Path-integrals in dynamics
Path integrals in dynamics - quantum mechanics and classical wave motion in one dimension
CLASSICAL MECHANICS↗
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Results for “Path integrals”
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Path-integrated growth of auroral kilometric radiation
Using Poeverlein's graphical method, three dimensional ray path calculations are performed to evaluate the path-integrated growth of auroral kilometric radiation (AKR). The ray tracing results indicate that waves whose initial wave vector lie in the local meridian plane continue to propagate in that plane and that among these waves, those with frequencies near the cutoff frequency (f sub R = 0) refract substantially, where as those with frequencies well above the cutoff frequency suffer little refraction. It is also shown that waves whose initial wave vector lie outside of the local meridian plane propagate in the longitudinal as well as the radial and the latitudinal directions. The refraction of these waves is also highly dependent upon the wave frequency, i.e., waves with frequencies near f sub R = 0 refract substantially, whereas waves with frequencies much above f sub R = 0 undergo little refraction. In order to test the electron cyclotron maser mechanisms as a method for generation of AKR, a typical electron distribution function measured in the auroral zone by the S3-3 satellite, is used to calculate path-integrated growths of representative rays. The results of this study indicate that electron distribution functions like those measured by the S3-3 satellite are not capable of amplifying cosmic noise background to the observed intensities of auroral kilometric radiation, and that much steeper slopes at the edges of the loss cone are required. The presence of such distribution functions in the auroral zone is plausible if one assumes that backscattered electrons in this region have energies less than a few hundred eV.
Omidi, N.↗
Intensity moments by path integral techniques for wave propagation through random media, with application to sound in the ocean
A theory is developed which describes intensity moments for wave propagation through random media. It is shown using the path integral technique that these moments are significantly different from those of a Rayleigh distribution in certain asymptotic regions. The path integral approach is extended to inhomogeneous, anisotropic media possessing a strong deterministic velocity profile. The behavior of the corrections to Rayleigh statistics is examined, and it is shown that the important characteristics can be attributed to a local micropath focusing function. The correction factor gamma is a micropath focusing parameter defined in terms of medium fluctuations. The value of gamma is calculated for three ocean acoustic experiments, using internal waves as the medium fluctuations. It is found that all three experiments show excellent agreement as to the relative values of the intensity moments. The full curved ray is found to yield results that are significantly different from the straight-line approximations. It is noted that these methods are applicable to a variety of experimental situations, including atmospheric optics and radio waves through plasmas.
Bernstein, D. R.↗
Self-Calibration and Laser Energy Monitor Validations for a Double-Pulsed 2-Micron CO2 Integrated Path Differential Absorption Lidar Application
Double-pulsed 2-micron integrated path differential absorption (IPDA) lidar is well suited for atmospheric CO2 remote sensing. The IPDA lidar technique relies on wavelength differentiation between strong and weak absorbing features of the gas normalized to the transmitted energy. In the double-pulse case, each shot of the transmitter produces two successive laser pulses separated by a short interval. Calibration of the transmitted pulse energies is required for accurate CO2 measurement. Design and calibration of a 2-micron double-pulse laser energy monitor is presented. The design is based on an InGaAs pin quantum detector. A high-speed photo-electromagnetic quantum detector was used for laser-pulse profile verification. Both quantum detectors were calibrated using a reference pyroelectric thermal detector. Calibration included comparing the three detection technologies in the single-pulsed mode, then comparing the quantum detectors in the double-pulsed mode. In addition, a self-calibration feature of the 2-micron IPDA lidar is presented. This feature allows one to monitor the transmitted laser energy, through residual scattering, with a single detection channel. This reduces the CO2 measurement uncertainty. IPDA lidar ground validation for CO2 measurement is presented for both calibrated energy monitor and self-calibration options. The calibrated energy monitor resulted in a lower CO2 measurement bias, while self-calibration resulted in a better CO2 temporal profiling when compared to the in situ sensor.
