Study on the Growth of Nb3Sn Superconductor in Cu(Sn)/Nb Diffusion Couple

Nb3Sn growth following the bronze technique, (i.e. by interdiffusion between Cu(Sn) alloy (bronze) and Nb) is one of the important methodologies to produce this superconductor. In this study, we have addressed the confusion over the growth rate of the Nb3Sn phase. Furthermore, a possible explanation for the corrugated layer in the multifilamentary structure is discussed. Kirkendall marker experiments were conducted to study the relative mobilities of the species, which also explained the reason for finding pores in the product phase layer. Based on the parabolic growth constant at different temperatures, the activation energy for the growth is determined. We have further explained the dramatic increase in the growth rate of the prod

Polynomial Decompositions in Polynomial Time

Fix a prime p. Given a positive integer k, a vector of positive integers Delta = (Delta(1), Delta(2), ... , Delta(k)) and a function Gamma : F-p(k) -> F-p, we say that a function P : F-p(n) -> F-p is (k, Delta, Gamma)-structured if there exist polynomials P-1, P-2, ..., P-k : F-p(n) -> F-p with each deg(P-i) <= Delta(i) such that for all x is an element of F-p(n), P(x) = Gamma(P-1(x), P-2(x), ..., P-k(x)). For instance, an n-variate polynomial over the field Fp of total degree d factors nontrivially exactly when it is (2, (d - 1, d - 1), prod)- structured where prod(a, b) = a . b. We show that if p > d, then for any fixed k, Delta, Gamma, we can decide whether a given polynomial P(x(1), x(2), ..., x(n)) of degree d is (k, Delta, Gamma)-structured and if so, find a witnessing decomposition. The algorithm takes poly(n) time. Our approach is based on higher-order Fourier analysis.