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At least 73 records · Page 4

The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions.

Ferguson, D. R.↗

Finite element solution of low bond number sloshing

The dynamics of liquid propellant in a low Bond number environment which are critical to the design of spacecraft systems with respect to orbital propellant transfer and attitude control system were investigated. Digital computer programs were developed for the determination of liquid free surface equilibrium shape, lateral slosh natural vibration mode shapes, and frequencies for a liquid in a container of arbitrary axisymmetric shape with surface tension forces the same order of magnitude as acceleration forces. A finite volume element representation of the liquid was used for the vibration analysis. The liquid free surface equilibrium shapes were computed for several tanks at various contact angles and ullage volumes. A configuration was selected for vibration analysis and lateral slosh mode shapes and natural frequencies were obtained. Results are documented.

Wohlen, R. L.↗

Structure of the atmosphere of Jupiter from Pioneer 10 and 11 radio occultation measurements

A technique for incorporating effects of the oblateness of Jupiter's atmosphere into the data analysis procedure for radio-occultation measurements is described which makes use of a spherical harmonic representation of the gravity field to compute the shape of the planet. With this technique, the center of refraction is located by the radius of curvature and the normal direction at the closest approach point of the ray. The present technique, a subsequent approximation involving the use of a constant center of refraction, and the Abel integral transform inversion method for spherical planets are applied to Pioneer 10 and 11 data. All the intermediate results obtained show a temperature inversion between 10 and 100 mb, with temperatures from 130 to 170 K at 10 mb and from 80 to 120 K at 100 mb. Comparison of the radio-occultation profiles with radiative-convective equilibrium models and the temperature profile based on Pioneer 10 IR radiometer data indicates good agreement between the models and the occultation results.

Kliore, A. J.↗

Icing testing in the large Modane wind-tunnel on full-scale and reduced scale models

Icing tests on full scale models of parts of aircraft (wings, tailplanes, radome) equipped with actual de-icing systems were carried out in the large Modane wind tunnel of ONERA. For studying icing on the Concorde, it was necessary to use a 1/6 scale half model. The equations governing the relevant parameter ratios to obtain reasonably good similitude water catching and ice accretion are recalled. Despite the inherent limitations of this particular kind of testing, i.e., the impossibility of duplicating both the Mach and Reynolds conditions for the main flow pattern, it is possible to obtain on a reduced scale model a reasonably good representation of icing cloud catching and of the shape of resulting ice accretion.

Charpin, F.↗

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗

Remote Sensing of Crystal Shapes in Ice Clouds

Ice crystals in clouds exist in a virtually limitless variation of geometries. The most basic shapes of ice crystals are columnar or plate-like hexagonal prisms with aspect ratios determined by relative humidity and temperature. However, crystals in ice clouds generally display more complex structures owing to aggregation, riming and growth histories through varying temperature and humidity regimes. Crystal shape is relevant for cloud evolution as it affects microphysical properties such as fall speeds and aggregation efficiency. Furthermore, the scattering properties of ice crystals are affected by their general shape, as well as by microscopic features such as surface roughness, impurities and internal structure. To improve the representation of ice clouds in climate models, increased understanding of the global variation of crystal shape and how it relates to, e.g., location, cloud temperature and atmospheric state is crucial. Here, the remote sensing of ice crystal macroscale and microscale structure from airborne and space-based lidar depolarization observations and multi-directional measurements of total and polarized reflectances is reviewed. In addition, a brief overview is given of in situ and laboratory observations of ice crystal shape as well as the optical properties of ice crystals that serve as foundations for the remote sensing approaches. Lidar depolarization is generally found to increase with increasing cloud height and to vary with latitude. Although this variation is generally linked to the variation of ice crystal shape, the interpretation of the depolarization remains largely qualitative and more research is needed before quantitative conclusions about ice shape can be deduced. The angular variation of total and polarized reflectances of ice clouds has been analyzed by numerous studies in order to infer information about ice crystal shapes from them. From these studies it is apparent that pristine crystals with smooth surfaces are generally inconsistent with the data and thus crystal impurity, distortion or surface roughness is prevalent. However, conclusions about the dominating ice shapes are often inconclusive and contradictory and are highly dependent on the limited selection of shapes included in the investigations. Since ice crystal optical properties are mostly determined by the aspect ratios of the crystal components and their microscale structure, it is advised that remote sensing applications focus on the variation of these ice shape characteristics, rather than on the macroscale shape or habit. Recent studies use databases with nearly continuous ranges of crystal component aspect ratio and-or roughness levels to infer the variation of ice crystal shape from satellite and airborne remote sensing measurements. Here, the rationale and results of varying strategies for the remote sensing of ice crystal shape are reviewed. Observed systematic variations of ice crystal geometry with location, cloud height and atmospheric state suggested by the data are discussed. Finally, a prospective is given on the future of the remote sensing of ice cloud particle shapes.

