Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “path integrals”

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 487 records · Page 27

A Model Predictive Control Approach for In-Flight Acoustic Constraint Compliance

Vehicle noise remains one of the major barriers to public acceptance of Urban Air Mobility-class aircraft. This work focuses on motion planning for aircraft in noise-sensitive areas. A nonlinear Model Predictive Path Integral (MPPI) control law is used to generate a finite-horizon trajectory that satisfies acoustic level constraints at a set of (three-dimensional) observer locations. The MPPI framework places no restrictions on the class of state-dependent cost functionals that can be employed, making it well-suited for use with sophisticated acoustic models and metrics, in addition to dynamic and mission-relevant constraints. The model predictive control architecture is also suitable for implementation in a real-time application. A simulation example demonstrates the ability of the controller to modify the flight trajectory in order to satisfy acoustic constraints at multiple measurement locations.

acoustically-aware vehicle↗

Retrieval Algorithm for the Column CO2 Mixing Ratio from Pulsed Multi-Wavelength Lidar Measurements

The retrieval algorithm for the column mixing ratio of CO2 from the measurements of a pulsed multi-wavelength integrated path differential absorption (IPDA) lidar is described. The lidar samples the shape of the 1572.33 nm CO2 absorption line at 15 or 30 wavelengths. The algorithm uses a least-squares fit between the CO2 line shape computed from a layered 10 atmosphere model to that sampled by the lidar. In addition to the column average CO2 dry air mole fraction (XCO2), several other parameters are also solved simultaneously from the fit. These include the Doppler shift in the received laser signal wavelengths, the product of the surface reflectivity and atmospheric transmission and a linear trend in the lidar receiver’s spectral response. The algorithm can also be used to solve for the average water vapor mixing ratio, which causes a secondary absorption in the wings of the CO2 absorption line under high humidity conditions. The least-squares fit is linearized about the 15 expected XCO2 value which allows the use of a standard linear least-squares fitting method and software tools. The standard deviation of the retrieved XCO2 is obtained from covariance matrix of the fit. An averaging kernel is defined similarly to that used for passive trace-gas sounding. Examples are presented of using the algorithm to retrieve XCO2 from the measurements from NASA Goddard’s airborne CO2 Sounder lidar made at a constant altitude and during spiral-down maneuvers.

Xiaoli Sun↗

A New Laser Transmitter for Methane and Water Vapor Measurements at 1.65 μm

Atmospheric methane trends over the last few years have been increasing at a rate of 7-12 parts per billion (ppb) per year after brief a pause in the first decade of this century. The reasons for the pause and subsequent increase remains unclear. Thus, there is a critical need for additional, precise and accurate methane observations to understand the natural and anthropogenic processes that drive the trends in atmospheric methane and to constrain its sources, and sinks. At NASA Goddard Space Flight Center (GSFC), in collaboration with Freedom Photonics Inc., we have been developing a lidar to measure atmospheric methane using Integrated Path Differential Absorption (IPDA) from an airborne platform as a precursor to a future space mission. In this paper we present the design of a laser transmitter operating at ~1651 nmbased on a newly developed Distributed Bragg Grating (DBR) seed laser and an Optical parametric oscillator (OPO). The DBR is rapidly step-tuned over the methane absorption at several discrete wavelengths. This multi-wavelength approach enables us to sample the entire methane lineshape and reduce systematic errors.

Atmospheric methane trends↗

1.6-μm Er:YGG Waveguide Amplifiers

We report on the fabrication and characterization of Er:YGG films suitable for waveguide amplifiers that could in principle be used in integrated path differential absorption lidar systems. Presented is our fabrication technique, comprising pulsed-laser-deposition growth of ~10 μm-thick crystalline films, their channeling via ultraprecision ductile dicing with a diamond-blade, producing optical quality facets and sidewalls, and amplifier performance. Net gain at 1572 nm and 1651 nm is obtained for the first time in Er-doped YGG waveguide amplifiers. Additionally, in a channel waveguide a maximum internal gain of 3.5 dB/cm at the 1533nm peak was realized. Recent crystal film quality improvements promise further performance enhancements needed for the intended application for high-peak power sources in the 1.6-μm spectral region targeting Earth observation systems for monitoring greenhouse gases.

greenhouse gases; planar waveguide amplifiers↗

Convective precipitation retrievals from space-borne dual frequency (Ka- and W-band) radar observations

