We explore the stability of equilibrium solution(s) of a simple model of microvascular blood flow in a two-node network. The model takes the form of convection equations for red blood cell concentration, and contains two important rheological effects—the Fåhræus–Lindqvist effect, which governs viscosity of blood flow in a single vessel, and the plasma skimming effect, which describes the separation of red blood cells at diverging nodes. We show that stability is governed by a linear system of integral equations, and we study the roots of the associated characteristic equation in detail. We demonstrate using a combination of analytical and numerical techniques that it is the relative strength of the Fåhræus–Lindqvist effect and the plasma skimming effect which determines the existence of a set of network parameter values which lead to a Hopf bifurcation of the equilibrium solution. We confirm these predictions with direct numerical simulation and suggest several areas for future research and application.
The Lexmark team will design and prototype novel applications for their multifunction printers. The target platform is a printer-scanner-copier with fax and phone capability, network access, USB memory device support, a hard disk, an LCD display / touch screen, and the ability to connect to other periferals through USB. The software environment is a Java Virtual Machine that provides access to all of the hardware as well as libraries of functions for generating a graphical user interface and managing electronic documents. The goal of this project is to design a software or hardware-software system that makes creative use of this technology, develops and improves user-interaction, or identifies novel applications that address the needs of users.