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At least 1,063 records · Page 59

Modification of Eye Movements and Motion Perception during Off-Vertical Axis Rotation

Constant velocity Off-Vertical Axis Rotation (OVAR) imposes a continuously varying orientation of the head and body relative to gravity. The ensuing ocular reflexes include modulation of both torsional and horizontal eye movements as a function of the varying linear acceleration along the lateral plane, and modulation of vertical and vergence eye movements as a function of the varying linear acceleration along the sagittal plane. Previous studies have demonstrated that tilt and translation otolith-ocular responses, as well as motion perception, vary as a function of stimulus frequency during OVAR. The purpose of this study is to examine normative OVAR responses in healthy human subjects, and examine adaptive changes in astronauts following short duration space flight at low (0.125 Hz) and high (0.5 Hz) frequencies. Data was obtained on 24 normative subjects (14 M, 10 F) and 14 (13 M, 1F) astronaut subjects. To date, astronauts have participated in 3 preflight sessions (n=14) and on R+0/1 (n=7), R+2 (n= 13) and R+4 (n= 13) days after landing. Subjects were rotated in darkness about their longitudinal axis 20 deg off-vertical at constant rates of 45 and 180 deg/s, corresponding to 0.125 and 0.5 Hz. Binocular responses were obtained with video-oculography. Perceived motion was evaluated using verbal reports and a two-axis joystick (pitch and roll tilt) mounted on top of a two-axis linear stage (anterior-posterior and medial-lateral translation). Eye responses were obtained in ten of the normative subjects with the head and trunk aligned, and then with the head turned relative to the trunk 40 deg to the right or left of center. Sinusoidal curve fits were used to derive amplitude, phase and bias of the responses over several cycles at each stimulus frequency. Eye responses during 0.125 Hz OVAR were dominated by modulation of torsional and vertical eye position, compensatory for tilt relative to gravity. While there is a bias horizontal slow phase velocity (SPV), the modulation of horizontal and vergence SPV is negligible at this lower stimulus frequency. Eye responses during 0.5 Hz OVAR; however, are characterized by modulation of horizontal and vergence SPV, compensatory for translation in the lateral and sagittal planes, respectively. Neither amplitude nor bias velocities were significantly altered by head-on-trunk position. The phases of the ocular reflexes, on the other hand, shifted towards alignment with the head. During the lower frequency OVAR, subjects reported the perception of progressing along the edge of a cone. During higher frequency OVAR, subjects reported the perception of progressing along the edge of an upright cylinder. In contrast to the eye movements, the phase of both perceived tilt and translation motion is not altered by stimulus frequency. Preliminary results from astronaut data suggest that the ocular responses are not substantially altered by short-duration spaceflight. However, compared to preflight averages, astronauts reported greater amplitude of both perceived tilt and translation at low and high frequency, respectively, during early post-flight testing. We conclude that the neural processing to distinguish tilt and translation linear acceleration stimuli differs between eye movements and motion perception. The results from modifying head-on-trunk position are consistent with the modulation of ocular reflexes during OVAR being primarily mediated by the otoliths in response to the sinusoidally varying linear acceleration along the interaural and naso-occipital head axis. While the tilt and translation ocular reflexes appear to operate in an independent fashion, the timing of perceived tilt and translation influence each other. We conclude that the perceived motion path during linear acceleration in darkness results from a composite representation of tilt and translation inputs from both vestibular and somatosensory systems.

Wood, S. J.↗

Multispacecraft Observations of Solar Flare Particles in the Inner Heliosphere

For a number of impulsive solar particle events we examine variations of maximum intensities and times to maximum intensity as a function of longitude, using observations from the two Helios spacecraft and near the Earth. We find that electrons in the MeV range can be detected more than 80 deg. from the flare longitude, corresponding to a considerably wider "well connected" region than that (approx. 20 deg. half width) reported for He-3-rich impulsive solar events. This wide range and the decrease of peak intensities with increasing connection angle revive the concept of some propagation process in the low corona that has a diffusive nature. Delays to the intensity maximum are not systematically correlated with connection angles. We argue that interplanetary scattering parallel to the average interplanetary magnetic field, that varies with position in space, plays an important role in flare particle events. In a specific case variations of the time profiles with radial distance and with particle rigidity are used to quantitatively confirm spatial diffusion. For a few cases near the edges of the well connected region the very long times to maximum intensity might result from interplanetary lateral transport.

