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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Some Recent Observations on the Burning of Isolated N-Heptane and Alcohol Droplets

In a joint program involving Prof F.A. Williams of the University of California, San Diego and Dr. Vedha Nayagam of the National Center for Microgravity Research on Fluid and Combustion, the combustion of liquid fuel droplets having initial diameters between about 1 mm and 6 mm is being studied. The objectives of the work are to improve fundamental knowledge of droplet combustion dynamics through microgravity experiments and theoretical analyses. The Princeton contributions to the collaborative program supports the engineering design, data analysis, and data interpretation requirements for the study of initially single component, spherically symmetric, isolated droplet combustion studies through experiments and numerical modeling. The complementary UCSD contributions apply asymptotic theoretical analyses and are described in the published literature and in a companion communication in this volume. Emphases of the Princeton work are on the study of simple alcohols (methanol, ethanol), alcohol/water mixtures, and pure alkanes (n-heptane, n-decane) as fuels, with time dependent measurements of drop size, flame-stand-off, liquid-phase composition, and finally, extinction. Ground based experiments have included bench-scale studies at Princeton and collaborative experimental studies in the 2.2 and 5.18 second drop towers at NASA-Glenn Research Center. Spacelab studies have included fiber-supported droplet combustion (FSDC) experiments in the Glovebox facility with accompanying numerical analyses. Experiments include FSDC-1, performed on the USML-2 mission in October, 1995 (STS-73) and FSDC-2, on the second flight of the MSL-1 mission in July, 1997 (STS-94).

Dryer, F. L.↗
NASA NTRS1989

Utilization of non-conventional systems for conversion of biomass to food components

The potential use of micro-algae in yielding useful macronutrients for the CELSS is investigated. Algal proteins were isolated and characterized from green algae (Scenedesmus obliquus) grown under controlled conditions. The RNA and DNA contents were determined, and methodology for reduction of the nucleic acid content to acceptable levels developed. Lipid extraction procedures using supercritical fluids were tailored to removal of undesirable lipids and pigments. Initial steps toward preparation of model foods for potential use in the CELSS were taken. The goal was to fabricate food products which contain isolated algal macronutrients such as proteins and lipids and also some components derived from higher plants including wheat flour, soy flour, potato powder (flakes), soy oil, and corn syrup.

Karel, M.↗
NASA NTRS1975

Design of a heat pipe governed thermal control system for the Solar Electric Propulsion Stage /SEPS/

A 2200-w capacity spacecraft heat rejection system designed for the SEPS and utilizing heat pipe radiator panels has been investigated. The total thermal control system consists of two radiator panels connected to the heat source by variable conductance heat pipes (VCHP's). The system was designed to operate in the 223 to 333 temperature range. The radiators have an emittance of 0.88 at their operational temperature and a fin efficiency of approximately 80 percent. The radiators are thermally isolated from the SEPS and environment by multilayer insulation and thermal shields. Butane was selected as the working fluid for the VCHP because of its low freezing point (135), which is necessary to prevent diffusion freezeout of the liquid during the cold outbond missions. Helium was selected for the control gas. This paper describes the VCHP system, discusses the system design parameters and presents the results of the analyses.

Ruttner, L. E.↗
NASA NTRS1981

High power densities from high-temperature materials interactions

Thermionic energy converters and metallic-fluid heat pipes are well suited to serve together synergistically. The two operating cycles appear as simple and isolated as their material problems seem forebodingly deceptive and complicated. Simplified equations verify material properties and interactions as primary influences on the operational effectiveness of both. Each experiences flow limitations in thermal emission and vaporization because of temperature restrictions redounding from thermophysicochemical stability considerations. Topics discussed include: (1) successful limitation of alkali-metal corrosion; (2) protection against external hot corrosive gases; (3) coping with external and internal vaporization; (4) controlling interfacial reactions and diffusion; and (5) meeting other thermophysical challenges; expansion matches and creep.

