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At least 559 records · Page 31

Performance Evaluation and Modeling Techniques for Parallel Processors

In practice, the performance evaluation of supercomputers is still substantially driven by singlepoint estimates of metrics (e.g., MFLOPS) obtained by running characteristic benchmarks or workloads. With the rapid increase in the use of time-shared multiprogramming in these systems, such measurements are clearly inadequate. This is because multiprogramming and system overhead, as well as other degradations in performance due to time varying characteristics of workloads, are not taken into account. In multiprogrammed environments, multiple jobs and users can dramatically increase the amount of system overhead and degrade the performance of the machine. Performance techniques, such as benchmarking, which characterize performance on a dedicated machine ignore this major component of true computer performance. Due to the complexity of analysis, there has been little work done in analyzing, modeling, and predicting the performance of applications in multiprogrammed environments. This is especially true for parallel processors, where the costs and benefits of multi-user workloads are exacerbated. While some may claim that the issue of multiprogramming is not a viable one in the supercomputer market, experience shows otherwise. Even in recent massively parallel machines, multiprogramming is a key component. It has even been claimed that a partial cause of the demise of the CM2 was the fact that it did not efficiently support time-sharing. In the same paper, Gordon Bell postulates that, multicomputers will evolve to multiprocessors in order to support efficient multiprogramming. Therefore, it is clear that parallel processors of the future will be required to offer the user a time-shared environment with reasonable response times for the applications. In this type of environment, the most important performance metric is the completion of response time of a given application. However, there are a few evaluation efforts addressing this issue.

Dimpsey, Robert Tod↗

Computational parametric study of sidewall-compression scramjet inlet performance at Mach 10

A computational parametric study of three-dimensional, sidewall-compression scramjet inlets was performed to identify the effects of geometric parameters on inlet performance. The parameters were the leading-edge sweep angle, varied between 30 and 60 deg, and the leading-edge position of the cowl, located at the throat and at two forward positions. A laminar boundary layer with cold-wall (T(sub wall) = 300 K (540 R)) boundary conditions was imposed. The parametric study was performed for a Mach number of 10 and a unit free-stream Reynolds number of 7.06 x 10(exp 6) per meter (2.15 x 10(exp 6) per foot) at a geometric contraction ratio of 5. The performance of each configuration was evaluated in terms of the mass capture, throat Mach number, total pressure recovery, kinetic energy efficiency, and internal compression. One computation of an unswept configuration was included as a baseline to determine the effects of introducing leading-edge sweep on the flow-field parameters. The purpose of the computational parametric study was to perform a trade-off of the effects of various parameters on the global performance of the inlet. Although no single optimal configuration emerged, trade-offs among the stated performance parameters identified a leading-edge sweep angle of 45 deg as possessing the most attractive performance characteristics.

Holland, Scott D.↗

An Analytical Method of Estimating Turbine Performance

A method is developed by which the performance of a turbine over a range of operating conditions can be analytically estimated from the blade angles and flow areas. In order to use the method, certain coefficients that determine the weight flow and friction losses must be approximated. The method is used to calculate the performance of the single-stage turbine of a commercial aircraft gas-turbine engine and the calculated performance is compared with the performance indicated by experimental data. For the turbine of the typical example, the assumed pressure losses and turning angles give a calculated performance that represents the trends of the experimental performance with reasonable accuracy. The exact agreement between analytical performance and experimental performance is contingent upon the proper selection of the blading-loss parameter. A variation of blading-loss parameter from 0.3 to 0.5 includes most of the experimental data from the turbine investigated.

Kochendorfer, Fred D↗

An analytical method of estimating turbine performance

A method is developed by which the performance of a turbine over a range of operating conditions can be analytically estimated from the blade angles and flow areas. In order to use the method, certain coefficients that determine the weight flow and the friction losses must be approximated. The method is used to calculate the performance of the single-stage turbine of a commercial aircraft gas-turbine engine and the calculated performance is compared with the performance indicated by experimental data. For the turbine of the typical example, the assumed pressure losses and the tuning angles give a calculated performance that represents the trends of the experimental performance with reasonable accuracy. The exact agreement between analytical performance and experimental performance is contingent upon the proper selection of a blading-loss parameter.

