For plane singly-connected domains with insulating boundary and four point-sized contacts, C<sub>0</sub> …C<sub>3</sub>, van der Pauw derived a famous equation relating the two trans-...For plane singly-connected domains with insulating boundary and four point-sized contacts, C<sub>0</sub> …C<sub>3</sub>, van der Pauw derived a famous equation relating the two trans-resistances R<sub>01,23</sub>, R<sub>12,30</sub> with the sheet resistance without any other parameters. If the domain has one hole van der Pauw’s equation becomes an inequality with upper and lower bounds, the envelopes. This was conjectured by Szymański et al. in 2013, and only recently it was proven by Miyoshi et al. with elaborate mathematical tools. The present article gives new proofs closer to physical intuition and partly with simpler mathematics. It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also given.展开更多
The marginal sea and back-arc basins in the Western Pacific Ocean have become the focus of tectonics due to their unique tectonic location.To understand the deep crustal structure in the back-arc region,we present a 5...The marginal sea and back-arc basins in the Western Pacific Ocean have become the focus of tectonics due to their unique tectonic location.To understand the deep crustal structure in the back-arc region,we present a 545-kmlong active-source ocean bottom seismometer(OBS)wide-angle reflection/refraction profile in the East China Sea.The P wave velocity model shows that the Moho depth rises significantly,from approximately 30 km in the East China Sea shelf to approximately 16 km in the axis of the Okinawa Trough.The lower crustal high-velocity zone(HVZ)in the southern Okinawa Trough,with V_(p) of 6.8-7.3 km/s,is a remarkable manifestation of the mantle material upwelling and accretion to the lower crust.This confirms that the lower crustal high-velocity mantle accretion is developed in the southern Okinawa Trough.During the process of back-arc extension,the crustal structure of the southern Okinawa Trough is completely invaded and penetrated by the upper mantle material in the axis region.In some areas of the southern central graben,the crust may has broken up and entered the initial stage of seafloor spreading.The discontinuous HVZs in the lower crust in the back-arc region also indicate the migration of spreading centers in the back-arc region since the Cenozoic.The asthenosphere material upwelling in the continent-ocean transition zone is constantly driving the lithosphere eastward for episodic extension,and is causing evident tectonic migration in the Western Pacific back-arc region.展开更多
文摘For plane singly-connected domains with insulating boundary and four point-sized contacts, C<sub>0</sub> …C<sub>3</sub>, van der Pauw derived a famous equation relating the two trans-resistances R<sub>01,23</sub>, R<sub>12,30</sub> with the sheet resistance without any other parameters. If the domain has one hole van der Pauw’s equation becomes an inequality with upper and lower bounds, the envelopes. This was conjectured by Szymański et al. in 2013, and only recently it was proven by Miyoshi et al. with elaborate mathematical tools. The present article gives new proofs closer to physical intuition and partly with simpler mathematics. It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also given.
基金supported by the National Key Basic Research Program of China(Grant No.2013CB429701)the National Natural Science Foundation of China(Grant Nos.41606083,91958210,41606050 and 41210005)+1 种基金AoShan Technological Innovation Projects of National Laboratory for Marine Science and Technology(Qingdao)(2015ASKJ03)National Marine Geological Special Project(DD20190236,DD20190365,DD20190377)。
文摘The marginal sea and back-arc basins in the Western Pacific Ocean have become the focus of tectonics due to their unique tectonic location.To understand the deep crustal structure in the back-arc region,we present a 545-kmlong active-source ocean bottom seismometer(OBS)wide-angle reflection/refraction profile in the East China Sea.The P wave velocity model shows that the Moho depth rises significantly,from approximately 30 km in the East China Sea shelf to approximately 16 km in the axis of the Okinawa Trough.The lower crustal high-velocity zone(HVZ)in the southern Okinawa Trough,with V_(p) of 6.8-7.3 km/s,is a remarkable manifestation of the mantle material upwelling and accretion to the lower crust.This confirms that the lower crustal high-velocity mantle accretion is developed in the southern Okinawa Trough.During the process of back-arc extension,the crustal structure of the southern Okinawa Trough is completely invaded and penetrated by the upper mantle material in the axis region.In some areas of the southern central graben,the crust may has broken up and entered the initial stage of seafloor spreading.The discontinuous HVZs in the lower crust in the back-arc region also indicate the migration of spreading centers in the back-arc region since the Cenozoic.The asthenosphere material upwelling in the continent-ocean transition zone is constantly driving the lithosphere eastward for episodic extension,and is causing evident tectonic migration in the Western Pacific back-arc region.
