On the Nusselt number in heat transfer between multiple parallel blood vessels.

Arrays of two or more parallel blood vessels in a tissue matrix have been studied extensively in the context of bioheat transfer. The average vessel Nusselt number (based on the difference between the mixed-mean blood temperature and the average vessel surface temperature) is a crucial parameter in such studies. Various workers have noted tht in particular cases the average Nusselt number is identical to that for fully developed flow in a single vessel in an infinite medium. In other words, the Nusselt number is unaffected by the presence of other vessels. It is proven here that this surprising result holds true for arbitrary number, size, flow direction, and velocity profile in the blood vessels, and for very general boundary conditions on the outer tissue boundary. A useful corollary is that the average wall temperature in a particular vessel may be found by evaluating the temperature fields due to the other vessels and the tissue boundaries at a single point, the center of the vessels in question.

Scalable aspheric corrective mirror for end-pumped solid-state lasers.

A procedure is presented to design an aspheric corrective mirror to remove the effects of thermally induced optical aberrations in end-pumped solid-state lasers. The design is based on solving the inverse problem of bending a thin plate of variable thickness; i.e., given the plate deflection profile a thickness profile must be calculated by solving the differential equation for bending. The advantage of this type of aberration correction is the fact that it can be scaled to different pump powers during operation while still matching the aspheric profile in question. Guidelines for fabrication of the mirror are also presented.

Application of the impedance formalism to diffraction gratings with multiple coating layers.

The standard method of matching boundary conditions at the interfaces of a multilayer plane dielectric stack is shown to be numerically unstable for the evanescent orders when a large number of layers is present. For an isolated dielectric stack with an incident propagating beam there is no need to calculate the evanescent orders; however, when a diffraction grating is buried under the stack there is mixing of orders, and it may be important to calculate the evanescent as well as the propagating orders. It is shown that the impedance formalism removes the numerical instability completely. This method may be coupled to either boundary integral or differential equation methods for the grating to provide the complete solution for the grating-stack system.