Computer program to calculate convective heat-transfer coefficients from harmonic temperature oscillations
Computer program for calculation convective heat transfer coefficients from harmonic temperature oscillations
Amling, G. E.↗
SEARCH · Engineering Papers
Results for “harmonic oscillator”
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.
Formationkeeping of Spacecraft via Differential Drag
This paper examines the use of differential drag in the formationkeeping of spacecraft. In many future space missions one satellite will be required to fly in a specific position with respect to another satellite; this action is referred to as formationkeeping. In this study, differential drag is the difference in drag between the two satellites. Reasons to use differential drag as an actuator for formationkeeping include the avoidance of jet plume impingement effects on closely spaced satellites and possible fuel savings. The equations of relative motion between the two satellites are derived and a mathematical transformation is made to reduce the formationkeeping problem to the simultaneous solution of a double integrator and a harmonic oscillator. A two-part control law is developed that simultaneously and dependently solves the double oscillator and harmonic integrator. Results are presented of eight test cases being driven to a target position; two different simulations are used. The validity of assumptions made in the derivation of the control law is examined in the comparison of similar test cases run through different simulations. The control law developed can drive a satellite from an initial position to a target position and maintain the satellite at that location.
Leonard, Carolina Lee↗
Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles
The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
When action is not least for systems with action-dependent Lagrangians
The dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action according to the variational principle of Herglotz. This is directly analogous to the variational principle of Hamilton commonly used to derive the dynamics of conservative systems. In a similar fashion, just as the second variation of a conservative system’s action can be used to infer whether that system’s possible trajectories are dynamically stable, so too can the second variation of the action-dependent action be used to infer whether the possible trajectories of non-conservative and dissipative systems are dynamically stable. In this paper, I show, generalizing earlier analyses of the second variation of the action for conservative systems, how to calculate the second variation of the action-dependent action and how to apply it to two physically important systems: a time-independent harmonic oscillator and a time-dependent harmonic oscillator.
Physics↗
Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH 3 OH–Cu(111)
A method for computing anharmonic thermophysical properties for adsorbates on metal surfaces has been extended to include libration, or frustrated rotation. Classical phase space integration is used with Monte Carlo sampling of the configuration space to obtain the partition function of CO on Pt(111) and CH 3 OH on Cu(111). A minima-preserving neural network potential energy surrogate is used within the integration routines. Direct state counting using discrete variable representation is used to benchmark the results. We find that the phase space integration approach is in excellent agreement with the direct state counting results. Comparison with standard models such as the harmonic oscillator indicates that anharmonicity contributes significantly to the thermodynamic properties of CH 3 OH on Cu(111). We find that there is also a considerable difference between the harmonic oscillator and phase space integration for CO on Pt(111), although the discrepancy can largely be attributed to the presence of multiple binding sites within the unit cell. We demonstrate that a multisite harmonic oscillator model might be sufficient for CO-Pt(111). A more thorough description of the potential energy surface, which can be achieved with phase space integration, is necessary for weakly bound adsorbates such as CH 3 OH. In conclusion, the thermophysical properties were used to calculate free energies of adsorption on the respective metals, and subsequently the equilibrium constants and Langmuir isotherms in relevant temperature ranges. The results show that the choice of model to obtain partition functions greatly affects the resulting surface coverages in kinetic models.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Beyond the universal Dyson singularity for 1-D chains with hopping disorder
We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Two Different Squeeze Transformations
Lorentz boosts are squeeze transformations. While these transformations are similar to those in squeezed states of light, they are fundamentally different from both physical and mathematical points of view. The difference is illustrated in terms of two coupled harmonic oscillators, and in terms of the covariant harmonic oscillator formalism.
Han, D.↗
Phase-Locking of a Second-Harmonic Gyrotron Oscillator Using a Quasi-Optical Circulator to
Explore the source record for details and available documents.
Second-Harmonic Gyrotron Oscillator↗
ELM Suppression by Boron Powder Injection and Comparison with Lithium Powder Injection on EAST
Type I edge-localized modes (ELMs) in the Experimental Advanced Superconducting Tokamak (EAST) were completely suppressed via boron powder injection into the X-point region of an upper-single null configuration over a wide range of operating conditions (2.8 < P aux < 7.5 MW, 3.8 × 10 19 < n e < 6 × 10 19 m -3 , RF-only and RF + NBI heating scenarios, both grad-B drift directions, and even He ion majority plasmas) (Sun et al. in Nucl. Fusion, 2020). A window of edge B concentration for stable long pulse operation was identified: too low and ELMs return, too high and the discharge suffers radiative collapse. The injection of boron powder above the minimum for ELM suppression coincided with the occurrence of an edge harmonic oscillation detected in magnetics (both on the high-field side and low-field side), in AXUV diodes near the upper X-point, divertor Dα emission, and in a range of other diagnostics (Diallo et al. in: Proceedings of 2020 IAEA fusion energy conference, 2021). Furthermore, no harmonic oscillation was observed when ELMs were present, and stored energy was slightly increased at constant density during ELM suppression. Core tungsten emission during ELM suppression either increased or decreased relative to ELMy H-mode, but the W emission was maintained at acceptable levels. The threshold B injection rate was measured for several conditions, and found to increase with heating power. Li powder injection into comparable discharges also resulted in a short phase of ELM suppression, but density and stored energy both decreased due to the strong pumping effect of lithium; no edge harmonic oscillation was observed with Li injection, indicating that the ELM suppression mechanisms differ. The new set of B-seeded, ELM-suppressed discharges exhibited certain characteristics of quiescent H-mode (Burrell et al. in Phys Plasmas 8:2153, 2001), but did not require high shear, counter beams, etc. The wide operating window and compatibility with RF-only discharges paves the way for future experiments targeting long pulse H-mode discharges with complete ELM suppression.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates
Here, phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.
