Characteristics of the Bright Band Based on Quasi-Vertical Profiles of Polarimetric Observations from an S-Band Weather Radar Network

Bright band (BB) characteristics obtained via dual-polarization weather radars elucidate thermodynamic and microphysical processes within precipitation systems. This study identified BB using morphological features from quasi-vertical profiles (QVPs) of polarimetric observations, and their geometric, thermodynamic, and polarimetric characteristics were statistically examined using nine operational S-band weather radars in South Korea. For comparable analysis among weather radars in the network, the calibration biases in reflectivity (ZH) and differential reflectivity (ZDR) were corrected based on self-consistency. The cross-correlation coefficient (ρHV) bias in the weak echo regions was corrected using the signal-to-noise ratio (SNR). First, we analyzed the heights of BBPEAK derived from the ZH as a function of season and compared the heights of BBPEAK derived from the ZH, ZDR, and ρHV. The heights of BBPEAK were highest in the summer season when the surface temperature was high. However, they showed distinct differences depending on the location (e.g., latitude) within the radar network, even in the same season. The height where the size of melting particles was at a maximum (BBPEAK from the ZH) was above that where the oblateness of these particles maximized (BBPEAK from ZDR). The height at which the inhomogeneity of hydometeors was at maximum (BBPEAK from the ρHV) was also below that of BBPEAK from the ZH. Second, BB thickness and relative position of BBPEAK were investigated to characterize the geometric structure of the BBs. The BB thickness increased as the ZH at BBBOTTOM increased, which indicated that large snowflakes melt more slowly than small snowflakes. The geometrical structure of the BBs was asymmetric, since the melting particles spent more time forming the thin shell of meltwater around them, and they rapidly collapsed to form a raindrop at the final stage of melting. Third, the heights of BBTOP, BBPEAK, and BBBOTTOM were compared with the zero-isotherm heights. The dry-temperature zero-isotherm heights were between BBTOP and BBBOTTOM, while the wet-bulb temperature zero-isotherm heights were close to the height of BBPEAK. Finally, we examined the polarimetric observations to understand the involved microphysical processes. The correlation among ZH at BBTOP, BBPEAK, and BBBOTTOM was high (>0.94), and the ZDR at BBBOTTOM was high when the BB’s intensity was strong. This proved that the size and concentration of snowflakes above the BB influence the size and concentration of raindrops below the BB. There was no depression in the ρHV for a weak BB. Finally, the mean profile of the ZH and ZDR depended on the ZH at BBBOTTOM. In conclusion, the growth process of snowflakes above the BB controls polarimetric observations of BB.

The Relationship between Nil-Strength Temperature, Zero Strength Temperature and Solidus Temperature of Carbon Steels

The nil-strength temperature, zero strength temperature and solidus temperature are significant parameters with respect to the processes of melting, casting and welding steels. With the use of physical tests performed on the universal plastometer Gleeble 3800 and calculations in the IDS software, the nil-strength temperatures, zero strength temperatures and solidus temperatures of nine non-alloy carbon steels have been determined. Apart from that, solidus temperatures were also calculated by the use of four equations expressing a mathematical relation of this temperature to the chemical composition of the investigated steels. The nil-strength and zero strength temperatures and the solidus temperatures decreased with increasing carbon content in the investigated steels. Much higher content of sulfur in free-cutting steel resulted in a decrease of all the temperatures investigated. The zero strength temperatures determined by calculation in the IDS software during solidification were approximately 43–85 °C higher than the nil-strength temperatures determined experimentally during heating of the investigated steels. The linear dependence of experimentally measured nil-strength temperature on the calculated zero strength temperature for the investigated steels was determined. Based on regression analyses, there were determined mathematical relations which described with high accuracy a linear dependence of the nil-strength and zero strength temperatures on the solidus temperature of the investigated steels.

The Toeplitz noncommutative solenoid and its Kubo–Martin–Schwinger states

We use Katsura’s topological graphs to define Toeplitz extensions of Latrémolière and Packer’s noncommutative-solenoid $C^{\ast }$-algebras. We identify a natural dynamics on each Toeplitz noncommutative solenoid and study the associated Kubo–Martin–Schwinger (KMS) states. Our main result shows that the space of extreme points of the KMS simplex of the Toeplitz noncommutative torus at a strictly positive inverse temperature is homeomorphic to a solenoid; indeed, there is an action of the solenoid group on the Toeplitz noncommutative solenoid that induces a free and transitive action on the extreme boundary of the KMS simplex. With the exception of the degenerate case of trivial rotations, at inverse temperature zero there is a unique KMS state, and only this one factors through Latrémolière and Packer’s noncommutative solenoid.