Kochendorfer, Fred D↗

Preliminary supersonic flight test evaluation of performance seeking control

Digital flight and engine control, powerful onboard computers, and sophisticated controls techniques may improve aircraft performance by maximizing fuel efficiency, maximizing thrust, and extending engine life. An adaptive performance seeking control system for optimizing the quasi-steady state performance of an F-15 aircraft was developed and flight tested. This system has three optimization modes: minimum fuel, maximum thrust, and minimum fan turbine inlet temperature. Tests of the minimum fuel and fan turbine inlet temperature modes were performed at a constant thrust. Supersonic single-engine flight tests of the three modes were conducted using varied after burning power settings. At supersonic conditions, the performance seeking control law optimizes the integrated airframe, inlet, and engine. At subsonic conditions, only the engine is optimized. Supersonic flight tests showed improvements in thrust of 9 percent, increases in fuel savings of 8 percent, and reductions of up to 85 deg R in turbine temperatures for all three modes. The supersonic performance seeking control structure is described and preliminary results of supersonic performance seeking control tests are given. These findings have implications for improving performance of civilian and military aircraft.

Orme, John S.↗

Reach performance while wearing the Space Shuttle launch and entry suit during exposure to launch accelerations

Crewmen aboard the Space Shuttle are subjected to accelerations during ascent (the powered flight phase of launch) which range up to +3 G(sub x). Despite having 33 missions and nine years experience, not to mention all the time spent in development prior to the first flight, no truly quantitative reach study wearing actual crew equipment, using actual Shuttle seats and restraints has ever been done. What little information exists on reach performance while under acceleration has been derived primarily from subjective comments gathered retrospectively from Shuttle flight crews during their post mission debrief. This lack of reach performance data has resulted in uncertainty regarding emergency procedures that can realistically be performed during and actual Shuttle ascent versus what is practiced in the ground-fixed and motion-based Shuttle Simulators. With the introduction on STS-26 of the current Shuttle escape system, the question of reach performance under launch accelerations was once again raised. The escape system's requirement that each crewman wear a Launch/Entry Suit (LES), parachute harness, and parachute were all anticipated to contribute to a further degradation of reach performance during Shuttle ascent accelerations. In order to answer the reach performance question in a quantitative way, a photogrammetric method was chosen so that the actual reach values and associated envelopes could be captured. This would allow quantitative assessment of potential task performance impact and identify areas where changes to our Shuttle ascent emergency procedures might be required. Also, such a set of reach values would be valid for any similar acceleration profile using the same crew equipment. Potential Space Station applications of this data include predicting reach performance during Assured Crew Return Vehicle (ACRV) operations.

Bagian, James P.↗

Sailplane Glide Performance and Control Using Fixed and Articulating Winglets

An experimental study was conducted to investigate the effects of controllable articulating winglets on glide performance and yawing moments of high performance sailplanes. Testing was conducted in the Texas A&M University 7 x 10 foot Low Speed Wind Tunnel using a full-scale model of the outboard 5.6 feet of a 15 meter class high performance sailplane wing. Different wing tip configurations could be easily mounted to the wing model. A winglet was designed in which the cant and toe angles as well as a rudder on the winglet could be adjusted to a range of positions. Cant angles used in the investigation consisted of 5, 25, and 40 degrees measured from the vertical axis. Toe-out angles ranged from 0 to 22.5 degrees. A rudder on the winglet was used to study the effects of changing the camber of the winglet airfoil on wing performance and wing yawing moments. Rudder deflections consisted of-10, 0, and 10 degrees. Test results for a fixed geometry winglet and a standard wing tip are presented to show the general behavior of winglets on sailplane wings, and the effects of boundary-layer turbulators on the winglets are also presented. By tripping the laminar boundary-layer to turbulent before laminar separation occurs, the wing performance was increased at low Reynolds numbers. The effects on the lift and drag, yawing moment, pitching moment, and wing root bending moment of the model are presented. Oil flows were used on the wing model with the fixed geometry winglet and the standard wing tip to visualize flow directions and areas of boundary layer transition. A cant angle of 25 degrees and a toe-out angle of 2.5 degrees provided an optimal increase in wing performance for the cant and toe angles tested. Maximum performance was obtained when the winglet rudder remained in the neutral position of zero degrees. By varying the cant, toe, and rudder angles from their optimized positions, wing performance decreases. Although the winglet rudder proved to be more effective in increasing the yawing moment compared to varying the cant and toe angles, the amount of increased yawing moment was insignificant when compared to that produced by the vertical tail. A rudder on the winglet was determined to be ineffective for providing additional yaw control.

