymond L.↗

Freak waves in white dwarfs and magnetars

We report properties of ion acoustic freak waves that propagate in a plasma composed of warm ions and ultrarelativistic electrons and positrons. The dynamics of the nonlinear freak waves is governed by the nonlinear Schroedinger equation. The possible region for the freak waves to exist is defined precisely for typical parameters of white dwarfs and magnetars corona. It is found that for low wave number, the nonlinear ion-acoustic wave packets are structurally stable in magnetars corona than in white dwarfs. However, for large wave numbers the situation is opposite. The critical wave number threshold (k{sub c}), which indicates where the modulational instability sets in, is defined for both applications. It is seen that near to k{sub c} the freak wave amplitude becomes high, but it decreases whenever we stepped away from k{sub c}. For the wave numbers close to k{sub c}, the increase of the unperturbed density ratio of positrons-to-electrons ({beta}) would lead to increase the freak wave amplitude, but for larger wave numbers the amplitude decreases with the increase of {beta}.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