Search NASA⌕ Search

SEARCH · Search NASA

Results for “vertex”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Vertex evoked potentials in a rating-scale detection task: Relation to signal probability

Vertex evoked potentials were recorded from human subjects performing in an auditory detection task with rating scale responses. Three values of a priori probability of signal presentation were tested. The amplitudes of the N1 and P3 components of the vertex potential associated with correct detections of the signal were found to be systematically related to the strictness of the response criterion and independent of variations in a priori signal probability. No similar evoked potential components were found associated with signal absent judgements (misses and correct rejections) regardless of the confidence level of the judgement or signal probability. These results strongly support the contention that the form of the vertex evoked response is closely correlated with the subject's psychophysical decision regarding the presence or absence of a threshold level signal.

Squires, K. C.↗

Stress singularities at the vertex of a cylindrically anisotropic wedge

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Delale, F.↗

Vertex implications of stability for a class of delay-differential interval system

Although vertex implication in parameter space does not hold for stability of general delay-differential interval systems, it is shown that in an important special case when the characteristic equation of the system is describable by certain quasi-polynomials the vertex implication for stability does hold. It is also pointed out that vertex implication for stability does not hold in general for delay-differential systems with interval delay.

Kim, K. D.↗

Vertex evoked potentials in a rating-scale detection task - Relation to signal probability

Results of vertex-evoked potential studies conducted to determine how decision confidence level and decision probability interact to determine P3 amplitude for both signal-present and signal-absent decisions. They support the contention that the form of the vertex-evoked response is closely correlated with the subject's psychophysical response regarding the presence or absence of a threshold-level signal.

Squires, K. C.↗

Hubble Space Telescope secondary mirror vertex radius/conic constant test

The Hubble Space Telescope backup secondary mirror was tested to determine the vertex radius and conic constant. Three completely independent tests (to the same procedure) were performed. Similar measurements in the three tests were highly consistent. The values obtained for the vertex radius and conic constant were the nominal design values within the error bars associated with the tests. Visual examination of the interferometric data did not show any measurable zonal figure error in the secondary mirror.

Parks, Robert↗

Optimized Vertex Method and Hybrid Reliability

A method of calculating the fuzzy response of a system is presented. This method, called the Optimized Vertex Method (OVM), is based upon the vertex method but requires considerably fewer function evaluations. The method is demonstrated by calculating the response membership function of strain-energy release rate for a bonded joint with a crack. The possibility of failure of the bonded joint was determined over a range of loads. After completing the possibilistic analysis, the possibilistic (fuzzy) membership functions were transformed to probability density functions and the probability of failure of the bonded joint was calculated. This approach is called a possibility-based hybrid reliability assessment. The possibility and probability of failure are presented and compared to a Monte Carlo Simulation (MCS) of the bonded joint.

Smith, Steven A.↗

Picometer Level Modeling of a Shared Vertex Double Corner Cube in the Space Interferometry Mission Kite Testbed

The Space Interferometry Mission (SIM) is a microarcsecond interferometric space telescope that requires picometer level precision measurements of its truss and interferometer baselines. Single-gauge metrology errors due to non-ideal physical characteristics of corner cubes reduce the angular measurement capability of the science instrument. Specifically, the non-common vertex error (NCVE) of a shared vertex, double corner cube introduces micrometer level single-gauge errors in addition to errors due to dihedral angles and reflection phase shifts. A modified SIM Kite Testbed containing an articulating double corner cube is modeled and the results are compared to the experimental testbed data. The results confirm modeling capability and viability of calibration techniques.

metrology↗

Measurement of the Non-common Vertex Error of a Double Corner Cube

The Space Interferometry Mission (SIM) requires the control of the optical path of each interferometer with picometer accuracy. Laser metrology gauges are used to measure the path lengths to the fiiducial corner cubes at the siderostats. Due to the geometry of SIM a single corner cube does not have sufficient acceptance angle to work with all the gauges. Therefore SIM employs a double corner cube. Current fabrication methods are in fact not capable of producing such a double corner cube with vertices having sufficient commonality. The plan for SIM is to measure the non-commonalty of the vertices and correct for the error in orbit. SIM requires that the non-common vertex error (NCVE) of the double corner cube to be less than 6 (mu)m. The required accuracy for the knowledge of the NCVE is less than 1 (mu)m. This paper explains a method of measuring non-common vertices of a brassboard double corner cube with sub-micron accuracy. The results of such a measurement will be presented.

Space Interferometry Mission (SIM)↗

Vertex potentials evoked during auditory signal detection - Relation to decision criteria

Vertex potentials were recorded from eight subjects performing in an auditory threshold detection task with rating scale responses. The amplitudes and latencies of both the N1 and the late positive (P3) components were found to vary systematically with the criterion level of the decision. These changes in the waveshape of the N1 component were comparable to those produced by varying the signal intensity in a passive condition, but the late positive component in the active task was not similarly related to the passively evoked P2 component. It was suggested that the N1 and P3 components represent distinctive aspects of the decision process, with N1 signifying the quantity of signal information received and P3 reflecting the certainty of the decision based upon that information.

Squires, K. C.↗

Selective attention and the auditory vertex potential. 2: Effects of signal intensity and masking noise

A randomized sequence of tone bursts was delivered to subjects at short inter-stimulus intervals with the tones originating from one of three spatially and frequency specific channels. The subject's task was to count the tones in one of the three channels at a time, ignoring the other two, and press a button after each tenth tone. In different conditions, tones were given at high and low intensities and with or without a background white noise to mask the tones. The N sub 1 component of the auditory vertex potential was found to be larger in response to attended channel tones in relation to unattended tones. This selective enhancement of N sub 1 was minimal for loud tones presented without noise and increased markedly for the lower tone intensity and in noise added conditions.

Schwent, V. L.↗

Error estimates for cell-vertex solutions of the compressible Euler equations

The cell-vertex schemes due to Ni and Jameson, et al. have been subjected to a theoretical analysis of their truncation error. The analysis confirms the authors' claims for second-order accuracy on smooth grids, but shows that the same accuracy cannot be obtained on arbitrary grids. It is shown that the schemes have a unique generalization to axisymmetric flow that preserves the second-order accuracy.

Roe, P. L.↗

A cell-vertex multigrid method for the Navier-Stokes equations

A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.

Radespiel, R.↗

A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations

The solution of the two-dimensional Euler equations is based on the two-dimensional linear convection equation and the Euler-equation decomposition developed by Hirsch et al. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative, and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.

Powell, Kenneth G.↗

A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations

A scheme of solving the two-dimensional Euler equations is developed. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.

Powell, Kenneth G.↗

An investigation of cell centered and cell vertex multigrid schemes for the Navier-Stokes equations

Two efficient and robust finite-volume multigrid schemes for solving the Navier-Stokes equations are investigated. These schemes employ either a cell centered or a cell vertex discretization technique. An explicit Runge-Kutta algorithm is used to advance the solution in time. Acceleration techniques are applied to obtain faster steady-state convergence. Accuracy and convergence of the schemes are examined. Computational results for transonic airfoil flows are essentially the same, even for a coarse mesh. Both schemes exhibit good convergence rates for a broad range of artificial dissipation coefficients.

Radespiel, R.↗