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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Evidence of an Intrinsic Intraseasonal Oscillation over Tropical South America During Austral Summer

The intraseasonal variation (ISV) in the 30-60 day band, also known as Madden-Julian oscillation (MJO), has been studied for decades. Madden and Julian showed that the oscillation originated from the western Indian Ocean, propagated eastward, got enhanced over the maritime continent and weakened after passing over the dateline. Composite studies showed evidences of a signal in upper and lower level zonal wind propagating around the globe during an oscillation. Theoretical studies pointed out that the interaction with the warm ocean surface and the coupling with the convective and radiative processes in the atmosphere could manifest the oscillation, which propagates eastward via mutual feedbacks between the wave motions and the cumulus heating. Over tropical South America, no independent 30-60 day oscillation has been reported so far, despite that Amazon is the most distinct tropical convection center over the western hemisphere and the fluxes from its surface of tropical rainforests are close to that from the warm tropical ocean. Liebmann et al. showed a distinct spectral peak of 40-50 day oscillation in outgoing longwave radiation (OLR) over tropical South America and considered that was manifested by the MJO propagation. Nogues-Paegle et al. (2000) focused on a dipole pattern of the OLR anomaly with centers of action over the South Atlantic Convergence Zone (SACZ) and the subtropical plain. They used the regional 10-90 day filtered data and demonstrated this pattern could be represented by the fifth mode of the rotated empirical orthogonal function. Its principal component was further analyzed using the singular spectrum analysis. Their result showed two oscillatory modes with periods of 36-40 days and 22-28 days, of which the former was related to the MJO influence and the latter linked to the remote forcing over southwest of Australia, which produced a wave train propagating southeastward, rounding the southern tip of South America and returning back toward the northeast. The 22-28 day mode has distinct impact on SACZ, responsible for the regional seesaw pattern of alternating dry and wet conditions. In this study we will focus on the 30-60-day spectral band and investigate whether the independent oscillation source over tropical South America is existed. First, we will show the seasonal dependence of the tropical South American ISV in Section 3. Then, the leading principal modes of 30-60 day bandpass filtered 850-hPa velocity potential (VP850) will be computed to distinguish the stationary ISV over tropical South America (SISA) from the propagating MJO in the austral summertime in Section 4. The importance of SISA in representing the regional ISV over South America will be discussed. In Section 5, we will demonstrate the mass oscillation regime of SISA, which is well separated from that of MJO by the Andes, and the convective coupling with rainfall. The dynamical response of SISA and the impact on the South American summer monsoon (SASM) will be presented. Finally, we will give the concluding remarks.

Zhou, Jiayu↗
NASA NTRS2010

Automated Detection of Oscillating Regions in the Solar Atmosphere

Recently observed oscillations in the solar atmosphere have been interpreted and modeled as magnetohydrodynamic wave modes. This has allowed for the estimation of parameters that are otherwise hard to derive, such as the coronal magnetic-field strength. This work crucially relies on the initial detection of the oscillations, which is commonly done manually. The volume of Solar Dynamics Observatory (SDO) data will make manual detection inefficient for detecting all of the oscillating regions. An algorithm is presented that automates the detection of areas of the solar atmosphere that support spatially extended oscillations. The algorithm identifies areas in the solar atmosphere whose oscillation content is described by a single, dominant oscillation within a user-defined frequency range. The method is based on Bayesian spectral analysis of time series and image filtering. A Bayesian approach sidesteps the need for an a-priori noise estimate to calculate rejection criteria for the observed signal, and it also provides estimates of oscillation frequency, amplitude, and noise, and the error in all of these quantities, in a self-consistent way. The algorithm also introduces the notion of quality measures to those regions for which a positive detection is claimed, allowing for simple post-detection discrimination by the user. The algorithm is demonstrated on two Transition Region and Coronal Explorer (TRACE) datasets, and comments regarding its suitability for oscillation detection in SDO are made.

