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An Algorithm for Integrated Subsystem Embodiment and System Synthesis

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft.

Lewis, Kemper↗

Performance of the Microwave Anisotropy Probe AST-201 Star Trackers

The Microwave Anisotropy Probe (MAP) was launched to create a full-sky map of the cosmic microwave background. MAP incorporates two modified Lockheed Martin AST-201 (Autonomous Star Tracker) star trackers. The AST-201 employs an eight element radiation hardened lens assembly which is used to focus an image on a charge coupled device (CCD). The CCD image is then processed by a star identification algorithm which outputs a three-axis attitude. A CCD-shift algorithm called Time Delayed Integration (TDI) was also included in each star tracker. In order to provide some radiation effect filtering during MAP's three to five phasing loop passes through the Van Allen radiation belts, a simple pixel filtering scheme was implemented, rather than using a more complex, but more robust windowing algorithm. The trackers also include a fiber optic data interface. This paper details the ground testing that was accomplished on the MAP trackers.

Ward, David K.↗

Particle Generation And Evolution In Silane (SiH4)/Acetylene (C2H2) Flames In Microgravity

The objective of this experimental program is to advance the understanding of the coupling of particle formation with gas phase combustion processes. The work utilizes the unique SiH4/C2H2 combustion system which generates particulate products ranging from high purity, white SiC to carbonaceous soot depending on equivalence ratio (Ref. 1). A goal of this work is to identify gas phase or particle formation processes that provide the enthalpy release needed to drive the combustion wave, and to locate the steps of the particle formation process that determine SiC stoichiometry and crystallinity. In a real sense, these SiH4/C2H2 flames act like highly sooty hydrocarbon flames, but with simpler chemistry. This simplification is expected to allow them to be used as surrogates to advance understanding of soot formation in such rich hydrocarbon flames. It is also expected that this improved understanding of SiC particle generation and evolution in these self-sustaining flames will advance the commercial potential of the flame process for the generation of high purity SiC powders.

Keil, D. G.↗

Aqueous Alteration of Carbonaceous Chondrites: New Insights from Comparative Studies of Two Unbrecciated CM2 Chondrites, Y 791198 and ALH 81002

Carbonaceous chondrites are an important resource for understanding the physical and chemical conditions in the early solar system. In particular, a long-standing question concerns the role of water in the cosmochemical evolution of carbonaceous chondrites. It is well established that extensive hydration of primary nebular phases occurred in the CM and CI chondrites, but the location where this alteration occurred remains controversial. In the CM2 chondrites, hydration formed secondary phases such as serpentine, tochilinite, pentlandite, carbonate and PCP. There are several textural observations which suggest that alteration occurred before the accretion of the final CM parent asteroid, i.e. preaccretionary alteration. Conversely, there is a significant body of evidence that supports parent-body alteration. In order to test these two competing hypotheses further, we studied two CM chondrites, Y-791198 and ALH81002, two meteorites that exhibit widely differing degrees of aqueous alteration. In addition, both meteorites have primary accretionary textures, i.e. experienced minimal asteroidal brecciation. Brecciation significantly complicates the task of unraveling alteration histories, mixing components that have been altered to different degrees from different locations on the same asteroidal parent body. Alteration in Y-791198 is mostly confined to chondrule mesostases, FeNi metal and fine-grained matrix and rims. In comparison, the primary chondrule silicates in ALH81002 have undergone extensive replacement by secondary hydrous phases. This study focuses on compositional and textural relationships between chondrule mesostasis and the associated rim materials. Our hypothesis is: both these components are highly susceptible to aqueous alteration and should be sensitive recorders of the alteration process. For parent body alteration, we expect systematic coupled mineralogical and compositional changes in rims and altered mesostasis, as elemental exchange between these components occurs. Conversely, for preaccretionary alteration, there should be no clear relationships between the rims and mesostases.

Chizmadia, L. J.↗

An Arabidopsis Ran-binding protein, AtRanBP1c, is a co-activator of Ran GTPase-activating protein and requires the C-terminus for its cytoplasmic localization