Wibberenz, G.↗

NASA Tech Briefs, November 2003

Topics covered include: Computer Program Recognizes Patterns in Time-Series Data; Program for User-Friendly Management of Input and Output Data Sets; Noncoherent Tracking of a Source of a Data-Modulated Signal; Software for Acquiring Image Data for PIV; Detecting Edges in Images by Use of Fuzzy Reasoning; A Timer for Synchronous Digital Systems; Prototype Parts of a Digital Beam-Forming Wide-Band Receiver; High-Voltage Droplet Dispenser; Network Extender for MIL-STD-1553 Bus; MMIC HEMT Power Amplifier for 140 to 170 GHz; Piezoelectric Diffraction-Based Optical Switches; Numerical Modeling of Nanoelectronic Devices; Organizing Diverse, Distributed Project Information; Eigensolver for a Sparse, Large Hermitian Matrix; Modified Polar-Format Software for Processing SAR Data; e-Stars Template Builder; Software for Acoustic Rendering; Functionally Graded Nanophase Beryllium/Carbon Composites; Thin Thermal-Insulation Blankets for Very High Temperatures; Prolonging Microgravity on Parabolic Airplane Flights; Device for Locking a Control Knob; Cable-Dispensing Cart; Foam Sensor Structures Would be Self-Deployable and Survive Hard Landings; Real-Gas Effects on Binary Mixing Layers; Earth-Space Link Attenuation Estimation via Ground Radar Kdp; Wedge Heat-Flux Indicators for Flash Thermography; Measuring Diffusion of Liquids by Common-Path Interferometry; Zero-Shear, Low-Disturbance Optical Delay Line; Whispering-Gallery Mode-Locked Lasers; Spatial Light Modulators as Optical Crossbar Switches; Update on EMD and Hilbert-Spectra Analysis of Time Series; Quad-Tree Visual-Calculus Analysis of Satellite Coverage; Dyakonov-Perel Effect on Spin Dephasing in n-Type GaAs; Update on Area Production in Mixing of Supercritical Fluids; and Quasi-Sun-Pointing of Spacecraft Using Radiation Pressure.

Source record↗

Fabrication of Feedhorn-Coupled Transition Edge Sensor Arrays for Measurement of the Cosmic Microwave Background Polarization

Characterization of the minute cosmic microwave background (CMB) polarization signature requires multi-frequency high-throughput precision instrument systems. We have previously described the detector fabrication of a 40 gigahertz focal plane and now describe the fabrication of a 37-element dual-polarization detector module for measurement of the CMB at 90 gigahertz. The 72-TES (Transition Edge Sensor)-based bolometers in each module are coupled to a niobium-based planar orthomode transducer with integrated band defining filters implemented in microstrip transmission line. A single crystal silicon dielectric substrate serves as microstrip dielectric and as a thermal link between the membrane isolated MoAu TES operating at 150 millikelvins and the heat bath. A short silicon leg between the heat bath and the TES bolometer is designed for ballistic phonon transport and provides improved process control and uniformity of thermal conductance in the presence of phonon scattering on roughened surfaces. Micro-machined structures are used to realize the orthomode transducer backshort, provide out of band signal rejection, and a silicon photonic choke for feedhorn coupling are described. The backshort, choke wafer, and detector wafer are indium bump-bonded to create a single 37-element dual-polarization detector module. Fourteen such hexagonally shaped modules each 80 millimeters in size comprise two focal planes. These, along with the recently delivered 40 gigahertz focal plane, will survey a large fraction of the sky as part of the Johns Hopkins University-led ground-based CLASS (Cosmology Large Angular Scale Surveyor) telescope.

Detectors↗

Measurements of noise produced by flow past lifting surfaces

Wind tunnel studies have been conducted to determine the specific locations of aerodynamic noise production within the flow field about various lifting-surface configurations. The models tested included low aspect ratio shapes intended to represent aircraft flaps, a finite aspect ratio NACA 0012 wing, and a multi-element wing section consisting of a main section, a leading edge flap, and dual trailing edge flaps. Turbulence was induced on the models by surface roughness. Lift and drag were measured for the flap models. Hot-wire anemometry was used for study of the flap-model vortex roll-up. Apparent noise source distributions were measured by use of a directional microphone system, located outside the tunnel, which was scanned about the flow region to be analyzed under computer control. These distributions exhibited a diversity of pattern, suggesting that several flow processes are important to lifting-surface noise production. Speculation concerning these processes is offered.

