Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references

Immunochemical study of the plasma low and high density lipoproteins in Tangier disease

AbstractMajor disturbances of the lipoproteins in Tangier serum have been investigated using electrophoretic and immunochemical techniques. Previously described anomalies concerning the striking deficiency in HDL and the very low levels of apo A-I and apo A-II in Tangier patients are illustrated and explained. Anomalies concerning the fast LDL of Tangier serum are attributed to different forms of apo B not previously described. These data are strengthened by the features of a 2-dimensional electrophoresis method elaborated in the laboratory which allows apoproteins to separate in the second dimension. These apoproteins are obtained by the delipidation of the lipoproteins fractionated in a first polyacrylamide discontinuous gel. This method clearly shows the distribution of apoproteins in the first lipoprotein track and is in perfect accordance with the new concept of lipoprotein particles