Ireland, J.↗
NASA NTRS2011

Cryogenic Behavior of the High Temperature Crystal Oscillator PX-570

Microprocessors, data-acquisition systems, and electronic controllers usually require timing signals for proper and accurate operation. These signals are, in most cases, provided by circuits that utilize crystal oscillators due to availability, cost, ease of operation, and accuracy. Stability of these oscillators, i.e. crystal characteristics, is usually governed, amongst other things, by the ambient temperature. Operation of these devices under extreme temperatures requires, therefore, the implementation of some temperature-compensation mechanism either through the manufacturing process of the oscillator part or in the design of the circuit to maintain stability as well as accuracy. NASA future missions into deep space and planetary exploration necessitate operation of electronic instruments and systems in environments where extreme temperatures along with wide-range thermal swings are countered. Most of the commercial devices are very limited in terms of their specified operational temperature while very few custom-made and military-grade parts have the ability to operate in a slightly wider range of temperature. Thus, it is becomes mandatory to design and develop circuits that are capable of operation efficiently and reliably under the space harsh conditions. This report presents the results obtained on the evaluation of a new (COTS) commercial-off-the-shelf crystal oscillator under extreme temperatures. The device selected for evaluation comprised of a 10 MHz, PX-570-series crystal oscillator. This type of device was recently introduced by Vectron International and is designed as high temperature oscillator [1]. These parts are fabricated using proprietary manufacturing processes designed specifically for high temperature and harsh environment applications [1]. The oscillators have a wide continuous operating temperature range; making them ideal for use in military and aerospace industry, industrial process control, geophysical fields, avionics, and engine control. They exhibit low jitter and phase noise, consume little power, and are suited for high shock and vibration applications. The unique package design of these crystal oscillators offers a small ceramic package footprint, as well as providing both through-hole mounting and surface mount options.

Patterson, Richard↗
NASA NTRS2012

Characterization of the Vectron PX-570 Crystal Oscillator for Use in Harsh Environments

Computing hardware, data-acquisition systems, communications systems, and many electronic control systems require well-controlled timing signals for proper and accurate operation. These signals are, in most cases, provided by circuits that employ crystal oscillators due to availability, cost, ease of operation, and accuracy. In some cases, the electronic systems are expected to survive and operate under harsh conditions that include exposure to extreme temperatures. These applications exist in terrestrial systems as well as in aerospace products. Well-logging, geothermal systems, and industrial process control are examples of ground-based applications, while distributed jet engine control in aircraft, space-based observatories (such as the James Webb Space Telescope), satellites, and lunar and planetary landers are typical environments where electronics are exposed to harsh operating conditions. To ensure these devices produce reliable results, the digital heartbeat from the oscillator must deliver a stable signal that is not affected by external temperature or other conditions. One such solution is a recently introduced commercial-off-the-shelf (COTS) oscillator, the PX-570 series from Vectron International. The oscillator was designed for high-temperature applications and as proof, the crystal oscillator was subjected to a wide suite of tests to determine its ruggedness for operation in harsh environments. The tests performed by Vectron included electrical characterization under wide range of temperature, accelerated life test/aging, shock and vibration, internal moisture analysis, ESD threshold, and latch-up testing. The parametric evaluation was performed on the oscillator's frequency, output signal rise and fall times, duty cycle, and supply current over the temperature range of -125 C to +230 C. The evaluations also determined the effects of thermal cycling and the oscillator's re-start capability at extreme hot and cold temperatures. These thermal cycling and restart tests were performed at the NASA Glenn Research Center. Overall, the crystal oscillator performed well and demonstrated very good frequency stability. This paper will discuss the test procedures and present details of the performance results.