Kendall, J. M.↗

Numerical modeling of chemical vapor deposition (CVD) in a horizontal reactor

In the present numerical prediction of the deposition rate of silicon from silane in a CVD process, the conservation equations for mass, momentum, energy, and chemical species are solved on a staggered grid using the SIMPLE algorithm, while the rate of chemical reactions in the gas phase and on the susceptor surface is obtained from an Arrhenius rate equation. Predicted deposition rates as a function of position along the susceptor with and without the gas phase chemical reaction are compared with the available experimental and numerical data; agreement is excellent except at the leading edge of the susceptor, where the deposition rate is overpredicted.

Sheikholeslami, M. Z.↗

Subband/transform functions for image processing

Functions for image data processing written for use with the MATLAB(TM) software package are presented. These functions provide the capability to transform image data with block transformations (such as the Walsh Hadamard) and to produce spatial frequency subbands of the transformed data. Block transforms are equivalent to simple subband systems. The transform coefficients are reordered using a simple permutation to give subbands. The low frequency subband is a low resolution version of the original image, while the higher frequency subbands contain edge information. The transform functions can be cascaded to provide further decomposition into more subbands. If the cascade is applied to all four of the first stage subbands (in the case of a four band decomposition), then a uniform structure of sixteen bands is obtained. If the cascade is applied only to the low frequency subband, an octave structure of seven bands results. Functions for the inverse transforms are also given. These functions can be used for image data compression systems. The transforms do not in themselves produce data compression, but prepare the data for quantization and compression. Sample quantization functions for subbands are also given. A typical compression approach is to subband the image data, quantize it, then use statistical coding (e.g., run-length coding followed by Huffman coding) for compression. Contour plots of image data and subbanded data are shown.

Glover, Daniel↗

Numerical prediction of transition of the F-16 wing at supersonic speeds

A parametric study is being conducted as an effort to numerically predict the extent of natural laminar flow (NLF) on finite swept wings at supersonic speeds. This study is one aspect of a High Speed Research Program (HSRP) to gain an understanding of the technical requirements for high-speed aircraft flight. The parameters that are being addressed in this study are Reynolds number, angle of attack, and leading-edge wing sweep. These parameters were analyzed through the use of an advanced Computational Fluid Dynamics (CFD) flow solver, specifically the ARC 3-D Compressible Navier-Stokes (CNS) flow solver. From the CNS code, pressure coefficients (Cp) are obtained for the various cases. These Cp's are then used to compute the boundary-layer profiles through the use of the 'Kaups and Cebeci' compressible 2-D boundary layer code. Finally, the boundary-layer parameters are processed into a 3-D compressible boundary layer stability code (COSAL) to predict transition. The parametric study then consisted of four geometries which addressed the effects of sweep, and three angles of attack from zero to ten degrees to yield a total of 12 cases. The above process was substantially automated through a procedure that was developed by the work conducted under this study. This automation procedure then yields a 3-D graphical measure of the extent of laminar flow by predicting the transition location of laminar to turbulent flow.

Cummings, Russell M.↗

PVD TBC experience on GE aircraft engines

The higher performance levels of modern gas turbine engines present significant challenges in the reliability of materials in the turbine. The increased engine temperatures required to achieve the higher performance levels reduce the strength of the materials used in the turbine sections of the engine. Various forms of thermal barrier coatings (TBC's) have been used for many years to increase the reliability of gas turbine engine components. Recent experience with the physical vapor deposition (PVD) process using ceramic material has demonstrated success in extending the service life of turbine blades and nozzles. Engine test results of turbine components with a 125 micron (0.005 in) PVD TBC have demonstrated component operating temperatures of 56-83 C (100-150 F) lower than non-PVD TBC components. Engine testing has also revealed the TBC is susceptible to high angle particle impact damage. Sand particles and other engine debris impact the TBC surface at the leading edge of airfoils and fracture the PVD columns. As the impacting continues, the TBC erodes away in local areas. Analysis of the eroded areas has shown a slight increase in temperature over a fully coated area, however a significant temperature reduction was realized over an airfoil without TBC.

