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Circular domains frequently appear in mathematical modeling in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a two-dimensional disk. The properties of these bifurcations at equilibriums are analyzed rigorously by studying the equivariant normal forms. Two reaction–diffusion systems with discrete time delays are selected as numerical examples to verify the theoretical results, in which spatially inhomogeneous periodic solutions including standing waves and rotating waves, and spatially homogeneous periodic solutions are found near the bifurcation points. [ABSTRACT FROM AUTHOR]

Electronegative S-filled skutterudite compounds have attracted considerable attention due to scattering of low-frequency phonons (35–50 cm − 1 ), but there are few reports on S-filled double-substituted skutterudite. In this work, a series of S-filled Te-Sn double-substituted skutterudite compounds were synthesized using high pressure and high temperature (HPHT) method. The phase composition, microstructure, and thermoelectric properties of SxCo4Sb 1 1 Te 0. 7 Sn 0. 3 (x = 0 , 0.05, 0.10, 0.20) samples were systematically determined. The results show that the introduction of S increases the substitution limit of Te in the Sb site. Under the combined effect of the sample synthesis pressure and S filling, the nucleation density of the sample grains increases and the grain size decreases. At the same time, there are numerous special microstructures in the samples synthesized in a high-pressure environment. Thermoelectric performance studies show that a small amount of S filling optimizes the Seebeck coefficient of the sample and increases the power factor (PF). With an increase of the amount of S introduced, the thermal conductivity of the samples decreases significantly. Therefore, the maximum zT value of an S 0. 0 5 Co4Sb 1 1 Te 0. 7 Sn 0. 3 sample synthesized at 2.5 GPa pressure is 0.17 at room temperature. The maximum zT value of the sample is 1.26 at 773 K. [ABSTRACT FROM AUTHOR]