Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

The intensity distribution in Fresnel diffraction through a slit includes numerous small fluctuations referred to as ripples. These ripples make the modelling of the intensity distribution complicated. In this study, we examine the characteristics of the Fresnel diffraction intensity distribution to deduce the rule for the peak position and then propose two types of quantum-mathematical models to obtain the distance between the edge and the peak point. The analysis and simulation indicate that the error in the models is below 0.50 μm. The models can also be used to detect the edges of a diffraction object, and we conduct several experiments to measure the slit width. The experimental results reveal that the repetition accuracy of the method can reach 0.23 μm.

A late Holocene winter monsoon record inferred from the palaeo-aeolian sand dune in the southeastern Mu Us Desert, northern China

The variation of the Asian winter monsoonal strength has seriously affected the climate and environmental conditions in the Asian monsoonal region, and even in marginal islands and the ocean in the East Asian region. However, relevant under-standing remains unclear due to the lack of suitable geological materials and effective proxies in the key study areas. Here, we present a grain-size record derived from the palaeo-aeolian sand dune in the southeastern Mu Us Desert, together with other proxies and OSL dating, which reflect a relatively detailed history of the winter monsoon and abrupt environmental events during the past 4.2 ka. Our grain-size standard deviation model indicated that 〉224 μm content can be considered as an indicator of the intensity of Asian winter monsoon, and it shows declined around 4.2–2.1 ka, enhanced but unstable in 2.1–0.9 ka, and obviously stronger since then. In addition, several typical climate events were also documented, forced by the periodic variation of winter monsoonal intensity. These include the cold intervals of 4.2, 2.8, 1.4 ka, and the Little Ice Age （LIA）, and relatively warm sub-phases around 3.0, 2.1, 1.8 ka, and the Medieval Warm Period （MWP）, which were roughly accordant with the records of the aeolian materials, peat, stalagmites, ice cores, and sea sediments in various latitudes of the Northern Hemisphere. Combined with the previous progresses of the Asian summer monsoon, we prelimi-narily confirmed a millennial-scale anti-correlation of Asian winter and summer monsoons in the Late Holocene epoch. This study suggests that the evolution of the palaeo-aeolian sand dune has the potential for comprehending the history of Asian monsoon across the desert regions of the modern Asian monsoonal margin in northern China.