The behavior of a fluid with a thin capillary meniscus can be modelled on a one-dimensional domain Ω = [−L, L] by the thin film equation ht = −(hnhxxx)x with boundary conditions hx(±L) = ±α (giving a fixed contact angle) and hxxx(±L) = 0 (prohibiting mass flux). It is desirable to know whether or not such a film experiences rupture; that is, whether there exists some x0, t0 (with t0 possibly ∞) such that h(x0, t0) = 0, corresponding to the appearance of a dry spot. We approach this problem using energy methods, which use the conservation or dissipation of quantities such as mass, surface area, coating energy, and other more abstract quantities to describe the behavior of the fluid. We present a brief analysis of the behavior of some of these energies, as well as a proof that, given certain assumptions, rupture cannot occur in a thin capillary meniscus for n > 4 and, in more restricted cases, for n > 7/2. We also show that rupture must occur for 0 < n < 1/2. We describe the asymptotic behavior of the regions in which rupture occurs. We also describe the numerical implementation of this problem and the advantages and drawbacks of using certain prewritten solvers in MATLAB and new implementations of θ-weighted schemes and the Newton-Raphson method. We propose uses of these numerical methods to make further progress on the problem.

Development and character analysis of software programs, which compute minimum information probability distributions. / Entwicklung und Charakteranalyse von Softwareprogrammen, welche Minimuminformations Wahrscheinlichkeitsverteilungen berechnen.

Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaf 53). Also available on the World Wide Web.

Une reconstruction critique du parcours qui a porté Newton à l'établissement de sa théorie des fluxions entre 1664 et 1666, visant l'identification des contributions que ce travail apporte à la mise en place de l'analyse en tant que théorie mathématique (théorie des fonctions).

Thèse doctorat : Informatique : Nancy 1 : 2006. / Titre provenant de l'écran-titre.

Thesis (M.S.)--Utah State University, Dept. of Wildlife Resources, 1971. / Includes vita. Includes bibliographical references (leaves 67-70).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Newton; globalized; inexact Newton. Includes bibliographical references (p. 61).

A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and the quasi-Newton optimizer to find the optimum. A Krylov subspace method with approximate-Schur preconditioning is used to solve both the flow equation and the adjoint equation. Basis spline surfaces are used to parameterize the geometry, and a fast algebraic algorithm is used for grid movement. Accurate discrete-adjoint gradients can be obtained in approximately one-fourth the time required for a converged flow solution. Single- and multi-point lift-constrained drag minimization optimization cases are presented for wing design at transonic speeds. In all cases, the optimizer is able to efficiently decrease the objective function and gradient for problems with hundreds of design variables.

A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and the quasi-Newton optimizer to find the optimum. A Krylov subspace method with approximate-Schur preconditioning is used to solve both the flow equation and the adjoint equation. Basis spline surfaces are used to parameterize the geometry, and a fast algebraic algorithm is used for grid movement. Accurate discrete-adjoint gradients can be obtained in approximately one-fourth the time required for a converged flow solution. Single- and multi-point lift-constrained drag minimization optimization cases are presented for wing design at transonic speeds. In all cases, the optimizer is able to efficiently decrease the objective function and gradient for problems with hundreds of design variables.

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