Past Differential Equations and Applications Seminar

28 April 2005
16:30
Abstract
We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplications of the model allow a general investigation of the r\^{o}les played by gain and delay, and the effects of ageing. <i>View diagram: </i>&nbsp;<a href="texshop_image.pdf">Download PDF</a>
  • Differential Equations and Applications Seminar
10 March 2005
16:30
Abstract
The classical gravity-capillary water-wave problem is the study of the irrotational flow of a three-dimensional perfect fluid bounded below by a flat, rigid bottom and above by a free surface subject to the forces of gravity and surface tension. In this lecture I will present a survey of currently available existence theories for travelling-wave solutions of this problem, that is, waves which move in a specific direction with constant speed and without change of shape. The talk will focus upon wave motions which are truly three-dimensional, so that the free surface of the water exhibits a two-dimensional pattern, and upon solutions of the complete hydrodynamic equations for water waves rather than model equations. Specific examples include (a) doubly periodic surface waves; (b) wave patterns which have a single- or multi-pulse profile in one distinguished horizontal direction and are periodic in another; (c) so-called 'fully-localised solitary waves' consisting of a localised trough-like disturbance of the free surface which decays to zero in all horizontal directions. I will also sketch the mathematical techniques required to prove the existence of the above waves. The key is a formulation of the problem as a Hamiltonian system with infinitely many degrees of freedom together with an associated variational principle.
  • Differential Equations and Applications Seminar

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