Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Quarter Two”

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 559 records · Page 31

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗

Switched steerable multiple beam antenna system

A steerable multibeam five element cross-feed cluster antenna system is described. The feed power is divided into five branches. Each branch includes a switching network comprised of a plurality of time delay elements each individually controlled by a respective electromagnetic latching switch. Frequency independent individual two-dimensional beam steering at intermediate (IF) scanning frequencies is thereby provided wherein discrete incremental time delays are introduced by the switching networks into each branch and the signals recombined thereafter to form each beam. The electromagnetic latched switching reduces power consumption and permits higher power switching and reciprocal coincident tranmsit and receive operation. Frequency independence due to incremental time delay switching permits coincident reciprocal operation and steering for transmit-receive signal paths carrying different transmit-receive frequencies. Diagonal quarter wave plates in the waveguides alter polarization from the circular to orthogonal linear to provide transmitter-receiver isolation.

Richard S Iwasaki↗

Risk to civilization: A planetary science perspective

One of the most profound changes in our perspective of the solar system resulting from the first quarter century of planetary exploration by spacecraft is the recognition that planets, including Earth, were bombarded by cosmic projectiles for 4.5 aeons and continue to be bombarded today. Although the planetary cratering rate is much lower now than it was during the first 0.5 aeons, sizeable Earth-approaching asteroids and comets continue to hit the Earth at a rate that poses a finite risk to civilization. The evolution of this planetary perspective on impact cratering is gradual over the last two decades. It took explorations of Mars and Mercury by early Mariner spacecraft and of the outer solar system by the Voyagers to reveal the significance of asteroidal and cometary impacts in shaping the morphologies and even chemical compositions of the planets. An unsettling implication of the new perspective is addressed: the risk to human civilization. Serious scientific attention was given to this issue in July 1981 at a NASA-sponsored Spacewatch Workshop in Snowmass, Colorado. The basic conclusion of the 1981 NASA sponsored workshop still stands: the risk that civilization might be destroyed by impact with an as-yet-undiscovered asteroid or comet exceeds risk levels that are sometimes deemed unacceptable by modern societies in other contexts. Yet these impact risks have gone almost undiscussed and undebated. The tentative quantitative assessment by some members of the 1981 workshop was that each year, civilization is threatened with destruction with a probability of about 1 in 100,000. The enormous spread in risk levels deemed by the public to be at the threshold of acceptability derives from a host of psychological factors that were widely discussed in the risk assessment literature. Slovic shows that public fears of hazards are greatest for hazards that are uncontrollable, involuntary, fatal, dreadful, globally catastrophic, and which have consequences that seem inequitable, especially if they affect future generations.

Chapman, Clark R.↗

Comparative Soot Diagnostics: Preliminary Results

The motivation for the Comparative Soot Diagnostics (CSD) experiment lies in the broad practical importance of understanding combustion generated particulate. Depending upon the circumstances, particulate matter can affect the durability and performance of combustion equipment, can be a pollutant, can be used to detect fires and, in the form of soot, can be the dominant source of radiant energy from flames. The nonbuoyant structure of most flames of practical interest makes understanding of soot processes in low gravity flames important to our ability to predict fire behavior on earth. These studies also have direct applications to fire safety in human-crew spacecraft, since smoke is the indicator used for automated detection in current spacecraft. In the earliest missions (Mercury, Gemini and Apollo), the crew quarters were so cramped that it was considered reasonable that the astronauts would rapidly detect any fire. The Skylab module, however, included approximately 20 UV-sensing fire detectors. The Space Shuttle has 9 particle-ionization smoke detectors in the mid-deck and flight deck and Spacelab has six additional particle-ionization smoke detectors. The designated detectors for the ISS are laser-diode, forward-scattering, smoke or particulate detectors. Current plans for the ISS call for two detectors in the open area of the module, and detectors in racks that have both cooling air flow and electrical power. Due to the complete absence of data concerning the nature of particulate and radiant emission from incipient and fully developed low-g fires, all three of these detector systems were designed based upon l-g test data and experience. As planned mission durations and complexity increase and the volume of spacecraft increases, the need for and importance of effective, crew-independent, fire detection grows significantly. To provide this level of protection, more knowledge is needed concerning low-gravity fire phenomena and, in particular, how they might be detected and suppressed. Prior to CSD, no combustion-generated particulate samples had been collected near the flame zone for well-developed microgravity flames. All of the extant data either came from drop tower tests and therefore only corresponded to the early stages of a fire or were collected far from the flame zone. The fuel sources in the drop tower tests were restricted to laminar gas-jet diffusion flames and very rapidly overheated wire insulation. The gas-jet tests indicated, through thermophoretic sampling, (2) that soot primaries and aggregates (groups of primary particles) in low-gravity may be significantly larger than those in normal gravity (1-g). This raises new scientific questions about soot processes as well as practical issues for particulate size sensitivity and detection alarm threshold levels used in on-orbit smoke detectors. Preliminary tests in the 2.2 second drop tower suggest that particulate generated by overheated wire insulation may be larger in low-g than in 1-g. Transmission Electron Microscope (TEM) grids downstream of the fire region in the Wire Insulation Flammability experiment as well as visual observation of long string-like aggregates, further confirm this suggestion. The combined impact of these limited results and theoretical predictions is that, as opposed to extrapolation from l-g data, direct knowledge of low-g combustion particulate is needed for more confident design of smoke detectors for spacecraft. This paper describes the operation and preliminary results of the CSD, a project conceived and developed at NASA Lewis Research Center. The CSD flight experiment was conducted in the Middeck Glovebox Facility (MGBX) on USMP-3. The project is support by NASA Headquarters Microgravity Science and Applications Division and Code Q. The results presented here are from the microgravity portion of the experiment, including the temporal response of the detectors and average sizes of the primary and aggregate particles captured on the thermophoretic probes.