The 2017 Decadal Survey highlighted Earth System Science themes, science and application questions that led to the inclusion aerosols (A), clouds, convection, and precipitation (CCP) in the list of designated observables (DOs) to be pursued within the decade following the survey. Multiple observing system architectures were considered during the NASA A-CCP study, and dual frequency Ka-W band radars have been identified as components of the most likely architectures due to their ability to significantly contribute to the achievement of the science objectives and their synergy with other essential instruments. We present an algorithm to estimate convective precipitation from dual frequency, Ka- and W-band, observations applicable to the observing system architectures considered in the A-CCP study. The algorithm is based on the radar profiling algorithm used within the operational NASA GPM combined algorithm but features an additional module that makes the retrieval problem well-posed in cases of severe attenuation and potential loss of signal below the freezing level. The additional module is developed from GPM combined retrievals and consists of a procedure that generates an ensemble of potential retrievals consistent with the portions of the Ka-band and W-band observation profiles above the noise level. The ensemble solution is refined based on estimates of Path Integrated Attenuation (PIA) from the Surface Reference Technique (SRT) and radiometric observations.

Mircea Grecu↗

GPM DPR Retrievals: Algorithm, Evaluation, and Validation

The primary goal of the Dual-frequency Precipitation Radar (DPR) aboard the Global Precipitation Measurement (GPM) core satellite is to infer precipitationrate and raindrop/particle size distributions (DSD/PSD). The focus of this paper is threefold: 1)description of the DPR retrieval algorithm that uses an adjustable relationship between rainrate (R) and the mass-weighted diameter (Dm) or an R-Dm relationship in solving for R and Dmsimultaneously; 2) evaluation of the DPR algorithm based on the physical simulationsthat employ measured DSD/PSD to understand the mechanism and errorcharacteristics of the retrieval method; 3) review of ground validation studies for theDPR product as well as analysis of the strengths and weaknesses of the ground radarand rain gauge/disdrometer validations. Overall, the DPR Version-6 algorithmprovides reasonably accurate estimates of R and Dm in rain. Non-uniformity in therain profile, however, tends to degrade the accuracy of the R and Dm estimates tosome extent as the range-independent assumption of the adjustable parameter () ofthe R-Dm relation is not able to fully account for natural variation of DSD in the verticalprofile. Underestimation of the DPR snow rate is found when compared with theindependent dual-frequency ratio (DFR) technique. This is possibly the result of theconstraint associated with the path integral attenuation (PIA)/differential PIA (dPIA)used in the DPR algorithm to find the best  and range-independent  assumption. Arange-variable  model, proposed in the DPR Version-7 algorithm, is expected toimprove rain and snow retrieval.

Liang Liao↗

Guidelines for Schlieren Systems at Langley Research Center

The original Langley Working Paper (LWP 448) published on July 27th, 1967, provided guidance to NASA Langley Research Center personnel on how to set up conventional path-integrated schlieren flow visualization systems and what pitfalls could be expected with such setups. The guidance and information contained in the document continues to be used for schlieren setups at NASA Langley Research Center to this day.

Schlieren↗

Airborne lidar measurements of atmospheric CO 2 column concentrations to cloud tops made during the 2017 ASCENDS/ABoVE campaign

We measured the column-averaged atmospheric CO 2 mixing ratio (XCO 2 ) to a variety of cloud tops with an airborne pulsed multi-wavelength integrated path differential absorption (IPDA) lidar during NASA's 2017 ASCENDS/ABoVE airborne campaign. Measurements of height-resolved atmospheric backscatter profiles allow this lidar to retrieve XCO 2 to cloud tops, as well as to the ground, with accurate knowledge of the photon path length. We validated these measurements with those from an onboard in situ CO 2 sensor during spiral-down maneuvers. These lidar measurements were 2–3 times better than those from previous airborne campaigns due to our using a wavelength step-locked laser transmitter and a high-efficiency detector for this campaign. Precisions of 0.6 parts per million (ppm) were achieved for 10 s average measurements to mid-level clouds and 0.9 ppm to low-level clouds at the top of the planetary boundary layer. This study demonstrates the lidar's capability to fill in XCO 2 measurement gaps in cloudy regions and to help resolve the vertical and horizontal distributions of atmospheric CO 2 . Future airborne campaigns and spaceborne missions with this capability can be used to improve atmospheric transport modeling, flux estimation and carbon data assimilation.