Morris, J. F.↗
NASA NTRS2000

The Low Temperature Microgravity Physics Experiments Project

The Low Temperature Microgravity Physics Facility (LTMPF) is being developed by NASA to provide long duration low temperature and microgravity environment on the International Space Station (ISS) for performing fundamental physics investigations. Currently, six experiments have been selected for flight definition studies. More will be selected in a two-year cycle, through NASA Research Announcement. This program is managed under the Low Temperature Microgravity Physics Experiments Project Office at the Jet Propulsion Laboratory. The facility is being designed to launch and returned to earth on a variety of vehicles including the HII-A and the space shuttle. On orbit, the facility will be connected to the Exposed Facility on the Japanese Experiment Module, Kibo. Features of the facility include a cryostat capable of maintaining super-fluid helium at a temperature of 1.4 K for 5 months, resistance thermometer bridges, multi-stage thermal isolation system, thermometers capable of pico-Kelvin resolution, DC SQUID magnetometers, passive vibration isolation, and magnetic shields with a shielding factor of 80dB. The electronics and software architecture incorporates two VME buses run using the VxWorks operating system. Technically challenging areas in the design effort include the following: 1) A long cryogen life that survives several launch and test cycles without the need to replace support straps for the helium tank. 2) The minimization of heat generation in the sample stage caused by launch vibration 3) The design of compact and lightweight DC SQUID electronics. 4) The minimization of RF interference for the measurement of heat at pico-Watt level. 5) Light weighting of the magnetic shields. 6) Implementation of a modular and flexible electronics and software architecture. The first launch is scheduled for mid-2003, on an H-IIA Rocket Transfer Vehicle, out of the Tanegashima Space Center of Japan. Two identical facilities will be built. While one facility is onboard the ISS, the other is re-integrated on the ground with new experiments. When the cryogen of the facility in space are exhausted, it will be swapped with the other facility with the new experiment. A total of 20 science missions are envisioned over the next 20 years.

Holmes, Warren↗
NASA NTRS1999

Fluid/Solid Boundary Conditions in Non-Isothermal Systems

The existing theoretical research concerned with thermal creep at fluid/solid interfaces is briefly reviewed, and the importance of microgravity-based experimental data is then discussed. It is noted that the ultimate goal of this research is a rational molecular level theory that predicts the dependence of a dimensionless thermal creep coefficient, Ctc, on relevant dimensionless parameters describing the way fluid molecules interact with the solid surface and how they interact among themselves. The discussion covers thermophoresis of isolated solid spheres and aggregates in gases; solid sphere thermophoresis in liquids and dense vapors; thermophoresis of small immiscible liquid droplets; and applications of the direct simulation Monte Carlo method.

Rosner, Daniel E.↗
NASA NTRS2001

Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic and Structural Design Optimization (SASDO) is shown as an extension of the Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) method. It is extended by the inclusion of structure element sizing parameters as design variables and Finite Element Method (FEM) analysis responses as constraints. The method aims to reduce the computational expense. incurred in performing shape and sizing optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, FEM structural analysis and sensitivity analysis tools. SASDO is applied to a simple. isolated, 3-D wing in inviscid flow. Results show that the method finds the saine local optimum as a conventional optimization method with some reduction in the computational cost and without significant modifications; to the analysis tools.

Gumbert, Clyde R.↗
NASA NTRS1998

Damping Mechanisms for Microgravity Vibration Isolation (MSFC Center Director's Discretionary Fund Final Report, Project No. 94-07)

As a research facility for microgravity science, the International Space Station (ISS) will be used for numerous investigations such as protein crystal growth, combustion, and fluid mechanics experiments which require a quiescent acceleration environment across a broad spectrum of frequencies. These experiments are most sensitive to low-frequency accelerations and can tolerate much higher accelerations at higher frequency. However, the anticipated acceleration environment on ISS significantly exceeds the required acceleration level. The ubiquity and difficulty in characterization of the disturbance sources precludes source isolation, requiring vibration isolation to attenuate the anticipated disturbances to an acceptable level. This memorandum reports the results of research in active control methods for microgravity vibration isolation.