Urban, David L.↗

M.I.N.G., Mars Investment for a New Generation: Robotic construction of a permanently manned Mars base

A basic procedure for robotically constructing a manned Mars base is outlined. The research procedure was divided into three areas: environment, robotics, and habitat. The base as designed will consist of these components: two power plants, communication facilities, a habitat complex, and a hangar, a garage, recreation and manufacturing facilities. The power plants will be self-contained nuclear fission reactors placed approx. 1 km from the base for safety considerations. The base communication system will use a combination of orbiting satellites and surface relay stations. This system is necessary for robotic contact with Phobos and any future communication requirements. The habitat complex will consist of six self-contained modules: core, biosphere, science, living quarters, galley/storage, and a sick bay which will be brought from Phobos. The complex will be set into an excavated hole and covered with approximately 0.5 m of sandbags to provide radiation protection for the astronauts. The recreation, hangar, garage, and manufacturing facilities will each be transformed from the four one-way landers. The complete complex will be built by autonomous, artificially intelligent robots. Robots incorporated into the design are as follows: Large Modular Construction Robots with detachable arms capable of large scale construction activities; Small Maneuverable Robotic Servicers capable of performing delicate tasks normally requiring a suited astronaut; and a trailer vehicle with modular type attachments to complete specific tasks; and finally, Mobile Autonomous Rechargeable Transporters capable of transferring air and water from the manufacturing facility to the habitat complex.

Amos, Jeff↗

Flow-induced birefringence measurement system using dual-crystal transverse electro-optic modulator for microgravity fluid physics applications

We have developed a new instrument that can measure fast transient birefringence and polymer chain orientation angle in complex fluids. The instrument uses a dual-crystal transverse electro-optic modulator with the second crystal's modulation voltage applied 180 deg out of phase from that of the first crystal. In this manner, the second crystal compensates for the intrinsic static birefringence of the first crystal, and it doubles the modulation depth. By incorporating a transverse electro-optic modulator with two lithium-niobate (LiNbO3) crystals oriented orthogonal to each other with a custom-designed optical system, we have produced a very small robust instrument capable of fast transient retardation measurements. By measuring the sample thickness or optical path length through the sample, we can calculate the transient birefringence. This system can also measure dichroism. We have compared the calibration results and retardation and orientation angle measurements of this instrument with those of a photoelastic modulator (PEM) based system using a quarter wave plate and a high-precision 1/16-wave plate to simulate a birefringent sample. Transient birefringence measurements on the order of 10(exp -9) can be measured using either modulator.

