Gas sensor array modeling and cuprate superconductivity from correlated spin disorder

In part I, a kernel regression method is developed for modeling gas sensor response functions, for the purpose of identifying the composition of gas mixtures. A quantitative measure of orthogonality in sensor arrays is introduced. The method is applied to TiO₂ sensor arrays exposed to O₂ and CO. A sensing mechanism is analyzed by applying Wolkenstein's theory of chemisorption to the single grain TiO₂ response to O₂ and CO. It is found that this mechanism, in combination with Wolkenstein's theory, can adequately describe the response of granular TiO₂ sensors.; In part II, a spin-dependent tight-binding model for the hole-doped cuprates is developed. The model incorporates the effects of antiferromagnetism and spin disorder. In the coherent potential approximation, the effective medium Green's function is derived and single-particle properties are obtained. When the spin disorder is correlated, an effective interaction between holes leads to d_x2−y2 superconductivity. The pseudogap region of the cuprate phase diagram is interpreted within this theory.