Refaat, Tamer F.↗
Path integrals and Liapunov functionals.
Liapunov functionals for time delay systems by path integrals in state space, using convolution equations involving distributions with compact support
Gruber, M.↗
Path integrals and Lyapunov functionals
Liapunov functionals for time delay systems generated by path integrals in state space in terms of convolution equations
Gruber, M.↗
Squeezed states and path integrals
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
Daubechies, Ingrid↗
A 2-Micron Pulsed Integrated Path Differential Absorption Lidar Development For Atmospheric CO2 Concentration Measurements
A 2-micron pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This instrument will provide an alternate approach to measure atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement.
Yu, Jirong↗
Path integrals, Liapunov functions, and quadratic minimization.
Nonlinear DC circuits analyzed by digital computer for application to path integrals and stability problems
SYSTEM STABILITY↗
Path integrals, differential renormalization-group, and stochastic systems near criticality
It is demonstrated, using the techniques of path integrals and renormalization-group, that nonlinear stochastic systems near criticality (including self-organized criticality) generally exhibit low-dimensional behavior. The symmetry which characterizes a particular criticality can be broken by the appearance of relevant scaling fields. A connection is made between the fractal dimensions of finite-dimensional chaotic systems and the anomalous dimensions in stochastic systems near criticality. The effect of additional random noise on stochastic systems is also delineated.
Chang, Tom↗
Path Planning: Differential Dynamic Programming and Model Predictive Path Integral Control on VTOL Aircraft
This paper explores two optimal control approaches, widely used in robotics, to establish their viability as real-time trajectory planners for vehicle configurations envisioned for the emerging aviation sector of Urban Air Mobility (UAM). Differential Dynamic Programming (DDP) enables planning over highly nonlinear dynamics using second-order approximations along a nominal trajectory, and displays quadratic convergence to a local solution. Model Predictive Path Integral (MPPI) is a stochastic sampling-based algorithm that can optimize for general cost criteria, including potentially highly nonlinear formulations, and supports parallel computation through the use of modern GPU hardware. In this work, DDP and MPPI were implemented using model predictive control (MPC), and the results indicate they are able to successfully transition the aircraft over different flight envelopes and generate trajectories unique to UAM vehicles.
Differential Dynamic Programming↗
Airborne Demonstration of Atmospheric Oxygen Optical Depth Measurements with an Integrated Path Differential Absorption Lidar
We report on an airborne demonstration of atmospheric oxygen (O2) optical depth measurements with an Integrated Path Differential Absorption (IPDA) lidar using a fiber-based laser transmitter and photon counting detectors. Accurate atmospheric temperature and pressure measurements are needed for NASA's Active Sensing of CO2 Emissions over Nights, Days and Seasons (ASCENDS) mission. Since O2 is uniformly mixed in the atmosphere, its spectrum can be used to estimate the dry mixing ratio of CO2. In its airborne configuration, the IPDA lidar uses an Erbium Doped Fiber amplifier, a frequency doubler and single photon counting detectors to measure O2 absorption at multiple wavelengths near 765 nm. This instrument was deployed in 2013 and 2014 aboard NASA's DC-8 airborne laboratory as part of two campaigns to measure CO2 mixing ratios over a wide range of topography and weather conditions from altitudes ranging between 3 km and 13 km. In this paper we will review a summary of the results from our flights, discuss the errors that limit the precision and accuracy of the measurement and identify possible areas of improvement.
