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Results for “Conformal Field Theory”

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NASA NTRS1956

Formation of a vortex at the edge of a plate

The flow about the plate of infinite width may be represented as a potential flow with discontinuity surfaces which extend from the plate edges. For prescribed form and vortex distribution of the discontinuity surfaces, the velocity field may be calculated by means of a conformal representation. One condition is that the velocity at the plate edges must be finite. However, it is not sufficient for determination of the form and vortex distribution of the surface. However, on the basis of a similitude requirement one succeeds in finding a solution of this problem for the plate of infinite width which is correct for the very beginning of the motion of the fluid. Starting from this solution, the further development of the vortex distribution and shape of the surface are observed in the case of a plate of finite width.

THEORIES - VORTEX↗

NASA NTRS1995

Solar wind theory and modelling

The outflow of coronal plasma into interplanetary space is a consequence of the coronal heating process. Therefore the formation of the corona and the acceleration of the solar wind should be treated as a single problem. Traditionally the mass or particle flux emanating from the extended corona has been thought of as being determined by the coronal temperature or scale height and the coronal (base) density. This argument follows from considerations of the momentum balance of the corona-wind system from which one obtains models of a close to hydrostatic corona out to the critical point where the flow becomes supersonic. With this approach to the acceleration of the wind is has been difficult to reconcile the relatively small variation observed in the proton flux at 1 AU with the predicted exponential dependence of the proton flux on the coronal temperature. In this talk we would like to emphasize another approach in which coronal energetics play the primary role. The deposition of energy into the corona through some 'mechanical' energy flux is balanced by the various energy sinks available to the corona and the sum of these processes determine the coronal structure, i.e. its temperature and density. The corona loses energy through heat conduction into the transition region, through radiative losses, and through the gravitational potential energy and kinetic energy put into the solar wind itself. We will show from a series of models of the chromosphere transition region-corona-solar wind system that most of the energy deposited in a magnetically open region will go into the solar wind, with roughly half going into kinetic energy and half into lifting the plasma out of the solar gravity field. The coronal base density will adjust itself in such a way that the heat conductive flux flowing into the transition region is radiated away in the upper chromosphere. The coronal temperature is set by the requirements that most of the deposited energy goes into accelerating the solar wind; the coronal scale height will adjust itself so that the solar wind energy losses conform to the amplitude of the input energy. These processes are modified by the 'mode' of energy deposition, and we will show the effects on coronal structure of changing the parameters describing coronal heating as well as the effects of including a helium fluid in the models. However, the location, scale height and/or form of the energy deposition (i.e. heating or direct acceleration) are not too important for the solar wind, the coronal density and temperature structure will vary with the 'mode' of energy deposition, but the solar wind mass flux depends mainly on the amplitude of the energy flux.

Hansteen, Viggo H.↗

NASA NTRS2002

Spatial distribution and yield of DNA double-strand breaks induced by 3-7 MeV helium ions in human fibroblasts

Accelerated helium ions with mean energies at the target location of 3-7 MeV were used to simulate alpha-particle radiation from radon daughters. The experimental setup and calibration procedure allowed determination of the helium-ion energy distribution and dose in the nuclei of irradiated cells. Using this system, the induction of DNA double-strand breaks and their spatial distributions along DNA were studied in irradiated human fibroblasts. It was found that the apparent number of double-strand breaks as measured by a standard pulsed-field gel assay (FAR assay) decreased with increasing LET in the range 67-120 keV/microm (corresponding to the energy of 7-3 MeV). On the other hand, the generation of small and intermediate-size DNA fragments (0.1-100 kbp) increased with LET, indicating an increased intratrack long-range clustering of breaks. The fragment size distribution was measured in several size classes down to the smallest class of 0.1-2 kbp. When the clustering was taken into account, the actual number of DNA double-strand breaks (separated by at least 0.1 kbp) could be calculated and was found to be in the range 0.010-0.012 breaks/Mbp Gy(-1). This is two- to threefold higher than the apparent yield obtained by the FAR assay. The measured yield of double-strand breaks as a function of LET is compared with theoretical Monte Carlo calculations that simulate the track structure of energy depositions from helium ions as they interact with the 30-nm chromatin fiber. When the calculation is performed to include fragments larger than 0.1 kbp (to correspond to the experimental measurements), there is good agreement between experiment and theory.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS1997

