Application of the Laplace transformation to the solution of the lateral and longitudinal stability equations
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STABILITY, LONGITUDINAL - DYNAMIC↗
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Parameter estimation technique for boundary value problems by spline collocation method
A parameter-estimation technique for boundary-integral equations of the second kind is developed. The output least-squares identification technique using the spline collocation method is considered. The convergence analysis for the numerical method is discussed. The results are applied to boundary parameter estimations for two-dimensional Laplace and Helmholtz equations.
Kojima, Fumio↗
U.S. National Congress of Applied Mechanics, 7th, University of Colorado, Boulder, Colo., June 3-7, 1974, Proceedings
A series of experimental, theoretical, and review papers dealing with various aspects of applied mechanics, including structural analysis, mathematical methods, and fluid dynamics. Some of the topics covered are: the direct formulation of two-dimensional mechanics problems, the mechanical aspects of athletics, Laplace's tidal equations, cochlear mechanics, dynamic constitutive equations, optical techniques for the determination of displacement and strain fields, chemical and biochemical problems involving nonlinear diffusion processes, thermal stresses, the rotating rod viscometer, finite-element methods in plasticity, ships of minimum resistance, and wide-band random vibration of structures. Individual items are announced in this issue.
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Open ocean tide modelling
Two trends evident in global tidal modelling since the first GEOP conference in 1972 are described. The first centers on the incorporation of terms for ocean loading and gravitational self attraction into Laplace's tidal equations. The second centers on a better understanding of the problem of near resonant modelling and the need for realistic maps of tidal elevation for use by geodesists and geophysicists. Although new models still show significant differences, especially in the South Atlantic, there are significant similarities in many of the world's oceans. This allows suggestions to be made for future locations for bottom pressure gauge measurements. Where available, estimates of M2 tidal dissipation from the new models are significantly lower than estimates from previous models.
Parke, M. E.↗
The inverse problem: Ocean tides derived from earth tide observations
Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.
Kuo, J. T.↗
M2, S2, K1 models of the global ocean tide
Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each contituent are presented.
Parke, M. E.↗
Modelling the pole tide and its effect on the earth's rotation
The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, both analytical and numerical models for the pole tide are constructed. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.
Carton, J. A.↗
New estimates of oceanic tidal energy dissipation from satellite altimetry
As a novel approach to computing the flux of tidal power into shelf areas, tidal maps of an oceanic area near the Patagonian Shelf are derived from 11 months of altimetry records from the GEOSAT satellite. Power fluxes are computed from the maps through Laplace's tidal equations. Flux vectors for M2 clearly show a convergence on to the southern portion of the shelf sea and their total is nearly twice the loss computed by Miller for that area. A decrease of 'quality factor' with frequency from M2 to S2 is in keeping with Webb's hypothesis of shelf resonances at frequencies a little higher than the tidal band.
Cartwright, David E.↗
Research on diabatic initialization
The objective was to contribute to the improvement of the analyses of irrotational wind and moisture fields in the trophics through advancement in the technique of initialization by incorporating diabatic effects. Significant accomplishments made during the period May 1990 to April 1991 in the following areas are presented: (1) estimation of the uncertainty of daily synoptic analyses in the tropics; (2) normal modes of Laplace's tidal equations for zonal wavenumber zero; and (3) tropical initialization to ameliorate the spin-up problem of precipitation forecasts. The focus of current research and plans for next year are also presented.
Kasahara, Akira↗
Gravitational tides in the outer planets. I - Implications of classical tidal theory. II - Interior calculations and estimation of the tidal dissipation factor
Classical tidal theory is applied to the atmospheres of the outer planets. The tidal geopotential due to satellites of the outer planets is discussed, and the solution of Laplace's tidal equation for Hough modes appropriate to tides on the outer planets is examined. The vertical structure of tidal modes is described, noting that only relatively high-order meridional mode numbers can propagate vertically with growing amplitude. Expected magnitudes for tides in the visible atmosphere of Jupiter are discussed. The classical theory is extended to planetary interiors taking the effects of spherically and self-gravity into account. The thermodynamic structure of Jupiter is described and the WKB theory of the vertical structure equation is presented. The regions for which inertial, gravity, and acoustic oscillations are possible are delineated. The case of a planet with a neutral interior is treated, discussing the various atmospheric boundary conditions and showing that the tidal response is small.
