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Coherent states on the m-sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied. They are eigenstates of the operators a(sub m)(+), a(sub m) which create and annihilate clusters of m-particles. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.
Fracture tests were conducted on 2.3mm thick, 305mm wide sheets of 2024-T3 aluminum alloy with from one to five collinear cracks. The cracks were introduced (crack history) into the specimens by three methods: saw cutting, fatigue precracking at a low stress range, and fatigue precracking at a high stress range. For the single crack tests, the initial crack history influenced the stress required for the onset of stable crack growth and the first 10mm of crack growth. The effect on failure stress was about 4 percent or less. For the multiple crack tests, the initial crack history was shown to cause differences of more than 20 percent in the link-up stress and 13 percent in failure stress. An elastic-plastic finite element analysis employing the CTOA fracture criterion was used to predict the fracture behavior of the single and multiple crack tests. The numerical predictions were within 7 percent of the observed link-up and failure stress in all the tests.
A series of fracture tests on large-scale, pre-cracked, aluminum alloy panels is being carried out to examine and to characterize the process by which cracks propagate and link up in this material. Extended grips and test fixtures were specially designed to enable the panel specimens to be loaded in tension, in a 1780-kN-capacity universal testing machine. Twelve panel specimens, each consisting of a single sheet of bare 2024-T3 aluminum alloy, 3988 mm high, 2286 mm wide, and 1.016 mm thick are being fabricated with simulated through-cracks oriented horizontally at mid-height. Using existing information, a test matrix has been set up that explores regions of failure that are controlled by fracture mechanics, with additional tests near the boundary between plastic collapse and fracture. In addition, a variety of multiple site damage (MSD) configurations have been included to distinguish between various proposed linkage mechanisms. All tests but one use anti-buckling guides. At this writing seven specimens have been tested. Three were fabricated with a single central crack, three others had multiple cracks on each side of the central crack, and one had a single crack but no anti-buckling guides. Each fracture event was recorded on film, video, computer, magnetic tape, and occasionally optical microscopy. The visual showed the crack tip with a load meter in the field of view, using motion picture film for one tip and SVHS video tape for the other. The computer recorded the output of the testing machine load cell, the stroke, and twelve strain gages at 1.5 second intervals. A wideband FM magnetic tape recorder was used to record data from the same sources. The data were analyzed by two different procedures: (1) the plastic zone model based on the residual strength diagram; and (2) the R-curve. The first three tests were used to determine the basic material properties, and these results were then used in the analysis of the two subsequent tests with MSD cracks. There is good agreement between measured values and results obtained from the model.
A small strain theory, three-dimensional elastic-plastic finite element analysis was used to simulate fracture in thin sheet 2024-T3 aluminum alloy in the T-L orientation. Both straight and tunneled cracks were modeled. The tunneled crack front shapes as a function of applied stress were obtained from the fracture surface of tested specimens. The stable crack growth behavior was measured at the specimen surface as a function of applied stress. The fracture simulation modeled the crack tunneling and extension as a function of applied stress. The results indicated that the global constraint factor, alpha(sub g), initially dropped during stable crack growth. After peak applied stress was achieved, alpha(sub g) began to increase slightly. The effect of crack front shape on alpha(sub g) was small, but the crack front shape did greatly influence the local constraint and through-thickness crack-tip opening angle (CTOA) behavior. The surface values of CTOA for the tunneled crack front model agreed well with experimental measurements, showing the same initial decrease from high values during the initial 3mm of crack growth at the specimen's surface. At the same time, the interior CTOA values increased from low angles. After the initial stable tearing region, the CTOA was constant through the thickness. The three-dimensional analysis appears to confirm the potential of CTOA as a two-dimensional fracture criterion.
