Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

This chapter provides an overview of the recent developments concerning Saint-Venant's principle The task of determining, within the framework of the linear theory of elasticity, the stresses and displacements in an elastic cylinder in equilibrium, under the action of loads that arise solely from tractions applied to its plane ends has come to be called Saint- Venant's problem Saint-Venant's construction does not permit the arbitrary preassignment of the point-by-point variation of the end tractions giving rise to these forces and moments; indeed, this variation is essentially determined as a consequence of the special assumptions made in connection with his so-called semi-inverse procedure The early work of Saint-Venant and Boussinesq furnished the seeds from which grew a large number of more general assertions, most referring to elastic solids of arbitrary shape and many being rather imprecise, concerning the effect on stresses within the body of replacing the tractions acting over a portion of its surface by statically equivalent ones Such propositions usually went by the name of Saint-Venunt's principle, despite the fact that Saint-Venant's original conjecture was intended to apply only to cylinders This chapter discusses in detail about flow in a cylinder, a representation for the exact solution, and energy decay for other linear elliptic second-order problem Linear elastostatic problems are also stated in the chapter

Recent Developments Concerning Saint-Venant's Principle

Mode localization and eigenvalue loci veering phenomena in disordered structures

Chaos on the pseudosphere

Comments on curve veering in eigenvalue problems

The eigenvalue problem for the Laplace operator in two dimensions is classical in mathematics and physics. Nevertheless, computational methods for estimating the eigenvalues are still of much current interest, particularly in applications to acoustic and electromagnetic waveguides. Although our primary interest is with the computational methods, there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and, in addition, are of interest in themselves. These results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds. Some of the more powerful techniques available are illustrated by applying them to a model problem.

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Eigenvalues of the Laplacian in Two Dimensions

Inequalities for membrane and Stekloff eigenvalues

On curve veering

Neural networks are a computer architecture, implementable in software or hardware, that allow an entirely new approach to the computerized perception of data. These so-called connectionist models are inspired by what is known about the architecture of biological neurons, in which the "intelligence" or processing capability of the network is a result of the interconnection strengths between large arrays of nonlinear processing nodes. Neural networks are described and then are used to analyze the common radiological problem of pattern recognition on a noisy background. Classical signal detection theory is used to compare network performance against that of human observers, using computer-generated sets of very simple "nodules." The neural network performed with better accuracy, relative to human observer performance, in the detection of this elementary test object. Although these results may not scale up with more complex images, the favorable performance of neural networks at this level suggests that further investigation is warranted.

Neural networks in radiology: An introduction and evaluation in a signal detection task

We present a method which bounds the error between an estimate for a point in the spectrum and an eigenvalue of self-adjoint elliptic operators The method makes use of trial functions which need not satisfy the boundary conditions of the problem By using rough preliminary estimates for the eigenvalues this method gives both upper and lower bounds

V.G. Sigillito

Papers

Eigenvalues of the Laplacian in Two Dimensions

Inequalities for membrane and Stekloff eigenvalues

On curve veering

Neural networks in radiology: An introduction and evaluation in a signal detection task

Bounding Eigenvalues of Elliptic Operators