Li, Jacob↗
NASA NTRS2015

Evaluation of Start Transient Oscillations with the J-2X Engine Gas Generator Assembly

During development of the gas generator for the liquid oxygen/liquid hydrogen propellant J-2X rocket engine, distinctive and oftentimes high-amplitude pressure oscillations and hardware vibrations occurred during the start transient of nearly every workhorse gas generator assembly test, as well as during many tests of engine system hardware. These oscillations appeared whether the steady-state conditions exhibited stable behavior or not. They occurred similarly with three different injector types, and with every combustion chamber configuration tested, including chamber lengths ranging over a 5:1 range, several different nozzle types, and with or without a side branch line simulating a turbine spin start gas supply line. Generally, two sets of oscillations occurred, one earlier in the start transient and at higher frequencies, and the other almost immediately following and at lower frequencies. Multiple dynamic pressure measurements in the workhorse combustion chambers indicated that the oscillations were associated with longitudinal acoustic modes of the combustion chambers, with the earlier and higher frequency oscillation usually related to the second longitudinal acoustic mode and the later and lower frequency oscillation usually related to the first longitudinal acoustic mode. Given that several early development gas generator assemblies exhibited unstable behavior at frequencies near the first longitudinal acoustic modes of longer combustion chambers, the start transient oscillations are presumed to provide additional insight into the nature of the combustion instability mechanisms. Aspects of the steadystate oscillations and combustion instabilities from development and engine system test programs have been reported extensively in the three previous JANNAF Liquid Propulsion Subcommittee meetings (see references below). This paper describes the hardware configurations, start transient sequence operations, and transient and dynamic test data during the start transient. The implications of these results on previous analyses and understanding of the combustion instability observed during steady-state conditions, especially the effects of injector influences, is discussed.

Hulka, J. R.↗
NASA NTRS2018

Temperature Oscillations in Loop Heat Pipes - A Revisit

Three types of temperature oscillation have been observed in the loop heat pipes. The first type is an ultra-high frequency temperature oscillation with a period on the order of seconds or less. This type of temperature oscillation is of little significance in spacecraft thermal control because the amplitude is in the noise level. The second type is a high frequency, low amplitude temperature oscillation with a period on the order of seconds to minutes and an amplitude on the order of one Kelvin. It is caused by the back-and-forth movement of the vapor front near the inlet or outlet of the condenser. The third type is a low frequency, high amplitude oscillation with a period on the order of hours and an amplitude on the order of tens of Kelvin. It is caused by the modulation of the net heat load into the evaporator by the attached large thermal mass which absorbs and releases energy alternately. Several papers on LHP temperature oscillation have been published. This paper presents a further study on the underlying physical processes during the LHP temperature oscillation, with an emphasis on the third type of temperature oscillation. Specifically, equations governing the thermal and hydraulic behaviors of LHP operation will be used to describe interactions among LHP components, heat source, and heat sink. The following sequence of events and their interrelationship will also be explored: 1) maxima and minima of reservoir and thermal mass temperatures; 2) the range of the vapor front movement inside the condenser; 3) rates of change of the reservoir and thermal mass temperatures; 4) the rate of heat absorption and heat release by the thermal mass and the rate of vapor front movement; and 5) inflection points of the reservoir and thermal mass temperatures.

Fluid Mechanics and Thermodynamics↗
NASA NTRS2018

Dawn- Dusk Auroral Oval Oscillations Associated with High- Speed Solar Wind

We report evidence of global-scale auroral oval oscillations in the millihertz range, using global auroral images acquired from the Ultraviolet Imager on board the decommissioned Polar satellite and concurrent solar wind measurements. On the basis of two events (15 January 1999 and 6 January 2000) studied, it is found that (1) quasi-periodic auroral oval oscillations (approximately 3 megahertz) can occur when solar wind speeds are high at northward or southward interplanetary magnetic field turning, (2) the oscillation amplitudes range from a few to more than 10 degrees in latitudes, (3) the oscillation frequency is the same for each event irrespective of local time and without any azimuthal phase shift (i.e., propagation), (4) the auroral oscillations occur in phase within both the dawn and dusk sectors but 180 degrees out of phase between the dawn and dusk sectors, and (5) no micropulsations on the ground match the auroral oscillation periods. While solar wind conditions favor the growth of the Kelvin-Helmholtz (K-H) instability on the magnetopause as often suggested, the observed wave characteristics are not consistent with predictions for K-H waves. The in-phase and out-of-phase features found in the dawn-dusk auroral oval oscillations suggest that wiggling motions of the magnetotail associated with fast solar winds might be the direct cause of the global-scale millihertz auroral oval oscillations. Plain Language Summary: We utilize global auroral image data to infer the motion of the magnetosphere and show, for the first time, the entire magnetospheric tail can move east-west in harmony like a windsock flapping in wind. The characteristic period of the flapping motion may be a major source of global long-period ULF (Ultra Low Frequency) waves, adding an extra source of the global mode ULF waves.

