We compute time-periodic and relative-periodic solutions of the free-surface Euler equations that take the form of overtaking collisions of unidirectional solitary waves of different amplitude on a periodic domain. As a starting guess, we superpose two Stokes waves offset by half the spatial period. Using an overdetermined shooting method, the background radiation generated by collisions of the...

A shooting method is developed to approximate the eigenvalues and eigenfunctions of a 4th order Sturm-Liouville problem. The main tool is a miss-distance function M(), which counts the number of eigenvalues less than. The method approximates the coeecients of the diierential equation by piecewise-constant functions, which enables an exact solution to be found on each mesh interval. In order to ...

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtaine...

Abstract: In this paper we present a mathematical analysis for a steady-state laminar boundary layer flow, governed by the Ostwald-de Wael power-law model of an incompressible nonNewtonian fluid past a semi-infinite power-law stretched flat plate with uniform free stream velocity. A generalization of the usual Blasius similarity transformation is used to find similarity solutions [1]. Under app...

Airborne wind energy systems are capable of extracting energy from higher wind speeds at higher altitudes. The configuration considered in this paper is based on a tethered kite flown in a pumping orbit. This pumping cycle generates energy by winching out at high tether forces and driving a generator while flying figures-of-eight, or lemniscates, as crosswind pattern. Then, the tether is reeled...

Many practical optimal control problems include discrete decisions. These may be either time–independent parameters or time–dependent control functions as gears or valves that can only take discrete values at any given time. While great progress has been achieved in the solution of optimization problems involving integer variables, in particular mixed–integer linear programs, as well as in cont...

In the present study, an analysis is carried out to study the variable viscosity and chemical reaction effects on the flow, heat, and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equati...

An analysis for the axisymmetric laminar boundary layer mixed convection flow of a viscous and incompressible fluid towards a stretching cylinder immersed in a thermally stratified medium is presented in this paper. Similarity transformation is employed to convert the governing partial differential equations into highly nonlinear ordinary differential equations. Numerical solutions of these equ...

We use recent innovative solution techniques to investigate the problem of MHD viscous flow due to a shrinking sheet with a chemical reaction. A comparison is made of the convergence rates, ease of use, and expensiveness the number of iterations required to give convergent results of three seminumerical techniques in solving systems of nonlinear boundary value problems. The results were validat...

Amethod for generating a near-minimum-time control input for  exible structures is presentedwith the objective of minimizing the maneuver time and the residual energy of the  exible modes. The method is based on smoothing the bang–bang, time-optimal control input designed for the rigid-body mode. Smoothing is accomplished through the addition, to the basic time-optimal control problem for the...