Positive Solutions and Extremal Points for Differential Equations

Extremal point properties are examined for the boundary value problem x⁽ⁿ⁾ + ? ^n-2 _i=0 A_i(t)x⁽ⁱ⁾ = 0, x⁽ⁱ⁾(0) = x^(n-2)(T) = 0, 0?i?n-2, where the A_i's, a characterization for the first extremal point is given in terms of the existence of a solution which is positive with respect to a cone in a Banach space. Also, an existence theorem is obtained for a related nonlinear problem     

Optimization of corrugated-QWIPs for large format, high quantum efficiency, and multi-color FPAs

Previously, we demonstrated a large format 1024 × 1024 corrugated quantum well infrared photodetector focal plane array (C-QWIP FPA). The FPA has a cutoff at 8.6 μm and is BLIP at 76 K with f/1.8 optics. The pixel had a shallow trapezoidal geometry that simplified processing but limited the quantum efficiency QE. In this paper, we will present two approaches to achieve a larger QE for the C-QWIPs. The first approach increases the size of the corrugations for more active volume and adopts a nearly triangular pixel geometry for larger light reflecting surfaces. With these improvements, QE is predicted to be about 35% for a pair of inclined sidewalls, which is more than twice the previous value. The second approach is to use Fabry–Perot resonant oscillations inside the corrugated cavities to enhance the vertical electric field strength. With this approach, a larger QE of 50% can be achieved within certain spectral regions without using either very thick active layers or anti-reflection coatings. The former approach has been adopted to produce two FPAs, and the preliminary experimental results will be discussed. In this paper, we also describe using voltage tunable detector materials to achieve multi-color capability for these FPAs.     

Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers

The process by which polymeric materials hydrolyze and disappear into their environments is often called erosion. Two types of erosion have been defined according to how the hydrolysis takes place. If hydrolysis occurs throughout the entire specimen at the same time, it is called bulk erosion. If the hydrolysis is mainly confined to a region near the surface of the specimen and the surface continuously degrades by moving inward, it is termed surface erosion. In this article, a kinetic relationship for bulk erosion is developed. This relationship provides a method for estimating the hydrolysis kinetic constants for bulk‐eroding polymers. This same relationship is also applicable to surface erosion at a microscopic level. Through its combination with a diffusion–reaction equation and the provision of moving boundary conditions, an analytical solution to the steady‐state surface‐erosion problem is obtained. The erosion rate, erosion front width, and induction time can all be expressed as simple functions of the rate of polymer bond hydrolysis, water diffusivity, and solubility, plus other parameters that can be experimentally determined. The erosion front width is the product of the induction time and the erosion rate. The ratio of the erosion front width to the polymer specimen thickness is a parameter that determines whether the specimen undergoes surface or bulk erosion. Theoretical results are compared with experimental observations from the literature, and agreement is found. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 383–397, 2005