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At least 145 records · Page 8

Approximate-factorization algorithms - Theory and applications in viscous-flow computations

A systematic development of implicit approximate-factorization algorithms in delta form for both unsteady and steady viscous flow is presented. The algorithms are cast in conservation-law form and simplified by using a thin-layer approximation to the governing equations. The implementation of implicit surface viscous boundary conditions is discussed in detail, and an example is presented illustrating the advantage of using the implicit boundary conditions. Three-dimensional results from the steady form of the algorithm are presented and compared with experimental data.

Chaussee, D. S.

Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation

Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.

Spreiter, John R.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Fabiano, R. H.

The diffusion approximation and transport theory for cosmic rays in relativistic flows

Equations describing the transport of cosmic rays in relativistic flows in the diffusion approximation are obtained. The analysis is based on the zeroth, first, and second differential moment equations of the relativistic Boltzmann equation with a BGK collision term. A perturbation solution of the moment equations in the diffusion approximation yields both the co-moving frame particle current and viscous stresses. The resultant cosmic-ray continuity equation contains three readily recognized energy change terms: the adiabatic energy change term; the viscous shear energy change term; and a term proportional to the scalar product of the acceleration vector of the scattering frame and the heat flux.

Webb, G. M.

Sudden bending of cracked laminates

A dynamic approximate laminated plate theory is developed with emphasis placed on obtaining effective solution for the crack configuration where the 1/square root of r stress singularity and the condition of plane strain are preserved. The radial distance r is measured from the crack edge. The results obtained show that the crack moment intensity tends to decrease as the crack length to laminate plate thickness is increased. Hence, a laminated plate has the desirable feature of stabilizing a through crack as it increases its length at constant load. Also, the level of the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers. The present theory, although approximate, is useful for analyzing laminate failure to crack propagation under dynamic load conditions.

Sih, G. C.

Schwinger-Keldysh effective action for hydrodynamics with approximate symmetries

We study hydrodynamic theories with approximate symmetries in the recently developed effective action approach on the Schwinger-Keldysh contour. We employ the method of spurious symmetry transformation for small explicit symmetry-breaking parameters to systematically constrain symmetry-breaking effects in the nonequilibrium effective action for hydrodynamics. We apply our method to the hydrodynamic theory of chiral symmetry in quantum chromodynamics at finite temperature and density and its explicit breaking by quark masses. We show that the spurious symmetry and the Kubo-Martin-Schwinger relation dictate that the Ward-Takahashi identity for the axial symmetry, i.e., the partial conservation of axial vector current (PCAC) relation, contains a relaxational term proportional to the axial chemical potential, whose kinetic coefficient is at least of the second order in the quark mass. In the phase where the chiral symmetry is spontaneously broken, and the pseudo-Nambu-Goldstone pions appear as hydrodynamic variables, this relaxation effect is subleading compared to the conventional pion mass term in the PCAC relation, which is of the first order in the quark mass. On the other hand, in the chiral symmetry restored phase, we show that our relaxation term, which is of the second order in the quark mass, becomes the leading contribution to the axial charge relaxation. Therefore, the leading axial charge relaxation mechanism is parametrically different in the quark mass across a chiral phase transition.

Goldstone bosons

Impedance characteristics of coaxial and planar magnetoplasma capacitors

A theory has been developed for the impedance of a homogeneous magnetoplasma enclosed between two specular reflecting coaxial electrodes, with a static magnetic field parallel to the electrode axes. The parallel-plate magnetoplasma capacitor is treated as a sub-case. Starting with the Vlasov equation, an integral equation is derived for the electric field. Solving this equation, and integrating to obtain the voltage, gives the capacitor impedance. This includes a capacitive component, and a resistive component expressing the Landau damping associated with the open orbits of electrons reflected at the electrodes. A direct numerical solution of the field integral equation has been carried out for a range of values of magnetic field, plasma density, and signal frequency. The values of impedance so obtained are compared with the predictions of macroscopic theory, and of an approximate microscopic theory in which open orbits are ignored and solutions are obtained using finite Fourier transform methods. The mathematical relations between these theories are demonstrated.

Harker, K. J.

Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

Prosser, W. H.

An analytical theory of planetary rotation rates

An approximate analytical theory is derived for the rate of rotation acquired by a planet as it grows from the solar nebula. This theory was motivated by a numerical study by Giuli, and yields fair agreement with his results. The periods of planetary rotation obtained are proportional to planetesimal encounter velocity, and appear to suggest lower values of this velocity than are commonly assumed to have existed during planetary formation.

Harris, A. W.

Scattering by non-spherical particles of size comparable to a wavelength - A new semi-empirical theory

An approximate method is proposed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound x(o) (about 5), Mie theory is used. For x greater than x(o), the interaction is divided into three components: diffraction, external reflection, and transmission. Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third. The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes. Limitations of the theory are also noted.

Pollack, J. B.

Bidirectional reflectance spectroscopy. I - Theory

An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Hapke, B.

Ostwald ripening theory

An approximate analytical technique for extracting the concentration dependence of the interdiffusion coefficient was derived from diffusion measurements carried out with the diaphragm cell. The systematic error incurred in using the technique was estimated and found to be no greater than the random error ordinarily encountered in these experiments.

Baird, J. K.