Numerical analysis of the Navier-Stokes equations

summary:This paper discusses some conceptional questions of the numerical simulation of viscous incompressible flow which are related to the presence of boundaries

Interaction between Experiment, Modeling and Simulation of Spatial Aspects in the JAK2/STAT5 Signaling Pathway

Fundamental progress in systems biology can only be achieved if experimentalists and theoreticians closely collaborate. Mathematical models cannot be formulated precisely without deep knowledge of the experiments while complex biological systems can often not be understood fully without mathematical interpretation of the dynamic processes involved. In this article, we describe how these two approaches can be combined to gain new insights on one of the most extensively studied signal transduction pathways, the Janus kinase (JAK)/ signal transducer and activator of transcription (STAT) pathway. We focus on the parameters of a model describing how STAT proteins are transported from the membrane to the nucleus where STATs regulate gene expression. We discuss which parameters can be measured experimentally in different cell types and how the unknown parameters are estimated, what the limits of these techniques and how accurate the determinations are

Incompressible Viscous Flows

In this article, we describe some approaches to the efficient numerical computation of viscous incompressible flows governed by the Navier-Stokes equations. We concentrate on laminar flows, stationary as well as nonstationary, for Reynolds numbers of moderate size, and in general domains. The emphasis is on spatial discretization by the finite element method. We discuss the treatment of the incompressibility constraint, the time-stepping process, techniques of error control and mesh adaptation and the solution of the resulting indefinite algebraic equations