Nonlinear Generalisation of Quantum Mechanics

It is known since Madelung that the Schrödinger equation can be thought of as governing the evolution of an incompressible fluid, but the current theory fails to mathematically express this incompressibility in terms of the wavefunction without facing problem. In this paper after showing that the current definition of quantum-mechanical momentum as a linear operator is neither the most general nor a necessary result of the de Broglie hypothesis, a new definition is proposed that can yield both a meaningful mathematical condition for the incompressibility of the Madelung fluid, and nonlinear generalisations of Schrödinger and Klein-Gordon equations. The derived equations satisfy all conditions that are expected from a proper generalisation: simplification to their linear counterparts by a well-defined dynamical condition; Galilean and Lorentz invariance (respectively); and signifying only rays in the Hilbert space.

The Southwest China Flood of July 2018 and Its Causes

Excessive rainfall was observed over Southwest China in July 2018, leading to floods in several major tributaries of the Yangtze River and landslide and debris flow in the neighboring provinces. The rainfall during 7–11 July was unusually heavy and broke the record that can be traced back to 1961. The occurrence of the excessive rain can be attributed to the anomalous convection over the western North Pacific and the presence of a mid-latitude Rossby wave train. On one hand, the convection over the western North Pacific was anomalously strong in July 2018, and it could have excited the negative phase of the Pacific–Japan pattern and led to a northwestward shift of the western Pacific subtropical high. Hence, the water vapor transport toward inland China including Southwest China was enhanced, providing a favorable moisture environment for precipitation. On the other hand, a mid-latitude Rossby wave train was observed to propagate from Northern Europe towards East Asia, which was conducive to anomalous ascending motion over Southwest China via warm advection and differential vorticity advection, creating a favorable dynamical condition for precipitation. As a result, the combination of the two effects mentioned above led to the occurrence of the flood over Southwest China in July 2018.

The 2017–2018 Winter Drought in North China and Its Causes

A meteorological drought was observed over North China in the 2017–2018 winter, which was accompanied by record-breaking consecutive non-precipitation days over many regions of central North China. Inspection on historical observations beginning in 1951 suggest that it was the fourth driest winter during the past 67 years. The possible cause of this drought was then analyzed. It has been suggested that the co-occurrence of the positive phase of the Eurasian (EU) teleconnection pattern and La Niña have played a crucial role. On one hand, both the positive phase of the EU pattern and La Niña could have enhanced the lower-tropospheric northerly winds over East Asia. The northward water vapor transport towards North China was thereby weakened, providing an unfavorable moisture environment for precipitation. On the other hand, the EU-like wave pattern in the mid-latitude was conducive to anomalous descending motion over mid-latitude East Asia, creating an unfavorable dynamical condition for precipitation. A combination of the above two effects lead to the occurrence of the North China drought in the 2017 winter.

HRV Analysis: A Clinical and Diagnostic Tool in Chronic Obstructive Pulmonary Disease

This study’s aim is to analyze heart rate dynamics in subjects with chronic obstructive pulmonary disease (COPD) by measures of heart rate variability (HRV). HRV is a simple and noninvasive measure of autonomic impulses. 38 adults were divided into two equal groups based on respiratory function: COPD and normal. HRV was monitored in the supine position for 30 minutes. After tests of normality, Kruskal-Wallis was used for the statistical analysis, with the level of significance set at P<0.05. Principal component analysis identified two components representing 99.5% of total variance. Furthermore, it is suggested that the chaos forward parameter (CFP) which applies all three “chaotic globals” is the most influential, although others are statistically more significant. The COPD subjects exhibited a decrease in the CFP. COPD can be termed a dynamical condition, decreasing the chaotic response. The perceived benefits of such analysis include quantitative assessment and suitable pharmacological intervention in the respiratory condition, especially of other related dynamical diseases such as cardiac failure.