Ran-binding proteins (RanBPs) are a group of proteins that bind to Ran (Ras-related nuclear small GTP-binding protein), and thus either control the GTP/GDP-bound states of Ran or help couple the Ran GTPase cycle to a cellular process. AtRanBP1c is a Ran-binding protein from Arabidopsis thaliana (L.) Heynh. that was recently shown to be critically involved in the regulation of auxin-induced mitotic progression [S.-H. Kim et al. (2001) Plant Cell 13:2619-2630]. Here we report that AtRanBP1c inhibits the EDTA-induced release of GTP from Ran and serves as a co-activator of Ran-GTPase-activating protein (RanGAP) in vitro. Transient expression of AtRanBP1c fused to a beta-glucuronidase (GUS) reporter reveals that the protein localizes primarily to the cytosol. Neither the N- nor C-terminus of AtRanBP1c, which flank the Ran-binding domain (RanBD), is necessary for the binding of PsRan1-GTP to the protein, but both are needed for the cytosolic localization of GUS-fused AtRanBP1c. These findings, together with a previous report that AtRanBP1c is critically involved in root growth and development, imply that the promotion of GTP hydrolysis by the Ran/RanGAP/AtRanBP1c complex in the cytoplasm, and the resulting concentration gradient of Ran-GDP to Ran-GTP across the nuclear membrane could be important in the regulation of auxin-induced mitotic progression in root tips of A. thaliana.

NASA Discipline Plant Biology↗

Detection, Identification, Location, and Remote Sensing using SAW RFID Sensor Tags

In this presentation, we will consider the problem of simultaneous detection, identification, location estimation, and remote sensing for multiple objects. In particular, we will describe the design and testing of a wireless system capable of simultaneously detecting the presence of multiple objects, identifying each object, and acquiring both a low-resolution estimate of location and a high-resolution estimate of temperature for each object based on wireless interrogation of passive surface acoustic wave (SAW) radiofrequency identification (RFID) sensor tags affixed to each object. The system is being studied for application on the lunar surface as well as for terrestrial remote sensing applications such as pre-launch monitoring and testing of spacecraft on the launch pad and monitoring of test facilities. The system utilizes a digitally beam-formed planar receiving antenna array to extend range and provide direction-of-arrival information coupled with an approximate maximum-likelihood signal processing algorithm to provide near-optimal estimation of both range and temperature. The system is capable of forming a large number of beams within the field of view and resolving the information from several tags within each beam. The combination of both spatial and waveform discrimination provides the capability to track and monitor telemetry from a large number of objects appearing simultaneously within the field of view of the receiving array. In the presentation, we will summarize the system design and illustrate several aspects of the operational characteristics and signal structure. We will examine the theoretical performance characteristics of the system and compare the theoretical results with results obtained from experiments in both controlled laboratory environments and in the field.

Barton, Richard J.↗

The Evolution and Development of the Lunar Regolith and Implications for Lunar Surface Operations and Construction

The lunar regolith consists of about 90% submillimeter particles traditionally termed lunar soil. The remainder consists of larger particles ranging up to boulder size rocks. At the lower size end, soil particles in the 10s of nanometer sizes are present in all soil samples. Lunar regolith overlies bedrock which consists of either lava flows in mare regions or impact-produced megaregolith in highland regions. Lunar regolith has been produced over billions of years by a combination of breaking and communition of bedrock by meteorite bombardment coupled with a variety of complex space weathering processes including solar wind implantation, solar flare and cosmic ray bombardment with attendant radiation damage, melting, vaporization, and vapor condensation driven by impact, and gardening and turnover of the resultant soil. Lunar regolith is poorly sorted compared to most terrestrial soils, and has interesting engineering properties including strong grain adhesion, over-compacted soil density, an abundance of agglutinates with sharp corners, and a variety of properties related to soil maturity. The NASA program has supported a variety of engineering test research projects, the production of bricks by solar or microwave sintering, the production of concrete, the in situ sintering and glazing of regolith by microwave, and the extraction of useful resources such as oxygen, hydrogen, iron, aluminum, silicon and other products. Future requirements for a lunar surface base or outpost will include construction of protective berms, construction of paved roadways, construction of shelters, movement and emplacement of regolith for radiation shielding and thermal control, and extraction of useful products. One early need is for light weight but powerful digging, trenching, and regolith-moving equipment.

McKay, David↗

Detection, Identification, Location, and Remote Sensing Using SAW RFID Sensor Tags

