Geochemical Characteristics of Pb Isotope of High-Pressure Metamorphic Rocks and Foliated Granites from HP Unit of Tongbai-Dabie Orogenic Belt

Whole-rock Pb isotopic compositions of the high-pressure (HP) metamorphic rocks, consisting of two-mica albite gneisses and eclogites, and foliated granites from the HP metamorphic unit of the Tongbai-Dabie orogenic belt are firstly reported in this paper. The results show that the HP metamorphic rocks in different parts of this orogenic belt have similar Pb isotopic compositions. The two- mica albite gneisses have 206 Pb/ 204 Pb=17.657-18.168, 207 Pb/ 204 Pb=15.318-15.573, 208 Pb/ 204 Pb=38.315-38.990, and the eclogites have 206 Pb/ 204 Pb=17.599-18.310, 207 Pb/ 204 Pb=15.465- 15.615 , 208 Pb/ 204 Pb=37.968-39.143. The HP metamorphic rocks are characterized by upper crustal Pb isotopic composition. Although the Pb isotopic composition of the HP metamorphic rocks partly overlaps that of the ultrahigh-pressure (UHP) metamorphic rocks, as a whole, the former is higher than the latter. The high radiogenic Pb isotopic composition for the HP metamorphic rocks confirms that the subducted Yangtze continental crust in the Tongbai-Dabie orogenic belt has the chemical structure of increasing radiogenic Pb isotopic composition from lower crust to upper crust. The foliated granites, intruded in the HP metamorphic rocks post the HP/UHP metamorphism, have 206 Pb/ 204 Pb=17.128-17.434, 207 Pb/ 204 Pb=15.313-15.422 and 208 Pb/ 204 Pb=37.631-38.122, which are obviously different from the Pb isotopic compositions of the HP metamorphic rocks but similar to those of the UHP metamorphic rocks and the foliated garnet-bearing granites in the UHP unit. This shows that the foliated granites from the HP and UHP units have common magma source. Combined with the foliated granites having the geochemical characteristics of A-type granites, it is suggested that the magma for the foliated granites in the UHP and HP unit would be derived from the partial melting of the retrometamorphosed UHP metamorphic rocks exhumed into middle to lower crust, and partial magmas were intruded into the HP unit.

Transverse Dimension of R^n Actions on Compact Foliated Manifolds

Consider a foliate Rn-action on a compact connected foliated manifold (M,F). Let mand r be the codimension of F and the (transverse)rank of (M,F)respectively. Suppose r<m.In this paper we prove that either there exists an orbit of the Rn-action of transverse dimension< (m + r)/2 or F can be arbitrarily approached by foliations with rank≥r+1. Moreover weshow that this kind of orbits exists in the following three cases: if F is Riemannian ;when all itsleaves are closed or if X(M)≠0(then r=0).On the other hand all foliate Rn-action on (S3,F) has a fixed leaf if dimF=1.Our result generalies a well known Lima's theorem about Rn-actions on surfaces.

Harmonic Maps and Bi-Harmonic Maps on CR-Manifolds and Foliated Riemannian Manifolds

This is a survey on our recent works on bi-harmonic maps on CR-manifolds and foliated Riemannian manifolds, and also a research paper on bi-harmonic maps principal G-bundles. We will show, (1) for a complete strictly pseudoconvex CR manifold , every pseudo bi-harmonic isometric immersion into a Riemannian manifold of non-positive curvature, with finite energy and finite bienergy, must be pseudo harmonic;(2) for a smooth foliated map of a complete, possibly non-compact, foliated Riemannian manifold into another foliated Riemannian manifold, of which transversal sectional curvature is non-positive, we will show that if it is transversally bi-harmonic map with the finite energy and finite bienergy, then it is transversally harmonic;(3) we will claim that the similar result holds for principal G-bundle over a Riemannian manifold of negative Ricci curvature.

U-Pb zircon age of the foliated garnet-bearing granites in western Dabie Mountains,Central China

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.

