EXPRESS: A Piecewise Model for In Situ Raman Measurement of the Chlorinity of Deep-Sea High-Temperature Hydrothermal Fluids

The chlorinity of deep-sea hydrothermal fluids, representing one of the crucial deep-sea hydrothermal indicators, indicates the degree of deep phase separation of hydrothermal fluids and water/rock reactions. However, accurately measuring the chlorinity of high-temperature hydrothermal fluids is still a significant challenge. In this paper, a piecewise chlorinity model to measure the chlorinity of high-temperature hydrothermal fluids was developed based on the OH stretching band of water, exhibiting an accuracy of 96.20%. The peak position, peak area ratio and F value were selected to establish the chlorinity piecewise calibration model within the temperature ranges of 0-50°C, 50-200°C and 200-300°C. Compared with that of the chlorinity calibration model built based on a single parameter, the accuracy of this piecewise model increased by approximately 4.83-12.33%. This chlorinity calibration model was applied to determine the concentrations of Cl for high-temperature hydrothermal fluids in the Okinawa Trough hydrothermal field.

Improved Zenith Tropospheric Delay Modeling Using the Piecewise Model of Atmospheric Refractivity

As one of the atmosphere propagation delays, the tropospheric delay is a significant error source that should be properly handled in high-precision global navigation satellite system (GNSS) applications. We propose an improved zenith tropospheric delay (ZTD) modeling method whereby the piecewise model of the atmospheric refractivity is introduced. Compared with using the exponential model to fit ZTD in vertical direction, the ZTD piecewise model has a better performance. Based on ERA5 2.5° × 2.5° reanalysis data produced by the European Centre for Medium-Range Weather Forecasting (ECMWF) from 2013 to 2017, we establish the regional gridded ZTD model (RGZTD) using a trigonometric function for China and the surrounding areas, which ranges from 70° E to 135° E in longitude and from 15° N to 55° N in latitude. To verify the performance of RGZTD model, the ERA5 ZTD data in 2017–2018, the radiosonde ZTD data from 86 radiosonde stations over China in 2017–2018, and the tropospheric delay products on 251 GNSS stations from Crustal Movement Observation Network of China (CMONOC) in 2016–2017 are used as external compliance check data. The results show that the overall accuracy of RGZTD model is better than that of exponential model, UNB3m model, and GPT3 model. Moreover, the accuracy can be improved by about 13.4%, 7.1%, and 6.2% when ERA5 reanalysis data, radiosonde data, and CMONOC data are used as reference values, respectively. High-accuracy ZTD data can be provided because the RGZTD model takes into account the vertical variation of ZTD through the new piecewise model.

Active Chatter Suppression in Low Immersion Intermittent Milling Process

Chatter in low immersion milling behaves differently from that in full immersion milling, mainly because of the non-negligible time-variant dynamics and the occurrence of period doubling bifurcation. The intermittent and time-variant characteristics make the active chatter suppression based on Lyaponov theorem a non-trivial problem. The main challenges lie in how to deal with the time-variant directional coefficient and how to construct a suitable Lyaponov function so as to alleviate the conservation, as well as the saturation of the controller. Generally, the Lyaponov stability of time-invariant dynamics is more tractable. Hence, in our paper, a first-order piecewise model is proposed to approximate the low immersion milling system as two time-invariant sub-ones that are cyclically switched. To alleviate the conservation, a novel piecewise Lyaponov function is constructed to determine the stability of each subsystem independently. The inequality conditions for determining the stability and stabilization are derived. The validity of the proposed stabilization algorithm to suppress both the hopf and period doubling bifurcation, as well as to reduce the conservation of the controller parameters have been verified.

An Empirical Model of Submicrocrystalline Structure Formation and Hardening upon Severe Plastic Deformation in Iron

The evolution of metals micro/nano-structure upon severe plastic deformation (SPD) is still far to be theoretically explained, while experimental datasets are persistently growing for several decades. Major problem associated with understanding of SPD is related to a fact that the latter is a synergetic product of several competing physical effects which alter the material micro/nano-structure. In attempt to find deformational boundaries, where predominantly one mechanism determines the micro/nano-structure, in this paper we propose a continuous piecewise model for the analysis of experiments on material hardness vs strain of SPD processed materials. The novelty of this approach lies in its ability to find, as free-fitting parameters, the strain breakpoints which separate different micro/nano-structure modes generated upon SPD process. The model is applied to analyse experimental data for polycrystalline samples of pure iron and two distinctive strain breakpoints are revealed with good accuracies. This finding is in a good agreement with our earlier results on TEM microscopy studies on pure iron polycrystals after SPD treatment.

Variation among states in rate of coronavirus spread

The corona virus, COVID-19, has been spreading rapidly across the USA since early March, but at a decreasing rate, where the rate r is defined as the exponential increase. I modeled the way the rate of increase y = ln(er − 1) has declined through time in each of the 51 states with the goal of determining how quickly the rate has declined, whether the decline has changed, and whether states differ. A piecewise linear regression was used, with a single break point. This model can identify whether there was a change in the rate of decline, when the change happened, and which states have shown the greatest improvement in reducing the spread of COVID-19. The piecewise model identified a significant breakpoint on 24 Mar for all states combined, and all states had nearly the same breakpoint. Prior to 24 Mar, the average change in y was −0.013 d−1, meaning a reduction in the rate of spread from 23.5 pct. d−1 to 19.5 pct. d−1; after 24 Mar, the average change in y was −0.070 d−1, a reduction from 19.5 pct. d−1 to 7.5 pct. d−1. Prior to 24 Mar there was no significant variation among states in the decline in y, but after 24 Mar there was substantial variation. Montana, Idaho, and Vermont showed the greatest improvement, while Nebraska, South Dakota, and Iowa the least. The improvement as measured by the reduction after 24 Mar did not correlate with case density in a state, nor state population. The next question is whether it correlates with differences among states in the health measures taken to combat the spread.

Observer-Based Piecewise Multi-Linear Controller Designs for Nonlinear Systems Using Feedback and Observer Linearizations

This paper proposes observer-based piecewise multi-linear controllers for nonlinear systems using feedback and observer linearizations. The piecewise model is a nonlinear approximation and fully parametric. Feedback linearizations are applied to stabilize the piecewise multi-linear control system. Furthermore, observer linearizations are more conservative in modeling errors compared with feedback linearizations. In this paper, we propose robust observer designs for piecewise multi-linear systems. Moreover, we design piecewise multi-linear controllers that combine the robust observer with various performance such as a regulator and tracking controller. These design methods realize a separation principle that allows an observer and a regulator to be designed separately. Examples are demonstrated through computer simulation to confirm the feasibility of our proposals.