clouds↗

A Parametric Study of Fine-scale Turbulence Mixing Noise

The present paper is a study of aerodynamic noise spectra from model functions that describe the source. The study is motivated by the need to improve the spectral shape of the MGBK jet noise prediction methodology at high frequency. The predicted spectral shape usually appears less broadband than measurements and faster decaying at high frequency. Theoretical representation of the source is based on Lilley's equation. Numerical simulations of high-speed subsonic jets as well as some recent turbulence measurements reveal a number of interesting statistical properties of turbulence correlation functions that may have a bearing on radiated noise. These studies indicate that an exponential spatial function may be a more appropriate representation of a two-point correlation compared to its Gaussian counterpart. The effect of source non-compactness on spectral shape is discussed. It is shown that source non-compactness could well be the differentiating factor between the Gaussian and exponential model functions. In particular, the fall-off of the noise spectra at high frequency is studied and it is shown that a non-compact source with an exponential model function results in a broader spectrum and better agreement with data. An alternate source model that represents the source as a covariance of the convective derivative of fine-scale turbulence kinetic energy is also examined.

Khavaran, Abbas↗

Modeling concepts for communication of geometric shape data

ANSI5, an abbreviation for Section 5 of the American National Standard under Engineering Drawing and Related Documentation Practices (Committee Y14) on Digital Representation for Communication of Product Definition Data (ANSI Y14.26M-1981), allows encoding of a broad range of geometric shapes to be communicated through digital channels. A brief review of its underlying concepts is presented. The intent of ANSI5 is to devise a unified set of concise language formats for transmission of data pertaining to five types of geometric entities in Euclidean 3 space (E(3)). These are regarded as point like, curve like, surface like, solid like, and a combination of these types. For the first four types, ANSI5 makes a distinction between the geometry and topology. Geometry is a description of the spatial occupancy of the entity, and topology discusses the interconnectedness of the entity's boundary components.

Collins, M. F.↗

Mapping of the solar wind electric field on the earth's polar caps

A quantitative model of a magnetically interconnected (open) magnetosphere is developed as a perturbation of Voight's closed magnetosphere model with a given magnetopause shape. The model is shown to give a reasonable representation of the open magnetosphere configuration and is especially useful in testing the magnetospheric consequences of various merging theories. The convection pattern obtained for southward IMF is in reasonable agreement with observations, especially in the manifestation of a convection 'throat' near noon. For northward IMF, this region of constricted flow is rotated in local time in the direction of the IMF, also in accordance with observations.

