Percolation of Superconductivity

In case of superconductors whose electrons attract each other only if they are near certain centers, the question arises 'How many such centers are needed to make the ground state superconducting?' We shall examine it in the context of a random U Hubbard model. In short we study the case where U_i is -|U| and 0 with probability c and 1-c respectively on a lattice whose sites are labelled i using the Gorkov decoupling and the Coherent Potential Approximation (CPA). We argue that for this model there is a critical concentration c_0 below which the system is not a superconductor.Comment: 18 pages, 10 figure

Superconducing Alloys with Weak and Strong Scattering: Anderson's Theorem and a Superconductor-Insulator Transition

We have studied the effects of strong impurity scattering on disordered superconductors beyond the low impurity concentration limit. By applying the full CPA to a superconductiong A-B binary alloy, we calculated the fluctuations of the local order parameters $\Delta_{A}, \Delta_{B}$ and charge densities, $n_{A}, n_{B}$ for weak and strong on site disorder. We find that for narrow band alloy s-wav e superconductors the conditions for Anderson's theorem are satisfied in general only for the case of particle-hole symmetry. In this case it is satisfied regardless whether we are in the weak or strong scattering regimes. Interestingly, we find that strong scattering leads to band splitting and in this regime for any band filling we have a critical concentration where a superconductor-insulator quantum phase transition occurs at T=0.Comment: 28 pages, 13 figure

Combustion Process in a Spark Ignition Engine: Dynamics and Noise Level Estimation

We analyse the experimental time series of internal pressure in a four cylinder spark ignition engine. In our experiment, performed for different spark advance angles, apart from usual cyclic changes of engine pressure we observed oscillations. These oscillations are with longer time scales ranging from one to several hundred engine cycles depending on engine working conditions. Basing on the pressure time dependence we have calculated the heat released per cycle. Using the time series of heat release to calculate the correlation coarse-grained entropy we estimated the noise level for internal combustion process. Our results show that for a smaller spark advance angle the system is more deterministic.Comment: 15 pages, 7 figures, submitted to CHAO