Whorton, M. S.↗
NASA NTRS2021

CubeSat Active Thermal Control in Support of Advanced Payloads: The Active Thermal Architecture Project

The Active Thermal Architecture (ATA) is an advanced sub-1U Active Thermal Control technology (ATC) for high power payload support in 6U CubeSat form factors and above. The design utilizes a two-stage, single-phase mechanically pumped fluid loop coupled through a two-axis flexible rotary fluid hinge, to reject thermal power to a deployable tracking radiator. A COTS Ricor K508N cryocooler forms the second stage and provides cryogenic cooling to a custom Kevlar detector mount through a TMT pyrolytic graphene thermal strap. Passive vibration isolation and damping technologies prevent the transfer of jitter to the satellite systems. The ATA design utilizes state-of-the-art 3D fabrication techniques such as Ultrasonic Additive Manufacturing (UAM) to directly embed the working fluid channels into the HX, radiator, and CubeSat chassis allowing for the miniaturization and simplification of the ATA system into an integrated thermal control solution. This paper will focus on the design and ground-based characterization and qualification of the ATA system and provide performance metrics for its use as a thermal support subsystem for advanced infrared electro-optical CubeSat payloads. The ATA project is funded through a NASA Small Satellite Technology Program (SSTP) and is a partnership between the Center for Space Engineering at Utah State University and the Jet Propulsions Laboratory. The ATA active thermal control system has been raised to a TRL of 6 and hopes to provide payload support to advanced missions such as the SABER-Lite and JPL CIRAS projects.

Mok, Mason↗
NASA NTRS1993

Modeling of PCG fluid dynamics: Salient results

Materials processing in space-based laboratories has already yielded higher quality crystals during previous space flights, and opportunities for several fluids experiments are anticipated during the extended duration missions planned for the future. Crystal growth in space benefits not only from its reduced gravity environment but also from the absence of the hydrostatic pressure which assists certain crystal growth and refinement methods. Gravity-driven phenomena are thus reduced in strength, and a purely diffusive fluid's behavior can be attained. In addition, past materials science experiments have shown that microgravity can also help produce larger crystals. While gravity-related effects are definitely curtailed in space, they are nevertheless present to some degree due to the acceleration environment onboard the spacecraft. This residual acceleration level is comprised of quasi-steady, oscillatory, and transient components, and is caused by a variety of mechanisms. For example, gravity gradient forces produce low frequency disturbances, and the operation of machinery, control thrusters, solar panels, human activity, etc. contribute to higher frequency accelerations. These disturbances are collectively referred to as g-jitter, and they can be deleterious to certain experiments where the minimization of the acceleration level is important. Advanced vibration isolation techniques can be utilized to actively filter out some of the detrimental frequencies and help in obtaining optimum results. However, the successful application of this technology requires the detailed analysis of candidate fluids experiments to gauge their response to g-jitter and to determine their acceleration sensitivities. Several crystal growth experiments in the Protein Crystal Growth (PCG) area, besides others, are expected to be carried out on future shuttle flights and on Space Station Freedom. The need for vibration isolation systems or components for microgravity science experiments can be expected to grow as experiments and available hardware becomes more complex. This technology will also find increased application as the science community develops an awareness of their specific needs relative to the environment available in manned space missions. Vibration isolation research strives to develop a microgravity environment requirement that defines tolerance limits on the allowable g-level, and provides the required technology to achieve it. This effort will assist in establishing the tolerable acceleration levels for specific fluids experiments. The primary effort is directed towards modeling PCG and the approach undertaken for this investigation is outlined. The objectives of this research are: (1) to computationally determine vibration sensitivity of protein crystal growth experiments; (2) determine if these experiments can benefit from vibration isolation techniques; and (3) provide realistic requirements for vibration isolation technology.

