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1,140 records · Page 64

Correspondence between discrete and continuous models of excitable media: trigger waves

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Non-NASA Center↗

Surface Modeling and Grid Generation for Iced Airfoils (SmaggIce)

Many of the troubles associated with problem solving are alleviated when there is a model that can be used to represent the problem. Through the Advanced Graphics and Visualization (G-VIS) Laboratory and other facilities located within the Research Analysis Center, the Computer Services Division (CSD) is able to develop and maintain programs and software that allow for the modeling of various situations. For example, the Icing Research Branch is devoted to investigating the effect of ice that forms on the wings and other airfoils of airplanes while in flight. While running tests that physically generate ice and wind on airfoils within the laboratories and wind tunnels on site are done, it would be beneficial if most of the preliminary work could be done outside of the lab. Therefore, individuals from within CSD have collaborated with Icing Research in order to create SmaggIce. This software allows users to create ice patterns on clean airfoils or open files containing a variety of icing situations, manipulate and measure these forms, generate, divide, and merge grids around these elements for more explicit analysis, and specify and rediscretize subcurves. With the projected completion date of Summer 2005, the majority of the focus of the Smagglce team is user-functionality and error handling. My primary responsibility is to test the Graphical User Interface (GUI) in SmaggIce in order to ensure the usability and verify the expected results of the events (buttons, menus, etc.) within the program. However, there is no standardized, systematic way in which to test all the possible combinations or permutations of events, not to mention unsolicited events such as errors. Moreover, scripting tests, if not done properly and with a view towards inevitable revision, can result in more apparent errors within the software and in effect become useless whenever the developers of the program make a slight change in the way a specific process is executed. My task therefore requires a brief yet intense study into GUI coverage criteria and creating algorithms for GUI implementation. Nevertheless, there are still heavily graphical features of SmaggIceSmaggIce that must be either corrected or redesigned before its release. A particular feature of SmaggIce is the ability to smooth out curves created by control points that form an arbitrary shape into something more acquiescent to gridding (while maintaining the integrity of the data). This is done by a mathematical model known as Non-Uniform Rational B-Spline (NURBS) curves. Existing NURBS code is written in FORTRAN-77 with static arrays for holding information. My new assignment is to allow for dynamic memory allocation within the code and to make it possible for the developers to call out functions from the NURBS code using C.

Hammond, Brandy M.↗

Using Coupled Models to Study the Effects of River Discharge on Biogeochemical Cycling and Hypoxia in the Northern Gulf of Mexico

We describe emerging capabilities to understand physical processes and biogeoehemical cycles in coastal waters through the use of satellites, numerical models, and ship observations. Emerging capabilities provide significantly improved ability to model ecological systems and the impact of environmental management actions on them. The complex interaction of physical and biogeoehemical processes responsible for hypoxic events requires an integrated approach to research, monitoring, and modeling in order to fully define the processes leading to hypoxia. Our efforts characterizes the carbon cycle associated with river plumes and the export of organic matter and nutrients form coastal Louisiana wetlands and embayments in a spatially and temporally intensive manner previously not possible. Riverine nutrients clearly affect ecosystems in the northern Gulf of Mexico as evidenced in the occurrence of regional hypoxia events. Less known and largely unqualified is the export of organic matter and nutrients from the large areas of disappearing coastal wetlands and large embayments adjacent to the Louisiana Continental Shelf. This project provides new methods to track the river plume along the shelf and to estimate the rate of export of suspended inorganic and organic paniculate matter and dissolved organic matter form coastal habitats of south Louisiana.