Colling, James David↗

Integrating Reliability Analysis with a Performance Tool

A large number of commercial simulation tools support performance oriented studies of complex computer and communication systems. Reliability of these systems, when desired, must be obtained by remodeling the system in a different tool. This has obvious drawbacks: (1) substantial extra effort is required to create the reliability model; (2) through modeling error the reliability model may not reflect precisely the same system as the performance model; (3) as the performance model evolves one must continuously reevaluate the validity of assumptions made in that model. In this paper we describe an approach, and a tool that implements this approach, for integrating a reliability analysis engine into a production quality simulation based performance modeling tool, and for modeling within such an integrated tool. The integrated tool allows one to use the same modeling formalisms to conduct both performance and reliability studies. We describe how the reliability analysis engine is integrated into the performance tool, describe the extensions made to the performance tool to support the reliability analysis, and consider the tool's performance.

Nicol, David M.↗

Performance Testing of a Trace Contaminant Control Subassembly for the International Space Station

As part of the International Space Station (ISS) Trace Contaminant Control Subassembly (TCCS) development, a performance test has been conducted to provide reference data for flight verification analyses. This test, which used the U.S. Habitation Module (U.S. Hab) TCCS as the test article, was designed to add to the existing database on TCCS performance. Included in this database are results obtained during ISS development testing; testing of functionally similar TCCS prototype units; and bench scale testing of activated charcoal, oxidation catalyst, and granular lithium hydroxide (LiOH). The present database has served as the basis for the development and validation of a computerized TCCS process simulation model. This model serves as the primary means for verifying the ISS TCCS performance. In order to mitigate risk associated with this verification approach, the U.S. Hab TCCS performance test provides an additional set of data which serve to anchor both the process model and previously-obtained development test data to flight hardware performance. The following discussion provides relevant background followed by a summary of the test hardware, objectives, requirements, and facilities. Facility and test article performance during the test is summarized, test results are presented, and the TCCS's performance relative to past test experience is discussed. Performance predictions made with the TCCS process model are compared with the U.S. Hab TCCS test results to demonstrate its validation.

Perry, J. L.↗

High-Performance Monitoring Architecture for Large-Scale Distributed Systems Using Event Filtering

Monitoring is an essential process to observe and improve the reliability and the performance of large-scale distributed (LSD) systems. In an LSD environment, a large number of events is generated by the system components during its execution or interaction with external objects (e.g. users or processes). Monitoring such events is necessary for observing the run-time behavior of LSD systems and providing status information required for debugging, tuning and managing such applications. However, correlated events are generated concurrently and could be distributed in various locations in the applications environment which complicates the management decisions process and thereby makes monitoring LSD systems an intricate task. We propose a scalable high-performance monitoring architecture for LSD systems to detect and classify interesting local and global events and disseminate the monitoring information to the corresponding end- points management applications such as debugging and reactive control tools to improve the application performance and reliability. A large volume of events may be generated due to the extensive demands of the monitoring applications and the high interaction of LSD systems. The monitoring architecture employs a high-performance event filtering mechanism to efficiently process the large volume of event traffic generated by LSD systems and minimize the intrusiveness of the monitoring process by reducing the event traffic flow in the system and distributing the monitoring computation. Our architecture also supports dynamic and flexible reconfiguration of the monitoring mechanism via its Instrumentation and subscription components. As a case study, we show how our monitoring architecture can be utilized to improve the reliability and the performance of the Interactive Remote Instruction (IRI) system which is a large-scale distributed system for collaborative distance learning. The filtering mechanism represents an Intrinsic component integrated with the monitoring architecture to reduce the volume of event traffic flow in the system, and thereby reduce the intrusiveness of the monitoring process. We are developing an event filtering architecture to efficiently process the large volume of event traffic generated by LSD systems (such as distributed interactive applications). This filtering architecture is used to monitor collaborative distance learning application for obtaining debugging and feedback information. Our architecture supports the dynamic (re)configuration and optimization of event filters in large-scale distributed systems. Our work represents a major contribution by (1) survey and evaluating existing event filtering mechanisms In supporting monitoring LSD systems and (2) devising an integrated scalable high- performance architecture of event filtering that spans several kev application domains, presenting techniques to improve the functionality, performance and scalability. This paper describes the primary characteristics and challenges of developing high-performance event filtering for monitoring LSD systems. We survey existing event filtering mechanisms and explain key characteristics for each technique. In addition, we discuss limitations with existing event filtering mechanisms and outline how our architecture will improve key aspects of event filtering.