Toffoletto, F. R.↗

Coupled Stochastic Time-Inverted Lagrangian Transport/Weather Forecast and Research/Vegetation Photosynthesis and Respiration Model: Simulations of Tower-Based and Airborne CO2 Measurements - Part II

This paper evaluates simulations of atmospheric CO2 measured in 2004 at continental surface and airborne receptors, intended to test the capability to use data with high temporal and spatial resolution for analyses of carbon sources and sinks at regional and continental scales. The simulations were performed using the Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by the Weather Forecast and Research (WRF) model, and linked to surface fluxes from the satellite-driven Vegetation Photosynthesis and Respiration Model (VPRM). The simulations provide detailed representations of hourly CO2 tower data and reproduce the shapes of airborne vertical profiles with high fidelity. WRF meteorology gives superior model performance compared with standard meteorological products, and the impact of including WRF convective mass fluxes in the STILT trajectory calculations is significant in individual cases. Important biases in the simulation are associated with the nighttime CO2 build-up and subsequent morning transition to convective conditions, and with errors in the advected lateral boundary condition. Comparison of STILT simulations driven by the WRF model against those driven by the Brazilian variant of the Regional Atmospheric Modeling System (BRAMS) shows that model-to-model differences are smaller than between an individual transport model and observations, pointing to systematic errors in the simulated transport. Future developments in the WRF model s data assimilation capabilities, basic research into the fundamental aspects of trajectory calculations, and intercomparison studies involving other transport models, are possible venues for reducing these errors. Overall, the STILT/WRF/VPRM offers a powerful tool for continental and regional scale carbon flux estimates.

Eluszkiewicz, Janusz↗

Shape Servoing of Deformable Objects Using Model Estimation and Barrier Lyapunov Function

An adaptive shape servoing control method is presented in this article to manipulate a deformable object into a desired shape in 3-D. A finite-point-based representation of the deformable object is used and the deformation Jacobian matrix is approximated using Fourier series basis functions. The unknown parameters of the deformation Jacobian are learned by using the velocity applied to a control point on the object and corresponding change of positions of the points describing the entire object. An integral concurrent learning (ICL)-based parameter update law is designed along with a constrained controller to satisfy the state constraints on the motion of the control point using Barrier Lyapunov function analysis. ICL-based parameter update law uses data history of velocity and corresponding positions of the points along with their current values. An efficient algorithm to update the history stack using singular value maximization is proposed based on the structure of the regressor matrix. Simulations using a physical simulator and experiments using a robot platform are performed to validate the performance of the proposed controller on two different deformable objects.

Vrithik Raj Guthikonda↗

Computational Characterization and Model Verification for 3D Microstructure Reconstruction of Additively-Manufactured Materials

The goal of this study is to characterize and validate the texture and grain topology of additively-manufactured anisotropic three-dimensional (3D) polycrystalline microstructures. The special focus is on developing methodologies to compare the grain shapes and orientations of two-dimensional (2D) and 3D microstructure representations using the same metric. To generate statistical data, synthetic microstructures are reconstructed from experimental data using Markov random field (MRF). The statistical similarity between the experimental and synthetic microstructures is verified by comparing their grain topologies. A universal measure to compare 2D and 3D grains is portrayed through the concept of image moments that are invariant to shape transformations. The graphical plots developed based on moment invariants to compare the 2D and 3D grains are used to verify the synthetic model

Materials Characterization↗

The Radiated Field Generated by a Monopole Source in a Short, Rigid, Rectangular Duct

This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.

Lakota, Barbara Anne↗

Calculations of the variability of ice cloud radiative properties at selected solar wavelengths

This study shows that there is surprising little difference in values of reflectance, absorptance, and transmittance for many of the intermediate-size particle spectra. Particle size distributions with mode radii ranging from approximately 50 to 300 microns, irrespective of particle shape and nearly independent of the choice of size distribution representation, give relatively similar flux values. The very small particle sizes, however, have significantly larger values of reflectance and transmittance with corresponding smaller values of absorptance than do the larger particle sizes. The very large particle modes produce very small values of reflectance and transmittance along with very large values of absorptance. Such variations are particularly noticeable when plotted as a function of wavelength.

Welch, R. M.↗

Nonlinear structural dynamics analysis using a modified modal method

The procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures which exhibit a stiffening behavior and to those with a softening behavior is presented.

