TY - BOOK A1 - Liu, Xiaochun A1 - Schulze, Bert-Wolfgang T1 - Ellipticity on Manifolds with edges and boundary T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Liu, Xiaochun A1 - Schulze, Bert-Wolfgang T1 - Boundary value problems in edge representation T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Liu, Xiaochun A1 - Schulze, Bert-Wolfgang T1 - Ellipticity on manifolds with edges and boundary N2 - Ellipticity of a manifold with edges and boundary is connected to boundary and edge conditions that complete corresponding operators to Fredholm operators between weighted Sobolev spaces. We study a new parameter-dependent calculus of elliptic operators, where the interior symbols have specific properties on the boundary. We construct elliptic operators with a prescribed number of edge conditions and obtain isomorphisms in the scale of edge Sobolev spaces Y1 - 2005 SN - 0026-9255 ER - TY - JOUR A1 - Liu, Xiaochun A1 - Witt, Ingo T1 - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types N2 - Given asymptotics types P, Q, pseudodifferential operators A is an element of L-cl(mu) (R+) are constructed in such a way that if u(t) possesses conormal asymptotics of type P as t --> +0, then Au(t) possesses conormal asymptotics of type Q as t --> +0. This is achieved by choosing the operators A in Schulze's cone algebra on the half-line R+, controlling their complete Mellin symbols {sigma(M)(u-j) (A); j is an element of N}, and prescribing the mapping properties of the residual Green operators. The constructions lead to a coordinate invariant calculus, including trace and potential operators at t = 0, in which a parametrix construction for the elliptic elements is possible. Boutet de Monvel's calculus for pseudodifferential boundary problems occurs as a special case when P = Q is the type resulting from Taylor expansion at t = 0. Y1 - 2004 SN - 0378-620X ER - TY - JOUR A1 - Liu, Xiaochun A1 - Jahn, Bor-Ming A1 - Dong, Shuwen A1 - Li, Huimin A1 - Oberhänsli, Roland T1 - Neoproterozoic granitoid did not record ultrahigh-pressure metamorphism from the Southern Dabieshan of China N2 - It has been often debated whether all granitic gneisses associated with coesite-bearing eclogites in southern Dabieshan, China, have also been subjected to ultrahigh-pressure (UHP) metamorphism. We show here that a metagranitoid adjacent to the Bixiling eclogite-ultramafic complex has preserved primary granitic textures and an igneous mineral assemblage of biotite + plagioclase + microcline + quartz + allanite +/- amphibole. The absence of UPH recrystallization for the metagranitoid is particularly manifested by the conservation of euhedral-zoned plagioclase phenocrysts, the lack of corona garnets around igneous biotite, and the presence of an igneous mineral assemblage in zircons. The only metamorphic overprint was the epidote-amphibolite facies metamorphism characterized by the assemblage of biotite + phengiticmica + epidote + albite + K-feldspar + quartz +/- amphibole Metamorphic conditions are estimated at ca. 550degrees-680degreesC and 6-13 kbar for the metagranitoid and its amphibolitic enclave. Geochemically, the metagranitoid is similar to its country gneiss and shows an affinity to volcanic arc granitoid. Zircon U-Pb dating suggests that the Bixiling metagranitoid was emplaced during the Neoproterozoic (729+/-4 Ma), when most other granitic rocks and the protoliths of eclogite were also formed in Dabieshan. Taking into account the discovery of non-UHP granitic gneisses in other places, we argue that part of Neoproterozoic granitic rocks in the Dabieshan and Sulu terranes have escaped UHP metamorphism during the Triassic deep subduction of the continental crust as a consequence of a lack of penetrative deformation and fluid-rock interaction Y1 - 2003 SN - 0022-1376 ER - TY - BOOK A1 - Liu, Xiaochun A1 - Witt, Ingo T1 - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Xiaochun, Liu A1 - Schulze, Bert-Wolfgang T1 - Boundary value problems in edge representation N2 - Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols. T3 - Preprint - (2004) 14 KW - Boundary value problems KW - edge singularities KW - ellipticity in the edge calculus Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26746 ER - TY - JOUR A1 - Dines, Nicoleta A1 - Liu, Xiaochun