Numerical analysis of the eutectic melting and relocation of the b4c control rod materials by the MPFI-MPS method

Eutectic melting and subsequent relocation of the boron-carbide (B4C) control rod materials were simulated by a particle method. In the past, it was difficult to simulate the eutectic melting by a particle method because the melting starts at the interface between two different materials, which leads to the instability of the particle motion due to the small amount of fluid particles and lack of the thermodynamic consistency of the particle system. Thus, the Moving Particle Full Implicit (MPFI)-Moving Particle Semi-implicit (MPS) method was developed and introduced in the current study. Specifically, the MPFI method was introduced for the momentum transfer calculation, and the MPS method was introduced for the heat and mass transfer calculation. The MPFIMPS method realized the simulation of the eutectic melting and subsequent relocation behaviour

An Lk1∩LkpL^1_k\cap L^p_k approach for the non-cutoff Boltzmann equation in R3\mathbb{R}^3

In the paper, we develop an $L^1_k\cap L^p_k$ approach to construct global solutions to the Cauchy problem on the non-cutoff Boltzmann equation near equilibrium in $\mathbb{R}^3$. In particular, only smallness of $\|\mathcal{F}_x{f}_0\|_{L^1\cap L^p (\mathbb{R}^3_k;L^2(\mathbb{R}^3_v))}$ with $3/2<p\leq \infty$ is imposed on initial data $f_0(x,v)$, where $\mathcal{F}_x{f}_0(k,v)$ is the Fourier transform in space variable. This provides the first result on the global existence of such low-regularity solutions without relying on Sobolev embedding $H^2(\mathbb{R}^3_x)\subset L^\infty(\mathbb{R}^3_x)$ in case of the whole space. Different from the use of sufficiently smooth Sobolev spaces in those classical results by Gressman-Strain and AMUXY, there is a crucial difference between the torus case and the whole space case for low regularity solutions under consideration. In fact, for the former, it is enough to take the only $L^1_k$ norm corresponding to the Weiner space as studied in Duan-Liu-Sakamoto-Strain. In contrast, for the latter, the extra interplay with the $L^p_k$ norm plays a vital role in controlling the nonlinear collision term due to the degenerate dissipation of the macroscopic component. Indeed, the propagation of $L^p_k$ norm helps gain an almost optimal decay rate $(1+t)^{-\frac{3}{2} (1-\frac{1}{p})_+}$ of the $L^1_k$ norm via the time-weighted energy estimates in the spirit of the idea of Kawashima-Nishibata-Nishikawa and in turn, this is necessarily used for establishing the global existence.Comment: 38 page

Mass-dependent evolution of the relation between supermassive black hole mass and host spheroid mass since z ~ 1

We investigate the evolution of supermassive black hole mass (M_BH) and the host spheroid mass (M_sph) in order to track the history of the M_BH-M_sph relationship. The typical mass increase of M_BH is calculated by a continuity equation and accretion history, which is estimated from the active galactic nucleus (AGN) luminosity function. The increase in M_sph is also calculated by using a continuity equation and a star formation model, which uses observational data for the formation rate and stellar mass function. We find that the black hole to spheroid mass ratio is expected to be substantially unchanged since z~1.2 for high mass objects (M_BH>10^8.5M_SUN and M_sph>10^11.3M_SUN). In the same redshift range, the spheroid mass is found to increase more rapidly than the black hole mass if M_sph>10^11M_SUN. The proposed mass-dependent model is consistent with the current available observational data in the M_BH-M_sph diagram.Comment: 15 pages, 8 figures, accepted to MNRA

Predicting reliable H2_2 column density maps from molecular line data using machine learning

The total mass estimate of molecular clouds suffers from the uncertainty in the H$_2$-CO conversion factor, the so-called $X_{\rm CO}$ factor, which is used to convert the $^{12}$CO (1--0) integrated intensity to the H$_2$ column density. We demonstrate the machine learning's ability to predict the H$_2$ column density from the $^{12}$CO, $^{13}$CO, and C$^{18}$O (1--0) data set of four star-forming molecular clouds; Orion A, Orion B, Aquila, and M17. When the training is performed on a subset of each cloud, the overall distribution of the predicted column density is consistent with that of the Herschel column density. The total column density predicted and observed is consistent within 10\%, suggesting that the machine learning prediction provides a reasonable total mass estimate of each cloud. However, the distribution of the column density for values $> \sim 2 \times 10^{22}$ cm$^{-2}$, which corresponds to the dense gas, could not be predicted well. This indicates that molecular line observations tracing the dense gas are required for the training. We also found a significant difference between the predicted and observed column density when we created the model after training the data on different clouds. This highlights the presence of different $X_{\rm CO}$ factors between the clouds, and further training in various clouds is required to correct for these variations. We also demonstrated that this method could predict the column density toward the area not observed by Herschel if the molecular line and column density maps are available for the small portion, and the molecular line data are available for the larger areas.Comment: Accepted for publication in MNRA

Distance determination of molecular clouds in the 1st quadrant of the Galactic plane using deep learning : I. Method and Results

Machine learning has been successfully applied in varied field but whether it is a viable tool for determining the distance to molecular clouds in the Galaxy is an open question. In the Galaxy, the kinematic distance is commonly employed as the distance to a molecular cloud. However, there is a problem in that for the inner Galaxy, two different solutions, the ``Near'' solution, and the ``Far'' solution, can be derived simultaneously. We attempted to construct a two-class (``Near'' or ``Far'') inference model using a Convolutional Neural Network (CNN), a form of deep learning that can capture spatial features generally. In this study, we used the CO dataset toward the 1st quadrant of the Galactic plane obtained with the Nobeyama 45-m radio telescope (l = 62-10 degree, |b| < 1 degree). In the model, we applied the three-dimensional distribution (position-position-velocity) of the 12CO (J=1-0) emissions as the main input. The dataset with ``Near'' or ``Far'' annotation was made from the HII region catalog of the infrared astronomy satellite WISE to train the model. As a result, we could construct a CNN model with a 76% accuracy rate on the training dataset. By using the model, we determined the distance to molecular clouds identified by the CLUMPFIND algorithm. We found that the mass of the molecular clouds with a distance of < 8.15 kpc identified in the 12CO data follows a power-law distribution with an index of about -2.3 in the mass range of M >10^3 Msun. Also, the detailed molecular gas distribution of the Galaxy as seen from the Galactic North pole was determined.Comment: 29 pages, 12 figure

Rotator Cuff Lesions in Patients with Stiff Shoulders A Prospective Analysis of 379 Shoulders

Background: Idiopathic adhesive capsulitis is defined as a frozen shoulder with severe and global range-of-motion los