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Mathematically, reliability is the probability of success. First, we will present the calculus needed to comprehend basic probability theory. Second, we will introduce The Reliability Function and its basic properties. Last, we will demonstrate The Reliability Function in a notional fatigue life example.
Previous missions to Mars have revealed that Mars surface is magnetic at DC frequency. Does this highly magnetic surface layer attenuate RADAR energy as it does in certain locations on Earth? It has been suggested that the active magnetic mineral on Mars is titanomaghemite and/or titanomagnetite. When titanium is incorporated into a maghemite or magnetite crystal, the Curie temperature can be significantly reduced. Mars has a wide range of daily temperature fluctuations (303K - 143K), which could allow for daily passes through the Curie temperature. Hence, the global dust layer on Mars could experience widely varying magnetic properties as a function of temperature, more specifically being ferromagnetic at night and paramagnetic during the day. Measurements of EM properties of magnetic minerals were made versus frequency and temperature (300K- 180K). Magnetic minerals and Martian analog samples were gathered from a number of different locations on Earth.
Nuclear irradiation effect on embrittlement of Ti and Ti alloys at cryogenic temperature, determining radiation damage threshold as function of tensile properties changes
The mass function of clusters of galaxies is derived separately from optical and X-ray observations of their respective properties. The mass function was extended to the faint end, to lower masses than the rich clusters, using small groups of galaxies. The derived mass function is within the mass range from approximately 10 exp 12 to not less than 10 exp 15/h solar masses. The deduced density range n is approximately 10 exp -2 to 10 exp -8 cubic h/cubic Mpc. The observed shape of the mass function exhibits a shallow power-law decrease with mass at the faint end, and a steep exponential decrease with mass at the massive end. A summary of some constraints placed by the observed mass function on current cosmological models is presented.
A stochastic design optimization methodology (SDO) has been developed to design components of an airframe structure that can be made of metallic and composite materials. The design is obtained as a function of the risk level, or reliability, p. The design method treats uncertainties in load, strength, and material properties as distribution functions, which are defined with mean values and standard deviations. A design constraint or a failure mode is specified as a function of reliability p. Solution to stochastic optimization yields the weight of a structure as a function of reliability p. Optimum weight versus reliability p traced out an inverted-S-shaped graph. The center of the inverted-S graph corresponded to 50 percent (p = 0.5) probability of success. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponds to unity for reliability p (or p = 1). Weight can be reduced to a small value for the most failure-prone design with a reliability that approaches zero (p = 0). Reliability can be changed for different components of an airframe structure. For example, the landing gear can be designed for a very high reliability, whereas it can be reduced to a small extent for a raked wingtip. The SDO capability is obtained by combining three codes: (1) The MSC/Nastran code was the deterministic analysis tool, (2) The fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and (3) NASA Glenn Research Center s optimization testbed CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life raked wingtip structure of the Boeing 767-400 extended range airliner made of metallic and composite materials.
Generalized formulations for dynamic capacity and life of ball bearings, based on the models introduced by Lundberg and Palmgren and Zaretsky, have been developed and implemented in the bearing dynamics computer code, ADORE. Unlike the original Lundberg-Palmgren dynamic capacity equation, where the elastic properties are part of the life constant, the generalized formulations permit variation of elastic properties of the interacting materials. The newly updated Lundberg-Palmgren model allows prediction of life as a function of elastic properties. For elastic properties similar to those of AISI 52100 bearing steel, both the original and updated Lundberg-Palmgren models provide identical results. A comparison between the Lundberg-Palmgren and the Zaretsky models shows that at relatively light loads the Zaretsky model predicts a much higher life than the Lundberg-Palmgren model. As the load increases, the Zaretsky model provides a much faster drop off in life. This is because the Zaretsky model is much more sensitive to load than the Lundberg-Palmgren model. The generalized implementation where all model parameters can be varied provides an effective tool for future model validation and enhancement in bearing life prediction capabilities.