Maly, K.↗

Performance Measurement, Visualization and Modeling of Parallel and Distributed Programs

This paper presents a methodology for debugging the performance of message-passing programs on both tightly coupled and loosely coupled distributed-memory machines. The AIMS (Automated Instrumentation and Monitoring System) toolkit, a suite of software tools for measurement and analysis of performance, is introduced and its application illustrated using several benchmark programs drawn from the field of computational fluid dynamics. AIMS includes (i) Xinstrument, a powerful source-code instrumentor, which supports both Fortran77 and C as well as a number of different message-passing libraries including Intel's NX Thinking Machines' CMMD, and PVM; (ii) Monitor, a library of timestamping and trace -collection routines that run on supercomputers (such as Intel's iPSC/860, Delta, and Paragon and Thinking Machines' CM5) as well as on networks of workstations (including Convex Cluster and SparcStations connected by a LAN); (iii) Visualization Kernel, a trace-animation facility that supports source-code clickback, simultaneous visualization of computation and communication patterns, as well as analysis of data movements; (iv) Statistics Kernel, an advanced profiling facility, that associates a variety of performance data with various syntactic components of a parallel program; (v) Index Kernel, a diagnostic tool that helps pinpoint performance bottlenecks through the use of abstract indices; (vi) Modeling Kernel, a facility for automated modeling of message-passing programs that supports both simulation -based and analytical approaches to performance prediction and scalability analysis; (vii) Intrusion Compensator, a utility for recovering true performance from observed performance by removing the overheads of monitoring and their effects on the communication pattern of the program; and (viii) Compatibility Tools, that convert AIMS-generated traces into formats used by other performance-visualization tools, such as ParaGraph, Pablo, and certain AVS/Explorer modules.

Yan, Jerry C.↗

High Performance Programming Using Explicit Shared Memory Model on Cray T3D1

The Cray T3D system is the first-phase system in Cray Research, Inc.'s (CRI) three-phase massively parallel processing (MPP) program. This system features a heterogeneous architecture that closely couples DEC's Alpha microprocessors and CRI's parallel-vector technology, i.e., the Cray Y-MP and Cray C90. An overview of the Cray T3D hardware and available programming models is presented. Under Cray Research adaptive Fortran (CRAFT) model four programming methods (data parallel, work sharing, message-passing using PVM, and explicit shared memory model) are available to the users. However, at this time data parallel and work sharing programming models are not available to the user community. The differences between standard PVM and CRI's PVM are highlighted with performance measurements such as latencies and communication bandwidths. We have found that the performance of neither standard PVM nor CRI s PVM exploits the hardware capabilities of the T3D. The reasons for the bad performance of PVM as a native message-passing library are presented. This is illustrated by the performance of NAS Parallel Benchmarks (NPB) programmed in explicit shared memory model on Cray T3D. In general, the performance of standard PVM is about 4 to 5 times less than obtained by using explicit shared memory model. This degradation in performance is also seen on CM-5 where the performance of applications using native message-passing library CMMD on CM-5 is also about 4 to 5 times less than using data parallel methods. The issues involved (such as barriers, synchronization, invalidating data cache, aligning data cache etc.) while programming in explicit shared memory model are discussed. Comparative performance of NPB using explicit shared memory programming model on the Cray T3D and other highly parallel systems such as the TMC CM-5, Intel Paragon, Cray C90, IBM-SP1, etc. is presented.

