The tensor renormalization group study of the general spin-S Blume-Capel model

We focus on the special situation of $D=2J$ of the general spin-S Blume-Capel model on the square lattice. Under the infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are discussed by the newly developed tensor renormalization group method. For the case of the integer spin-S, the system will undergo $S$ first-order phase transitions with the successive symmetry breaking with the magnetization $M=S,S-1,...0$. For the half-integer spin-S, there are similar $S-1/2$ first order phase transition with $M=S,S-1,...1/2$ stepwise structure, in addition, there is a continuous phase transition due to the spin-flip $Z_2$ symmetry breaking. In the low temperature regions, all first-order phase transitions are accompanied by the successive disappearance of the optional spin-component pairs($s,-s$), furthermore, the critical temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of the magnetic field, the visualization parameter characterizing the intrinsic degeneracy of the different phases clearly demonstrates the phase transition process.Comment: 6 pages, 7 figure

Fast micro-differential evolution for topological active net optimization

This paper studies the optimization problem of topological active net (TAN), which is often seen in image segmentation and shape modeling. A TAN is a topological structure containing many nodes, whose positions must be optimized while a predefined topology needs to be maintained. TAN optimization is often time-consuming and even constructing a single solution is hard to do. Such a problem is usually approached by a ``best improvement local search'' (BILS) algorithm based on deterministic search (DS), which is inefficient because it spends too much efforts in nonpromising probing. In this paper, we propose the use of micro-differential evolution (DE) to replace DS in BILS for improved directional guidance. The resultant algorithm is termed deBILS. Its micro-population efficiently utilizes historical information for potentially promising search directions and hence improves efficiency in probing. Results show that deBILS can probe promising neighborhoods for each node of a TAN. Experimental tests verify that deBILS offers substantially higher search speed and solution quality not only than ordinary BILS, but also the genetic algorithm and scatter search algorithm

First Abundance Measurement of Organic Molecules in the Atmosphere of HH 212 Protostellar Disk

HH 212 is one of the well-studied protostellar systems, showing the first vertically resolved disk with a warm atmosphere around the central protostar. Here we report a detection of 9 organic molecules (including newly detected ketene, formic acid, deuterated acetonitrile, methyl formate, and ethanol) in the disk atmosphere, confirming that the disk atmosphere is, for HH 212, the chemically rich component, identified before at a lower resolution as a "hot-corino". More importantly, we report the first systematic survey and abundance measurement of organic molecules in the disk atmosphere within $\sim$ 40 au of the central protostar. The relative abundances of these molecules are similar to those in the hot corinos around other protostars and in Comet Lovejoy. These molecules can be either (i) originally formed on icy grains and then desorbed into gas phase or (ii) quickly formed in the gas phase using simpler species ejected from the dust mantles. The abundances and spatial distributions of the molecules provide strong constraints on models of their formation and transport in star formation. These molecules are expected to form even more complex organic molecules needed for life and deeper observations are needed to find them.Comment: 12 pages, 4 figure