Methane↗
Path-Integrated Attenuation from Airborne X-Band Radar and Passive Radiometer Measurements: Implication for Rainfall Measurements
This study compares path-integrated attenuation (PIA), in precipitation over the ocean, derived from a single-frequency X-band radar, using the surface reference technique (SRT), with that deduced from a radiometer also operating at X band. The data were collected during TRMM field campaigns. The PIA derived from radar using the SRT does not involve any assumptions regarding the precipitation but it assumes that the cross-section of the surface is stable, that is, it is not significantly altered by factors such as surface roughness. The PIA deduced from the radiometer, however, involves assumptions regarding the temperature and emissivity of the surface and absorption and scattering by the intervening precipitation, which in turn depend upon the size, concentration and composition of the precipitation particles. The comparison of the PIA from the two instruments serves not only as a check between the radar and the radiometer but also may yield insights into the structure of the intervening precipitation. Such study can provide valuable information for TRMM in which both radar and radiometers are used for rain measurements. The radiometer PIA was first deduced from the brightness temperature using a simple one-layer radiative transfer model assuming no scattering, an isothermal atmosphere. The initial results show a general agreement between the PIAs deduced from the two instruments. Largo disagreement was found at high values of PIAs that may have been caused saturation of the X-band brightness temperature or by uncertainties in wind roughening of the sea surface that affects the SRT. Further results including the effects of scattering and a non-isothermal atmosphere will be shown at the conference.
Tian, Lin↗
Error Reduction Methods for Integrated-path Differential-absorption Lidar Measurements
We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log".
averging before log↗
Development of an Airborne Triple-Pulse 2-Micron Integrated Path Differential Absorption Lidar (IPDA) for Simultaneous Airborne Column Measurements of Carbon Dioxide and Water Vapor in the Atmosphere
This presentation will provide status and details of an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar being developed at NASA Langley Research Center with support from NASA ESTO Instrument Incubator Program. The development of this active optical remote sensing IPDA instrument is targeted for measuring both atmospheric carbon dioxide and water vapor in the atmosphere from an airborne platform. This presentation will focus on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of seed laser locking, wavelength control, receiver and detector upgrades, laser packaging and lidar integration. Future plan for IPDA lidar system for ground integration, testing and flight validation will also be presented.
Singh, Upendra N.↗
Measurement of Rainfall Path Integrated Attenuation at Nadir: A Comparison of Radar and Radiometer Methods at 13.8GHz
An approach for reducing the ambiguity in the retrieved rainfall profile from spaceborne rain radar is to use the path integrated attenuation as a constraint.
radar surface reference technique microwave radiom↗
Imaginary time path integral Monte Carlo route to rate coefficients for nonadiabatic barrier crossing
Nonadiabatic transitions are central to many areas of chemical and condensed matter physics, ranging from biological electron transfer to the optical properties of one-dimensional conductors. Here, a path integral Monte Carlo method is used to simulate such transitions, based on the observation that nonadiabatic rate coefficients are often dominated by saddle point trajectories that correspond to an imaginary time. Simple analytic theories can be used to continue these imaginary time correlation functions to determine rate coefficients. The advantages and drawbacks of this approach are discussed.
Wolynes, Peter G.↗
Integrated Path Differential Absorption Lidar Optimizations Based on Pre-Analyzed Atmospheric Data for ASCENDS Mission Applications
In this paper a modeling method based on data reductions is investigated which includes pre analyzed MERRA atmospheric fields for quantitative estimates of uncertainties introduced in the integrated path differential absorption methods for the sensing of various molecules including CO2. This approach represents the extension of our existing lidar modeling framework previously developed and allows effective on- and offline wavelength optimizations and weighting function analysis to minimize the interference effects such as those due to temperature sensitivity and water vapor absorption. The new simulation methodology is different from the previous implementation in that it allows analysis of atmospheric effects over annual spans and the entire Earth coverage which was achieved due to the data reduction methods employed. The effectiveness of the proposed simulation approach is demonstrated with application to the mixing ratio retrievals for the future ASCENDS mission. Independent analysis of multiple accuracy limiting factors including the temperature, water vapor interferences, and selected system parameters is further used to identify favorable spectral regions as well as wavelength combinations facilitating the reduction in total errors in the retrieved XCO2 values.
Pliutau, Denis↗