The Electromagnetic Systems Branch (EV4) of the Avionic Systems Division at NASA Johnson Space Center in Houston, TX is studying the utility of surface acoustic wave (SAW) radiofrequency identification (RFID) tags for multiple wireless applications including detection, identification, tracking, and remote sensing of objects on the lunar surface, monitoring of environmental test facilities, structural shape and health monitoring, and nondestructive test and evaluation of assets. For all of these applications, it is anticipated that the system utilized to interrogate the SAW RFID tags may need to operate at fairly long range and in the presence of considerable multipath and multiple-access interference. Towards that end, EV4 is developing a prototype SAW RFID wireless interrogation system for use in such environments called the Passive Adaptive RFID Sensor Equipment (PARSED) system. The system utilizes a digitally beam-formed planar receiving antenna array to extend range and provide direction-of-arrival information coupled with an approximate maximum-likelihood signal processing algorithm to provide near-optimal estimation of both range and temperature. The system is capable of forming a large number of beams within the field of view and resolving the information from several tags within each beam. The combination of both spatial and waveform discrimination provides the capability to track and monitor telemetry from a large number of objects appearing simultaneously within the field of view of the receiving array. In this paper, we will consider the application of the PARSEQ system to the problem of simultaneous detection, identification, localization, and temperature estimation for multiple objects. We will summarize the overall design of the PARSEQ system and present a detailed description of the design and performance of the signal detection and estimation algorithms incorporated in the system. The system is currently configured only to measure temperature (jointly with range and tag ID), but future versions will be revised to measure parameters other than temperature as SAW tags capable of interfacing with external sensors become available. It is anticipated that the estimation of arbitrary parameters measured using SAW-based sensors will be based on techniques very similar to the joint range and temperature estimation techniques described in this paper.

Barton, Richard J.↗

Automated Knowledge Discovery From Simulators

A computational method, SimLearn, has been devised to facilitate efficient knowledge discovery from simulators. Simulators are complex computer programs used in science and engineering to model diverse phenomena such as fluid flow, gravitational interactions, coupled mechanical systems, and nuclear, chemical, and biological processes. SimLearn uses active-learning techniques to efficiently address the "landscape characterization problem." In particular, SimLearn tries to determine which regions in "input space" lead to a given output from the simulator, where "input space" refers to an abstraction of all the variables going into the simulator, e.g., initial conditions, parameters, and interaction equations. Landscape characterization can be viewed as an attempt to invert the forward mapping of the simulator and recover the inputs that produce a particular output. Given that a single simulation run can take days or weeks to complete even on a large computing cluster, SimLearn attempts to reduce costs by reducing the number of simulations needed to effect discoveries. Unlike conventional data-mining methods that are applied to static predefined datasets, SimLearn involves an iterative process in which a most informative dataset is constructed dynamically by using the simulator as an oracle. On each iteration, the algorithm models the knowledge it has gained through previous simulation trials and then chooses which simulation trials to run next. Running these trials through the simulator produces new data in the form of input-output pairs. The overall process is embodied in an algorithm that combines support vector machines (SVMs) with active learning. SVMs use learning from examples (the examples are the input-output pairs generated by running the simulator) and a principle called maximum margin to derive predictors that generalize well to new inputs. In SimLearn, the SVM plays the role of modeling the knowledge that has been gained through previous simulation trials. Active learning is used to determine which new input points would be most informative if their output were known. The selected input points are run through the simulator to generate new information that can be used to refine the SVM. The process is then repeated. SimLearn carefully balances exploration (semi-randomly searching around the input space) versus exploitation (using the current state of knowledge to conduct a tightly focused search). During each iteration, SimLearn uses not one, but an ensemble of SVMs. Each SVM in the ensemble is characterized by different hyper-parameters that control various aspects of the learned predictor - for example, whether the predictor is constrained to be very smooth (nearby points in input space lead to similar output predictions) or whether the predictor is allowed to be "bumpy." The various SVMs will have different preferences about which input points they would like to run through the simulator next. SimLearn includes a formal mechanism for balancing the ensemble SVM preferences so that a single choice can be made for the next set of trials.

Burl, Michael↗

Reducing Centroid Error Through Model-Based Noise Reduction

A method of processing the digitized output of a charge-coupled device (CCD) image detector has been devised to enable reduction of the error in computed centroid of the image of a point source of light. The method involves model-based estimation of, and correction for, the contributions of bias and noise to the image data. The method could be used to advantage in any of a variety of applications in which there are requirements for measuring precise locations of, and/or precisely aiming optical instruments toward, point light sources. In the present method, prior to normal operations of the CCD, one measures the point-spread function (PSF) of the telescope or other optical system used to project images on the CCD. The PSF is used to construct a database of spot models representing the nominal CCD pixel outputs for a point light source projected onto the CCD at various positions incremented by small fractions of a pixel.