Antonio Maricocchi↗

User Manual for Beta Version of TURBO-GRD: A Software System for Interactive Two-Dimensional Boundary/ Field Grid Generation, Modification, and Refinement

TURBO-GRD is a software system for interactive two-dimensional boundary/field grid generation. modification, and refinement. Its features allow users to explicitly control grid quality locally and globally. The grid control can be achieved interactively by using control points that the user picks and moves on the workstation monitor or by direct stretching and refining. The techniques used in the code are the control point form of algebraic grid generation, a damped cubic spline for edge meshing and parametric mapping between physical and computational domains. It also performs elliptic grid smoothing and free-form boundary control for boundary geometry manipulation. Internal block boundaries are constructed and shaped by using Bezier curve. Because TURBO-GRD is a highly interactive code, users can read in an initial solution, display its solution contour in the background of the grid and control net, and exercise grid modification using the solution contour as a guide. This process can be called an interactive solution-adaptive grid generation.

Choo, Yung K.↗

High T(sub c) Superconducting Bolometer on Chemically Etched 7 Micrometer Thick Sapphire

A transition-edge IR detector, using a YBa2Cu3O(7-x) (YBCO) thin film deposited on a chemically etched, 7 micrometer thick sapphire substrate has been built. To our knowledge it is the first such high T(sub c) superconducting (HTS) bolometer on chemically thinned sapphire. The peak optical detectivity obtained is l.2 x 10(exp 10) cmHz(sup 1/2)/W near 4Hz. Result shows that it is possible to obtain high detectivity with thin films on etched sapphire with no processing after the deposition of the YBCO film. We discuss the etching process and its potential for micro-machining sapphire and fabricating 2-dimensional detector arrays with suspended sapphire membranes. A 30 micrometer thick layer of gold black provided IR absorption. Comparison is made with the current state of the art on silicon substrates.

Lakew, B.↗

Moonshine Versus Earthshine: Physics Makes a Difference

Introduction: Recently released, high-resolution images from the Mars Orbiter Camera (MOC) and the Thermal Emission Imaging System (THEMIS) reveal a myriad of intriguing landforms banked along the northern edge of Terby Crater located on the northern rim of Hellas (approx.28degS, 287degW). Landforms within this crater include north-trending troughs and ridges, a remarkable 2.5 km-thick sequence of exposed layers, mantled ramps that extend across and between layered sequences, fan-like structures, sinuous channels, collapse pits, a massive landslide and viscous flow features. The suite of diverse landforms in Terby and its immediate surroundings attest to a diversity of rock types and geologic processes, making this locality ideal for studying landform-climate relationships on Mars. In order to decipher the complicated geologic history of Terby Crater and the nature of the layered deposits, a generalized geomorphic map was created and the slope of the layered deposits was examined.

Wilson, T. L.↗

Shuttle Damage/Repair from the Perspective of Hypersonic Boundary Layer Transition - Experimental Results