On the basis of resistive MHD simulations we investigate the stability and dynamic evolution of the magnetotail for configurations with various degrees of plasma sheet thickening from midnight toward the tail flanks, associated with a similar increase of the B(sub z) component. This increase is varied by factors between 2 and 3.5, while the magnitude of B(sub z) at midnight is left unchanged. The increase of B(sub z) has a strong effect on the spatial extend of resistive tearing and reconnection across the tail and on the unstable evolution. For stronger thickening the cross-tail extent of the near-Earth neutral line, formed by reconnection, and correspondingly the amount of reconnected magnetic flux get reduced and the dipolarization effects earthward of the neutral line are more concentrated near midnight. An increase of B(sub z) from midnight toward the flanks by more than a factor of about 3 can possibly even suppress the resistive tearing instability. This indicates the possibility of a stability transition due to a reduction of B(sub z) in the flank regions in response to changes in the solar wind, even when the magnitude of B(sub z) near midnight and the fluctuation level in that region are unchanged (provided that a sufficient fluctuation level exists).
A three-dimensional (3-D) magnetohydrodynamic (MHD) numerical model is used to trace global deformations of the heliospheric current sheet (HCS) caused by large-scale dynamical interactions associated with corotating solar wind flows. Configurations incorporating the tilted-dipole geometry are investigated out past 30 AU for a variety of dipole tilt angles, alpha. Inclusion of the full, 3-D interplanetary dynamics allows north-south displacements and the east-west warping of the HCS by advective corotational effects to be accurately assessed for the first time. It is found that large-scale spatial correlations between velocity and density imposed at the coronal source (i.e., the geometric arrangement whereby regions of high-speed low-density material lying adjacent to areas of slow, dense flow interact obliquely under the influence of solar rotation) result in a distinctive pattern of deformation of the HCS. For an alpha = 30 deg tilted-dipole example, it is shown that typical zonal variations in radial velocity lead to significant folding of the HCS within about 5 AU of the Sun. By 10 AU, additional sharp bends appear near the latitudinal extremes of the HCS surface, where it is overtaken by shock fronts driven by 3-D corotating interaction regions (CIRs). Moreover, the model suggests that inside about 20 AU, major plasma structures are systematically organized, about the HCS, such that the greatest concentrations of material and magnetic field (the centroids of the 3-D CIR structures) are coincident with the folded crests of the HCS (near heliographic latitudes lambda = +/- alpha). Thus, in these circumstances many of the more interesting dynamical features inconveniently lie well away from the heliographic equator. At larger heliocentric distances, where neighboring CIRs begin to interact strongly, the warping of the HCS abates dramatically and the association between folds in the HCS and major field and density concentrations is weakened and ultimately breaks down. On the basis of the model calculations, quasi-steady deformations and related phenomena should figure prominently in the interplanetary medium, except during those periods when the magnetic dipole and solar spin axes are nearly aligned (alpha is approximately less than 10 deg). Even then, they may be of significance if there are any substantial local warps or kinks in the streamer belt.
Contemporary applications of failure criteria frequently incorporate two-dimensional or simplified three-dimensional methodologies for prediction of stresses. Motivation behind the development of a new multi-dimensional failure criterion is due mainly to the lack of a sufficiently accurate mathematical tool that accounts for the behavior of brittle material with anisotropic properties. Such a criterion should be able to provide a reliable maximum load estimate so that design of the structure is not penalized in terms of excessive weight requirements. The failure criterion developed is represented by a fracture surface in a six-dimensional stress space. The criterion is applied for failure prediction of SR-200 beryllium sheet structures, a non-homogeneous orthotropic material used widely in space applications. Two experiments are used to verify the criterion.
We adopt a magnetotail model with stretched field lines where ion motions are generally nonadiabatic and where it is assumed that the pressure anisotropy resides only in the electron pressure tensor. We show that the magnetic field lines with p(perpendicular) greater than p(parallel) are less stretched than the corresponding field lines in the isotropic model. For p(parallel) greater than p(perpendicular), the magnetic field lines become more and more stretched as the anisotropy approaches the marginal firehose limit, p(parallel) = p(perpendicular) + B(exp 2)/mu(sub 0). We also show that the tail current density is highly enhanced at the firehose limit, a situation that might be subject to a microscopic instability. However, we emphasize that the enhancement in the current density is notable only near the center of the tail current sheet (z = 0). Thus it remains unclear whether any microscopic instability can significantly alter the global magnetic field configuration of the tail. By comparing the radius of the field-line curvature at z = 0 with the particle's gyroradius, we suspect that even the conventional adiabatic description of electrons may become questionable very close to the marginal firehose limit.