Mackey, Jeffrey R.↗

Method Development for In Situ Microbiome Profiling of the Water Recovery System’s Wastewater Tank Onboard the International Space Station

A distinctive microbial community has inhabited the International Space Station (ISS) Water Recovery System (WRS) for over 14 years and has experienced the stressors associated with the microgravity environment. The WRS generates potable water for the crew from urine distillate, humidity condensate, Sabatier product water, and the occasional off-loading of ground-supplied water (1). The reservoir for these products, the wastewater tank, does not have a means of microbial control. Current in situ microbial monitoring of the WRS is limited to quarterly culture-based assessments of the potable water product using a microbial capture device and coliform detection bag. Additional analysis of the wastewater and condensate sources are collected into Teflon bags for analysis following return to the ground. The time between sample collection and the return to Earth, as well as the lack of preservation, results in a skewed depiction of the microbiome. Routinely observed from these returned wastewater samples are high counts (105 – 106 colony forming units per mL) and two prevailing genera, Ralstonia and Cupriavidus, as well as a high abundance of unidentified organisms (Table 1). The wastewater tank likely contains a more diverse microbiome, as a higher diversity of bacteria and fungi has been noted upstream and downstream of the tank.

Sarah Stahl-Rommel↗

Transmission of sound through nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows.

Nayfeh, A. H.↗

Synchronous Separation, Seaming, Sealing and Sterilization (S4) using Brazing for Sample Containerization and Planetary Protection

The return of samples back to Earth in future missions would require protection of our planet from the risk of bringing uncontrolled biological materials back with the samples. This protection would require “breaking the chain of contact (BTC)”, where any returned material reaching Earth for further analysis would have to be sealed inside a container with extremely high confidence. Therefore, the acquired samples would need to be contained while destroying any potential biological materials that may contaminate the external surface of the container. A novel process that could be used to contain returning samples has been developed and demonstrated in a quarter scale size. The process consists of brazing using non-contact induction heating that synchronously separates, seams, seals and sterilizes (S4) the container. The use of brazing involves melting at temperatures higher than 500°C and this level of heating assures sterilization of the exposed areas since all carbon bonds (namely, organic materials) are broken at this temperature. The mechanism consists of a double wall container with inner and outer shells having Earth-clean interior surfaces. The process consists of two-steps, Step-1: the double wall container halves are fabricated and brazed (equivalent to production on Earth); and Step-2 is the S4 process and it is the equivalent to the execution on-orbit around Mars. In a potential future mission, the double wall container would be split into two halves and prepared on Earth. The potential on-orbit execution would consist of inserting the orbiting sample (OS) container into one of the halves and then mated to the other half and brazed. The latest results of this effort will be described and discussed in this manuscript.

Salazar, Eduardo↗

Properties of the new $ \mathcal{N} $ = 1 AdS 4 vacuum of maximal supergravity

The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new N = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × Z 2 -invariant truncation of the N = 8 theory to an N = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the N = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × Z 2 -invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional Z $3\atop{2}$ -invariant scalar manifold (SU(1, 1)/U(1)) 7 , for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new N = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an N = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predictive Engineering Tools for Injection-Molded Long-Carbon-Fiber Thermoplastic Composites - FY 2015 First Quarterly Report

During the first quarter of FY 2015, the following technical progress has been made toward project milestones: 1) Autodesk delivered a new research version of ASMI to PNNL. This version includes the improved 3D fiber orientation solver, and the reduced order model (ROM) for fiber length distribution using the proper orthogonal decomposition (POD) implemented in the mid-plane, dual-domain and 3D solvers. 2) Autodesk coordinated a conference paper with PNNL reporting ASMI mid-plane fiber orientation predictions compared with the measured data for two PlastiComp plaques. This paper was accepted for presentation at the 2015 Society for Plastics Engineers (SPE) ANTEC conference. 3) The University of Illinois (Prof. Tucker) assisted team members from Purdue with fiber orientation measurement techniques, including interpretation of off-axis cross sections. 4) The University of Illinois assisted Autodesk team members with software implementation of the POD approach for fiber length modeling, and with fiber orientation modeling. 5) The University of Illinois co-authored in the SPE ANTEC paper, participated with the team in discussions of plaque data and model results, and participated in the definition of go/no-go experiments and data. 6) Purdue University (Purdue) conducted fiber orientation measurements for 3 PlastiComp plaques: fast-fill 30wt% LCF/PP center-gated, fast-fill 50wt% LCF/PA66 edge-gated and fast-fill 50wt% LCF/PA66 center-gated plaques, and delivered the fiber orientation data for these plaques at the selected locations (named A, B, and C) to PNNL. However, the data for the fast-fill 50wt% LCF/PA66 edge-gated plaque exhibited unusual variations and could not be used for the model validation. Purdue will re-measure fiber orientation for this plaque. 7) Based on discussions with the University of Illinois Purdue explained the ambiguity in the measurements of the fiber orientation components. 8) PNNL discussed with team members to establish a go/no-go decision plan for the project and submitted the established plan to DOE. 9) PNNL performed ASMI mid-plane analyses for the fast-fill center-gated 30wt% LCF/PP and 50wt% LCF/PA66 plaques and compared the predicted fiber orientations with the measured data provided by Purdue at Locations A, B, and C on these plaques. 10) Based on discussions with the University of Illinois and Autodesk, PNNL proposed a procedure to adjust fiber orientation data for Location A of the center-gated plaques so that the data can be expressed and interpreted in the flow/cross-flow direction coordinate system. 11) PNNL tested the new ASMI version received from Autodesk, examined and discussed 3D fiber orientation predictions for PlastiComp plaques. 12) PlastiComp, Inc. (PlastiComp), Toyota Research Institute North America (Toyota) and Magna Exteriors and Interiors Corp. (Magna) participated in discussions with team members on the go/no-go plan and the issues related to fiber length measurements. Toyota continued the discussion with Magna on tool modification for molding the complex part in order to achieve the target fiber length in the part.

