This article is an attempt to understand harmonic and holomorphic maps between two bounded symmetric domains in special situations. We study foliations associated to a lattice-equivariant harmonic map of small rank fr...This article is an attempt to understand harmonic and holomorphic maps between two bounded symmetric domains in special situations. We study foliations associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex two ball quotients.Some open questions are raised as well.展开更多
Mixing and coherence are fundamental issues at the heart of understanding fluid dynamics and other non-autonomous dynamical systems. Recently the notion of coherence has come to a more rigorous footing, in particular,...Mixing and coherence are fundamental issues at the heart of understanding fluid dynamics and other non-autonomous dynamical systems. Recently the notion of coherence has come to a more rigorous footing, in particular, within the studies of finite-time nonautonomous dynamical systems. Here we recall “shape coherent sets” which is proven to correspond to slowly evolving curvature, for which tangency of finite time stable foliations (related to a “forward time” perspective) and finite time unstable foliations (related to a “backwards time” perspective) serve a central role. We compare and contrast this perspective to both the variational method of geodesics [17], as well as the coherent pairs perspective [12] from transfer operators.展开更多
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
Deciphering the relationship between polyphase tectonic foliations and their associated mineral assemblages is significant in understanding the process from diagenesis to low-/medium-/high-grade metamorphism.It can pr...Deciphering the relationship between polyphase tectonic foliations and their associated mineral assemblages is significant in understanding the process from diagenesis to low-/medium-/high-grade metamorphism.It can provide information related to strain,metamorphic conditions and overprinting relationships and so help reveal the tectonic evolution of orogenesis.In this study,we predominately focus on the formation of foliations and their related minerals,as developed in two separate basins.First of all,two stages of axial plane cleavages(S1 and S2)were recognized in the Hongyanjing inter-arc basin,the formation of the S1 axial plane cleavage is associated with mica rotation and elongation in mudstones in the local area.The pencil structure of S2 formed during the refolding phase,the minerals in the sedimentary rocks not changing their shape and orientation.Secondly,in the Liao-Ji backarc basin,foliations include diagenetic foliation(bedding parallel foliation),tectonic S1 foliation(secondary foliation or axial plane cleavage of S0 folding)and crenulation cleavage(S2).The formation mechanism of foliation changes from mineral rotation or elongation and mineral solution transfer in S1 to crystal-plastic deformation,dynamic recrystallization and micro-folding in S2.Many index metamorphic minerals formed from low-grade to medium-grade consist of biotites,garnets,staurolite and kyanite,constituting a typical Barrovian metamorphic belt.Accordingly,a new classification of foliation is presented in this study.The foliations can be divided into continuous and disjunctive foliations,based on the existence of microlithons,detectable with the aid of a microscope.Disjunctive foliation can be further sub-divided into spaced foliation and crenulation cleavage,according to whether(or not)crenulation(micro-folding)is present.The size of the mineral grains is also significant for classification of the foliations.展开更多
We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