Using IMP 6, 7, and 8 magnetic field and plasma data, we have determined statistical occurrance properties of bulk flow and magnetic field orientation near the midtail neutral sheet. Characteristics of bulk plasma flow and magnetic field significantly change according to the radial distance down the tail. High-speed flow events (v greater than 300 km/s) are essentially restricted to the region tailward of X = -2.5 R(sub E) and are predominatly sunward or tailward. The low-speed flows were nearly equally likely to be in any direction, with the occurace rate of dustward and sunward flow being larger than that of tailward and dawnward flow. Dustward flow occurrence is highest in the region Earthward of X = -2.5 R(sub E), while sunward flow occurrence is highest in the region tailward of X = -2.5 R(sub E). The significance of the dawn-to-dust flow in the near-Earth region obtained in our study supports the idea that there exists a very effective mechanism to accelerate ions in the dawn-to-dust direction and hence the relief of pressure buildup in the near-Earth region. During high-speed flow events the relationship between B(sub Z) polarity and plasma flow direction is largely consistent with that expected from the magnetic reconnenection processes associted with substorms. There are also significant numbers of negative B9sub Z) events that are not associated with tailward flow. Mechanism other than substorm neutral line should therefore also taken into account to explain general B(sub Z) polarity in the midtail region.
By comparing data from the Special Sensor Microwave Imager (SSM/I) to field data, a melt threshold of the cross-polarized gradient ratio (XPGR), which is a normalized difference between the 19 GHz horizontally-polarized and 37 GHz vertically polarized brightness temperatures, is determined. This threshold, XPGR = -0.025, is used to classify dry and wet snow. The annual areal extent of melt is mapped for the years 1988 through 1991, and inter-annual variations of melt extent are examined. The results show that the melt extent varied from a low of 38.3% of the ice sheet (1990) to a high of 41.7% (1991) during the years 1988-1991.
Ulysses has collected data between 1 and 5 AU during, and just following solar maximum, when the heliospheric current sheet (HCS) can be thought of as reaching its maximum tilt and being subject to the maximum amount of turbulence in the solar wind. The Ulysses solar wind plasma instrument measures the vector velocity and can be used to estimate the flow speed and direction in turbulent 'eddies' in the solar wind that are a fraction of an astronomical unit in size and last (have either a turnover or dynamical interaction time of) several hours to more than a day. Here, in a simple exercise, these solar wind eddies at the HCS are characterized using Ulysses data. This character is then used to define a model flow field with eddies that is imposed on an ideal HCS to estimate how the HCS will be deformed by the flow. This model inherently results in the complexity of the HCS increasing with heliocentric distance, but the result is a measure of the degree to which the observed change in complexity is a measure of the importance of solar wind flows in deforming the HCS. By comparison with randomly selected intervals not located on the HCS, it appears that eddies on the HCS are similar to those elsewhere at this time during the solar cycle, as is the resultant deformation of the interplanetary magnetic field (IMF). The IMF deformation is analogous to what is often termed the 'random walk' of interplanetary magnetic field lines.
Apparatus simple to make, operate, and maintain used to determine abilities of transparent polymeric seal materials to resist stress crazing when exposed to various cleaning solvents. Includes pulleys, cable, and weights to apply constant tension to specimen sheet immersed in test fluid in glass vessel. Provides visual observation of specimen at any time during test and ease of removal of fluid via drain port at bottom of glass vessel.
