Bayesian Reconstruction of Missing Observations

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framework of Bayesian reconstruction and its application to the traffic data reconstruction problem in the field of traffic engineering. In the latter part of this paper, we describe the evaluation of the statistical performance of our Bayesian traffic reconstruction model using a statistical mechanical approach and clarify its statistical behavior

Static compression of porous dust aggregates

Context: In protoplanetary disks, dust grains coagulate with each other and grow to form aggregates. As these aggregates grow by coagulation, their filling factor \phi decreases down to \phi << 1. However, comets, the remnants of these early planetesimals, have \phi ~ 0.1. Thus, static compression of porous dust aggregates is important in planetesimal formation. However, the static compression strength has been investigated only for relatively high density aggregates (\phi > 0.1). Aims: We investigate and find the compression strength of highly porous aggregates (\phi << 1). Methods: We perform three dimensional N-body simulations of aggregate compression with a particle-particle interaction model. We introduce a new method of static compression: the periodic boundary condition is adopted and the boundaries move with low speed to get closer. The dust aggregate is compressed uniformly and isotropically by themselves over the periodic boundaries. Results: We empirically derive a formula of the compression strength of highly porous aggregates (\phi << 1). We check the validity of the compression strength formula for wide ranges of numerical parameters, such as the size of initial aggregates, the boundary speed, the normal damping force, and material. We also compare our results to the previous studies of static compression in the relatively high density region (\phi > 0.1) and confirm that our results consistently connect to those in the high density region. The compression strength formula is also derived analytically.Comment: 12 pages, 14 figures, accepted for publication in A&

Opacity of fluffy dust aggregates

Context. Dust grains coagulate to form dust aggregates in protoplanetary disks. Their porosity can be extremely high in the disks. Although disk emission may come from fluffy dust aggregates, the emission has been modeled with compact grains. Aims. We aim to reveal the mass opacity of fluffy aggregates from infrared to millimeter wavelengths with the filling factor ranging from 1 down to $10^{-4}$. Methods. We use Mie calculations with an effective medium theory. The monomers are assumed to be 0.1 ${\rm \mu m}$ sized grains, which is much shorter than the wavelengths that we focus on. Results. We find that the absorption mass opacity of fluffy aggregates are characterized by the product $a\times f$, where $a$ is the dust radius and $f$ is the filling factor, except for the interference structure. The scattering mass opacity is also characterized by $af$ at short wavelengths while it is higher in more fluffy aggregates at long wavelengths. We also derive the analytic formula of the mass opacity and find that it reproduces the Mie calculations. We also calculate the expected difference of the emission between compact and fluffy aggregates in protoplanetary disks with a simple dust growth and drift model. We find that compact grains and fluffy aggregates can be distinguished by the radial distribution of the opacity index $\beta$. The previous observation of the radial distribution of $\beta$ is consistent with the fluffy case, but more observations are required to distinguish between fluffy or compact. In addition, we find that the scattered light would be another way to distinguish between compact grains and fluffy aggregates.Comment: 16 pages, 17 figures, published in A&A, 568, A4

Thermal conductivity of porous aggregates

$\mathit{Context.}$ The thermal conductivity of highly porous dust aggregates is a key parameter for many subjects in planetary science; however, it is not yet fully understood. $\mathit{Aims.}$ In this study, we investigate the thermal conductivity of fluffy dust aggregates with filling factors of less than $10^{-1}$. $\mathit{Methods.}$ We determine the temperature structure and heat flux of the porous dust aggregates calculated by $N$-body simulations of static compression in the periodic boundary condition. $\mathit{Results.}$ We derive an empirical formula for the thermal conductivity through the solid network $k_{\rm sol}$ as a function of the filling factor of dust aggregates $\phi$. The results reveal that $k_{\rm sol}$ is approximately proportional to ${\phi}^{2}$, and the thermal conductivity through the solid network is significantly lower than previously assumed. In light of these findings, we must reconsider the thermal histories of small planetary bodies.Comment: 4 pages, 4 figures. Accepted for publication in Astronomy & Astrophysic

Effect of dust size and structure on scattered light images of protoplanetary discs

We study scattered light properties of protoplanetary discs at near-infrared wavelengths for various dust size and structure by performing radiative transfer simulations. We show that different dust structures might be probed by measuring disk polarisation fraction as long as the dust radius is larger than the wavelength. When the radius is larger than the wavelength, disc scattered light will be highly polarised for highly porous dust aggregates, whereas more compact dust structure tends to show low polarisation fraction. Next, roles of monomer radius and fractal dimension for scattered light colours are studied. We find that, outside the Rayleigh regime, as fractal dimension or monomer radius increases, colours of the effective albedo at near-infrared wavelengths vary from blue to red. Our results imply that discs showing grey or slightly blue colours and high polarisation fraction in near-infrared wavelengths might be explained by the presence of large porous aggregates containing sub-microns sized monomers.Comment: Accepted for publication in MNRAS, 18 pages, 19 figure