Ramachandran, N.↗
NASA NTRS2000

Stereo Imaging Velocimetry of Mixing Driven by Buoyancy Induced Flow Fields

Mixing of two fluids generated by steady and particularly g-jitter acceleration is fundamental towards the understanding of transport phenomena in a microgravity environment. We propose to carry out flight and ground-based experiments to quantify flow fields due to g-jitter type of accelerations using Stereo Imaging Velocimetry (SIV), and measure the concentration field using laser fluorescence. The understanding of the effects of g-jitter on transport phenomena is of great practical interest to the microgravity community and impacts the design of experiments for the Space Shuttle as well as the International Space Station. The aim of our proposed research is to provide quantitative data to the community on the effects of g-jitter on flow fields due to mixing induced by buoyancy forces. The fundamental phenomenon of mixing occurs in a broad range of materials processing encompassing the growth of opto-electronic materials and semiconductors, (by directional freezing and physical vapor transport), to solution and protein crystal growth. In materials processing of these systems, crystal homogeneity, which is affected by the solutal field distribution, is one of the major issues. The understanding of fluid mixing driven by buoyancy forces, besides its importance as a topic in fundamental science, can contribute towards the understanding of how solutal fields behave under various body forces. The body forces of interest are steady acceleration and g-jitter acceleration as in a Space Shuttle environment or the International Space Station. Since control of the body force is important, the flight experiment will be carried out on a tunable microgravity vibration isolation mount, which will permit us to precisely input the desired forcing function to simulate a range of body forces. To that end, we propose to design a flight experiment that can only be carried out under microgravity conditions to fully exploit the effects of various body forces on fluid mixing. Recent flight experiments, by the P.I. through collaboration with the Canadian Space Agency (STS-85, August 1997), aimed at determining the stability of the interface between two miscible liquids inside an enclosure show that a long liquid column (5 cm) under microgravity isolation conditions can be stable, i.e. the interface remains sharp and vertical over a short time scale; thus transport occurs by molecular mass diffusion. On the other hand, when the two liquids were excited from a controlled vibration source (Microgravity Vibration Isolation Mount) two to four mode large amplitude quasi-stationary waves were observed. The data was limited to CCD recording of the dynamics of the interface between the two fluids. We propose to carry out flight experiments to quantify the dynamics of the flow field using Stereo Imaging Velocimetry and measure the concentration field using laser fluorescence. The results will serve as a basis to understand effects of g-jitter on transport phenomena, in this case mass diffusion. As the measurement of the kinematics of the flow field will shed light on the instability mechanism. The research will allow measurement of the flow field in microgravity environment to prove two hypotheses: (1) Maxwell's hypothesis: finite convection always exists in diffusing systems, and (2) Quasi-stationary waves inside a bounded enclosure in a microgravity environment is generated by Kelvin-Helmholtz instability; resonance of the interface which produces incipient mixing is due to Rayleigh-Taylor instability. The first hypothesis can be used as a benchmark experiment to illustrate diffusive mixing. The second hypothesis will lead to the understanding of g-jitter effects on buoyancy driven flow fields which occur in many situations involving materials processing, and other basic fluid physics phenomena. In addition, the second hypothesis will also provide insight in how Rayleigh-Taylor and Kelvin-Helmholtz instabilities propagate concentration fronts during mixing. Measurement of the flow field using SIV is important because it is the flow field which causes instability at the interface between the two fluids. Mixing driven by buoyancy induced flow fields will be addressed both experimentally and computationally. The experimental effort will address the kinematics of mixing: stretching, transport and chaos. Quantification of the mechanisms of mixing will consists of measuring the flow field using the SIV system at Glenn and capturing the dynamics of the interface, to measure mass transport, using a CCD camera. These experiments will be carried out within the framework of Earth's gravity and g-jitter microgravity acceleration as in a Space Shuttle environment or the International Space Station. The g-jitter will be induced and controlled using a tunable vibration isolation platform to isolate against vibration as well as input periodic and random vibration to the system. The parametric range of the microgravity experiment will be extended from the experiments on STS-85 to investigate higher mode quasi-stationary waves (8 to 12), as well as resonance regions which leads to chaos and turbulence. Ground-based experiments will focus on effects of vibration on stably stratified fluid layers in order to scale for possible scenarios in a microgravity environment. These vibrations will be subjected perpendicular to the concentration field on the ground since the parallel case can only be carried out in a microgravity environment. The concept of dynamical similarity will be applied to tune the experiments as closely as possible to a Space Shuttle environment or the International Space Station. The computational effort will take advantage of the Computational Laboratory at Glenn to corroborate the experimental findings with predictions of the dynamics of the flow field using the codes FLUENT (finite difference based) and FIDAP (finite element based). We will investigate two important cases, single-fluid model to address dilute systems with negligible jump in viscosity and the more general two-fluid model which accounts for finite jump in viscosity. Apart from its microgravity relevance, this experiment is well suited to study dynamics in nonlinear systems.