42 ENGINEERING↗

Automotive Stirling Engine Development Program

The third quarter (April-June, 1978) effort of the Ford/DOE Automotive Stirling Engine Development Program is reported, specifically Task 1 of that effort, which is Fuel Economy Assessment. At the end of this quarter the total fourth generation fuel economy projection was 26.12 MPG (gasoline) with a confidence level of 44%. This represents an improvement of 66.4% over the baseline M-H fuel economy of 15.7 MPG. The confidence level for the original 20.6 MPG goal has been increased from 53% to 57%. Engine 3X17 has accumulated a total of 213 hours of variable speed running. A summary of the individual sub-tasks of Task 1 are given. The sub-tasks are grouped into two categories: Category 1 consists of those sub-tasks which are directly related to fuel economy and Category 2 consists of those sub-tasks which are not directly related to fuel economy but are an integral part of the Task 1 effort.

Source record↗

Dynamic model verification of large structural systems

The objective of the present methodology is two-fold: (1) to process test data obtained from either modal survey tests, or slow sine-sweep tests, to extract a set of orthogonal modes best matching the test data while being commensurate with the dynamic model, and (2) to modify submatrices of the dynamic model mass and stiffness matrices to adjust the model to best fit the test data. The method has been implemented using a linear statistical sequential estimator for computation on a CDC computer. Demonstration problems involving Space Shuttle quarter-scale vibration test data and dynamic models have been run. This paper will discuss the general methodology and experience to date.

Lee, L. T.↗

Recent Progress and Development of Self-Aligned Focusing Schlieren

A broad range of developments and applications of self-aligned focusing schlieren (SAFS)systems is presented. The replacement of the Ronchi ruling (RR) with a𝜇LCD was demonstrated with digital SAFS, which provides the ability to modulate the pattern and orientation without physical intervention. Additionally, replacement of the traditional RR with spectral-spatial filters was demonstrated to yield the ability to simultaneously image horizontal and vertical index of refraction gradients using two separate wavelengths. The application of the Scheimpflug principle to SAFS systems enables off-axis imaging and allowed for extended fields-of-view to be captured using a two-camera system. The addition of a plenoptic camera to a baseline SAFS system enables refocusing capabilities, which is demonstrated on two jets offset along the optical axis. Furthermore, application of an event-based camera to SAFS was shown to enable acquisition of sparse, spatio-temporal data. Beyond the listed developments, SAFS was applied to difficult and constraining facilities, such as the National Full-Scale Aerodynamics Complex(NFAC) 80- by 120-ft Wind Tunnel and the Thermal Acoustic Engines (TAE) rig at NASA Ames Research Center and NASA Glenn Research Center, respectively. Behavior of Ronchi rulings, Rochon prisms, and the use of quarter-wave plates versus quarter-wave films are evaluated to provide insight for future experimental design of SAFS-systems.

Self-Aligned Focusing Schlieren↗

Recent Progress and Development of Self-Aligned Focusing Schlieren

A broad range of developments and applications of self-aligned focusing schlieren (SAFS)systems is presented. The replacement of the Ronchi ruling (RR) with a𝜇LCD was demonstrated with digital SAFS, which provides the ability to modulate the pattern and orientation without physical intervention. Additionally, replacement of the traditional RR with spectral-spatial filters was demonstrated to yield the ability to simultaneously image horizontal and vertical index of refraction gradients using two separate wavelengths. The application of the Scheimpflug principle to SAFS systems enables off-axis imaging and allowed for extended fields-of-view to be captured using a two-camera system. The addition of a plenoptic camera to a baseline SAFS system enables refocusing capabilities, which is demonstrated on two jets offset along the optical axis. Furthermore, application of an event-based camera to SAFS was shown to enable acquisition of sparse, spatio-temporal data. Beyond the listed developments, SAFS was applied to difficult and constraining facilities, such as the National Full-Scale Aerodynamics Complex(NFAC) 80- by 120-ft Wind Tunnel and the Thermal Acoustic Engines (TAE) rig at NASA Ames Research Center and NASA Glenn Research Center, respectively. Behavior of Ronchi rulings, Rochon prisms, and the use of quarter-wave plates versus quarter-wave films are evaluated to provide insight for future experimental design of SAFS-systems.

