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At least 37 records · Page 2

Parameter identification for an abstract Cauchy problem by quasilinearization

A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasi-linearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations.

Brewer, Dennis W.↗

An experimental study of wall adaptation and interference assessment using Cauchy integral formula

This paper summarizes the results of an experimental study of combined wall adaptation and residual interference assessment using the Cauchy integral formula. The experiments were conducted on a supercritical airfoil model in the Langley 0.3-m Transonic Cryogenic Tunnel solid flexible wall test section. The ratio of model chord to test section height was about 0.7. The method worked satisfactorily in reducing the blockage interference and demonstrated the primary requirement for correcting for the blockage effects at high model incidences to correctly determine high lift characteristics. The studies show that the method has potential for reducing the residual interference to considerably low levels. However, corrections to blockage and upwash velocities gradients may still be required for the final adapted wall shapes.

Murthy, A. V.↗

Parameter identification for an abstract Cauchy problem by quasilinearization

A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasi-linearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations.

Brewer, Dennis W.↗

Macroscopic Violation of Three Cauchy-Schwarz Inequalities Using Correlated Light Beams From an Infra-Red Emitting Semiconductor Diode Array

We briefly review quantum mechanical and semi-classical descriptions of experiments which demonstrate the macroscopic violation of the three Cauchy-Schwarz inequalities: g(sup 2)(sub 11)(0) greater than or equal to 1; g(sup 2)(sub 11)(0) greater than or equal to g(sup 2)(sub 11)(t), (t approaches infinity); (the absolute value of g(sup 2)(sub 11)(0))(exp 2) less than or equal to g(sup 2)(sub 11)(0) g(sup 2)(sub 11)(0). Our measurements demonstrate the violation, at macroscopic intensities, of each of these inequalities. We show that their violation, although weak, can be demonstrated through photodetector current covariance measurements on correlated sub-Poissonian Poissonian, and super Poissonian light beams. Such beams are readily generated by a tandem array of infrared-emitting semiconductor junction diodes. Our measurements utilize an electrically coupled array of one or more infrared-emitting diodes, optically coupled to a detector array. The emitting array is operated in such a way as to generate highly correlated beams of variable photon Fano Factor. Because the measurements are made on time scales long compared with the first order coherence time and with detector areas large compared with the corresponding coherence areas, first order interference effects are negligible. The first and second inequalities are violated, as expected, when a sub-Poissonian light beam is split and the intensity fluctuations of the two split beams are measured by two photodetectors and subsequently cross-correlated. The third inequality is violated by bunched (as well as anti-bunched) beams of equal intensity provided the measured cross correlation coefficient exceeds (F - 1)/F, where F is the measured Fano Factor of each beam. We also investigate the violation for the case of unequal beams.

Edwards, P. J.↗

A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations

The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.

Borzi, A.↗

An Efficient Filter for Measurements Corrupted with Cauchy Noise

This paper present a new sequential filter for state estimation using measurements corrupted with Cauchy noise. The new filter retains the familiar structure of the Kalman filter and is computationally efficient. In addition, it does not exhibit computational complexity which grows or varies in time like existing methods. These results are based upon a nearly 50 year old result by Masreliez in which the conditional mean estimator is approximated via linearization of the measurement predictive density. This work derives the new filter, provides discussion regarding practical implementation, and present Monte Carlo analyses to validate and assess the new filter's performance.

James S McCabe↗

Effects of hindlimb unweighting on the mechanical and structure properties of the rat abdominal aorta

Previous studies have shown that hindlimb unweighting of rats, a model of microgravity, reduces evoked contractile tension of peripheral conduit arteries. It has been hypothesized that this diminished contractile tension is the result of alterations in the mechanical properties of these arteries (e.g., active and passive mechanics). Therefore, the purpose of this study was to determine whether the reduced contractile force of the abdominal aorta from 2-wk hindlimb-unweighted (HU) rats results from a mechanical function deficit resulting from structural vascular alterations or material property changes. Aortas were isolated from control (C) and HU rats, and vasoconstrictor responses to norepinephrine (10(-9)-10(-4) M) and AVP (10(-9)-10(-5) M) were tested in vitro. In a second series of tests, the active and passive Cauchy stress-stretch relations were determined by incrementally increasing the uniaxial displacement of the aortic rings. Maximal Cauchy stress in response to norepinephrine and AVP were less in aortic rings from HU rats. The active Cauchy stress-stretch response indicated that, although maximum stress was lower in aortas from HU rats (C, 8.1 +/- 0.2 kPa; HU, 7.0 +/- 0.4 kPa), it was achieved at a similar hoop stretch. There were also no differences in the passive Cauchy stress-stretch response or the gross vascular morphology (e.g., medial cross-sectional area: C, 0.30 +/- 0.02 mm(2); HU, 0.32 +/- 0.01 mm(2)) between groups and no differences in resting or basal vascular tone at the displacement that elicits peak developed tension between groups (resting tension: C, 1.71 +/- 0.06 g; HU, 1.78 +/- 0.14 g). These results indicate that HU does not alter the functional mechanical properties of conduit arteries. However, the significantly lower active Cauchy stress of aortas from HU rats demonstrates a true contractile deficit in these arteries.

