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Ordinary Differential Equations and Applied Dynamics

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Articles 151 - 156 of 156

Full-Text Articles in Numerical Analysis and Computation

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06 Feb 2007

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06

All HMC Faculty Publications and Research

Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size h=1, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots

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Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill Feb 2005

Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.

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Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling Apr 1996

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

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Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling Apr 1993

Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling

Aviation Department Publications

Report LSTM 375/TE/93, Lehrstuhl fuer Stroemungsmechanik Universitaet Erlangen-Nuernberg Cauerstr. 4, 8520 Erlangen Germany.

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Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic May 1992

Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic

Aviation Department Publications

In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is …

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A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic Mar 1992

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

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