In this paper we use a method due to Williams (l) to discuss the scattering of surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending indefinitely downwards from a finite depth.1. Introduction. In 1966 Williams (l) presented a new approach to the problem of the scattering of two-dimensional surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending from above the free surface to a finite depth. This problem had previously been considered by Ursell (2), with whose results Williams agreed. Subsequently Faulkner (3,4) extended Wnliams's method, in conjunction with the Wiener-Hopf technique, to discuss the scattering of three-dimensional waves. However, the second of Faulkner's papers, which considers the case when the barrier extends downwards indefinitely from a finite depth, contains an error of formulation which vitiates his results.In this paper we first extend Williams's method to the two-dimensional case where the barrier extends indefinitely downwards from a finite depth and then give a correct formulation of the problem considered by Faulkner.2. Statement of the problem. We consider the scattering of surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending indefinitely downwards from a finite depth I. We take a non-dimensional Cartesian coordinate system with the axis of y vertically downwards, the mean free surface of the water being the plane y = 0, and such that the barrier is given by x = 0, y ^ 1, -oo < z < oo. Assuming the motion to be irrotational and simple harmonic in time, the velocity potential may be taken as the real part of x(z, y, z) e~i ai: , where (6) % is a single-valued harmonic function in the region occupied by the water satisfying the boundary conditions

Purpose-The purpose of this paper is to provide a framework for analysing and modelling detailed workflow of image-guided interventions to facilitate simulation and the re-engineering process for the development of new procedures in multi-modal imaging environments. Design/methodology/approach-The methodology presented includes a literature review on workflow simulation in surgery, focussing on radiology environments, an assessment of simulation tools, a data gathering and management framework and research on methods for conceptual modelling of the processes. Findings-The literature review reveals that few authors attempted to analyse the phases within image-guided interventions, and those that did, only did so partially. The framework developed for this work intends to fill the gap found in the survey. It allows the maintenance and management of large amounts of data, one of the most critical factors when modelling detailed workflow. In addition, selecting the appropriate simulation software plays an important role, saving time in later stages of the project. Originality/value-The framework presented for endovascular interventions can be extended to other types of image-guided interventions. Moreover, modelling the workflow processes in a modular way facilitates the re-engineering process when integrating different imaging modalities during the same procedure.