Lee, Shinhak↗

NASA Tech Briefs, March 2005

Topics covered include: Scheme for Entering Binary Data Into a Quantum Computer; Encryption for Remote Control via Internet or Intranet; Coupled Receiver/Decoders for Low-Rate Turbo Codes; Processing GPS Occultation Data To Characterize Atmosphere; Displacing Unpredictable Nulls in Antenna Radiation Patterns; Integrated Pointing and Signal Detector for Optical Receiver; Adaptive Thresholding and Parameter Estimation for PPM; Data-Driven Software Framework for Web-Based ISS Telescience; Software for Secondary-School Learning About Robotics; Fuzzy Logic Engine; Telephone-Directory Program; Simulating a Direction-Finder Search for an ELT; Formulating Precursors for Coating Metals and Ceramics; Making Macroscopic Assemblies of Aligned Carbon Nanotubes; Ball Bearings Equipped for In Situ Lubrication on Demand; Synthetic Bursae for Robots; Robot Forearm and Dexterous Hand; Making a Metal-Lined Composite-Overwrapped Pressure Vessel; Ex Vivo Growth of Bioengineered Ligaments and Other Tissues; Stroboscopic Goggles for Reduction of Motion Sickness; Articulating Support for Horizontal Resistive Exercise; Modified Penning-Malmberg Trap for Storing Antiprotons; Tumbleweed Rovers; Two-Photon Fluorescence Microscope for Microgravity Research; Biased Randomized Algorithm for Fast Model-Based Diagnosis; Fast Algorithms for Model-Based Diagnosis; Simulations of Evaporating Multicomponent Fuel Drops; Formation Flying of Tethered and Nontethered Spacecraft; and Two Methods for Efficient Solution of the Hitting- Set Problem.

Source record↗

Effects of Real-Time NASA Vegetation Data on Model Forecasts of Severe Weather

The NASA Short-term Prediction Research and Transition (SPoRT) Center has developed a Greenness Vegetation Fraction (GVF) dataset, which is updated daily using swaths of Normalized Difference Vegetation Index data from the Moderate Resolution Imaging Spectroradiometer (MODIS) data aboard the NASA-EOS Aqua and Terra satellites. NASA SPoRT started generating daily real-time GVF composites at 1-km resolution over the Continental United States beginning 1 June 2010. A companion poster presentation (Bell et al.) primarily focuses on impact results in an offline configuration of the Noah land surface model (LSM) for the 2010 warm season, comparing the SPoRT/MODIS GVF dataset to the current operational monthly climatology GVF available within the National Centers for Environmental Prediction (NCEP) and Weather Research and Forecasting (WRF) models. This paper/presentation primarily focuses on individual case studies of severe weather events to determine the impacts and possible improvements by using the real-time, high-resolution SPoRT-MODIS GVFs in place of the coarser-resolution NCEP climatological GVFs in model simulations. The NASA-Unified WRF (NU-WRF) modeling system is employed to conduct the sensitivity simulations of individual events. The NU-WRF is an integrated modeling system based on the Advanced Research WRF dynamical core that is designed to represents aerosol, cloud, precipitation, and land processes at satellite-resolved scales in a coupled simulation environment. For this experiment, the coupling between the NASA Land Information System (LIS) and the WRF model is utilized to measure the impacts of the daily SPoRT/MODIS versus the monthly NCEP climatology GVFs. First, a spin-up run of the LIS is integrated for two years using the Noah LSM to ensure that the land surface fields reach an equilibrium state on the 4-km grid mesh used. Next, the spin-up LIS is run in two separate modes beginning on 1 June 2010, one continuing with the climatology GVFs while the other uses the daily SPoRT/MODIS GVFs. Finally, snapshots of the LIS land surface fields are used to initialize two different simulations of the NU-WRF, one running with climatology LIS and GVFs, and the other running with experimental LIS and NASA/SPoRT GVFs. In this paper/presentation, case study results will be highlighted in regions with significant differences in GVF between the NCEP climatology and SPoRT product during severe weather episodes.

Case, Jonathan L.↗

Apparatus and Method for Assessing Vestibulo-Ocular Function

A system for assessing vestibulo-ocular function includes a motion sensor system adapted to be coupled to a user's head; a data processing system configured to communicate with the motion sensor system to receive the head-motion signals; a visual display system configured to communicate with the data processing system to receive image signals from the data processing system; and a gain control device arranged to be operated by the user and to communicate gain adjustment signals to the data processing system.

Shelhamer, Mark J.↗

Microphysics in the Multi-Scale Modeling Systems with Unified Physics

In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (l) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, the microphysics developments of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling system to study the heavy precipitation processes will be presented.

Tao, Wei-Kuo↗

Microphysics in Multi-scale Modeling System with Unified Physics

Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-land surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, a review of developments and applications of the multi-scale modeling system will be presented. In particular, the microphysics development and its performance for the multi-scale modeling system will be presented.

