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Effects of salinity on methane gas hydrate system

Science China Earth sciences 2007年第11期50卷 1733-1745页

作者： yang dinghui1 & xu wenyue2.1 department of mathematical sciences, tsinghua university,{2., China 2.School of Earth & Atmospheric sciences, Georgia Institute of Technology, Atlanta, GA 30332. USA 1. department of mathematical {2. Tsinghua University Beijing 100084 China 2. School of Earth & Atmospheric sciences Georgia Institute of Technology Atlanta GA 30332 USA

Using an approximately analytical formation, we extend the steady state model of the pure methane hydrate system to include the salinity based on the dynamic model of the methane hydrate system. The top and bottom boundaries of the methane hydrate stability zone (MHSZ) and the actual methane hy-drate zone (MHZ), and the top of free gas occurrence are determined by using numerical methods and the new steady state model developed in this paper. Numerical results show that the MHZ thickness becomes thinner with increasing the salinity, and the stability is lowered and the base of the MHSZ is shifted toward the seafloor in the presence of salts. As a result, the thickness of actual hydrate occur-rence becomes thinner compared with that of the pure water case. On the other hand, since lower solubility reduces the amount of gas needed to form methane hydrate, the existence of salts in sea-water can actually promote methane gas hydrate formation in the hydrate stability zone. Numerical modeling also demonstrates that for the salt-water case the presence of methane within the field of methane hydrate stability is not sufficient to ensure the occurrence of gas hydrate, which can only form when the methane concentration dissolved in solution with salts exceeds the local methane solubility in salt water and if the methane flux exceeds a critical value corresponding to the rate of diffusive methane transport. In order to maintain gas hydrate or to form methane gas hydrate in marine sedi-ments, a persistent supplied methane probably from biogenic or thermogenic processes, is required to overcome losses due to diffusion and advection.

关键词： methane gas hydrate,solubility,stability of hydrate,salinity,phase equilibrium

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SOME PROPERTIES OF LSQR FOR LARGE SPARSE LINEAR LEAST SQUARES PROBLEMS

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Journal of Systems Science & Complexity 2010年第4期23卷 815-821页

作者： Zhongxiao JIA department of mathematical {2.,tsinghua university,beijing 100084,China. department of mathematical {2. Tsinghua University

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual *** not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes *** for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov ***,there has not yet been an analogouslyelegant formula for residual *** paper derives such kind of *** addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.

关键词： CGLS krylov subspace lanczos bidiagonalization least squares lsqr normal equations.

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An eikonal equation-based earthquake location method by inversion of multiple phase arrivals

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Science China Earth sciences 2024年第6期67卷 1802-1817页

作者： Gaoyue LAO dinghui yang Shaolin LIU Guiju DONG Wenshuai WANG Kui LIU National Institute of Natural Hazards Ministry of Emergency Management of ChinaBeijing 100085China School of Earth sciences Yunnan UniversityKunming 650091China department of mathematical {2. Tsinghua UniversityBeijing 100084China School of Mathematics and Statistics Ningxia UniversityYinchuan 750021China

The precise determination of earthquake location is the fundamental basis in seismological community,and is crucial for analyzing seismic activity and performing seismic *** arrivals are generally used to practically determine earthquake ***,first-arrival traveltimes are not sensitive to focal ***,they cannot accurately constrain focal *** improve the accuracy,researchers have analyzed the depth phases of earthquake *** traveltimes of depth phases are sensitive to focal depths,and the joint inversion of depth phases and direct phases can be implemented to potentially obtain accurate earthquake ***,researchers can determine earthquake locations in layered *** layered models can only represent the first-order feature of subsurface structures,the advantages of joint inversion are not fully explored if layered models are *** resolve the issue of current joint inversions,we use the traveltimes of three seismic phases to determine earthquake locations in heterogeneous *** three seismic phases used in this study are the first P-,sPg-and *** calculate the traveltimes of the three seismic phases by solving an eikonal equation with an upwind difference scheme and use the traveltimes to determine earthquake *** verify the accuracy of the earthquake location method by the inversion of three seismic phases,we take the 2.2. M_(S)6.4 yangbi,Yunnan earthquake as an example and locate this earthquake using synthetic and real seismic *** tests demonstrate that the eikonal equation-based earthquake location method,which involves the inversion of multiple phase arrivals,can effectively improve earthquake location accuracy.