Anisotropic shearing mechanism of Kangding slate:Experimental investigation and numerical analysis

The shear mechanical behavior is regarded as an essential factor affecting the stability of the surrounding rocks in underground engineering.The shear strength and failure mechanisms of layered rock are significantly affected by the foliation angles.Direct shear tests were conducted on cubic slate samples with foliation angles of 0°,30°,45°,60°,and 90°.The effect of foliation angles on failure patterns,acoustic emission(AE)characteristics,and shear strength parameters was analyzed.Based on AE characteristics,the slate failure process could be divided into four stages:quiet period,step-like increasing period,dramatic increasing period,and remission period.A new empirical expression of cohesion for layered rock was proposed,which was compared with linear and sinusoidal cohesion expressions based on the results made by this paper and previous experiments.The comparative analysis demonstrated that the new expression has better prediction ability than other expressions.The proposed empirical equation was used for direct shear simulations with the combined finite-discrete element method(FDEM),and it was found to align well with the experimental results.Considering both computational efficiency and accuracy,it was recommended to use a shear rate of 0.01 m/s for FDEM to carry out direct shear simulations.To balance the relationship between the number of elements and the simulation results in the direct shear simulations,the recommended element size is 1 mm.

Meso-and Micro-structures of Foliated Eclogites in Dabie-Sulu UHP Belt and Implications for the Earliest Stages of Exhumation of UHP Metamorphic Rocks:An Example from Taohang,Southeastern Shandong,China

The sub-vertical meso-and micro-structures and fabrics developed in coesite-bearing foliated eclogites in the Taohang （桃行） area, southeastern Shandong （山东）, China. The diagnostic structures and fabrics, including penetrative foliation or mylonitic foliation containing mineral and stretching lineations, as well as sheath-like folds, appear to be the development of anastomosing UHP eciogite-facies shear belt arrays hosting massive eelogites. Textural relationships and mineral assem-blages indicate that the deformation of foliated eclogites developed closely after the formation of the massive eclogite, prior to the development of the granulite/amphibolite-facies symplectites and coronas, occurring over a very wide pressure range of （31-8）×10^2 MPa. It presents the structural records of the tectonometamorphic processes as being responsible for the earliest stages of exhumation of the UHP metamorphic rocks. Extensive regional field observations show that the meso-and micro-structures and fabrics recognized in the foliated eclogites at Taohang are remarkably similar or consistent in the whole Dabie （大别）-Sulu （苏鲁） UHP metamorphic belt. This article, thus, supports the idea that the earliest stages of exhumation of the UHP metamorphic rocks, from mantle depths to the Moho or the mantle-crust boundary layering, may be attributed mainly to a sub-vertical extrusion and ductile flow along the subduction channel, belonging to a syn-collision exhumation at about 235 to 220 Ma.

MINIMAL FOLIATIONS FOR THE HIGH-DIMENSIONAL FRENKEL-KONTOROVA MODEL

For the high-dimensional Frenkel-Kontorova(FK)model on lattices,we study the existence of minimal foliations by depinning force.We introduce the tilted gradient flow and define the depinning force as the critical value of the external force under which the average velocity of the system is zero.Then,the depinning force can be used as the criterion for the existence of minimal foliations for the FK model on a Z^(d)lattice for d>1.

The Gondwana Orogeny in northern North Patagonian Massif:Evidences from the Caita Có granite, La Se?a and Pangaré mylonites,Argentina

Structural analyses in the northern part of the North Patagonia Massif, in the foliated Caita Co granite and in La Sefia and Pangare mylonites, indicate that the pluton was intruded as a sheet-like body into an opening pull-apart structure during the Gondwana Orogeny. Geochronological studies in the massif indicate a first, lower to middle Permian stage of regional deformation, related to movements during indentation tectonics, with emplacement of foliated granites in the western and central areas of the North Patagonian Massif. Between the upper Permian and lower Triassic, evidence indicates emplacement of undeformed granitic bodies in the central part of the North Patagonian Massif. A second pulse of deformation between the middle and upper Triassic is related to the emplacement of the Caita CO granite, the development of mylonitic belts, and the opening of the Los Menucos Basin. During this pulse of deformation, compression direction was from the eastern quadrant.

Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

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.

Chemical U-Th-Pb Monazite Dating of Deformations versus Pluton Emplacement and the Proterozoic History of the Arkansas River Region,Colorado,USA

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.

Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method

We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.

Resolving the Routine Presence of Kyanite, Andalusite and Sillimanite across a Region using Foliation Intersection/Inflection Axes Preserved in Porphyroblasts, Petrographic Observations and Thermobarometry

Constraints from P-T pseudosections （MnNCKFMASH system）, foliation intersection/ inflection axes preserved in porphyroblasts （FIAs）, mineral assemblages and textural relationships for rocks containing all three Al2 SiO5 polymorphs indicate a kyanite→ andalusite→ sillimanite sequential formation at different times rather than stable coexistence at the Al2SiO5 triple point. All three Al2SiO5 polymorphs grew in the Chl, Bt, Ms, Grt, St, Pl and Crd bearing Ordovician Clayhole Schist in Balcooma, northeastern Australia separately along a looped P-T-t-D path that swaps from clockwise to anticlockwise in the tectono-metamorphic history of the region. Kyanite grew during crustal thickening in an Early Silurian Orogenic event followed by decompression/heating, andalusite and fibrolitic sillimanite growth during Early Devonian exhumation.

FIAs(Foliation Intersection/Inflection Axes) Preserved in Porphyroblasts,the DNA of Deformation:A Solution to the Puzzle of Deformation and Metamorphism in the Colorado,Rocky Mountains,USA

FIAs have been used extensively for more than a decade to unravel deformation and metamorphic puzzles. Orogenic processes developing early during the history or orogenesis challenge scientists because compositional layering in rocks always reactivates where multiple deformations have occurred, leaving little evidence of the history of foliation development preserved in the matrix. The foothills of the Rocky Mountains in Colorado, USA contain a succession of four FIA sets （trends） that would not have been distinguishable if porphyroblasts had not grown during the multiple deformation events that affected these rocks or if they had rotated as these events took place. They reveal that both the partitioning of deformation and the location of isograds changed significantly as the deformation proceeded.

Role of stress,slenderness and foliation on large anisotropic deformations at deep underground excavations

High stress concentrations around underground excavations can result in significant damage to deep hard-rock mines.These conditions can be the result of stopping activities,blasting,seismicity,or other mining activities.Large anisotropic deformation and excavation closure,especially under high-stress conditions,are expected if the excavation is located in a foliated or thin-bedded rock mass.In this research,the behaviour of excavations under deep and high-stress conditions was investigated and categorised.The main purpose was to enhance the existing knowledge of managing large anisotropic deformations and to help prepare suitable measures for handling such contingencies.Numerical simulations using the distinct element method(DEM)and model calibration were performed to reproduce the anisotropic deformation of an ore drive based on the collected field data.Then,the roles of key factors(i.e.stress ratio,slenderness ratio,foliation orientation,and foliation considering excavation orientation)on the large deformation and damage depth of the excavations were investigated.This study found that increasing both the stress ratio and slenderness ratio induced linear increases in wall closure and damage depth,whereas increasing the foliation angle first increases the deformation and damage depth and then reduces them both before and after 45.The wall closure and damage thickness decreased with increasing orientation intercept.The deformation and damage levels were classified based on these factors.