Tao, Wei-Kuo↗

Modeling Macro- and Micro-Scale Turbulent Mixing and Chemistry in Engine Exhaust Plumes

Simulation of turbulent mixing and chemical processes in the near-field plume and plume-vortex regimes has been successfully carried out recently using a reduced gas phase kinetics mechanism which substantially decreased the computational cost. A detailed mechanism including gas phase HOx, NOx, and SOx chemistry between the aircraft exhaust and the ambient air in near-field aircraft plumes is compiled. A reduced mechanism capturing the major chemical pathways is developed. Predictions by the reduced mechanism are found to be in good agreement with those by the detailed mechanism. With the reduced chemistry, the computer CPU time is saved by a factor of more than 3.5 for the near-field plume modeling. Distributions of major chemical species are obtained and analyzed. The computed sensitivities of major species with respect to reaction step are deduced for identification of the dominant gas phase kinetic reaction pathways in the jet plume. Both the near field plume and the plume-vortex regimes were investigated using advanced mixing models. In the near field, a stand-alone mixing model was used to investigate the impact of turbulent mixing on the micro- and macro-scale mixing processes using a reduced reaction kinetics model. The plume-vortex regime was simulated using a large-eddy simulation model. Vortex plume behind Boeing 737 and 747 aircraft was simulated along with relevant kinetics. Many features of the computed flow field show reasonable agreement with data. The entrainment of the engine plumes into the wing tip vortices and also the partial detrainment of the plume were numerically captured. The impact of fluid mechanics on the chemical processes was also studied. Results show that there are significant differences between spatial and temporal simulations especially in the predicted SO3 concentrations. This has important implications for the prediction of sulfuric acid aerosols in the wake and may partly explain the discrepancy between past numerical studies (that employed parabolic or temporal approximations) and the measured data. Finally to address the major uncertainty in the near-field plume modeling related to the plume processing of sulfur compounds and advanced model was developed to evaluate its impact on the chemical processes in the near wake. A comprehensive aerosol model is developed and it is coupled with chemical kinetics and the axisymmetric turbulent jet flow models. The integrated model is used to simulate microphysical processes in the near-field jet plume, including sulfuric acid and water binary homogeneous nucleation, coagulation, non-equilibrium heteromolecular condensation, and sulfur-induced soot activation. The formation and evolution of aerosols are computed and analyzed. The computed results show that a large number of ultra-fine (0.3--0.6 nm in radius) volatile HSO4 - HO embryos are generated in the near-field plume. These embryos further grow in size by self coagulation and condensation. Soot particles can be activated by both heterogeneous nucleation and scavenging of H2SO4-H2O aerosols. These activated soot particles can serve as water condensation nuclei for contrail formation. Conditions under which ice contrails can form behind aircrafts are studied. The sensitivities of the threshold temperature for contrail formation with respect to aircraft propulsion efficiency, relative humidity, and ambient pressure are evaluated. The computed aerosol properties for different extent of fuel sulfur conversion to S(VI) (SO3 and H2SO4) in engine are examined and the results are found to be sensitive to this conversion fraction.

Menon, Suresh↗

Integrated optics technology study

The materials and processes available for the fabrication of single mode integrated electrooptical components are described. Issues included in the study are: (1) host material and orientation, (2) waveguide formation, (3) optical loss mechanisms, (4) wavelength selection, (5) polarization effects and control, (6) laser to integrated optics coupling,(7) fiber optic waveguides to integrated optics coupling, (8) souces, (9) detectors. The best materials, technology and processes for fabrication of integrated optical components for communications and fiber gyro applications are recommended.

Chen, B.↗

The evolution of strongly modulated, low-frequency, moderate-amplitude wave packets in a dispersive plasma

The evolution of strongly modulated wave packets in a dispersive plasma that propagate parallel to the magnetic field is studied. Modulation effects are shown to reduce significantly (about 30 percent) the rate of spreading from that due to dispersion alone. For fluidlike behavior, nonlinearity has its greatest impact on evolution when the linear sound speed and initial wave packet speeds are well matched, resulting in a strong coupling between the wave magnetic and sonic components. Ion kinetic processes reduce the impact of nonlinearity and cause the rate of spreading to approach that expected from dispersion alone as the ratio of ion and electron temperatures, Ti/Te approaches 4. For Beta equal to or greater than 1 and Ti/Te of about 1, the coupled waveforms correspond qualitatively to kinetic treatments of the derivative nonlinear Schroedinger equation.

Vasquez, Bernard J.↗