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Black carbon (BC), normally existing as aggregates, significantly affects the Earth radiative forcing, energy balance, and climate by scattering and absorbing both solar radiation and terrestrial emission. The BC particles are usually treated as fractal aggregates with same-sized monomers. However, experimental studies show that monomer diameters of BC normally obey a lognormal distribution ranging from 10 nm to over 100 nm. This study investigates the effects of monomer size distribution on the radiative properties of BC particles. The fractal aggregates are generated by a cluster-cluster aggregation (CCA) algorithm, and the Multiple Sphere T-Matrix (MSTM) method is used to simulate the radiative properties of randomly oriented aggregates. The integral radiative properties of aggregates with different-sized monomers have normal distributions with large standard deviations, and it requires to average radiative properties of over 60 aggregate realizations to represent their ensemble-averaged properties. The aggregates with different-sized monomers exhibit much stronger scattering and absorption than the aggregates with same-sized monomers and the geometric mean diameter, whereas the absorption cross section becomes comparable to that given by aggregates with same-sized monomer and the equivalent volume diameter. Similar phase matrix elements are obtained for the aggregates with different-sized and same-sized monomers. Furthermore, the Rayleigh-Debye-Gans (RDG) approach is significantly challenged for approximating the absorption and scattering cross sections of the aggregates with different-sized monomers, whereas it performs quite accurately for the phase matrix elements.

Recently, Liu et al. [Opt. Commun. 284, 3160, 2011] proposed a protocol for quantum private comparison of equality (QPCE) based on symmetric W state. However, Li et al. [Eur. Phys. J. D. 66, 110, 2012] pointed out that there is a flaw of information leak, and they proposed a new protocol based on EPR pairs. While examining these two protocols, we find that there exists a same flaw: the third party (TP) can know the comparison result. In this paper, through introducing and constructing a special class of asymmetric W state, a secure QPCE protocol based on this asymmetric W state is presented. Analysis shows the present protocol can not only effectively avoid the information leak found by Li et al, but also ensure TP would not get any information about the comparison result.

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