Linearly Induced Mappings between Cones of Quadratic Forms
This paper deals with mappings between cones of positive quadratic forms which are induced by linear mappings between the underling vector spaces, i.e., the spaces which are the domains of the forms. Three fundamental results are proved, two of which were previously announced by the second author. The first result states that there is an inclusion-reversing one-to-one correspondence between the lattice of subspaces of a given space and the lattice of faces of the cone of quadratic forms on that space. The second result states that all cone-isomorphisms between cones of quadratic forms are induced by linear isomorphisms between the underlying spaces. The third result states that a given cone-linear mapping F between cones of quadratic forms is induced by some linear mapping between the underlying spaces if and only if both F and its transpose preserve faces.
Natural metrics on faceless cones
SummaryA genuine faceless cone is a non-empty linear cone that is open in some linear topology and includes no line. This paper describes all assignments of metrics to genuine faceless cones such that every linear mapping between cones is a contraction.
Computational fluid dynamics as a development tool for rotary blood pumps.
Computational fluid dynamics (CFD) is beginning to significantly impact the development of biomedical devices, in particular rotary cardiac assist devices. The University of Pittsburgh's McGowan Center for Artificial Organ Development has extensively used CFD as the primary tool to analyze and design a novel axial flow blood pump having a magnetically suspended rotor. The blood-contacting surfaces of the pump were developed using a design strategy based on CFD that involved closely coupling a Navier-Stokes solver to a parameterized geometry modeler and advanced mesh movement techniques. CFD-based blood damage models for shear-induced hemolysis as well as surrogate functions describing thrombosis potential were employed to help guide design improvements. This CFD-based design approach resulted in the timely development of a pump subjected to multiple geometric refinements without building expensive physical prototypes for each design iteration. A physical prototype of the final improved pump was fabricated and experimentally analyzed using particle imaging flow visualization. The CFD predicted results correlated well with the experimental data including pressure-flow (H-Q) performance and specific flow field features. It is estimated that the present CFD-based design approach shortened the overall design time frame from an order of years to months.