Theory of optimum shapes in free-surface flows. Part 2. Minimum drag profiles in infinite cavity flow

The problem considered here is to determine the shape of a symmetric two-dimensional plate so that the drag of this plate in infinite cavity flow is a minimum. With the flow assumed steady and irrotational, and the effects due to gravity ignored, the drag of the plate is minimized under the constraints that the frontal width and wetted arc-length of the plate are fixed. The extremization process yields, by analogy with the classical Euler differential equation, a pair of coupled nonlinear singular integral equations. Although analytical and numerical attempts to solve these equations prove to be unsuccessful, it is shown that the optimal plate shapes must have blunt noses. This problem is next formulated by a method using finite Fourier series expansions, and optimal shapes are obtained for various ratios of plate arc-length to plate width

Unsteady, Free Surface Flows; Solutions Employing the Lagrangian Description of the Motion

Numerical techniques for the solution of unsteady free surface flows are briefly reviewed and consideration is given to the feasibility of methods involving parametric planes where the position and shape of the free surface are known in advance. A method for inviscid flows which uses the Lagrangian description of the motion is developed. This exploits the flexibility in the choice of Lagrangian reference coordinates and is readily adapted to include terms due to inhomogeneity of the fluid. Numerical results are compared in two cases of irrotational flow of a homogeneous fluid for which Lagrangian linearized solutions can be constructed. Some examples of wave run-up on a beach and a shelf are then computed

Discussion of: Brownian distance covariance

Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]Comment: Published in at http://dx.doi.org/10.1214/09-AOAS312E the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Theory of optimum shapes in free-surface flows. Part 1. Optimum profile of sprayless planing surface

This paper attempts to determine the optimum profile of a two-dimensional plate that produces the maximum hydrodynamic lift while planing on a water surface, under the condition of no spray formation and no gravitational effect, the latter assumption serving as a good approximation for operations at large Froude numbers. The lift of the sprayless planing surface is maximized under the isoperimetric constraints of fixed chord length and fixed wetted arc-length of the plate. Consideration of the extremization yields, as the Euler equation, a pair of coupled nonlinear singular integral equations of the Cauchy type. These equations are subsequently linearized to facilitate further analysis. The analytical solution of the linearized problem has a branch-type singularity, in both pressure and flow angle, at the two ends of plate. In a special limit, this singularity changes its type, emerging into a logarithmic one, which is the weakest type possible. Guided by this analytic solution of the linearized problem, approximate solutions have been calculated for the nonlinear problem using the Rayleigh-Ritz method and the numerical results compared with the linearized theory

Interaction energy of Chern-Simons vortices in the gauged O(3) sigma model

The purpose of this Letter is to present a computation of the interaction energy of gauged O(3) Chern-Simons vortices which are infinitely separated. The results will show the behaviour of the interaction energy as a function of the constant coupling the potential, which measures the relative strength of the matter self-coupling and the electromagnetic coupling. We find that vortices attract each other for $\lambda > 1$ and repel when $\lambda < 1$. When $\lambda =1$ there is a topological lower bound on the energy. It is possible to saturate the bound if the fields satisfy a set of first order partial differential equations.Comment: 12 pages, LateX, 7 figures available on request from author. [email protected]

Dislocation scattering in a two-dimensional electron gas

A theory of scattering by charged dislocation lines in a two-dimensional electron gas (2DEG) is developed. The theory is directed towards understanding transport in AlGaN/GaN high-electron-mobility transistors (HEMT), which have a large number of line dislocations piercing through the 2DEG. The scattering time due to dislocations is derived for a 2DEG in closed form. This work identifies dislocation scattering as a mobility-limiting scattering mechanism in 2DEGs with high dislocation densities. The insensitivity of the 2DEG (as compared to bulk) to dislocation scattering is explained by the theory.Comment: 6 pages, 3 figure

An algorithm for the systematic disturbance of optimal rotational solutions

An algorithm for introducing a systematic rotational disturbance into an optimal (i.e., single axis) rotational trajectory is described. This disturbance introduces a motion vector orthogonal to the quaternion-defined optimal rotation axis. By altering the magnitude of this vector, the degree of non-optimality can be controlled. The metric properties of the distortion parameter are described, with analogies to two-dimensional translational motion. This algorithm was implemented in a motion-control program on a three-dimensional graphic workstation. It supports a series of human performance studies on the detectability of rotational trajectory optimality by naive observers