Ioannou, Petros J.↗
Unsteady subsonic and supersonic potential aerodynamics for complex configurations
A recently developed general theory for unsteady compressible potential fluid dynamics for complex-configuration aircraft is reviewed. The method is based on a combination of the following techniques: Green's function method (to transform the differential equation into an integral differential-delay equation), finite element method (to transform the equation into a set of differential-delay equations in time), and the Laplace transform method (to transform the differential-delay equations into algebraic equations).
Morino, L.↗
Application of the Laplace-Borel transformation to the representation of analytical solutions of Duffing's equation
Various features of the solutions of Duffing's equation are described using a representation of the solutions in the Laplace-Borel transform domain. An application of this technique is illustrated for the symmetry-breaking bifurcation of a hard spring.
Truong, K. V.↗
SINDA - Systems Improved Numerical Differencing Analyzer
Capability to model fluid flow added. SINDA is software system developed to solve physical problems governed by diffusion-type equations mathematically modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations. Adapted to wide range of problems represented by Fourier, Possion, Laplace, or other differential equations. Written in FORTRAN and Assembler.
Damico, Steve J.↗
Dynamic response of a semi-infinite elastic cylinder containing an acoustic medium.
The solutions developed in this paper are based on the finite Hankel-Fourier-Laplace transform. The Love-Timoshenko shell equations are reduced through the application of the Fourier-Laplace transforms to the axial space and time variables. The equation of motion for the acoustic fluid contained within the shell are reduced through the application of the finite Hankel-Fourier-Laplace transform to the radial, axial spatial, and time variables. The boundary conditions at the fixed end of the semi-infinite shell are met through the application of loadings symmetric with respect to the origin and the application of a ring loading at the origin which is chosen so as to make the radial deflection there zero. Expressions are found for the transforms of the axial, tangential, and radial shell displacements, the axial, tangential, and radial fluid velocities, and the radiated fluid pressure. Numerical inversion of the Fourier-Laplace transform is accomplished in terms of a series of ultraspherical polynomials and Gauss-Hermite or Gauss-Laguerre quadrature.
Carpenter, R. F., III↗
SINDA '85/FLUINT, Version 2.2
SINDA, Systems Improved Numerical Differencing Analyzer, software system developed for solving physical problems governed by diffusion-type equations modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations, adapted to wide range of problems represented by such differential equations as Fourier, Poisson, or LaPlace. Software system updated. FLUINT, FLUid INTegrator, is advanced, one-dimensional fluid-analysis program solving equations of arbitrary fluid-flow networks. Written in FORTRAN and ASSEMBLER.
Cullimore, Brent↗
I-BIEM, an iterative boundary integral equation method for computer solutions of current distribution problems with complex boundaries: A new algorithm. I - Theoretical
A new algorithm for an iterative computation of solutions of Laplace's or Poisson's equations in two dimensions, using Green's second identity, is presented. This algorithm converges strongly and geometrically and can be applied to curved, irregular, or moving boundaries with nonlinear and/or discontinuous boundary conditions. It has been implemented in Pascal on a number of micro- and minicomputers and applied to several geometries. Cases with known analytic solutions have been tested. Convergence to within 0.1 percent to 0.01 percent of the theoretical values are obtained in a few minutes on a microcomputer.
Cahan, B. D.↗
KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation
This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.
97 MATHEMATICS AND COMPUTING↗
Vibration of the hollow sphere in an acoustic medium
Radial vibrations of hollow elastic sphere in acoustic medium, considering Laplace transform of field equations with respect to time
Berger, B. S.↗