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The exchange of stabilities is demonstrated for a system with harmonic boundary conditions. The motion of fluid in the presence of temperatures gradients is described. It is shown that this principle holds under free, but not rigid or semirigid, boundary conditions.
A 3-dimensional model was developed to support mechanistic studies. The model solves the global primitive equations in isentropic coordinates, which directly characterize diabatic processes forcing the Brewer-Dobson circulation of the middle atmosphere. It's numerical formulation is based on Hough harmonics, which partition horizontal motion into its rotational and divergent components. These computational features, along with others, enable 3D integrations to be performed practically on RISC computer architecture, on which they can be iterated to support mechanistic studies. The model conserves potential vorticity quite accurately under adiabatic conditions. Forced by observed tropospheric structure, in which integrations are anchored, the model generates a diabatic circulation that is consistent with satellite observations of tracer behavior and diabatic cooling rates. The model includes a basic but fairly complete treatment of gas-phase photochemistry that represents some 20 chemical species and 50 governing reactions with diurnally-varying shortwave absorption. The model thus provides a reliable framework to study transport and underlying diabatic processes, which can then be compared against chemical and dynamical structure observed and in GCM integrations. Integrations with the Langley GCM were performed to diagnose feedback between simulated convection and the tropical circulation. These were studied in relation to tropospheric properties controlling moisture convergence and environmental conditions supporting deep convection, for comparison against mechanistic integrations of wave CISK that successfully reproduce the Madden-Julian Oscillation (MJO) of the tropical circulation. These comparisons were aimed at identifying and ultimately improving aspects of the convective simulation, with the objective of recovering a successful simulation of the MJO in the Langley GCM, behavior that should be important to budgets of upper-tropospheric water vapor and chemical species.
Several flight-critical aerodynamic problems such as buffet, flutter, stall, and wing rock are strongly affected or caused by abrupt changes in unsteady aerodynamic loads and moments. Advanced sensing and flow diagnostic techniques have made possible simultaneous identification and tracking, in real-time, of the critical surface, viscosity-related aerodynamic phenomena under both steady and unsteady flight conditions. The wind tunnel study reported here correlates surface hot-film measurements of leading edge stagnation point and separation point, with unsteady aerodynamic loads on a NACA 0015 airfoil. Lift predicted from the correlation model matches lift obtained from pressure sensors for an airfoil undergoing harmonic pitchup and pitchdown motions. An analytical model was developed that demonstrates expected stall trends for pitchup and pitchdown motions. This report demonstrates an ability to obtain unsteady aerodynamic loads in real-time, which could lead to advances in air vehicle safety, performance, ride-quality, control, and health management.
Several flight-critical aerodynamic problems such as buffet, flutter, stall, and wing rock are strongly affected or caused by abrupt changes in unsteady aerodynamic loads and moments. Advanced sensing and flow diagnostic techniques have made possible simultaneous identification and tracking, in realtime, of the critical surface, viscosity-related aerodynamic phenomena under both steady and unsteady flight conditions. The wind tunnel study reported here correlates surface hot-film measurements of leading edge stagnation point and separation point, with unsteady aerodynamic loads on a NACA 0015 airfoil. Lift predicted from the correlation model matches lift obtained from pressure sensors for an airfoil undergoing harmonic pitchup and pitchdown motions. An analytical model was developed that demonstrates expected stall trends for pitchup and pitchdown motions. This report demonstrates an ability to obtain unsteady aerodynamic loads in real time, which could lead to advances in air vehicle safety, performance, ride-quality, control, and health management.
We reexamine mass flow in a superfluid gyroscope containing a superfluid Josephson weak link. We introduce a frequency-dependent hydrodynamic inductance to account for an oscillatory flow of the normal fluid component in the sensing loop. With this hydrodynamic inductance, we derive the thermal phase noise, and hence the thermal rotational noise of the gyroscope. We examine the thermodynamic stability of the system based on an analysis of the free energy. We derive a quantum phase noise, which is analogous to the zero-point motion of a simple harmonic oscillator. The configuration of the studied gyroscope is analogous to a conventional superconducting RF SQUID. We show that the gyroscope has very low intrinsic noise (1.9x10(-13) rad s(-1)/root Hz), and it can potentially be applied to study general relativity, Earth science, and to improve global positioning systems (GPS).
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Harmonic and superharmonic liquid surface motions observed for longitudinally excited rigid cylindrical tank
The spherical harmonic coefficients in the gravity field of Mars are determined using a two stage filtering process. In the first stage, a weighted least squares orbit determination processor is applied to Mariner 9 Doppler tracking data to estimate Kepler elements and rates. In the second stage, the Kepler element rates are used as input to another weighted least squares processor that estimates gravity coefficients using the Lagrange perturbation equations. The novelty in this method is the fitting of element rates rather than the elements themselves. This procedure decouples the results from the effects of internal spacecraft dynamics.