Liou, Kan↗
NASA NTRS2018

NICER Discovers mHz Oscillations in the "Clocked" Burster GS 1826-238

We report the discovery with the Neutron Star Interior Composition Explorer (NICER) of mHz X-ray brightness oscillations from the "clocked burster" GS 1826−238. NICER observed the source in the periods 2017 June 20–29, July 11–13, and September 9–15, for a total useful exposure of 34 ks. Two consecutive dwells obtained on 2017 September 9 revealed highly significant oscillations at a frequency of 8 mHz. The fractional, sinusoidal modulation amplitude increases from 0.7% at 1 keV to ≈2% at 6 keV. Similar oscillations were also detected at lower significance in three additional dwells. The oscillation frequency and amplitude are consistent with those of mHz QPOs reported in other accreting neutron star systems. A thermonuclear X-ray burst was also observed on 2017 June 22. The burst properties and X-ray colors are both consistent with GS 1826 being in a soft spectral state during these observations, findings that are confirmed by ongoing monitoring with MAXI and SWIFT-BAT. Assuming that the mHz oscillations are associated with blackbody emission from the neutron star surface, modeling of the phase-resolved spectra shows that the oscillation is consistent with being produced by modulation of the temperature component of this emission. In this interpretation, the blackbody normalization, proportional to the emitting surface area, is consistent with being constant through the oscillation cycle. We place the observations in the context of the current theory of marginally stable burning and briefly discuss the potential for constraining neutron star properties using mHz oscillations.

Strohmayer, T. E.↗
NASA NTRS2022

Kink Oscillation of a Flux Rope During a Failed Solar Eruption

We report a decaying kink oscillation of a flux rope during a confined eruptive flare, observed off the solar limb by SDO/AIA, that lacked a detectable white-light coronal mass ejection. The erupting flux rope underwent kinking, rotation, and apparent leg–leg interaction during the event. The oscillations were observed simultaneously in multiple AIA channels at 304, 171, and 193 Å, indicating that multithermal plasma was entrained in the rope. After reaching the overlying loops in the active region, the flux rope exhibited large-amplitude, decaying kink oscillations with an apparent initial amplitude of 30 Mm, period of about 16 min, and decay time of about 17 min. We interpret these oscillations as a fundamental standing kink mode of the flux rope. The oscillation polarization has a clear vertical component, while the departure of the detected waveform from a sinusoidal signal suggests that the oscillation could be circularly or elliptically polarized. The estimated kink speed is 1080 km s−1, corresponding to an Alfv'en speed of about 760 km s−1. This speed, together with the estimated electron density in the rope from our DEM analysis, ne ≈ (1.5–2.0) ×109 cm−3, yields a magnetic field strength of about 15 G. To the best of our knowledge, decaying kink oscillations of a flux rope with non-horizontal polarization during a confined eruptive flare have not been reported before. These oscillations provide unique opportunities for indirect measurements of the magnetic-field strength in low-coronal flux ropes during failed eruptions.