A1 - Schulze, Bert-Wolfgang T1 - Edge quantisation of elliptic operators JF - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell N2 - The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy sigma = (sigma(psi), sigma(boolean AND)), where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the ellipticity of the principal edge symbol sigma(boolean AND) which includes the (in general not explicity known) number of additional conditions of trace and potential type on the edge. We focus here on these questions and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems. Y1 - 2009 UR - http://www.springerlink.com/content/103082 U6 - https://doi.org/10.1007/s00605-008-0058-y SN - 1437-739X ER - TY - JOUR A1 - Huang, Wentao A1 - Dupont-Nivet, Guillaume A1 - Lippert, Peter C. A1 - van Hinsbergen, Douwe J. J. A1 - Dekkers, Mark J. A1 - Guo, Zhaojie A1 - Waldrip, Ross A1 - Li, Xiaochun A1 - Zhang, Xiaoran A1 - Liu, Dongdong A1 - Kapp, Paul T1 - Can a primary remanence be retrieved from partially remagnetized Eocence volcanic rocks in the Nanmulin Basin (southern Tibet) to date the India-Asia collision? JF - Journal of geophysical research : Solid earth N2 - Paleomagnetic dating of the India-Asia collision hinges on determining the Paleogene latitude of the Lhasa terrane (southern Tibet). Reported latitudes range from 5 degrees N to 30 degrees N, however, leading to contrasting paleogeographic interpretations. Here we report new data from the Eocene Linzizong volcanic rocks in the Nanmulin Basin, which previously yielded data suggesting a low paleolatitude (similar to 10 degrees N). New zircon U-Pb dates indicate an age of similar to 52Ma. Negative fold tests, however, demonstrate that the isolated characteristic remanent magnetizations, with notably varying inclinations, are not primary. Rock magnetic analyses, end-member modeling of isothermal remanent magnetization acquisition curves, and petrographic observations are consistent with variable degrees of posttilting remagnetization due to low-temperature alteration of primary magmatic titanomagnetite and the formation of secondary pigmentary hematite that unblock simultaneously. Previously reported paleomagnetic data from the Nanmulin Basin implying low paleolatitude should thus not be used to estimate the time and latitude of the India-Asia collision. We show that the paleomagnetic inclinations vary linearly with the contribution of secondary hematite to saturation isothermal remanent magnetization. We tentatively propose a new method to recover a primary remanence with inclination of 38.1 degrees (35.7 degrees, 40.5 degrees) (95% significance) and a secondary remanence with inclination of 42.9 degrees (41.5 degrees,44.4 degrees) (95% significance). The paleolatitude defined by the modeled primary remanence21 degrees N (19.8 degrees N, 23.1 degrees N)is consistent with the regional compilation of published results from pristine volcanic rocks and sedimentary rocks of the upper Linzizong Group corrected for inclination shallowing. The start of the Tibetan Himalaya-Asia collision was situated at similar to 20 degrees N and took place by similar to 50Ma. KW - remagnetization KW - paleomagnetism applied to tectonics KW - rock and mineral magnetism KW - India-Asia collision Y1 - 2015 U6 - https://doi.org/10.1002/2014JB011599 SN - 2169-9313 SN - 2169-9356 VL - 120 IS - 1 SP - 42 EP - 66 PB - American Geophysical Union CY - Washington ER - TY - BOOK A1 - Liu, Xiaochun A1 - Witt, Ingo T1 - Asymptotic expansions for bounded solutions to semilinear fuchsian equations T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Xiaochun, Liu A1 - Witt, Ingo T1 - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types N2 - Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus T3 - Preprint - (2002) 06 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26255 ER - TY - INPR A1 - Xiaochun, Liu A1 - Witt, Ingo T1 - Asymptotic expansions for bounded solutions to semilinear Fuchsian equations N2 - It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions. T3 - Preprint - (2001) 01 KW - Calculus of conormal symbols KW - conormal asymptotic expansions KW - discrete saymptotic types KW - weighted Sobolev spaces with discrete saymptotics Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25912 ER -