Duval, W. M. B.↗
NASA NTRS2001

Some Recent Observations on the Burning of Isolated N-Heptane and Alcohol Droplets

In a joint program involving Prof. F.A. Williams of the University of California, San Diego and Dr. V. Nayagam of the National Center for Microgravity Research on Combustion and Fluid Dynamics, the combustion of liquid fuel droplets of n-heptane, n-decane, methanol, methanol-water, ethanol and ethanol-water having initial diameters between about 1 mm and 6 mm continues to be studied. The objectives of the work are to improve fundamental knowledge of droplet combustion dynamics for pure fuels and fuel-water mixtures through microgravity experiments and theoretical analyses. The Princeton contributions to the collaborative program supports the engineering design, data analysis, and data interpretation requirements for the study of initially single component, spherically symmetric, isolated droplet combustion studies through experiments and numerical modeling. The complementary UCSD contributions apply asymptotic theoretical analyses and are described in the published literature and in a companion communication in this conference. The combined program continues to focus on analyses of results obtained from Fiber Supported Droplet Combustion (FSDC) experiments (FSDC-2, STS- 94) conducted with the above fuels in shuttle cabin air and Droplet Combustion Experiment (DCE) data obtained for unsupported and fiber supported droplets of n-heptane in Helium-Oxygen mixtures and cabin air (STS-83, STS-94). The program is preparing for a second DCE experimental mission using methanol/methanol-water as fuels and helium-oxygen-nitrogen environments. DCE-2 is to be conducted aboard the International Space Station. Emphases of recent Princeton work are on the study of simple alcohols (methanol, ethanol) and alcohol/water mixtures as fuels, with time-dependent measurements of drop size, flame-standoff, liquid-phase composition, and finally, extinction. Ground based experiments have included bench-scale studies at Princeton and collaborative experimental studies in the 2.2 second drop tower at NASA-Glenn Research Center.

Dryer, F. L.↗
DOE OSTI2023

Impedance‐matching model‐in‐the‐loop simulation

Abstract Impedance matching is a novel approach to executing model‐in‐the‐loop (MIL) simulations. The concept, key features, and sample applications of this approach have been described in a series of publications. This paper advances theory and implementation for impedance‐matching MIL by: (1) developing a feedback linearization technique for implementing MIL for nonlinear virtual systems, (2) systematically characterizing MIL performance‐stability tradeoffs using three design‐oriented criteria—performance: defined as closeness of the controlled‐actuator impedance to the virtual‐boundary impedance;control effort: low controller response at high frequencies to reduce sensitivity to measurement noise and uncertainties in the actuator model; andstability: pursued using passivity of the controlled actuator system, and (3) assessing, through experimentation, the robustness of two ways to estimate feedback reaction force from the test article. These fundamental advancements to MIL are described using a one‐dimensional configuration consisting of a fluid‐filled cylindrical vessel as the physical test article and a uniaxial hydraulic shake table controlled to imitate different seismic isolation systems at the base of the vessel.

Engineering↗
DOE OSTI2024

Detection and Characterization of Influenza A Virus Endemic Circulation in Suckling and Nursery Pigs Originating from Vaccinated Farms in the Same Production System

Inactivated influenza A virus (IAV) vaccines help reduce clinical disease in suckling piglets, although endemic infections still exist. The objective of this study was to evaluate the detection of IAV in suckling and nursery piglets from IAV-vaccinated sows from farms with endemic IAV infections. Eight nasal swab collections were obtained from 135 two-week-old suckling piglets from four farms every other week from March to September 2013. Oral fluid samples were collected from the same group of nursery piglets. IAV RNA was detected in 1.64% and 31.01% of individual nasal swabs and oral fluids, respectively. H1N2 was detected most often, with sporadic detection of H1N1 and H3N2. Whole-genome sequences of IAV isolated from suckling piglets revealed an H1 hemagglutinin (HA) from the 1B.2.2.2 clade and N2 neuraminidase (NA) from the 2002A clade. The internal gene constellation of the endemic H1N2 was TTTTPT with a pandemic lineage matrix. The HA gene had 97.59% and 97.52% nucleotide and amino acid identities, respectively, to the H1 1B.2.2.2 used in the farm-specific vaccine. A similar H1 1B.2.2.2 was detected in the downstream nursery. These data demonstrate the low frequency of IAV detection in suckling piglets and downstream nurseries from farms with endemic infections in spite of using farm-specific IAV vaccines in sows.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2013