Pankaj Kumar↗
DOE OSTI2021

Tuned oscillator atomic force microscopy methods and apparatus

Techniques for operating an atomic force microscope, the atomic force microscope comprising a cantilever and configured to image a surface of a sample using a probe tip coupled to the cantilever, the techniques comprising using a controller to perform: obtaining, based on at least one intrinsic parameter of the cantilever, a first quality factor and a first free oscillation amplitude, wherein the cantilever exhibits only one stable oscillation state when oscillating at the first free oscillation amplitude and operating at the first quality factor; and controlling the cantilever to exhibit the only one stable oscillation state by controlling the cantilever to oscillate at a fixed frequency at or near a resonance frequency of the cantilever, oscillate at the first free oscillation amplitude, and operate at the first quality factor.

Schwarz, Udo↗
DOE OSTI2023

Oscillator for adiabatic computational circuitry

An adiabatic resonator, an adiabatic oscillator, and an adiabatic oscillator system are disclosed. An adiabatic system is one that ideally transfers no heat outside of the system, thereby reducing the required operating power. The adiabatic resonator, which includes a plurality of tank circuits, acts as an energy reservoir, the missing aspect of previously attempted adiabatic computational systems. By using the adiabatic resonator as a feedback element with an amplifier, an adiabatic oscillator is formed. An adiabatic oscillator system is formed with a primary adiabatic oscillator feeding a plurality of secondary adiabatic oscillators. In this manner, the adiabatic oscillator system may be used to generate the multiple clock signals required of adiabatic computational logic elements, such as Split-level Charge Recovery Logic and 2-Level Adiabatic Logic. The adiabatic oscillator system stores enough energy to drive many individual adiabatic computational logic elements, permitting implementation of complex logic circuits.

Brocato, Robert W.↗
DOE OSTI2020

Flow-induced oscillation patterns for two tandem cylinders with turbulence stimulation and variable stiffness and damping

Herein, the oscillation patterns of two 1-DOF cylinder oscillators, undergoing VIV and galloping, are investigated in a free surface water channel for 3.2 × 104 ≤ Re ≤ 1.2 × 10 5 . The cylinders are arranged in tandem and supported by springs for a range of different spring stiffness and damping parameters. The efficiency of a current energy converter (CEC), based on flow-induced oscillation (FIO) of multiple cylinders in tandem, is critically related to the cylinder oscillation patterns. Due to the limited number of studies on the FIO for multiple cylindrical or prismatic bodies, their oscillation patterns have neither been identified nor classified. The surfaces of the cylinders are modified by turbulence stimulation to enhance FIO. Three different center-to-center spacing, five stiffness, and six damping ratios, for a total of 90 sets of experiments were conducted. The current velocity range is from 0.34 m/s to 1.32 m/s. From more than 2000 tests, five major patterns, nine sub-patterns are identified and classified. The patterns are defined based on the amplitudes, frequencies and the phase angle differences between the two cylinders. The characteristics and mechanics of each oscillation pattern are explored and explained from the perspective of fluid-structure interaction (FSI). By systematically varying the parameters, the underlying hydrodynamic mechanisms, including the coupling level between vortices and cylinders, the shielding effect, the wake effect, and the stability states are revealed. Few preliminary observations on the connection between oscillation pattern and harnessed power by the tandem cylinders are reported.

42 ENGINEERING↗
DOE OSTI2024

Forced Oscillation Source Location in Power Systems Using MVMD-assisted DEF in TF Plane

Fast and accurate forced oscillation source location (FOSL) is critical for mitigating forced oscillations in power systems. Here, to overcome the shortcomings of traditional dissipating energy flow (DEF) in decomposing the forced oscillation components from the measurement responses, a multivariate variational mode decomposition (MVMD)-assisted FOSL is proposed in this paper to locate the forced oscillation sources from measurements in time-frequency (TF) plane. The multi-channel measurement matrix of each generator is formed, then the multi-channel modes are decomposed from the formed multi-channel measurement matrix using the MVMD. Further, the intrinsic mode functions (IMFs) associated with the forced oscillation mode are distinguished from the decomposed modes according to the relative energy weights. With the distinguished IMFs, the MVMD-assisted DEF calculation method is developed to locate the forced oscillation source. Finally, the performance of the proposed method is evaluated using the simulation data of the WECC 179-bus test system and IEEE-NASPI Oscillation Source Location Contest as well as the actual PMU data of ISO New England. The results validated the effectiveness and accuracy of the proposed method in the FOSL.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Injection Locking of Gigahertz‐Frequency Surface Acoustic Wave Phononic Crystal Oscillator