The spherical harmonic coefficients in the Mars gravity field are determined using a two-stage filtering process. In the first stage, a weighted least-squares orbit determination processor is applied to Mariner 9 radio data to estimate the mean Kepler elements of each orbit. A finite difference method is then used to generate orbital element rates. In the second stage, the gravity coefficients are determined using another weighted least-squares processor which fits the long period Lagrange perturbation equations to the estimated rates. The resulting gravity potential and associated equipotential surface is presented and error sources discussed. Gravity field results are applied to various physical properties of Mars, such as moments of inertia.-
Abstract The higher harmonics generated by nonlinear sheath motion would enhance the standing wave effect, and thus lead to center-peaked plasma density profile in very-high-frequency (VHF) capacitive discharges. In this work, a nonlinear transmission line (NTL) model introduced in Zhouet al(2021Plasma Sources Sci. Technol.30125017) has been extended, with radial transport of various particles and nonlinear sheath motion into account, to investigate the effects of CF 4 fraction α on the nonlinear standing wave excitation and plasma radial uniformity in VHF (60 MHz) capacitively coupled Ar/CF 4 plasmas at 3 Pa. The results indicate that for pure Ar discharges (i.e. α = 0%), the nonlinearly excited harmonics with short wavelength significantly enhance the electron power absorption at the radial center, resulting in a pronounced central-high plasma density profile. As α increases, the high-order harmonics are gradually damped due to the increase of resistance, as well as the longer wavelength caused by thicker sheath thickness. Thus, the radial profile of the electron absorbed power density shifts from center-peak to edge-high. Besides, at the radial center, the electron density and Ar + ion density decrease with α , CF 3 + ion density shows an increasing trend, while F − ion density initially rises and then decreases. Moreover, the density profiles of all the species become more uniform at higher CF 4 fraction, due to the suppressed nonlinear standing wave excitation and the longer wavelength of the nonlinear harmonics.
The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.
The equations of motion of an arbitrary flexible body in orbit are derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit is modeled. The example considers the inplane motion of the beam in orbit. In the case of planar motion with only flexural vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion is decoupled from the pitch motion. However, for small values of this ratio and small amplitude pitch motion, the elastic motion is governed by a Hill's 3-term equation. Numerical simulation of this equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate.
Abstract It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage V L on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage V L at 2 MHz varies from 0 to 700 V while the HF voltage V H at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. V L = 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as V L increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher V L , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔEbecomes wider with the increase of V L . The IEDF at the radial center of the powered electrode exhibits a broader ΔEthan that at the edge. For the IADF, an increased V L results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.
Abstract In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.
Here, we present a scenario in heavy-ion collisions where different modes of collective motions are noninterdependent, driven by factorized actions in the created nuclear medium. Such physics mechanisms could each dominate at a distinct evolution stage, or coexist simultaneously. If the probability of particle emission is modulated by each nondependent collective motion with a single-harmonic Fourier expansion, the particle azimuthal distribution should be the product of all these expansions. Consequently, nonleading cross terms between collectivity modes appear, and their contributions to experimental observables could be significant. In particular, we argue that the chiral magnetic effect (CME) and elliptic flow can develop separately, with their convolution affecting the observable that is sensitive to the shear-induced CME. We will use the event-by-event anomalous-viscous fluid dynamics model to illustrate the effects of this scenario. Besides giving insights into searches for the CME, we also propose feasible experimental tests based on conventional flow harmonics, and demonstrate the emergence of nonleading cross terms with a multiphase transport model.
Trapped vortices in superconductors introduce residual resistance in superconducting radio-frequency (SRF) cavities and disrupt the operation of superconducting quantum and digital electronic circuits. Understanding the detailed dynamics of trapped vortices under oscillating magnetic fields is essential for advancing these technologies. We have developed a near-field magnetic microwave microscope to study the dynamics of a limited number of trapped vortices under the probe when stimulated by a localized rf magnetic field. By measuring the local second-harmonic response (𝑃 2f ) at subfemto-Watt levels, we isolate signals exclusively arising from trapped vortices, excluding contributions from surface defects and Meissner screening currents. Toy models of niobium superconductor hosting vortex pinning sites are introduced and studied with time-dependent Ginzburg-Landau (TDGL) simulations of probe/sample interaction to better understand the measured second-harmonic response. The simulation results demonstrate that the second-harmonic response of trapped vortex motion under a localized rf magnetic field shares key features with the experimental data. Here, this measurement technique provides access to vortex dynamics at the micrometer scale, such as depinning events and spatially resolved pinning properties, as demonstrated in measurements on a niobium film with an antidot flux pinning array.
Harmonic and superharmonic liquid surface motions observed for longitudinally excited rigid cylindrical tank
Harmonics, pulsation amplitude, and vibratory motion of Cepheid variable stars