关键词： Earthquake location Eikonal equation Fast marching method Heterogeneous model

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Dimensions of a class of high-dimensional homogeneous Moran sets and Moran classes

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Progress in Natural Science:Materials International 2002年第9期12卷 17-22页

作者： YAN Ping(department of mathematical {2., tsinghua university, beijing 100084, China) Tsing Hua Univ Dept Math Sci Beijing 100084 Peoples R China

A class of high-dimensional homogeneous Moran sets and Moran classes are introduced and some dimensional properties are studied. The Hausdorff dimension, modified lower box-counting dimension, lower and upper box-counting dimension, and packing dimension of high-dimensional homogeneous and partial homogeneous Cantor sets are determined. Moreover, a kind of fractal E is obtained, which is not regular but with the property Dimw(Ed) = dDimw(E), where w denotes any of the dimensions mentioned above.

关键词： Moran set Moran class homogeneous Cantor set partial homogeneous Cantor set dimension.

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Γ-CONVERGENCE OF INTEGRAL FUNCTIONALS DEPENDING ON VECTOR-VALUED FUNCTIONS OVER PARABOLIC DOMAINS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 249-258页

作者： JIAN HUAIYU(department of mathematical {2., tsinghua university, beijing 100084, China.) department of mathematical {2. Tsinghua University Beijing 100084 China

This paper studies Γ-convergence for a sequence of parabolic functionals, where the integrand f is nonconvex, and periodic on the first variable. The author obtains the representation formula of the Γ-limit. The results in this paper support a conclusion which relates Γ-convergence of parabolic functionals to the associated gradiend flows and confirms one of De Giorgi’s conjectures partially.

关键词： Γ-convergence Parabolic-minima Nonconvex functionals Parabolic equations

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EXACT NONREFLECTING BOUNDARY CONDITIONS FOR AN ACOUSTIC PROBLEM IN THREE DIMENSIONS

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Journal of Computational Mathematics 2003年第1期21卷 15-24页

作者： Houde Han Chunxiong Zheng (department of mathematical {2., tsinghua university, beijing 100084, China) department of mathematical {2. Tsinghua University 北京 100084

In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.

关键词： Exterior problem Nonreflecting artificial boundary condition Acoustic equa-tion Three-dimensions.

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THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY

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Journal of Computational Mathematics 2003年第4期21卷 435-450页

作者： Hou-de Han Xin Wen (department of mathematical {2., tsinghua university, beijing 100084, China) department of mathematical {2. Tsinghua University Beijing 100084 China

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.

关键词： Ship wave Potential flow Global artificial boundary condition Finite element method.

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Remnant Paleoproterozoic Subduction or Lithospheric Drip Initiation at the Yilgarn Craton Margin: Constraints from P-wave Tomography

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Acta Geologica Sinica(English Edition) 2024年第S1期 72-74页

作者： xu Xiaobing WANG Kun yang {2. ZHAO Liang YUAN Huaiyu department of mathematical {2. Tsinghua University Institute of Geophysics China Earthquake Administration State Key Laboratory of Lithospheric Evolution Institute of Geology and Geophysics Chinese Academy of Sciences university of Chinese Academy of sciences ARC Centre of Excellence for Core to Crust Fluid Systems Department of Earth and Environmental SciencesMacquarie University Centre for Exploration Targeting University of Western Australia

The Paleoproterozoic was a critical time in whether modern-style plate tectonics had become globally dominant(e.g., Wan et al., 2.2.). The Capricorn Orogen witnessed the assembly of the Pilbara and Yilgarn Cratons and an exotic microcontinent, the Glenburgh Terrane, to form the West Australia Craton(WAC) through two collisional orogenic events, the 2.15–2.45 Ma Ophthalmian and 2.05–1950 Ma Glenburgh Orogenies(Johnson et al., 2.13; Fig. 1). Compared to other Proterozoic orogenic belts in Australia, the Capricorn Orogen preserves ‘complete' opposing continental margin successions, together with intervening arc fragments associated with oceanic closure and foreland basins associated with collisional loading(Cawood et al., 2.09).

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Extremal eigenvalues of measure differential equations with fixed variation

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Science China Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2.1 department of {2. {2.,tsinghua university,beijing 100084,China 2.Zhou Pei-Yuan Center for Applied Mathematics,tsinghua university,beijing 100084,China 1. department of mathematical {2. Tsinghua University Beijing 100084 China2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

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Maximal regularity of second order delay equations in Banach spaces

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Science China Mathematics 2010年第1期53卷 51-62页

作者： BU ShangQuan ? & FANG Yi department of mathematical {2., tsinghua university, beijing 100084, China department of mathematical {2., tsinghua university, beijing 100084, China 1. department of mathematical {2. Tsinghua University Beijing 100084 China

We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2.] with periodic boundary conditions u(0)=u(2.), u′(0)=u′(2.), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2., 0];X)(*** ,q([2., 0];X) or Fsp,q([-2., 0;X])).

关键词： maximal regularity second order delay equations Lebesgue-Bochner spaces Besov spaces Triebel-Lizorkin spaces

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