Random Latin square graphs

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and several similarities and differences are pointed out. For many properties our results for the general case are as strong as the known results for random Cayley graphs and sometimes improve the previously best results for the Cayley case. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

The Breakdown Phenomena in Micrometer Scale Direct-Current Gas Discharges

This paper reports on experimental and theoretical studies of the direct current breakdown voltage characteristics for several gases (argon, nitrogen, helium, hydrogen, dry air, oxygen and carbon dioxide) in discharges with parallel-plane electrodes separated from 1 to 100 μm. The breakdown phenomena have been discussed in terms of field emission of electrons from the cathode. Based on the measured breakdown voltage curves, realistic values of the effective yields and the field emission thresholds for considered gases have been estimated. It was found that the secondary electron emission due to high electric field generated in microgaps depends primarily on the electric field E leading directly to the violation of the Paschen’s law. The effective yields due to the field emission for all gases are determined for the first time. Experimental data are supported by the theoretical predicitions that suggest departure from the scaling law and a flattening of the Paschen curves at higher pressures. The obtained results may provide better understending of the breakdown phenomena in microgaps.