SYN-AND POST-THICKENING EXTENSIONS IN THE YULONG—HABA MOUNTAIN RANGE IN SOUTHWEST CHINA

The Yulong and Haba snowcapped ranges in the southeast side of the Qinghai—Xizang (Tibet) Plateau are situated structurally in a corner between the Dianxi Block to the west, the Yangzi Landmass to the southeast and Songpan—Ganzi folded belts to the north. Deformations in this area are strongly effected by the Tethys—Himalaya movement and defined by the Jinshajiang\|Honghe fault in the west and the Xiaojinhe fault in the southeast. A Jinshajiang river cut through in the middle with about 200 meters drop height that gives an exposed cross section.The Yulong—Haba range is an N—S trending anticline (F 3/D 3) comprising a metamorphic core of unknown ages and a sedimentary cover from mid\| Devonian onwards. Contact between the metamorphic core and the cover sequence is structurally. Although there is no evidence being found for the unconformity interface, deformation in the core, dominated by mica\|quartz schists, phyllites and quartzite, and the cover rocks, dominated by marbles, are different. The core rocks underwent a metamorphism with well developed foliations (S 1/D 1) in a greenschist facies condition. Occasionally an intrafolial fold (F 1, folded S 0) present in the S 1 layering. The S1 foliation was re\|folded by recumbent folds (F 2/D 2). Orientations of the axes of F 2 recumbent folds, the crenulation and mineral lineations now are shallowly plunged to S or N with angles less than 20° since the intensity of the D 3 deformation, during which both the core and cover rocks are involved to form the regional upright F 3 fold. All of the L\|S fabrics formed during D 2 in the core rocks are cut off by a set of near E—W or SWW—NEE trending normal faults that showing a top to the SSE extensional movement occurred during the D 3 event as a result of syn\|thickening extension (D 3′). Deformations D 4 are characterized by (1) numbers of near S—N trending high\|angle normal faults, and (2) interlayer gliding in the cover rocks, and lower angle detachment zones in the contact. Movement indicators in the D 4 structures showing a NEE in the east side of the F 3 fold, and a SWW in the west side, normal sense of shear that demonstrated a post\|thickening extension in the area.

Formation of Foliations and their Related Minerals from Diagenetic to Medium-grade Metamorphic Rocks:A Case Study of the Hongyanjing and Liao-Ji Backarc Basins,China

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.

Survival Conditions of Folding in Different Depth During Orogenesis-Deformation in Texas Creek and Chester Dome, USA

A succession of 5 FIA trends（foliation intersection or inflection axes in porphyroblasts） preserved in high temperature-low pressure regime PreCambrian rocks in the Texas Creek, Arkansas River region reflected by the fold axial plane traces and schistosity data in this region. Similar fold axial plane trace data measured in Palaeozoic rocks in Chester Dome, Vermont, which is high temperature to medium pressure regime, only preserve the effects of the youngest FIAs of the all 5 FIA sets that obtained in this region. The other three FIA sets have no equivalent fold axial planes. This difference from shallow to deeper orogenic regimes reflects decreasing competency at greater pressure with collapse and unfolding of earlier formed folds. The greater overlying load of rocks has tended to flatten all but the very largest early-formed structures, preserving only those folds that were more recently developed.

Functional Separable Solutions of Nonlinear Heat Equations in Non-Newtonian Fluids

We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.

ANALYSIS OF FOLDS SOUTH OF MALAKAND AND ADJOINING AREAS, NORTH PAKISTAN

North of the study area in lower Swat, the rocks have been found to have undergone multiple deformations with at least four periods of folding during a single Paleogene metamorphism (DiPietro and Lawrence, 1991). The earliest folds are composite W—SW vergent, syn\|metamorphic F 1/F 2 folds associated with the formation of the regional foliation. Late\|metamorphic, N—S trending open upright F 3 folds are associated with local foliation development, and E—W trending open F 4 folds are associated with retrograde metamorphism. These interfere with each other to produce dome/basin structures.

Multiple Successions of Soliation Development in Shallow Versus Deep Orogenic Regimes and Their Relationship to Regional Folding

With the realization that rocks with a schistosity parallel to bedding(S0 parallel S1)have undergone lengthy histories of deformation that predate the obvious first deformation(e.g.Bell et al.,2003; Sayab,2006;Yeh,2007)came recognition that large scale regional folds can form early during this process and be preserved throughout orogenesis(e.g.,Ham & Bell,2004;Bell & Newman,2006).This history is lost within the matrix because of reactivational shear