On Possibility of Determining Neutrino Mass Hierarchy by the Charged-Current and Neutral-Current Events of Supernova Neutrinos in Scintillation Detectors

One of the unresolved mysteries in neutrino physics is the neutrino mass hierarchy. We present a new method to determine neutrino mass hierarchy by comparing the events of inverse beta decays (IBD), $\bar{\nu}_e + p\rightarrow n + e^+$, and neutral current (NC) interactions, $\nu(\overline{\nu}) + p\rightarrow\nu(\overline{\nu}) + p$, of supernova neutrinos from accretion and cooling phases in scintillation detectors. Supernova neutrino flavor conversions depend on the neutrino mass hierarchy. On account of Mikheyev-Smirnov-Wolfenstein effects, the full swap of $\bar{\nu}_e$ flux with the $\bar{\nu}_x$ ($x=\mu,~\tau$) one occurs in the inverted hierarchy, while such a swap does not occur in the normal hierarchy. In consequence, the ratio of high energy IBD events to NC events for the inverted hierarchy is higher than in the normal hierarchy. Since the luminosity of $\bar{\nu}_e$ is larger than that of $\nu_x$ in accretion phase while the luminosity of $\bar{\nu}_e$ becomes smaller than that of $\nu_x$ in cooling phase, we calculate this ratio for both accretion and cooling phases. By analyzing the change of this event ratio from accretion phase to cooling phase, one can determine the neutrino mass hierarchy.Comment: one column, 16 pages, 3 figure

Precise Phase Transition of Total Variation Minimization

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error of a denoising problem and the high-dimensional convex geometry for TV minimization.Comment: 6 page

Colloidal Photonic Crystals Containing Copper-Oxide and Silver Nanoparticles with Tunable Structural Colors

In this chapter, we investigated polystyrene (PS) colloidal photonic crystal (CPhC) color films containing copper-oxide (CuO) nanoparticles (NPs) and silver (Ag) NPs and exhibiting tunable structural colors. PS CPhC color films containing CuO-NPs and Ag-NPs were prepared through thermal-assisted self-assembly by using a gravitational sedimentation method. Doped CuO-NPs and Ag-NPs deposited on the bottom of the substrate and acted as black materials that absorb background and scattering light. Experimental results showed that brilliant structural colors were enhanced because of the absorption of incoherently scattered light, and color saturation was increased by the distribution of metal NPs on PS CPhC surfaces. The brilliant structural colors of CuO-NPs/PS and Ag-NPs/PS hybrid CPhC color films were based on the scattering absorption and Bragg diffraction theory. The reflection peaks of metal-NPs/PS hybrid CPhCs and pure PS CPhCs were measured by UV-Visible reflection spectrometry and theoretically calculated based on the Bragg diffraction law. Additionally, the structural colors of metal-NPs/PS hybrid CPhC color films were assessed through color measurements based on the Commission International d’Eclairage 1931 standard colorimetric system. Finally, this chapter exhibits a simple method to generate tunable structural color of functional materials for numerous applications, such as in textile fabrics, bionic colors, catalysis, and paint