Study of a Solar X-Ray Telescope

The highly structured nature of the outer solar atmosphere seems to be intimately linked to the presence, at the solar surface, of magnetic fields that have been generated inside the Sun and have emerged to the surface. The corona is brightest (and also hottest) at just those locations where the magnetic field has emerged from inside the Sun. Dynamo theory predicts that strong magnetic fields will be generated deep in the solar interior and that bundles or 'ropes' of magnetic flux will float to the surface. When this happens, a magnetically bipolar region will become visible, extending above the surface in a three-dimensional structure. The field lines penetrate through the surface, showing two magnetic poles, and also exhibit a three-dimensional structure above the surface. The structure created by the field emergence is rooted in the (relatively) cool photosphere and extends through the chromosphere and transition region to the corona. Thus, the magnetic field creates a region, called an active region, which contains portions at temperatures from less than 10(exp 4) K to greater than 10(exp 6) K, and is therefore visible at wavelengths from the infrared through x-rays. The locations where the magnetic field leaves and reenters the visible surface are called the 'footpoints' of the coronal structures associated with the magnetic field. The magnetic fields themselves are not directly visible. However, the hot coronal plasma is, for the most part, constrained to follow the direction of the magnetic field lines in the atmosphere. Now, 100 years after the discovery of x-rays by Wilhelm Roentgen in 1896, we can routinely make observations of the solar corona from outside the Earth's atmosphere in this region of the electromagnetic spectrum. As shown by comparing x-ray images with magnetograms, the bright corona over these bipolar magnetic regions consists of closed structures that seem to follow the orientation of the magnetic field. Although we can see down to the photosphere at x-ray wavelengths when observing the disk of the Sun, this part of the solar atmosphere emits so little that far from the peak of its Planck curve it appears dark in x-ray images. This impression of hot plasma following the magnetic field direction is further strengthened by quantitative studies that calculate coronal magnetic field strength and direction based on photospheric measurements and compare them with the observed brightness and location of the x-ray emitting structures. Such comparisons make it clear that, for the most part, the hot plasma conforms to the geometry of the magnetic field and that the coronal brightness is strongly linked to the strength of the magnetic fields which have erupted to the solar surface from the interior. It is also the case that the larger-scale, fainter corona, as well as coronal holes, are strongly influenced by the large-scale solar magnetic field. We may get a small hint of the reason that the coronal plasma outlines the direction of B by examining the thermal conductivity of a hot plasma in the presence of a magnetic field. This quantity has enormously different values in the directions parallel and perpendicular to the field for a coronal temperature of 10(exp 6) K, a particle density of 10(exp 9)/cu cm and a magnetic field strength of 100 G, the conductivity along the field is approximately 13 orders of magnitude greater than that perpendicular to the field. It is therefore not surprising that a parcel of plasma which is locally heated would conduct that heat preferentially in the direction of the field. We also note that the thermal conductivity parallel to the magnetic field increases with temperature T, while the perpendicular conductivity decreases. To the extent that the loop aspect ratio, i.e., the ratio of loop length to loop width, is determined by the thermal conductivity, we would expect that higher temperature loops are longer and thinner than cooler ones. However, if the loop width becomes smaller than the spatial resolution of the observing instrument, this effect will not be directly observable. For organizational purposes, we provide a listing of some scientific objectives for a Solar-B x-ray telescope, arranged in terms of identifiable features in the corona.

Golub, Leon↗

NASA NTRS2014

Modeling and Prediction of the Noise from Non-Axisymmetric Jets

The new source model was combined with the original sound propagation model developed for rectangular jets to produce a new version of the rectangular jet noise prediction code. This code was validated using a set of rectangular nozzles whose geometries were specified by NASA. Nozzles of aspect ratios two, four and eight were studied at jet exit Mach numbers of 0.5, 0.7 and 0.9, for a total of nine cases. Reynolds-averaged Navier-Stokes solutions for these jets were provided to the contactor for use as input to the code. Quantitative comparisons of the predicted azimuthal and polar directivity of the acoustic spectrum were made with experimental data provided by NASA. The results of these comparisons, along with a documentation of the propagation and source models, were reported in a journal article publication (Ref. 4). The complete set of computer codes and computational modules that make up the prediction scheme, along with a user's guide describing their use and example test cases, was provided to NASA as a deliverable of this task. The use of conformal mapping, along with simplified modeling of the mean flow field, for noise propagation modeling was explored for other nozzle geometries, to support the task milestone of developing methods which are applicable to other geometries and flow conditions of interest to NASA. A model to represent twin round jets using this approach was formulated and implemented. A general approach to solving the equations governing sound propagation in a locally parallel nonaxisymmetric jet was developed and implemented, in aid of the tasks and milestones charged with selecting more exact numerical methods for modeling sound propagation, and developing methods that have application to other nozzle geometries. The method is based on expansion of both the mean-flowdependent coefficients in the governing equation and the Green's function in series of orthogonal functions. The method was coded and tested on two analytically prescribed mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant equations. Working with NASA Glenn Acoustics Branch personnel, numerical methods and boundary conditions appropriate for use in a high-resolution calculation of the full equations governing sound propagation in a steady base flow were identified. Computer codes were then written (by NASA) and tested (by OAI) for an increasingly complex set of flow conditions to validate the methods. The NASA-supplied codes were ported to the High-End Computing resources of the NASA Advanced Supercomputing facility for testing and validation against analytical (where possible) and independent numerical solutions. The cases which were completed during the course of this contract were solutions of the two-dimensional linearized Euler equations with no mean flow, a uniform mean flow and a nonuniform mean flow representative of a parallel flow jet.

Leib, Stewart J.↗