The purpose of this paper is to evaluate control of orientation of foliations and joints on the direction of valley axes in the Stribrne Hory area in the Bohemian-Moravian Highlands in central part of the Czech Republ...The purpose of this paper is to evaluate control of orientation of foliations and joints on the direction of valley axes in the Stribrne Hory area in the Bohemian-Moravian Highlands in central part of the Czech Republic. This area is predominantly built by metamorphic rocks. It is situated near the Pribyslav deep-seated fault. The data concerning of foliations, joints and valley axes were statistically analyzed and then visually compared according to their distribution using direction roses. Directions of valley axes have generally orientation of NNE-SSW, SE, E-W, NW and WNW and coincide with the system of foliations and ordinarily steep joints.展开更多
U-Pb zircon dating on two foliated garnet-bearing granite samples in the western Dabie ultra-high-pressure (UHP) metamorphic unit yields concordant ages of (234±4) Ma and (227±5) Ma, respectively. These ages...U-Pb zircon dating on two foliated garnet-bearing granite samples in the western Dabie ultra-high-pressure (UHP) metamorphic unit yields concordant ages of (234±4) Ma and (227±5) Ma, respectively. These ages, following the UHP peak metamorphism, represent the magma emplacement ages for the foliated garnet-bearing granites. This, for the first time, shows that there are the Triassic granites in the Dabie Mountains. The foliated garnet-bearing granites resemble A-type granite in geochemical characteristics, indicating that they were formed in exten-sional geodynamic setting. The magma formation reflects a reheating event in the Dabie orogenic belt and it enhances the transfer of tectonic regime from collision into extension and promotes the rapid exhumation into lower crust for the UHP metamorphic rocks.展开更多
Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to n...Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.展开更多
Five lengthy periods involving multiple phases of cordierite and andalusite growth were revealed by detailed studies of foliation inflection/intersection axes （FIA） preserved in porphyroblasts in schists from the Ar...Five lengthy periods involving multiple phases of cordierite and andalusite growth were revealed by detailed studies of foliation inflection/intersection axes （FIA） preserved in porphyroblasts in schists from the Arkansas River region in Colorado, USA. The regionally consistent character of the succession of five different FIA trends enabled the relative timing of each FIA with respect to the next to be determined. The FIA succession from first to last is： FIA 1 trending W-E, FIA 2 trending SSW- NNE, FIA 3 trending NNW-SSE, FIA 4 trending NW-SE and FIA 5 trending SW-NE. For four of the FIA sets, samples were found containing monazite grains preserved as inclusions. These were dated on an electron microprobe. The ages obtained concur exactly with the FIA succession, with FIA 1 at 1506±15 Ma, FIA 2 at 1467±23 Ma, FIA 3 at 1425±18 Ma, FIA 4 not dated and FIA 5 at 1366±20 Ma. These ages are directly reflected in a succession of plutons in the surrounding region dated by other isotopic approaches, suggesting that deformation, metamorphism and pluton emplacement occurred together episodically, but effectively continuously, for some 140 Ma.展开更多
基金supported by the National Science Foundation of USA(Grant No.DMS1501282
文摘This article is an attempt to understand harmonic and holomorphic maps between two bounded symmetric domains in special situations. We study foliations associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex two ball quotients.Some open questions are raised as well.
文摘Mixing and coherence are fundamental issues at the heart of understanding fluid dynamics and other non-autonomous dynamical systems. Recently the notion of coherence has come to a more rigorous footing, in particular, within the studies of finite-time nonautonomous dynamical systems. Here we recall “shape coherent sets” which is proven to correspond to slowly evolving curvature, for which tangency of finite time stable foliations (related to a “forward time” perspective) and finite time unstable foliations (related to a “backwards time” perspective) serve a central role. We compare and contrast this perspective to both the variational method of geodesics [17], as well as the coherent pairs perspective [12] from transfer operators.