Low-noise gigahertz (GHz) frequency sources are essential for applications in signal processing, sensing, and telecommunications. Surface acoustic wave (SAW) resonator-based oscillators offer compact form factors and low-phase noise due to their short mechanical wavelengths and high-quality (Q) factors. However, their small footprint makes them vulnerable to environmental variation, resulting in their poor long-term frequency stability. Injection locking is widely used to suppress frequency drift of lasers and oscillators by synchronizing to an ultra-stable reference. Here, injection locking of a 1-GHz SAW phononic-crystal oscillator is demonstrated, achieving 40-dB phase noise reduction at low offset frequencies and unperturbed low noise at large offset frequencies. Compared to a free-running SAW oscillator, which typically exhibits frequency drifts of several hundred hertz over minutes, the injection-locked oscillator reduces the frequency deviation to below 0.35 Hz. The locking range and oscillator dynamics is also investigated in the injection pulling region. The demonstrated injection-locked SAW oscillator could find applications in high-performance portable telecommunications and sensing systems.

injection locking↗
DOE OSTI2021

Synergistic data analytics for electromechanical oscillation in electric power systems

Accurate real-time estimation of the four electromechanical oscillation properties, i.e., dominant oscillation modes, mode shapes, participation factors, and coherent groups, is of great importance to assess and mitigate potential electromechanical oscillations in interconnected power systems. While eigenvalue analysis can realize such estimation, it requires precise linearized dynamic models and accurate parameters, which are highly difficult to obtain in practice. Data fusion-based modal estimation methods can extract the properties of electromechanical oscillations from measurement data without the power system model and parameters, but most of the time only one or two property assessments can be accomplished each time. To overcome this challenge, this paper presents a synergistic data analytics solution to characterize the dynamic behaviors of electromechanical oscillations from real-time measurement data. Here, the proposed method uses optimized variable projection, and it is capable of estimating all four electromechanical oscillation behavior properties from measured responses. Case studies are performed using the simulated measurement data of a 16-generator 68-bus test system and the field measurements collected by the PMUs deployed in the Yunnan Power Grid. The results demonstrate that the proposed synergistic data analytics solution can achieve satisfactory performance in capturing the properties of electromechanical oscillations from measurement data and exhibit strong robustness against measurement noise when compared with existing measurement-based methods.

42 ENGINEERING↗
DOE OSTI2013

Mechanism behind self-sustained oscillations in direct current glow discharges and dusty plasmas

An alternative explanation to the mechanism behind self-sustained oscillations of ions in direct current (DC) glow discharges is provided. Such description is distinguished from the one provided by the fluid models, where oscillations are attributed to the positive feedback mechanism associated with photoionization of particles and photoemission of electrons from the cathode. Here, oscillations arise as consequence of interaction between an ion and the surface charges induced by it at the bounding electrodes. Such mechanism provides an elegant explanation to why self-sustained oscillations occur only in the negative resistance region of the voltage-current characteristic curve in the DC glow discharges. Furthermore, this alternative description provides an elegant explanation to the formation of plasma fireballs in the laboratory plasma. It has been found that oscillation frequencies increase with ion's surface charge density, but at the rate which is significantly slower than it does with the electric field. The presented mechanism also describes self-sustained oscillations of ions in dusty plasmas, which demonstrates that self-sustained oscillations in dusty plasmas and DC glow discharges involve common physical processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Coupled-oscillator theory of dispersion and Casimir-Polder interactions

We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