Simon, Horst D.↗

Investigation of Fundamental Modeling and Thermal Performance Issues for a Metallic Thermal Protection System Design

A study was performed to develop an understanding of the key factors that govern the performance of metallic thermal protection systems for reusable launch vehicles. A current advanced metallic thermal protection system (TPS) concept was systematically analyzed to discover the most important factors governing the thermal performance of metallic TPS. A large number of relevant factors that influence the thermal analysis and thermal performance of metallic TPS were identified and quantified. Detailed finite element models were developed for predicting the thermal performance of design variations of the advanced metallic TPS concept mounted on a simple, unstiffened structure. The computational models were also used, in an automated iterative procedure, for sizing the metallic TPS to maintain the structure below a specified temperature limit. A statistical sensitivity analysis method, based on orthogonal matrix techniques used in robust design, was used to quantify and rank the relative importance of the various modeling and design factors considered in this study. Results of the study indicate that radiation, even in small gaps between panels, can reduce significantly the thermal performance of metallic TPS, so that gaps should be eliminated by design if possible. Thermal performance was also shown to be sensitive to several analytical assumptions that should be chosen carefully. One of the factors that was found to have the greatest effect on thermal performance is the heat capacity of the underlying structure. Therefore the structure and TPS should be designed concurrently.

Blosser, Max L.↗

Improving TCP Network Performance by Detecting and Reacting to Packet Reordering

There are many factors governing the performance of TCP-basec applications traversing satellite channels. The end-to-end performance of TCP is known to be degraded by the reordering, delay, noise and asymmetry inherent in geosynchronous systems. This result has been largely based on experiments that evaluate the performance of TCP in single flow tests. While single flow tests are useful for deriving information on the theoretical behavior of TCP and allow for easy diagnosis of problems they do not represent a broad range of realistic situations and therefore cannot be used to authoritatively comment on performance issues. The experiments discussed in this report test TCP s performance in a more dynamic environment with competing traffic flows from hundreds of TCP connections running simultaneously across the satellite channel. Another aspect we investigate is TCP's reaction to bit errors on satellite channels. TCP interprets loss as a sign of network congestion. This causes TCP to reduce its transmission rate leading to reduced performance when loss is due to corruption. We allowed the bit error rate on our satellite channel to vary widely and tested the performance of TCP as a function of these bit error rates. Our results show that the average performance of TCP on satellite channels is good even under conditions of loss as high as bit error rates of 10(exp -5)

Kruse, Hans↗

Numerical Modeling of Pulse Detonation Rocket Engine Gasdynamics and Performance

This paper presents viewgraphs on the numerical modeling of pulse detonation rocket engines (PDRE), with an emphasis on the Gasdynamics and performance analysis of these engines. The topics include: 1) Performance Analysis of PDREs; 2) Simplified PDRE Cycle; 3) Comparison of PDRE and Steady-State Rocket Engines (SSRE) Performance; 4) Numerical Modeling of Quasi 1-D Rocket Flows; 5) Specific PDRE Geometries Studied; 6) Time-Accurate Thrust Calculations; 7) PDRE Performance (Geometries A B C and D); 8) PDRE Blowdown Gasdynamics (Geom. A B C and D); 9) PDRE Geometry Performance Comparison; 10) PDRE Blowdown Time (Geom. A B C and D); 11) Specific SSRE Geometry Studied; 12) Effect of F-R Chemistry on SSRE Performance; 13) PDRE/SSRE Performance Comparison; 14) PDRE Performance Study; 15) Grid Resolution Study; and 16) Effect of F-R Chemistry on SSRE Exit Species Mole Fractions.

Source record↗

Sustained attention performance during sleep deprivation: evidence of state instability

Nathaniel Kleitman was the first to observe that sleep deprivation in humans did not eliminate the ability to perform neurobehavioral functions, but it did make it difficult to maintain stable performance for more than a few minutes. To investigate variability in performance as a function of sleep deprivation, n = 13 subjects were tested every 2 hours on a 10-minute, sustained-attention, psychomotor vigilance task (PVT) throughout 88 hours of total sleep deprivation (TSD condition), and compared to a control group of n = 15 subjects who were permitted a 2-hour nap every 12 hours (NAP condition) throughout the 88-hour period. PVT reaction time means and standard deviations increased markedly among subjects and within each individual subject in the TSD condition relative to the NAP condition. TSD subjects also had increasingly greater performance variability as a function of time on task after 18 hours of wakefulness. During sleep deprivation, variability in PVT performance reflected a combination of normal timely responses, errors of omission (i.e., lapses), and errors of commission (i.e., responding when no stimulus was present). Errors of omission and errors of commission were highly intercorrelated across deprivation in the TSD condition (r = 0.85, p = 0.0001), suggesting that performance instability is more likely to include compensatory effort than a lack of motivation. The marked increases in PVT performance variability as sleep loss continued supports the "state instability" hypothesis, which posits that performance during sleep deprivation is increasingly variable due to the influence of sleep initiating mechanisms on the endogenous capacity to maintain attention and alertness, thereby creating an unstable state that fluctuates within seconds and that cannot be characterized as either fully awake or asleep.