36 MATERIALS SCIENCE↗
Dissociation of diatomic gases
The Landau-Zener theory of reactive cross sections has been applied to diatomic molecules dissociating from a ladder of rotational and vibrational states. Although the preexponential factor of the Arrhenius rate expression is shown to be a complex function of the dimensionless activation energy, the average over all states in the ladder is well represented by a single factor that varies about as T exp (-n), where the coefficient n is the order of unity. This relation agrees very well with experimental data for dissociation of O2 and N2, for example. The results validate previous empirical assignment of a single preexponential factor in the Arrhenius expression and justify the extrapolation of the expression well beyond the range of data. The theory is then used to calculate the effect of vibrational nonequilibrium on dissociation rate. For Morse oscillators the results are about the same as for harmonic oscillators, and the dissociation from a ladder of equilibrium rotational and nonequilibrium vibrational states is close to an analytic approximation provided by Hammerling, Kivel, and Teare for harmonic oscillators all dissociating from the ground rotational state.
Hansen, C. F.↗
Point form relativistic quantum mechanics and relativistic SU(6)
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Klink, W. H.↗
Resonance absorption of magnetohydrodynamic surface waves Physical discussion
It is shown how the phenomenon of MHD surface wave resonance absorption can be described in simple terms, both physically and mathematically, by applying the 'thin flux tube equations' to the finite-thickness transition layer which supports the surface wave. The thin flux tubes support incompressible slow-mode waves that are driven by fluctuations in the total pressure which exist due to the presence of the surface wave. It is shown that the equations for the slow-mode waves can be reduced to a simple equation, equivalent to a driven harmonic oscillator. Certain field lines within the transition layer are equivalent to a harmonic oscillator driven at resonance, and neighboring field lines are effectively driven at resonance as long as a given condition is satisfied. Thus, a layer which secularly extracts energy from the surface wave develops. The analysis indicates that nonlinear effects may destroy the resonance which is crucial to the whole effect.
Hollweg, Joseph V.↗
The Duffin-Kemmer-Petiau oscillator
In view of current interest in relativistic spin-one systems and the recent work on the Dirac Oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since, in the non-relativistic limit, the spin 1 representation leads to a harmonic oscillator with a spin-orbit coupling of the Thomas form, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable. We calculate and discuss the eigenspectrum of the DKP oscillator in the spin 1 representation.
Nedjadi, Youcef↗
Linear canonical transformations of coherent and squeezed states in the Wigner phase space
It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.
Han, D.↗
Analysis of Transformer Magnetizing Reactance Using Describing Function in Direct Power Control of Back-to-Back Modular Multilevel Converter with Advanced Grid Support
This paper presents a Port Controlled Hamiltonian based direct power control architecture for a back-to-back modular multilevel converter system connecting two ac sources at different frequencies. The system features advanced grid support functionalities based on IEEE 1547-2018, implemented on the inverter side. The rectifier side controller ensures reference following for active and/or reactive powers and maintains the commanded dc bus voltage. The inverter side controller ensures power command following for active and reactive powers.The proposed control architecture is designed to suppress second harmonic oscillations in powers during unbalanced grid voltage sags by dynamically adjusting the currents on each ac side. This also ensures effective elimination of any second harmonic oscillations in the equivalent dc bus voltage. Validation is performed on an OPAL-RT real-time platform with case studies on unbalanced and balanced sags, demonstrating the controller's effectiveness during real time implementation. A reduced-scale laboratory prototype further verifies these case studies, with experimental results for balanced sags due to grid simulator limitations. The results confirm the robustness and efficiency of the proposed control strategy in ensuring stable and reliable operation under various grid conditions.
24 POWER TRANSMISSION AND DISTRIBUTION↗
User's Guide for ECAP2D: an Euler Unsteady Aerodynamic and Aeroelastic Analysis Program for Two Dimensional Oscillating Cascades, Version 1.0
This guide describes the input data required for using ECAP2D (Euler Cascade Aeroelastic Program-Two Dimensional). ECAP2D can be used for steady or unsteady aerodynamic and aeroelastic analysis of two dimensional cascades. Euler equations are used to obtain aerodynamic forces. The structural dynamic equations are written for a rigid typical section undergoing pitching (torsion) and plunging (bending) motion. The solution methods include harmonic oscillation method, influence coefficient method, pulse response method, and time integration method. For harmonic oscillation method, example inputs and outputs are provided for pitching motion and plunging motion. For the rest of the methods, input and output for pitching motion only are given.
Reddy, T. S. R.↗
A Canonical Transformation to Eliminate Resonant Perturbations. I
We study dynamical systems that admit action-angle variables at leading order, which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical evolution may be integrated by orbit-averaging over the high-frequency angles, thereby evolving the orbit-averaged effect of the perturbations. It is well known that such integrators may be constructed via a canonical transformation, which eliminates the high-frequency variables from the orbit-averaged quantities. An example of this algorithm in celestial mechanics is the von Zeipel transformation. However, if the perturbations are inside or close to a resonance, i.e., the frequencies of the unperturbed system are commensurate; these canonical transformations are subject to divergences. We introduce a canonical transformation that eliminates the high-frequency phase variables in the Hamiltonian without encountering divergences. This leads to a well-behaved symplectic integrator. We demonstrate the algorithm through two examples: a resonantly perturbed harmonic oscillator and the gravitational three-body problem in mean motion resonance.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