The persistent Be/X-ray binary RXJ0440.9+4431 flared in 2010 and 2011 and has been followed by various X-ray facilities (Swift, RXTE, XMM-Newton, and INTEGRAL).We studied the source timing and spectral properties as a function of its X-ray luminosity to investigate the transition from normal to flaring activity and the dynamical properties of the system. We have determined the orbital period from the long-term Swift/BAT light curve, but our determinations of the spin-period are not precise enough to constrain any orbital solution. The source spectrum can always be described by a bulk-motion Comptonization model of black body seed photons attenuated by a moderate photoelectric absorption. At the highest luminosity, we measured a curvature of the spectrum, which we attribute to a significant contribution of the radiation pressure in the accretion process. This allows us to estimate that the transition from a bulk-motion-dominated flow to a radiatively dominated one happens at a luminosity of approx 2 × 10(exp 36) erg/ s. The luminosity dependency of the size of the black body emission region is found to be r(sub BB) varies as L(sub x) (exp 0.39 +/- 0.02). This suggests that either matter accreting onto the neutron star hosted in RXJ0440.9+4431 penetrates through closed magnetic field lines at the border of the compact object magnetosphere or that the structure of the Neutron star magnetic field is more complicated than a simple dipole close to the surface.
This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross-Thick Li-Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple ]scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT ]based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three ]dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.
Photometric properties of the lunar surface derived theoretically - functions for differential and integral brightness
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
A systematic study of the properties of various polymer pottant materials and of the electrochemical corrosion mechanisms in solar cell materials is required for advancing the technology of terrestrial photovoltaic modules. The items of specific concern in this sponsored research activity involve: (1) kinetics of plasticizer loss in PVB, (2) kinetics of water absorption and desorption in PVB, (3) kinetics of water absorption and desorption in EVA, (4) the electrical properties at PVB as a function of temperature and humidity, (5) the electrical properties of EVA as a function of temperature and humidity, (6) solar cell corrosion characteristics, (7) water absorption effects in PVB and EVA, and (8) ion implantation and radiation effects in PVB and EVA.
This article describes the development of elastic and plastic constitutive relations as functions of relative density for partially consolidated -100 mesh aluminum powder. First, measurements of yield stress as a function of stress state and relative density are described. Measurements of the plastic strain increments associated with yielding in unconstrained compression tests and elastic properties, both as functions of relative density, are also described. The experimental results are combined with the associated flow rule to show that the yield surface is asymmetric with respect to hydrostatic tension and compression. Second, it is shown that the yield stress results can be represented by a two-part (capped Drucker-Prager) yield surface. The consolidation yield surface moves along the hydrostatic stress axis during densification, while the shear yield surface approaches the Mises yield surface. For the Al powder used in the present investigation, superposition of shear stress on a hydrostatic stress state aids the densification process. However, the hydrostatic stress requirement was found to be reduced by only about 20 pct for relative densities below 0.98.
The performance of infrared sensing systems is dependent upon the radiative properties of targets in addition to constraints imposed by system components. The unclassified state-of-the-art of infrared system performance figures is reviewed to indicate the relevance to system performance of target radiative properties. A theory of rough surface scattering is developed which allows the formulation of the reflective characteristics of extended targets. The thermal radiation emission from extended targets is formulated on the basis of internal radiation characteristics of natural materials and the transmissive scattering effects at the surface. Finally, the total radiative characteristics may be expressed as functions of material properties and incident and received directions, although the expressions are extremely complex functions and do not account for the effects of shadowing or multiple scattering. It is believed that the theory may be extended to include these effects and to incorporate the local radii of curvature of the surface.
This note considers codes for computer file transfer protocols when only upper-case ASCII characters are used as control characters. Such a restriction may be necessary to avoid dependence on unique machine features and to promote portability. If ten control functions are needed, a number used in a typical sufficiently rich protocol, we seek a subset of ten upper-case ASCII characters with good distance properties. The control functions form themselves naturally into three groups. Recognizing that only even distances can occur, the need to make the intragroup minimum distances as large as possible, and the number of control characters have distance 2 as small as possible is emphasized. The optimum solution to the above problem is found as well as an assignment that attains the optimum. The codes are essentially unique.
The presence of a stratospheric haze layer may produce increases in both the actinic flux and the irradiance below this layer. Such haze layers result from the injection of aerosol-forming material into the stratosphere by volcanic eruptions. Simple heuristic arguments show that the increase in flux below the haze layer, relative to a clear sky case, is a consequence of 'photon trapping'. The magnitude of these flux perturbations, as a function of aerosol properties and illumination conditions, is explored with a new radiative transfer model that can accurately compute fluxes in an inhomogeneous atmosphere with nonconservative scatterers having arbitrary phase function. One calculated consequence of the El Chichon volcanic eruption is an increase in the midday surface actinic flux at 20 deg N latitude, summer, by as much as 45 percent at 2900 A. This increase in flux in the UV-B wavelength range was caused entirely by aerosol scattering, without any reduction in the overhead ozone column.