Jianping Mao↗

Zemax Modeling of a Self-aligned Focusing Schlieren System with Simulated Compressible Flow

A self-aligned focusing schlieren system is simulated in the ANSYS Zemax OpticStudio software environment. The model uses a custom scatter-defining dynamic link library on the retroreflective background in order to scatter rays in the direction of the incident ray rather than the specular ray. Simulated compressible flow refractive index fields are imported into Zemax by use of the grid gradient object and a workaround to the maximum point limit is introduced. The Ronchi ruling is built as a high resolution bitmap image in MATLAB and set in Zemax as a slide object allowing the bitmap image to either transmit or terminate rays at each line pair. The Zemax simulations are compared to computational numerical schlieren and experimental conventional, path-integrated schlieren results from a hypersonic stagnation point injection flow configuration and an experimental image of a shock wave from a laser-induced breakdown. In the stagnation point injection simulations, the Zemax schlieren images capture complex flow features such as the Mach disk, shear layers, contact surface, and bow shock well, but contains long, curved features (striations) between the model and the bow shock that are not present in the synthetic schlieren image from the CFD or the experimental image. The image from Zemax of the spark-induced shock wave captures the shape and curvature of the shock but appears blurry due to grid discretization in the computational data.

Nicholas A Mejia↗

Time Evolution in Quantum Cosmology

The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained using a gauge fixed path integral, as long as one does not integrate over proper time. Using this gauge fixed action we can construct a Hamiltonian in the coherent - or classical - state basis. We show that by construction the coherent states satisfy the classical dynamical equations of General Relativity. They do not satisfy the Hamiltonian constraint. A consequence of this is that the Wheeler-DeWitt equation should not be satisfied in quantum gravity. Classical states have a natural non-trivial time evolution since they are not eigenstates of the Hamiltonian. A general feature of the unconstrained quantum theory of gravity is the prediction of a pressureless dark matter component of either sign energy density in the classical universe which may lead to novel phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Classical Equations of Motion of Quantized Gauge Theories, Part I: General Relativity

In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or Hamiltonian formulation of general relativity allows for classical states that do not satisfy the full set of Einstein's equations. This amounts to loosening the Hamiltonian and momentum constraints that are imposed on the initial state. Nevertheless, the quantum theory permits gauge invariant time evolution of these states. The time evolution of these states is such that at the classical level the full set of Einstein's equations would appear to hold, with the physical effects of these states being attributable to an auxiliary, covariantly conserved energy-momentum tensor with no internal degrees of freedom. We derive the generalized Einstein equations for these states and show that a homogeneous and isotropic initial background state contributes to expansion identical to cold dark matter. The inhomogeneous components of this state could source curvature perturbations that grow linearly at linear order. This auxiliary contribution to Einstein's equations could have either sign and thus provide a trivial way to violate the null energy condition, enabling novel gravitational dynamics such as cosmic bounces and wormholes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Signal-to-noise improvement through neural network contour deformations for 3D $SU(2)$ lattice gauge theory

Complex contour deformations of the path integral have been demonstrated to significantly improve the signal-to-noise ratio of observables in previous studies of two-dimensional gauge theories with open boundary conditions. In this work, new developments based on gauge fixing and a neural network definition of the deformation are introduced, which enable an effective application to theories in higher dimensions and with generic boundary conditions. Improvements of the signal-to-noise ratio by up to three orders of magnitude for Wilson loop measurements are shown in $SU(2)$ lattice gauge theory in three spacetime dimensions.

Detmold, William↗

Integrative genomics reveals paths to sex dimorphism in Salix purpurea L

Sex dimorphism and gene expression were studied in developing catkins in 159 F 2 individuals from the bioenergy crop Salix purpurea , and potential mechanisms and pathways for regulating sex development were explored. Differential expression, eQTL, bisulfite sequencing, and network analysis were used to characterize sex dimorphism, detect candidate master regulator genes, and identify pathways through which the sex determination region (SDR) may mediate sex dimorphism. Eleven genes are presented as candidates for master regulators of sex, supported by gene expression and network analyses. These include genes putatively involved in hormone signaling, epigenetic modification, and regulation of transcription. eQTL analysis revealed a suite of transcription factors and genes involved in secondary metabolism and floral development that were predicted to be under direct control of the sex determination region. Furthermore, data from bisulfite sequencing and small RNA sequencing revealed strong differences in expression between males and females that would implicate both of these processes in sex dimorphism pathways. These data indicate that the mechanism of sex determination in Salix purpurea is likely different from that observed in the related genus Populus . This further demonstrates the dynamic nature of SDRs in plants, which involves a multitude of mechanisms of sex determination and a high rate of turnover.

59 BASIC BIOLOGICAL SCIENCES↗

Design of supercritical cascades with high solidity

The method of complex characteristics of Garabedian and Korn was successfully used to design shockless cascades with solidities of up to one. A code was developed using this method and a new hodograph transformation of the flow onto an ellipse. This code allows the design of cascades with solidities of up to two and larger turning angles. The equations of potential flow are solved in a complex hodograph like domain by setting a characteristic initial value problem and integrating along suitable paths. The topology that the new mapping introduces permits a simpler construction of these paths of integration.

Sanz, J. M.↗