Graphlet frequency distribution (GFD) has recently become popular for characterizing large networks. However, the computation of GFD for a network requires the exact count of embedded graphlets in that network, which is a computationally expensive task. As a result, it is practically infeasible to compute the GFD for even a moderately large network. In this paper, we propose GUISE, which uses a Markov Chain Monte Carlo (MCMC) sampling method for constructing the approximate GFD of a large network. Our experiments on networks with millions of nodes show that GUISE obtains the GFD within few minutes, whereas the exhaustive counting based approach takes several days. Cit 92-94(V=4,340,E=12,917) Cit 92-96(V=9,186,E=53,183 ) Cit 92-98(V=14,572,E=125,346) Cit 92-00(V=8,000,E=20,523) Cit 92-03(V=27,770,E = 352, 8 07)
We report the effect of cathode structure on the field emission properties of
individual carbon nanotubes. Experimental field emission data are obtained for
two well-defined cathode structures: a multi-walled carbon nanotube (MWNT)
attached to an etched Ni metal wire and a MWNT attached to a flat Ni-coated
Si microstructure. We observed different macroscopic turn-on fields of 1.6 and
2.5 V µm−1, respectively, for the aforementioned experimental structures. This effect is investigated by
detailed finite element analysis. We demonstrate that the geometry of the cathode
structures significantly affects the microscopic tip field, leading to different turn-on voltages
and field distributions for such individual MWNT emitters. Simulations show
that changing the support geometry from a hemispherically capped shank to
a cylindrical shank produces an increase in the macroscopic threshold field of
0.91 V µm−1. This effect is further investigated by varying the support radius from 0.5 to
30 µm
for a cylindrically shaped support structure. The results show that such a variation in the radius
of the support structure produces an increase in the macroscopic turn on field from 0.72 to
5.89 V µm−1. We also report quantitative evidence for the nonlinear relationship between the field
enhancement factor as a function of support structure radius for nanostructures of three
different aspect ratios.
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