Non-NASA Center↗

Oscillation Amplitude Growth for a Decelerating Object with Constant Pitch Damping

The equations governing the deceleration and oscillation of a blunt body moving along a planar trajectory are re-expressed in the form of the Euler-Cauchy equation. An analytic solution of this equation describes the oscillation amplitude growth and frequency dilation with time for a statically stable decelerating body with constant pitch damping. The oscillation histories for several constant pitch damping values, predicted by the solution of the Euler-Cauchy equation are compared to POST six degree-of-freedom (6-DoF) trajectory simulations. The simulations use simplified aerodynamic coefficients matching the Euler-Cauchy approximations. Agreement between the model predictions and simulation results are excellent. Euler-Cauchy curves are also fit through nonlinear 6-DoF simulations and ballistic range data to identify static stability and pitch damping coefficients. The model os shown to closely fit through the data points and capture the behavior of the blunt body observed in simulation and experiment. The extracted coefficients are in reasonable agreement with higher fidelity, nonlinear parameter identification results. Finally, a nondimensional version of the Euler-Cauchy equation is presented and shown to be a simple and effective tool for designing dynamically scaled experiments for decelerating blunt capsule flight.

Schoenenberger, Mark↗

Arrangement of vortex lattices

A new method is developed for solving the lifting-surface equation for thin wings. The solution requires the downwash equation to be in the form of Cauchy integrals which can be interpreted as a vortex lattice with the positions of the vortices and control points dictated by the finite sum used to approximate the integrals involved. Lan's continuous loading method is employed for the chordwise integral since it properly accounts for the leading-edge singularity, Cauchy singularity, and Kutta condition. Unlike Lan, the spanwise loading is also continuous and the Cauchy singularity in the spanwise integral is also properly accounted for by using the midpoint trapezoidal rule and the theory of Chebyshev polynomials. This technique yields the exact classical solution to Prandtl's lifting-line equation.The solution to the lifting-surface equation for rectangular wings was found to compare well with other continuous loading methods, but with much smaller computational times, and to converge faster than other vortex lattice methods.

Dejarnette, F. R.↗

Lifting surface theory for rectangular wings

A new incompressible lifting-surface theory is developed for thin rectangular wings. The solution requires the downwash equation to be in the form of Cauchy-type integrals. Lan's method is employed for the chordwise integrals since it properly accounts for the leading-edge singularity, Cauchy singularity and Kutta condition. The Cauchy singularity in the spanwise integral is also accounted for by using the midpoint trapezoidal rule and theory of Chebychev polynomials. The resulting matrix equation, formed by satisfying the boundary condition at control points, is simpler and quicker to compute than other lifting surface theories. Solutions were found to converge with only a small number of control points and to compare favorably with results from other methods.

Dejarnette, F. R.↗

Subsonic, transonic, and supersonic nozzle flow by the inverse technique.

The inverse technique is used to obtain a mathematically and physically consistent solution of the flowfield in a nozzle from the mass generation surface through the supersonic region. The inverse method employs an assumed centerline function which is of the Cauchy type in that the values and the derivatives of the function are known. Since the Cauchy boundary conditions can give rise to numerical instabilities, the governing gasdynamic equations for rotational steady flow were transformed into a form which puts the geometry into a rectangular shape, and which spaces the network of interior points more finely in regions of the greatest gradients of the dependent variables. For arbitrarily specified centerline data, the solution of the governing flow equations may not exist, and if it does it may not depend continuously on the data.

Norton, D. J.↗

Stress-intensity factors for a thick-walled cylinder containing an annular imbedded or external or internal surface crack

The elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack is considered. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness.

Erdol, R.↗

A thick-walled cylinder with an axisymmetric internal or edge crack

The paper considers the elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress-intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress-intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress-intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness.

Erdol, R.↗

Analysis of airfoil leading edge separation bubbles

A local inviscid-viscous interaction technique was developed for the analysis of low speed airfoil leading edge transitional separation bubbles. In this analysis an inverse boundary layer finite difference analysis is solved iteratively with a Cauchy integral representation of the inviscid flow which is assumed to be a linear perturbation to a known global viscous airfoil analysis. Favorable comparisons with data indicate the overall validity of the present localized interaction approach. In addition numerical tests were performed to test the sensitivity of the computed results to the mesh size, limits on the Cauchy integral, and the location of the transition region.

Carter, J. E.↗

Crystallinity determination by curvefit procedure for a semi-crystalline polymer

Wide angle X-ray scattering (WAXS) data from poly(etheretherketone) (PEEK) was resolved into a crystalline contribution represented as four reflections and an amorphous contribution represented as a broad, smoothly varying curve. The crystalline scatter is described as a linear combination of Cauchy and Gaussian functions while that of the amorphous halo is expressed as a cubic polynomial. Statistical analysis of the measured scattered intensity from an amorphous specimen with that calculated from the cubic polynomial, as a function of the combination parameter (fraction of Cauchy and Gaussian functions), suggests that the crystalline fraction of the polymer specimen studied is about 0.39.

Wakelyn, N. T.↗