基金supported by National Natural Science Foundation of USA(Grant No.DMS0705284)National Natural Science Foundation of China(Grant No.10801027)
文摘In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.92062214,41430210 and 41888101)the NSFC Regional Science Foundation(Grant No.41962012)+3 种基金the Scientific Program of Jiangxi Educational Committee(Grant No.GJJ190586)the Chinese Geological Survey projects(Grant No.DD20190003)the Strategic Priority Research Program(B)of the Chinese Academy of Sciences(CAS)(Grant No.XDB18020203)the Basic Scientific Research Foundations of the Institute of Geology,Chinese Academy of Geological Sciences(Grant No.J2030,J2009)。
文摘Deciphering the relationship between polyphase tectonic foliations and their associated mineral assemblages is significant in understanding the process from diagenesis to low-/medium-/high-grade metamorphism.It can provide information related to strain,metamorphic conditions and overprinting relationships and so help reveal the tectonic evolution of orogenesis.In this study,we predominately focus on the formation of foliations and their related minerals,as developed in two separate basins.First of all,two stages of axial plane cleavages(S1 and S2)were recognized in the Hongyanjing inter-arc basin,the formation of the S1 axial plane cleavage is associated with mica rotation and elongation in mudstones in the local area.The pencil structure of S2 formed during the refolding phase,the minerals in the sedimentary rocks not changing their shape and orientation.Secondly,in the Liao-Ji backarc basin,foliations include diagenetic foliation(bedding parallel foliation),tectonic S1 foliation(secondary foliation or axial plane cleavage of S0 folding)and crenulation cleavage(S2).The formation mechanism of foliation changes from mineral rotation or elongation and mineral solution transfer in S1 to crystal-plastic deformation,dynamic recrystallization and micro-folding in S2.Many index metamorphic minerals formed from low-grade to medium-grade consist of biotites,garnets,staurolite and kyanite,constituting a typical Barrovian metamorphic belt.Accordingly,a new classification of foliation is presented in this study.The foliations can be divided into continuous and disjunctive foliations,based on the existence of microlithons,detectable with the aid of a microscope.Disjunctive foliation can be further sub-divided into spaced foliation and crenulation cleavage,according to whether(or not)crenulation(micro-folding)is present.The size of the mineral grains is also significant for classification of the foliations.
文摘We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
文摘The purpose of this paper is to evaluate control of orientation of foliations and joints on the direction of valley axes in the Stribrne Hory area in the Bohemian-Moravian Highlands in central part of the Czech Republic. This area is predominantly built by metamorphic rocks. It is situated near the Pribyslav deep-seated fault. The data concerning of foliations, joints and valley axes were statistically analyzed and then visually compared according to their distribution using direction roses. Directions of valley axes have generally orientation of NNE-SSW, SE, E-W, NW and WNW and coincide with the system of foliations and ordinarily steep joints.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 49794043 and 40073005) and the Ministry of Science and Technology of China (Grant No. G1999075506).
文摘U-Pb zircon dating on two foliated garnet-bearing granite samples in the western Dabie ultra-high-pressure (UHP) metamorphic unit yields concordant ages of (234±4) Ma and (227±5) Ma, respectively. These ages, following the UHP peak metamorphism, represent the magma emplacement ages for the foliated garnet-bearing granites. This, for the first time, shows that there are the Triassic granites in the Dabie Mountains. The foliated garnet-bearing granites resemble A-type granite in geochemical characteristics, indicating that they were formed in exten-sional geodynamic setting. The magma formation reflects a reheating event in the Dabie orogenic belt and it enhances the transfer of tectonic regime from collision into extension and promotes the rapid exhumation into lower crust for the UHP metamorphic rocks.
文摘Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.
文摘Five lengthy periods involving multiple phases of cordierite and andalusite growth were revealed by detailed studies of foliation inflection/intersection axes （FIA） preserved in porphyroblasts in schists from the Arkansas River region in Colorado, USA. The regionally consistent character of the succession of five different FIA trends enabled the relative timing of each FIA with respect to the next to be determined. The FIA succession from first to last is： FIA 1 trending W-E, FIA 2 trending SSW- NNE, FIA 3 trending NNW-SSE, FIA 4 trending NW-SE and FIA 5 trending SW-NE. For four of the FIA sets, samples were found containing monazite grains preserved as inclusions. These were dated on an electron microprobe. The ages obtained concur exactly with the FIA succession, with FIA 1 at 1506±15 Ma, FIA 2 at 1467±23 Ma, FIA 3 at 1425±18 Ma, FIA 4 not dated and FIA 5 at 1366±20 Ma. These ages are directly reflected in a succession of plutons in the surrounding region dated by other isotopic approaches, suggesting that deformation, metamorphism and pluton emplacement occurred together episodically, but effectively continuously, for some 140 Ma.
