Burnt offerings and harpies at Nasidienus’ dinner-party (Horace, Satires 2.8)

Horace's last Satire describes a disastrous dinner party hosted by the gourmet Nasidienus, which is ruined by a collapsing tapestry. The food served afterwards is presented in a dismembered state. This chapter argues that several elements of the scene recall the greedy Harpies of Apollonius' Argonautica, and that Horace's friend Virgil shows the influence of this Satire in his own Harpy-scene in Aeneid 3. It also argues that the confusion in the middle of the dinner causes the food cooking in the kitchen to be neglected and burned. This explains the state of the subsequent courses, which Nasidienus has salvaged from a separate disaster backstage.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.