The aero design of an inward pumping spiral groove face seal using an in-house spread sheet was compared with predictions from the NASA code SPIRALG. The high pressure compressor exit of an aero gas turbine was chosen as the location for the candidate seal. This is a challenging environment as rotational velocity, pressure drop, and temperature are high. This presentation compares the resulting lift forces, leakages, and friction loss for various ride heights. Within practical ranges of ride height, the lift force predictions agreed well. However, both leakage and friction loss predictions were significantly different.
We performed ice thickness measurements over the southern part of the Greenland ice sheet during June and July 1993. We used an airborne coherent radar depth sounder for these measurements. The radar was operated from a NASA P-3 aircraft equipped with GPS receivers. Radar data were collected in conjunction with laser altimeter and microwave altimeter measurements of ice surface elevation. This report provides radio echograms and thickness profiles from data collected during 1993.
Interplanetary shocks often propagate along the heliospheric plasma sheet (HPS) where the interplanetary magnetic field (IMF) changes its polarity. This problem is investigated by the time-dependent 2.5-D MHD numerical model in the meridional plane. An example of computation is shown in the figure using density (log) contours and IMF vectors. Values of plasma parameters along the HPS fluctuate in time due to the Kelvin-Helmholtz instability. The HPS with its decreased intensity of the IMF as well as with its increased mass density causes a dimple in the shock structure (relatively weak for the forward shock, significant for the reverse shock, and very large for the contact discontinuity). Beyond the forward shock, the HPS is slightly compressed due to the post-shock increase of the azimuthal IMF component. Then follows expansion of the HPS surrounded by the highly-deformed contact discontinuity. A significant draping of IMF lines occurs around this structure that increases the meridional component of the IMF. This can cause a favorable condition for initiation of a geomagnetic storm.
Results of a series of hypervelocity impact tests are presented. In these tests, 1.275-g, 9.53-mm-diameter, 2017-T4 aluminum spheres were fired at normal incidence at eight thicknesses of 6061-T6 aluminum sheet. Bumper thickness to projectile diameter (t/D) ratio ranged from 0.026 to 0.424. Nominal impact velocity was 6.7 km/s. Results of five tests using 6.35, 9.53, and 12.70-mm-diameter aluminum spheres and other aluminum alloy bumpers are also given. A large chunky fragment of projectile was observed at the center of the debris clouds produced by the impacts. The equivalent diameter of this large fragment ranged from 5.5 mm for the lowest t/D ratio to a minimum of 0.6 mm for the case where maximum breakup of the projectile occurred (t/D approximately 0.2 to 0.3). When the t/D ratio was 0.42, numerous large flaky fragments were evenly distributed in the external bubble of bumper debris. Velocity of the large central fragments decreased continuously with increasing t/D ratio, ranging from about 99 percent to less than 80 percent of the impact velocity. The change in the velocity of small fragments spalling from the rear of the projectile was used to obtain a relationship showing a linear increase in the size of the central projectile fragment with decrease in the shock-induced stress in the projectile.
Mean changes in the surface elevation near the west margin of the Greenland ice sheet are measured using Seasat altimetry and altimetry from the Geosat Exact Repeat Mission (ERM). The Seasat data extend from early July through early October 1978. The ERM data extend from winter 1986-87 through fall 1988. Both seasonal and multi-year changes are measured using altimetry referenced to GEM T2 orbits. The possible effects of orbit error are minimized by adjusting the orbits into a common ocean surface. Seasonal mean changes in the surface height are recognizable during the Geosat ERM. The multi-year measurements indicate the surface was lower by 0.4 +/- 0.4 m on average in late summer 1987 than in late summer 1978. The surface was lower by 0.2 +/- 0.5 m on average in late summer 1988 than in late summer 1978. As a control case, the computations art also carried out using altimetry referenced to orbits not adjusted into a common ocean surface.
The primary goals of this research were to identify and begin to comprehend the spatial and temporal variations in surface characteristics of the Greenland ice sheet using passive microwave observations, physically-based models of the snowpack and field observations of snowpack and firn properties.