A brief summary of the contents of this paper is presented here. In part I the differential equations of the problem of a gas flow in two dimensions is derived and the particular integrals by which the problem on jets is solved are given. Use is made of the same independent variables as Molenbroek used, but it is found to be more suitable to consider other functions. The stream function and velocity potential corresponding to the problem are given in the form of series. The investigation on the convergence of these series in connection with certain properties of the functions entering them forms the subject of part II. In part III the problem of the outflow of a gas from an infinite vessel with plane walls is solved. In part IV the impact of a gas jet on a plate is considered and the limiting case where the jet expands to infinity changing into a gas flow is taken up in more detail. This also solved the equivalent problem of the resistance of a gaseous medium to the motion of a plate. Finally, in part V, an approximate method is presented that permits a simpler solution of the problem of jet flows in the case where the velocities of the gas (velocities of the particles in the gas) are not very large.
This investigation is a collaboration between researchers at Cornell University, the University of Florida, and the University of Rennes 1, France. Flow modeling at Cornell University focused on mechanisms for the suspension and transport of wind-blown sand that are important in both terrestrial and Martian environments. These mechanisms include the saltation (or jumping) of grains, collisions between grains, and the interaction of grains with the velocity fluctuations of the turbulent wind. Of particular interest are sheet flows; these are relatively thin, highly concentrated regions of grains flowing near the ground under the influence of a strong turbulent wind. In them, the grains are suspended by interparticle collisions. Sheet flows may be relatively rare events, but they have the capacity to move great amounts of sand. In order to describe sheet flows, a turbulent mixture theory was formulated for particles in a fluid in which fluctuations in the volume fiaction of the particles take place on the scale of the turbulent eddies. Ensemble averaged equations for particle and fluid mass, momentum, and energy and fluid rate of dissipation were expressed in terms of Farve (concentration) averaged velocities and the associated velocity fluctuations. Correlations that describe the turbulent suspension of particles and dissipation of turbulent energy of both phases due to fluid particle interactions were modeled and boundary conditions at the bed and at the upper surface of the collisional flow were formulated. The boundary conditions at the upper surface were tested in a numerical simulation developed at the University of Florida. Steady and unsteady solutions for steady and unsteady fully-developed flows were obtained over a range of wind speeds fiom the lowest for which collisional between particles occurred to at which turbulent suspension is found to dominate collisional suspension. Below the value of the wind speed at which collisions between particles were unimportant, numerical solutions were obtained for the velocity distribution function and the resulting fields of concentration, particle and gas mean velocity, and particle shear stress for the steady two-dimensional saltation of spherical sand particles driven by a turbulent wind over a bed characterized by a simple relationship (the splash function) between the properties of incoming particles and those of the rebounding particles and other particles ejected fiom the bed. At the University of Rennes 1, experiments devoted to the characterization of the splash function for beds consisting of either random or ordered arrays of spheres in two- dimensions were completed. These indicated the role played by the packing geometry in the rebound and ejection of grains. Preliminary experiments on response of a three- dimensional collision bed to a collision with a single particle were performed. Data was taken with a single camera focused on the plane of collision. Here, for example, the decrease of the effective coefficient of restitution of the bed with an increase of the angle of incidence of the incoming particle has been measured. Other experiments on avalanches at Rennes studied the properties of the flows of particles that are responsible for the motion of the leeward side of a dune. In these, the dependence of the initiation of avalanches on the packing and depth of the particles was measured. Particle migration was studied in inclined flows of a binary mixture of disks and the mechanisms of diffision and segregation were isolated and characterized. The influence of side wall on dense, rapid inclined flows was measured and shown to be the reason why the angle of the free surface in such flows can exceed the static angle of repose. Future research will be devoted to a better understanding the transition between saltating (collisionless) and collisional flows as the wind speed the increases. This will involve the understanding of the evolution of the splash function as clisions with the bed become more numerous, more frequent, and more violent.
Microwave techniques at X and L band were used to determine the dependence of ocean-wave radar modulation transfer functions (MTFs) on various environmental and radar parameters during the Marine Remote Sensing experiment of 1979 (MARSEN 79). These MIF are presented, as are coherence functions between the AM and FM parts of the backscattered microwave signal. It is shown that they both depend on several of these parameters. Besides confirming many of the properties of transfer functions reported by previous authors, indications are found that MTFs decrease with increasing angle between wave propagation and antenna-look directions but are essentially independent of small changes in air-sea temperature difference. However, coherence functions are much smaller when the antennas are pointed perpendicular to long waves. It is found that X band transfer functions measured with horizontally polarized microwave radiation have larger magnitudes than those obtained by using vertical polarization.