Non-NASA Center↗

Analysis of Aircraft Control Performance using a Fuzzy Rule Base Representation of the Cooper-Harper Aircraft Handling Quality Rating

The Cooper-Harper rating of Aircraft Handling Qualities has been adopted as a standard for measuring the performance of aircraft since it was introduced in 1966. Aircraft performance, ability to control the aircraft, and the degree of pilot compensation needed are three major key factors used in deciding the aircraft handling qualities in the Cooper- Harper rating. We formulate the Cooper-Harper rating scheme as a fuzzy rule-based system and use it to analyze the effectiveness of the aircraft controller. The automatic estimate of the system-level handling quality provides valuable up-to-date information for diagnostics and vehicle health management. Analyzing the performance of a controller requires a set of concise design requirements and performance criteria. Ir, the case of control systems fm a piloted aircraft, generally applicable quantitative design criteria are difficult to obtain. The reason for this is that the ultimate evaluation of a human-operated control system is necessarily subjective and, with aircraft, the pilot evaluates the aircraft in different ways depending on the type of the aircraft and the phase of flight. In most aerospace applications (e.g., for flight control systems), performance assessment is carried out in terms of handling qualities. Handling qualities may be defined as those dynamic and static properties of a vehicle that permit the pilot to fully exploit its performance in a variety of missions and roles. Traditionally, handling quality is measured using the Cooper-Harper rating and done subjectively by the human pilot. In this work, we have formulated the rules of the Cooper-Harper rating scheme as fuzzy rules with performance, control, and compensation as the antecedents, and pilot rating as the consequent. Appropriate direct measurements on the controller are related to the fuzzy Cooper-Harper rating system: a stability measurement like the rate of change of the cost function can be used as an indicator if the aircraft is under control; the tracking error is a good measurement for performance needed in the rating scheme. Finally, the change of the control amount or the output of a confidence tool, which has been developed by the authors, can be used as an indication of pilot compensation. We use a number of known aircraft flight scenarios with known pilot ratings to calibrate our fuzzy membership functions. These include normal flight conditions and situations in which partial or complete failure of tail, aileron, engine, or throttle occurs.

Tseng, Chris↗

Preliminary Performance Analyses of the Constellation Program ARES 1 Crew Launch Vehicle

By the time NASA's Exploration Systems Architecture Study (ESAS) report had been released to the public in December 2005, engineers at NASA's Marshall Space Flight Center had already initiated the first of a series of detailed design analysis cycles (DACs) for the Constellation Program Crew Launch Vehicle (CLV), which has been given the name Ares I. As a major component of the Constellation Architecture, the CLV's initial role will be to deliver crew and cargo aboard the newly conceived Crew Exploration Vehicle (CEV) to a staging orbit for eventual rendezvous with the International Space Station (ISS). However, the long-term goal and design focus of the CLV will be to provide launch services for a crewed CEV in support of lunar exploration missions. Key to the success of the CLV design effort and an integral part of each DAC is a detailed performance analysis tailored to assess nominal and dispersed performance of the vehicle, to determine performance sensitivities, and to generate design-driving dispersed trajectories. Results of these analyses provide valuable design information to the program for the current design as well as provide feedback to engineers on how to adjust the current design in order to maintain program goals. This paper presents a condensed subset of the CLV performance analyses performed during the CLV DAC-1 cycle. Deterministic studies include development of the CLV DAC-1 reference trajectories, identification of vehicle stage impact footprints, an assessment of launch window impacts to payload performance, and the computation of select CLV payload partials. Dispersion studies include definition of input uncertainties, Monte Carlo analysis of trajectory performance parameters based on input dispersions, assessment of CLV flight performance reserve (FPR), assessment of orbital insertion accuracy, and an assessment of bending load indicators due to dispersions in vehicle angle of attack and side slip angle. A short discussion of the various customers for the dispersion results, along with results and ramifications of each study, are also provided.

Phillips, Mark↗