COUPLED MODEL↗

IYL Blog: Astronomers travel in time and space with light

As an astronomer, I use light to travel through the universe, and to look back in time to when the universe was young. So do you! All of us see things as they were when the light was emitted, not as they are now. The farthest thing you can easily see without a telescope is the Andromeda Nebula, which is a galaxy like the Milky Way, about 2.5 million light years away. You see it as it was 2.5 million years ago, and we really don't know what it looks like today; the disk will have rotated a bit, new stars will have been born, there could have been all kinds of exploding stars, and the black hole in the middle could be lighting up. People may be skeptical of the Big Bang theory, even though we have a TV show named for it, but we (I should say Penzias and Wilson) measured its heat radiation 51 years ago at Bell Telephone Labs in New Jersey. Their discovery marks the beginning of the era of cosmology as a measurement science rather than speculation. Penzias and Wilson received the Nobel Prize in 1978 for their finding, which had been predicted in 1948 by Alpher and Herman. By the way, heat radiation is just another form of light - we call it radiation because we can't see it, but it's exactly the same phenomenon of electromagnetic waves, and the only difference is the wavelength. In the old days of analog television, if you tuned your TV in between channels, about 1% of the snow that you could see came from the Big Bang. So when we look at the heat radiation of the early universe, we really are gazing right at what seems to us a cosmic fireball, which surrounds us completely. It's a bit of an illusion; if you can imagine what astronomers in other galaxies would see, they would also feel surrounded by the fireball, and they would also think they were in the middle. So from a mathematical version of imagination, we conclude that there is no observable center and no edge of our universe, and that the heat of the fireball fills the entire universe uniformly. Astronomers are also using light to find out whether we are alone in the universe. The Kepler observatory showed that thousands of stars blink a little when their orbiting planets pass between us and them, and other observatories use light to measure the wobble of stars as their planets pull on them. Eventually, we will find out whether planets like Earth have atmospheres like Earth's too - with water, carbon dioxide, oxygen, methane, and other gases that would be evidence of photosynthetic life. I think in a few decades we will have evidence that some planets do have life, and it will be done using light for remote chemical analysis. Also, astronomers at the SETI project are using light (long wavelength light we can pick up with radio telescopes) to look for signals from intelligent civilizations. That's a harder project because we don't know what to look for. But if we wanted to send signals all the way across the Milky Way, we could do it with laser beams, and if somebody over there knew what to look for, he or she could decode the message. On with the search! Dr. John C. Mather is a Senior Astrophysicist and is the Senior Project Scientist for the James Webb Space Telescope at NASA's Goddard Space Flight Center in Greenbelt, MD. His research centers on infrared astronomy and cosmology. With the Cosmic Background Explorer (COBE) team, he showed that the cosmic microwave background radiation has a blackbody spectrum within 50 parts per million, confirming the expanding universe model (aka the Big Bang Theory) to extraordinary accuracy, and initiating the study of cosmology as a precision science. The COBE team also made the first map of the hot and cold spots in the background radiation. The COBE maps have been confirmed and improved by two succeeding space missions, the Wilkinson Microwave Anisotropy Probe (WMAP, built by GSFC with Princeton University), and the Planck mission built by ESA. Based on these maps, astronomers have now developed a "standard model" of cosmology and have built detailed numerical simulations that begin to match Hubble observations, and require the existence of both "dark matter" and "dark energy", neither of which has been detected or deduced in laboratory experiments. Dr. Mather is the recipient of numerous awards, including the Nobel Prize in Physics (2006) with George Smoot, for the COBE work, and the NASA Distinguished Service Medal (2007). He is a member of many professional societies including the National Academy of Sciences and the American Academy of Arts and Sciences. Dr. Mather is now working with teams and committees to develop plans for a future great telescope capable of observing signs of life on planets orbiting other stars.

telescopes↗

"Electrostructural Phase Changes" In Charged Particulate Clouds: Planetary and Astrophysical Implications