Knight, N. F., Jr.↗

Surface generation and editing operations applied to structural support of aerospace vehicle fuselages

The Solid Modeling Aerospace Research Tool (SMART) is a computer aided design tool used in aerospace vehicle design. Modeling of structural components using SMART includes the representation of the transverse or cross-wise elements of a vehicle's fuselage, ringframes, and bulkheads. Ringframes are placed along a vehicle's fuselage to provide structural support and maintain the shape of the fuselage. Bulkheads are also used to maintain shape, but are placed at locations where substantial structural support is required. Given a Bezier curve representation of a cross sectional cut through a vehicle's fuselage and/or an internal tank, this project produces a first-guess Bezier patch representation of a ringframe or bulkhead at the cross-sectional position. The grid produced is later used in the structural analysis of the vehicle. The graphical display of the generated patches allows the user to edit patch control points in real time. Constraints considered in the patch generation include maintaining 'square-like' patches and placement of longitudinal, or lengthwise along the fuselage, structural elements called longerons.

Schwartz, Susan K.↗

Three-dimensional canard-wing shape optimization in aircraft cruise and maneuver environments

This paper demonstrates a numerical technique for canard-wing shape optimization at two operating conditions. For purposes of simplicity, a mean surface wing paneling code is employed for the aerodynamic calculations. The optimization procedures are based on the method of feasible directions. The shape functions for describing the thickness, camber, and twist are based on polynomial representations. The primary design requirements imposed restrictions on the canard and wing volumes and on the lift coefficients at the operating conditions. Results indicate that significant improvements in minimum drag and lift-to-drag ratio are possible with reasonable aircraft geometries. Calculations were done for supersonic speeds with Mach numbers ranging from 1 to 6. Planforms were mainly of a delta shape with aspect ratio of 1.

De Silva, B. M. E.↗

Decoupling in the Vertical Shape of HCHO During a Sea Breeze Event: the Effect on Trace Gas Satellite Retrievals and Column-to-Surface Translation

The effect of sea breeze circulation on stratification of the vertical formaldehyde (HCHO) concentration vertical profiles is explored using a regional atmospheric chemical transport model (CTM) for three synoptically stagnant days focused on the east coast of the U.S in June 2018. During this event, a significant thermal contrast between the Atlantic Ocean and the terrestrial regions (12–17 °C), observed by moderate resolution imaging spectroradiometer (MODIS) and well-captured by the WRF-CMAQ model (15–18 °C), is conducive to monsoon-like flow, perpendicular to the shorelines, carrying clean marine air masses over the land within a few hundreds of meters above the surface. In contrast, the westerly continental polluted air masses prevail in higher altitudes. These two conflicting flows result in atypical vertical shapes of HCHO concentrations increasing with altitude. This decoupling pattern is so pronounced that we observe total column HCHO negatively correlate with surface concentrations. Comparisons of an accredited global model, GEOS-CF, to surface wind measurements and MODIS skin temperature indicate its poor representation of the sea breeze timing and strength, resulting in GEOS-CF HCHO vertical shapes being drastically different from the WRF-CMAQ. Based on radiative transfer calculations, the differences in the vertical distribution of HCHO between the WRF-CMAQ and that of GEOS-CF in the first 3 km are sufficient to induce a 20–30% error in air mass factors (thus total vertical HCHO column abundances). Through an experiment involving converting HCHO total columns to surface mixing ratios, we demonstrate that GEOS-CF allocates noticeably more HCHO molecules (40–150%) to the surface layer due to the misrepresentation of the vertical shape of HCHO during the sea breeze event. It is known that a significant fraction of the human population lives in coastal areas prone to detrimental effects caused by air pollution, and elevated pollutant concentrations usually occur in synoptically stagnant atmospheric conditions when local circulation patterns come into play; accordingly, our experiments emphasize the importance of the effect a priori profiles can have on satellite-derived applications under such conditions. To ensure that the quantitative representation of satellite-based trace gas retrievals on a daily basis is trustworthy and useable for air quality applications, atmospheric models providing a priori profiles for satellite retrievals should be well-tuned to reproduce complex local circulation such as sea-land breezes.

sea breeze↗