Temperature-dependent reflectivity of silicon carbide

The spectral reflectivity of a commercial silicon carbide (SiC) ceramic surface was measured at wavelengths from 2.5 to 14.5 microns and at temperatures ranging from 358 to 520 K using a NASA-developed multiwavelength pyrometer. The SiC surface reflectivity was low at the short wavelengths, decreasing to almost zero at 10 microns, then increasing rapidly to a maximum at approximately 12.5 microns, and decreasing gradually thereafter. The reflectivity maximum increased in magnitude with increasing surface temperature. The wavelength and temperature dependence can be explained in terms of the classical dispersion theory of crystals and the Lorentz electron theory. Electronic transitions between the donor state and the conduction band states were responsible for the dispersion. The concentration of the donor state in SiC was determined to be approximately 4 x 10 exp 18 and its ionization energy was determined to be approximately 71 meV

Multiwavelength pyrometry for nongray surfaces in the presence of interfering radiation

A NASA developed multiwavelength pyrometry technique for nongray surfaces was extended to also measure surface temperature in the presence of interfering radiation. This radiation is produced by heat lamps used to raise the temperature of the surface. The necessary instruments are a spectral radiometer, an auxiliary radiation source, and a computer. Four radiation spectra are recorded: (1) the unobstructed spectrum characterizing an auxiliary radiation source; (2) the unobstructed spectrum characterizing the interfering radiation; (3) the radiation spectrum consisting of surface emission plus the interfering radiation; and (4) a spectrum consisting of the radiations of (3) plus the reflected radiation due to the incidence of the auxiliary radiation source on this surface. With these spectra, application of two variable, nonlinear, least squares, curve fitting computer software determines the surface temperature and the spectral emissivity. Use of the method to measure the surface temperature of silicon carbide under a simulated interference condition is shown at a low temperature just above ambient. The instrumentation necessary to extend the method to elevated temperatures is discussed

Lower bounds for the stable marriage problem and its variants

In an instance of the stable marriage problem of size n, n men and n women each ranks members of the opposite sex in order of preference. A stable marriage is a complete matching M = {(m_1, w_i_1), (m_2, w_i_2), ..., (m_n, w_i_n)} such that no unmatched man and woman prefer each other to their partners in M.A pair (m_i, w_j) is stable if it is contained in some stable marriage. In this paper, we prove that determining if an arbitrary pair is stable requires Ω(n^2) time in the worst case. We show, by an adversary argument, that there exists instances of the stable marriage problem such that it is possible to find at least one pair that exhibits the Ω(n^2) lower bound.As corollaries of our results, the lower bound of Ω(n^2) is established for several stable marriage related problems. Knuth, in his treatise on stable marriage, asks if there is an algorithm that finds a stable marriage in less than Θ(n^2) time. Our results show that such an algorithm does not exist

Complexity of the stable marriage and stable roommate problems in three dimensions

The stable marriage problem is a matching problem that pairs members of two sets. The objective is to achieve a matching that satisfies all participants based on their preferences. The stable roommate problem is a variant involving only one set, which is partitioned into pairs with a similar objective. There exist asymptotically optimal algorithms that solve both problems.In this paper, we investigate the complexity of three dimensional extensions of these problems. This is one of twelve research directions suggested by Knuth in his book on the stable marriage problem. We show that these problems are NP-complete, and hence it is unlikely that there exist efficient algorithms for their solutions.Applying the polynomial tranformation developed in this paper, we extend the NP-completeness result to include the problem of matching couples - who are both medical school graduates - to pairs of hospital resident positions. This problem is important in practice and is dealth with annually by NRMP, the centralized program that matches all medical school graduates in the United States to available resident positions

Non-contact heat flux measurement using a transparent sensor

A working non-contact heat flux sensor was demonstrated using a transparent material (sapphire) and a multiwavelength pyrometer. The pyrometer is used to measure the temperatures of the two surfaces of the sensor from the spectrum of radiation originating from them. The heat conducted through the material is determined from the temperature difference of the two surfaces and the thermal conductivity of the material. The measured heat flux is equal to the incident heat flux within experimental error indicating that no calibration would be necessary. A steady state heat flux of 100 kW/sq m was easily achieved