Normal State Response

Since it is much more convenient to weigh a sample than to measure its volume accurately, the magnetic response is often expressed as the moment per unit mass, m/W, where W is the weight of the cylinder. The proportionality between the internal field and the moment per unit mass is termed the mass magnetic susceptibility xg with units of cm3/g. Obviously, xv and Xg are simply related by the density of the cylinder p = W/V  

It is useful to consider typical values of different contributions to the magnetic susceptibility. One important component is the Curie susceptibility arising from isolated (i.e., noninteracting) paramagnetic ions with g-factor g and spin S which is given by  

The superconducting material YBa2Cus07 weighs 666 g/mole or 222 g/mole Cu. If all the Cu ions were divalent and acted as isolated spins, N in Eq. 4 would be 2.7 x 1021 Cu+2 ions per gram. Hence, the mass susceptibility xg would be 5.6 x 10 6 cms/g at room temperature (295 K) and would increase inversely with decreasing temperature, tripling to 1.7 x 10 5 cms/g at 100 K. 

Another additive term in the magnetic susceptibility arises from the temperature-independent core diamagnetism of all the ions in a solid. For YBa2Cu307 the core diamagnetism is approximately -2 x 10 7 based on a calculation using Pascal s constants (9). This small negative contribution serves to reduce the total susceptibility. A third possible contribution arises from Van Vleck paramagnetism (10) caused by excited states in the atoms of the 

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Fig. 19. Low-energy, commensurate [Q = (n ,n), acoustic mode] response in the normal state of fbur different compositions of 835011307., measured at lOOK. As the doping is increased the feature at (ji,jl) broadens and weakens, and there is very little normal state response at the commensurate position for the overdoped sample. From Bourges (1998).

There is a clear anomaly in the temperature dependence at the superconducting transition, with an abrupt jump in intensity above the level of a weaker normal-state response. The existence of a weak normal-state feature was disputed (see Fong et al. 1995) however, the different measurements were not performed on samples with the same oxygen content. The general trend of the normal-state response shown in fig. 19 indicates a gradual elimination of the intensity at (jr,jr) in the normal state as the oxygen content is increased beyond optimal doping (x 0.07). 

Protection is the branch of electric power engineering concerned with the principles of design and operation of equipment (called relays nr protective relays ) which detect abnormal power system conditions and initiate corrective action as quickly as possible in order to return the power system to its normal state. The quickness of response is an essential element of protective relaying systems—response times of the order of a few milliseconds are often required. Consequently, human intervention in the protection of system operation is not possible. The response must be automatic, quick, and should cause a minimum amount of disruption to the power system. 

There are several methods that can be used to select well-distributed calibration samples from a set of such happenstance data. One simple method, called leverage-based selection, is to run a PCA analysis on the calibration data, and select a subset of calibration samples that have extreme values of the leverage for each of the significant PCs in the model. The selected samples will be those that have extreme responses in their analytical profiles. In order to cover the sample states better, it would also be wise to add samples that have low leverage values for each of the PCs, so that the center samples with more normal analytical responses are well represented as well. Otherwise, it would be very difficult for the predictive model to characterize any non-linear response effects in the analytical data. In PAC, where spectroscopy and chromatography methods are common, it is better to assume that non-linear effects in the analytical responses could be present than to assume that they are not. 

This is a central result of our paper. Here, xo(q> °>) is the usual BCS-like Lind-hard response function, n(q, co) and Z(q, co) result from the strong electronic correlation effects. In the normal state the expression for n(q, co) has been obtained by Hubbard and Jain [15]. In the superconducting state it is given by... 

We looked at the far-infrared equilibrium and photo-induced reflectivity of a MgB2 thin film and at the ESR spectra of powder samples. The photo-induced response shows one gap at 3 meV and another at 7 meV. However, excess quasiparticles are only found at the edge of the smaller gap. ESR data on the normal state shows a break down, around room temperature, of the... 

The symbol P is normally rendered as p, but this collides with our p for the dimensionless potential. For LSV, a small P value means a slow LSV sweep rate and a sigmoidal steady-state response, while a large value means a fast sweep rate, with the UMDE behaving more like a planar (shrouded) electrode. It will be seen later that the above impinges on the choice of a maximum Z... 

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