There is empirical evidence that freely-suspended triboelectrostatically charged particulate clouds of dielectric materials undergo rapid conversion from (nominally) monodispersed "aerosols" to a system of well-defined grain aggregates after grain motion or fluid turbulence ceases within the cloud. In United States Microgravity Laboratory Space Shuttle experiments USML-1 and USML-2, it was found that ballistically-energized grain dispersions would rapidly convert into populations of filamentary aggregates after natural fluid (air) damping of grain motion. Unless continuously disrupted mechanically, it was impossible to maintain a non-aggregated state for the grain clouds of sand-size materials. Similarly, ground- based experiments with very fine dust-size material produced the same results: rapid, impulsive "collapse" of the dispersed grains into well-defined filamentary structures. In both ground-based and microgravity experiments, the chains or filaments were created by long-range dipole electrostatic forces and dipole-induced dielectric interactions, not by monopole interactions. Maintenance of the structures was assisted by short-range static boundary adhesion forces and van der Waals interactions. When the aggregate containers in the USML experiments were disturbed after aggregate formation, the quiescently disposed filaments would rearrange themselves into fractal bundles and tighter clusters as a result of enforced encounters with one another. The long-range dipole interactions that bring the grains together into aggregates are a product of randomly-distributed monopole charges on the grain surfaces. In computer simulations, it has been shown that when the force vectors of all the random charges (of both sign) on a grain are resolved mathematically by assuming Coulombic interaction between them, the net result is a dipole moment on individual grains, even though the grains are electrically neutral insofar as there is no predominance, on their surface, of one charge sign over another. The random charges of both sign derive from natural grain-to-grain interactions that produce triboelectrification via charge exchange every time grain surfaces make contact with one another. The conversion from a random distribution of grains (upon which there are randomly distributed charges) into an organization of electrostatically-ordered aggregates, can be regarded (within the framework of granular-material science) as an "electrical or Coulombic phase change" of the particulate cloud. It is not totally dissimilar from the more normal phase-change concept in which, for example, a gas with long free-path-molecules suddenly becomes a solid as a result of structural ordering of the molecules (notably, also the result of electronic forces, albeit at a different scale). In both the gas-to-solid case, and the aerosol-to-aggregate case, the same materials and charges are present before and after the phase change, but their arrangement now has a higher degree of order and a lower-energy configuration. An input of energy into the system is required to reverse the situation. The aggregates in the USML experiments were observed to undergo at least two phase changes as noted above. The point about phase changes, and by implication, the "electrostructural" reorganizations in particulate clouds, is the following: (a) they can occur very rapidly, almost spontaneously, above a critical cloud density, (b) in going from a higher energy state to a lower energy state, they convert to a denser system, (c) energy must be required to reverse the situation, implying that energy is released during the high-to-low energy phase change. In applying this information to natural particulate clouds, some inferences can be made (it is stressed that reference is still to dielectric materials attracted by dipole forces). There are several natural settings to which the USML observations apply, and to which the phase-change implications likewise apply. Dense clouds of triboelectrically-charged, kinetically-energized grains are to be found in volcanic eruptions (particularly on earth), aeolian dust storms (particularly on Mars), meteorite impact ejecta curtains (on all planets), in "immature" debris rings around planets (e.g., that from which our own Moon may have condensed), and in gravitationally collapsing protoplanetary dust/planetesimal debris disks where dielectric granules are being increasingly brought into collisional relationships with one another (increasing both charge exchange and physical proximity). It is noted that in many of these cases, the degree of electrical charging on the grains is likely to be much higher than that in the USML experiments where charging was not enhanced above the "normal", naturally encountered level for the particular materials (quartz, glass, and various silicate minerals). Application of the phase-change concept suggests that volcanic, aeolian, and impact debris clouds may, under certain circumstances, undergo rapid, impulsive, or even catastrophic collapse into a denser state that will lead to rapid precipitation or fall-out of suspended particulates. Although this idea has been suggested previously by the author , the phase change concept possibly permits some new insights into cloud-system behavior. For example, in a protoplanetary debris disk, the work of gravity may suddenly be enhanced by electrostatically driven collapse of the system when materials reach a critical intergranular spacing or grain number density. This might reduce the rate of planet formation by orders of magnitude (considering the ratio of g-forces to electrostatic ones for very small grains in close proximity), and indeed, it might drive the collapse into a system configuration that would perhaps not be created by gravity alone. Additional information is contained in the original.

Marshall, J. R.↗

Computational Modeling of Space Physiology for Informing Spaceflight Countermeasure Design and Predictions of Efficacy

MOTIVATION: Spaceflight countermeasures mitigate the harmful effects of the space environment on astronaut health and performance. Exercise has historically been used as a countermeasure to physical deconditioning, and additional countermeasures including lower body negative pressure, blood flow occlusion and artificial gravity are being researched as countermeasures to spaceflight-induced fluid shifts. The NASA Digital Astronaut Project uses computational models of physiological systems to inform countermeasure design and to predict countermeasure efficacy.OVERVIEW: Computational modeling supports the development of the exercise devices that will be flown on NASAs new exploration crew vehicles. Biomechanical modeling is used to inform design requirements to ensure that exercises can be properly performed within the volume allocated for exercise and to determine whether the limited mass, volume and power requirements of the devices will affect biomechanical outcomes. Models of muscle atrophy and bone remodeling can predict device efficacy for protecting musculoskeletal health during long-duration missions. A lumped-parameter whole-body model of the fluids within the body, which includes the blood within the cardiovascular system, the cerebral spinal fluid, interstitial fluid and lymphatic system fluid, estimates compartmental changes in pressure and volume due to gravitational changes. These models simulate fluid shift countermeasure effects and predict the associated changes in tissue strain in areas of physiological interest to aid in predicting countermeasure effectiveness. SIGNIFICANCE: Development and testing of spaceflight countermeasure prototypes are resource-intensive efforts. Computational modeling can supplement this process by performing simulations that reduce the amount of necessary experimental testing. Outcomes of the simulations are often important for the definition of design requirements and the identification of factors essential in ensuring countermeasure efficacy.

biomedical data↗