An overview is provided of the experimental wind tunnel program conducted at the NASA Langley Research Center Aerothermodynamics Laboratory in support of an agency-wide effort to prepare the Shuttle Orbiter for Return-to-Flight. The effect of an isolated protuberance and an isolated rectangular cavity on hypersonic boundary layer transition onset on the windward surface of the Shuttle Orbiter has been experimentally characterized. These experimental studies were initiated to provide a protuberance and cavity effects database for developing hypersonic transition criteria to support on-orbit disposition of thermal protection system damage or repair. In addition, a synergistic experimental investigation was undertaken to assess the impact of an isolated mass-flow entrainment source (simulating pyrolysis/outgassing from a proposed tile repair material) on boundary layer transition. A brief review of the relevant literature regarding hypersonic boundary layer transition induced from cavities and localized mass addition from ablation is presented. Boundary layer transition results were obtained using 0.0075-scale Orbiter models with simulated tile damage (rectangular cavities) of varying length, width, and depth and simulated tile damage or repair (protuberances) of varying height. Cavity and mass addition effects were assessed at a fixed location (x/L = 0.3) along the model centerline in a region of near zero pressure gradient. Cavity length-to-depth ratio was systematically varied from 2.5 to 17.7 and length-to-width ratio of 1 to 8.5. Cavity depth-to-local boundary layer thickness ranged from 0.5 to 4.8. Protuberances were located at several sites along the centerline and port/starboard attachment lines along the chine and wing leading edge. Protuberance height-to-boundary layer thickness was varied from approximately 0.2 to 1.1. Global heat transfer images and heating distributions of the Orbiter windward surface using phosphor thermography were used to infer the state of the boundary layer (laminar, transitional, or turbulent). Test parametrics include angles-of-attack of 30 deg and 40 deg, sideslip angle of 0 deg, freestream Reynolds numbers from 0.02x106 to 7.3x106 per foot, edge-to-wall temperature ratio from 0.4 to 0.8, and normal shock density ratios of approximately 5.3, 6.0, and 12 in Mach 6 air, Mach 10 air, and Mach 6 CF4, respectively. Testing to simulate the effects of ablation from a proposed tile repair concept indicated that transition was not a concern. The experimental protuberance and cavity databases highlighted in this report were used to formulate boundary layer transition correlations that were an integral part of an analytical process to disposition observed Orbiter TPS damage during STS- 114.

Horvath, Thomas J.↗

Preliminary Geological Map of the Fortuna Tessera (V-2) Quadrangle, Venus

The Fortuna Tessera quadrangle (50-75 N, 0-60 E) is a large region of tessera [1] that includes the major portion of Fortuna and Laima Tesserae [2]. Near the western edge of the map area, Fortuna Tessera is in contact with the highest moun-tain belt on Venus, Maxwell Montes. Deformational belts of Sigrun-Manto Fossae (extensional structures) and Au ra Dorsa (contractional structures) separate the tessera regions. Highly deformed terrains correspond to elevated regions and mildly deformed units are with low-lying areas. The sets of features within the V-2 quadrangle permit us to address the following important questions: (1) the timing and processes of crustal thickening/thinning, (2) the nature and origin of tesserae and deformation belts and their relation to crustal thickening processes, (3) the existence or absence of major evolutionary trends of volcanism and tectonics. The key feature in all of these problems is the regional sequence of events. Here we present description of units that occur in the V-2 quadrangle, their regional correlation chart (Fig. 1), and preliminary geological map of the region (Fig. 2).

Ivanov, M. A.↗

Using PHP/MySQL to Manage Potential Mass Impacts

This paper presents a new application using commercially available software to manage mass properties for spaceflight vehicles. PHP/MySQL(PHP: Hypertext Preprocessor and My Structured Query Language) are a web scripting language and a database language commonly used in concert with each other. They open up new opportunities to develop cutting edge mass properties tools, and in particular, tools for the management of potential mass impacts (threats and opportunities). The paper begins by providing an overview of the functions and capabilities of PHP/MySQL. The focus of this paper is on how PHP/MySQL are being used to develop an advanced "web accessible" database system for identifying and managing mass impacts on NASA's Ares I Upper Stage program, managed by the Marshall Space Flight Center. To fully describe this application, examples of the data, search functions, and views are provided to promote, not only the function, but the security, ease of use, simplicity, and eye-appeal of this new application. This paper concludes with an overview of the other potential mass properties applications and tools that could be developed using PHP/MySQL. The premise behind this paper is that PHP/MySQL are software tools that are easy to use and readily available for the development of cutting edge mass properties applications. These tools are capable of providing "real-time" searching and status of an active database, automated report generation, and other capabilities to streamline and enhance mass properties management application. By using PHP/MySQL, proven existing methods for managing mass properties can be adapted to present-day information technology to accelerate mass properties data gathering, analysis, and reporting, allowing mass property management to keep pace with today's fast-pace design and development processes.

Hager, Benjamin I.↗

Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This proposal describes an approach to validate the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft. The research described here is absolutely cutting edge. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional"validation by test only'' mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computationaf Fluid Dynamics can be used to veritY these requirements; however, the model must be validated by test data. The proposed research project includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT and OPEN FOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid . . . Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. To date, the author is the only person to look at the uncertainty in the entire computational domain. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Groves, Curtis E.↗

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

Joanna N Schmidt↗

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

robust design↗