Time Averaged Pressure Measurement in Fundamentally Unsteady Pressure Gain Combustion Systems

Experimental results and analysis are presented on a technique for obtaining time averaged pressure in the harsh and highly unsteady environment of a pressure gain combustor. The technique utilizes a long, narrow, stand-off tube leading from the measurement point to a pressure transducer. The tube damps the fluctuations (which may result from strong shocks and/or detonations) and thermally isolates the transducer. The damping must be sufficient to ensure that net gasdynamic work exchange does not occur on the fluid in the stand-off tube, and it must be linear to insure that the time-averaged pressure at the transducer end is the same as that at the combustor end. The paper presents experimental and analytical results from two rigs which indicate that, using certain stand-off tube dimensions, these criteria are met. Physical rational for the tube dimensions (i.e., guidelines) are also presented.

detonation↗
NASA NTRS1987

Passive isolation/damping system for the Hubble space telescope reaction wheels

NASA's Hubble Space Telescope contain large, diffraction limited optics with extraordinary resolution and performance for surpassing existing observatories. The need to reduce structural borne vibration and resultant optical jitter from critical Pointing Control System components, Reaction Wheels, prompted the feasibility investigation and eventual development of a passive isolation system. Alternative design concepts considered were required to meet a host of stringent specifications and pass rigid tests to be successfully verified and integrated into the already built flight vehicle. The final design employs multiple arrays of fluid damped springs that attenuate over a wide spectrum, while confining newly introduced resonances to benign regions of vehicle dynamic response. Overall jitter improvement of roughly a factor of 2 to 3 is attained with this system. The basis, evolution, and performance of the isolation system, specifically discussing design concepts considered, optimization studies, development lessons learned, innovative features, and analytical and ground test verified results are presented.

Hasha, Martin D.↗
DOE OSTI2023

Characterizing the seismic response of a molten salt nuclear reactor

Abstract One Generation IV nuclear reactor, which uses a fluoride salt as a coolant, graphite reflector blocks as a moderator, and circulating buoyant TRISO pebbles as fuel is at an advanced stage of development. To characterize the seismic behavior of components of this reactor, validate numerical models for analysis, and develop recommendations for design, a set of earthquake‐simulator experiments on a scaled model of the reactor vessel and its internals was executed on a six‐degree‐of‐freedom earthquake simulator. The model was seismically isolated at its base using two types of spherical sliding bearings. The scaled model involved representations of the prototype reactor vessel, core barrel, reflector blocks, coolant, and spherical fuel pebbles. The material and geometric properties of different test components were selected based on a dynamic similitude scaling analysis and an approximate length scale of 0.4. Four sets of three‐component earthquake motions were used as inputs for testing. Instrumentation on the test specimen recorded the dynamic responses of the outer vessel, core barrel, and reflector‐block assembly, the hydrodynamic responses (sloshing and hydrodynamic pressure) of the liquid coolant, pebble consolidation under earthquake shaking, and the behavior of the isolation systems. This paper describes the design of the experiments and presents key results from the tests. The dynamic responses of the outer vessel, core barrel, and the reflector blocks revealed that the components responded as a unit for the intense shaking used in the experiments. The sloshing response of the fluid in a thin annulus near the perimeter of the vessel was heavily damped. The change in the packing fraction of the pebble bed under repeated, intense 3D earthquake shaking was less than 3%. Seismically isolating the vessel substantially reduced demands on its internal components.

Engineering↗
NASA NTRS1985

The method of complex characteristics for transonic airfoil design, with an application to compressors

The use of mathematical models to study physical problems of current interest to aeronautical engineers has been made possible by the development of numerical techniques to compute solutions of the differential equations of transonic aerodynamics. These advances have encouraged the improvement of supercritical wing technology. A method to determined steady, shockless flow of an inviscid, compressible fluid past a cascade of airfoils in the (x,y)-plane is considered, taking into account also the case of an isolated airfoil. The method of complex characteristics solves the equations in the hodograph plane by extending all variables into the complex domain, where the notion of type is no longer significant. Attention is given to the mathematical background, the method of complex characteristics, and numerical calculations.

Bledsoe, M.↗