Self-Aligned Focusing Schlieren↗

Comparison of oscillation parameters measured from $\nu_\mu$ and $\bar{\nu}_\mu$ disappearance in the NOvA experiment

The NOvA experiment is a neutrino oscillation experiment designed to make precise measurements of \nueD and \nuebarD appearance and \numuD and \numubarD disappearance at long distances and GeV energy scales. Using Fermilab's Neutrinos at the Main Injector (NuMI) beam, the experiment is provided with a highly pure and abundant source of either \numuD or $\numubar$. NOvA’s \numuD and \numubarD disappearance measurement is particularly sensitive to constraining the \snD vs.~\dmD space of oscillation parameters. Any difference between \numuD and \numubarD disappearance in vacuum could be an indication of the combination of Charge Conjugation, Parity and Time reversal (CPT) symmetry not being conserved in the neutrino sector or something else beyond our current understanding of physics.\medskip This thesis presents results from two \numuD and \numubarD disappearance analyses, one where \snD and \dmD are assumed to be identical as in the standard three neutrino flavour model, and t he other where the oscillation parameters can differ between neutrinos and antineutrinos. In the later, the core analysis of this thesis, the parameters \snD and \dmD are measured using just the information from neutrinos, and the parameters \snbarD and \dmbarD are measured using just the information from antineutrinos. The results for the mass splitting are $\Delta m^2_{32}=2.48^{+0.07}_{-0.09} \times 10^{-3}~\rm{eV}^2$ and $\Delta\bar{m}^2_{32}=2.55^{+0.12}_{-0.13} \times 10^{-3}~\rm{eV}^2$. The results for the mixing angle are $\rm{sin}^2\theta_{23}= 0.51$ in the range $[0.45, 0.57]$, and two degenerate best fits for $\rm{sin}^2\bar{\theta}_{23}$ at 0.41 and 0.61 in the ranges $[0.38, 0.45]$ and $[0.57, 0.64]$ allowed at $1~\sigma$. No significant difference between the oscillation parameters measured using \numuD or \numubarD was found. The data analysed in this thesis was collected between 2014 and 2019, for which the NOvA detectors collected an exposure of \potFHC and \potRHC protons-on-target (POT) for the production of the \n! umuD and \numubarD beams respectively. This data is about a quarter and a third of what NOvA is expected to collect in \nuD and \nubarD mode, respectively.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Observations of sodium in the tenuous lunar atmosphere

Spectra showing the sodium D lines above the moon's bright limb (subsolar point) were obtained at first and last quarters, May 27 and June 7, 1988. The number density at the surface is 57 + or - 20 atoms/cu cm and the scale height is 79 + or - 8 km, compatible with the temperature of the surface. Comparison with the Mercurian density of 26,000 atoms/cu cm reveals an enigma. Despite the apparent general similarity of the surfaces, the sodium densities are in a ratio of about 400. The difference may be attributed to differences in source or loss mechanisms or to some fundamental compositional difference between the two planets. The possibility that the source is rapid diffusion of sodium through Mercury's crust and regolith is discussed, as well as recent observational evidence that Mercury's regolith is of intermediate rock type and may be more sodium-rich than the moon's.

Tyler, Ann L.↗

Visualizing Spatially Varying Distribution Data

Box plot is a compact representation that encodes the minimum, maximum, mean, median, and quarters information of a distribution. In practice, a single box plot is drawn for each variable of interest. With the advent of more accessible computing power, we are now facing the problem of visual icing data where there is a distribution at each 2D spatial location. Simply extending the box plot technique to distributions over 2D domain is not straightforward. One challenge is reducing the visual clutter if a box plot is drawn over each grid location in the 2D domain. This paper presents and discusses two general approaches, using parametric statistics and shape descriptors, to present 2D distribution data sets. Both approaches provide additional insights compared to the traditional box plot technique

Kao, David↗