Search

Thermoelectric measurement of the dimensionless zT parameter requires multiple physical quantities to be measured, therefore there is great interest to find an experimental setup capable of measuring all these properties at once. Previous works on impedance spectroscopy have shown promising results in this direction, however, this technique does not lead to a complete characterization of the thermoelectric system without additional measurement. In order to extend impedance spectroscopy, we have investigated the measurement of the non-linear harmonic response of a Peltier device. The experiments are analyzed using an analytic model obtained by solving the heat equation in the frequency regime. Our work shows that fitting the experimental response of the system in the harmonic regime can lead to a complete characterization of the thermoelectric properties without the need of additional measurement., Comment: 9 pages 6 figures Change from the previous version: add Kramers-Kronig analysis add DC response analysis add the influence of temperature dependence of material properties in the model add references

The interval number of a graph $G$ is the minimum $k$ such that one can assign to each vertex of $G$ a union of $k$ intervals on the real line, such that $G$ is the intersection graph of these sets, i.e., two vertices are adjacent in $G$ if and only if the corresponding sets of intervals have non-empty intersection. In 1983 Scheinerman and West [The interval number of a planar graph: Three intervals suffice. \textit{J.~Comb.~Theory, Ser.~B}, 35:224--239, 1983] proved that the interval number of any planar graph is at most $3$. However the original proof has a flaw. We give a different and shorter proof of this result., Comment: 12 pages, 4 figures