The geochemical characteristics of two sections—the Permian–Triassic boundary(PTB) Guryul Ravine section, Kashmir Valley, Jammu and Kashmir,India; and the Attargoo section, Spiti Valley, Himachal Pradesh, India—hav...The geochemical characteristics of two sections—the Permian–Triassic boundary(PTB) Guryul Ravine section, Kashmir Valley, Jammu and Kashmir,India; and the Attargoo section, Spiti Valley, Himachal Pradesh, India—have been studied in the context of provenance, paleo-weathering, and plate tectonic setting.These sections represent the siliciclastic sedimentary sequence from the Tethys Himalaya. The PTB siliciclastic sedimentary sequence in these regions primarily consists of sandstones and shales with variable thickness. Present studied sandstones and shales of both sections had chemical index of alteration values between 65 and 74; such values reveal low-to-moderate degree of chemical weathering. The chemical index of weathering in studied samples ranged from 71 to 94, suggesting a minor K-metasomatism effect on these samples. Plagioclase index of alteration in studied sections ranged from 68 to 92, indicating a moderate degree of weathering of plagioclase feldspars. The provenance discriminant function diagram suggests that the detritus involved in the formation of present studied siliciclastic sedimentary rocks fall in quartzose sedimentary and felsic igneous provenances. These sediments were deposited in a passive continental margin plate tectonic setting according to their location on a Si_2 O versus K_2O/Na_2 O tectonic setting diagram.展开更多
For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geomet...For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.展开更多
In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relat...In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relatively smooth level set function with a local optimality condition.The objective of topology optimization is tond an optimal conguration of theuid and solid materials that minimizes power dissipation under a prescribeduid volume fraction constraint.An articial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition.Although a great deal of work has been carried out for topology optimization ofuidow in recent years,there are few researches on the topology optimization ofuidow with physical body forces.To simulate theuidow in reality,the constant body force(e.g.,gravity)is considered in this paper.Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design,and demonstrate the feasibility and superiority of the proposed method in dealing with unstructuredmesh problems.Three 3D numerical examples demonstrate the proposedmethod is feasible in three-dimensional.展开更多
During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions for the numerical solution of Partial Differential Equations (PDEs). A level set method...During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions for the numerical solution of Partial Differential Equations (PDEs). A level set method is a promising design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. In the conventional level set methods, the level set equation is solved to evolve the interface using a capturing Eulerian approach. The solving procedure requires an appropriate choice of the upwind schemes, reinitialization, etc. Our goal is to include Multiquadric Radial Basis Functions (MQ RBFs) into the level set method to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm. This paper presents an alternative approach to the conventional level set methods for solving moving-boundary problems. The solution was compared to the solution calculated by the exact explicit lime integration scheme. The examples show that MQ RBFs and adaptive greedy algorithm is a very promising calculation scheme.展开更多
目的:探讨体质量指数(body mass index,BMI)对乳腺癌患者治疗中位移误差的影响,为乳腺癌放射治疗中计划靶区外放边界提供数据支持。方法:回顾性分析本中心乳腺癌治疗的患者153例,利用CBCT获取摆位误差,并对数据进行挖掘,计算出两组因BM...目的:探讨体质量指数(body mass index,BMI)对乳腺癌患者治疗中位移误差的影响,为乳腺癌放射治疗中计划靶区外放边界提供数据支持。方法:回顾性分析本中心乳腺癌治疗的患者153例,利用CBCT获取摆位误差,并对数据进行挖掘,计算出两组因BMI的不同而导致的误差和PTV外放的差别。结果:从左乳和右乳的摆位误差分析计算得出:在考虑BMI情况下,左乳在腹背Z方向的摆位误差随BMI的增大而略有增大。右乳在Rx方向的摆位误差随BMI的增大而增大。左乳中,腹背Z方向外扩边界随BMI增大而逐渐增大。右乳中,头脚Y方向外扩边界随BMI增大而增大。结论:医师可根据乳腺癌的左右位置和BMI的大小来判断Mptv的扩大或者缩小,从而为患者提供更个性化精准化治疗。展开更多
This paper is a sequel to a previous paper (Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69(2), 1364-1375 (2008)) in which the n...This paper is a sequel to a previous paper (Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69(2), 1364-1375 (2008)) in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.展开更多
Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinea...Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.展开更多
Let Ω R d and ξ∈Ω. Let E be any non tangential subset of Ω.We prove that if E is internal thin at ξ, then it is minimal thin at any minimal Martin boundary point of Ω.
This paper deals with the quenching behavior of positive solutions to the Newton filtration equations coupled with boundary singularities.We determine quenching rates for non-simultaneous quenching at first,and then e...This paper deals with the quenching behavior of positive solutions to the Newton filtration equations coupled with boundary singularities.We determine quenching rates for non-simultaneous quenching at first,and then establish the criteria to identify the simultaneous and non-simultaneous quenching in terms of the parameters involved.展开更多
Eco-geographical regionalization involves dividing land into regions by considering both intra-regional consistency and interregional disparity and is based on the pattern of differentiation of eco-geographical elemen...Eco-geographical regionalization involves dividing land into regions by considering both intra-regional consistency and interregional disparity and is based on the pattern of differentiation of eco-geographical elements.Owing to the complexity of the land surface,and the limitation of data and appropriate methods,regions in China have hitherto been mapped manually,meaning that the process of mapping was non-repeatable.To make the regionalization technique repeatable,this study aimed to extract and quantify the expert knowledge of regionalization using an automated method.The rough set method was adopted to extract rules of regionalization based on the existing eco-geographical regionalization map of China,as well as its corresponding meteorological and geological datasets.Then,the rules for regionalization were obtained hierarchically for each natural domain,each temperature zone,and each humidity region.Owing to differences in zonal differentiation,the rule extraction sequence for the eastern monsoon zone and Tibetan Alpine zone was temperature zone first followed by humidity region,with the reverse order being applied for the northwest arid/semi-arid zone.Results show that the extracted indicators were similar to those of the existing(expert-produced)regionalization scheme but more comprehensive.The primary indicator for defining temperature zones was the≥10℃ growing season,and the secondary indicators were the January and July mean temperatures.The primary and secondary indicators for identifying humid regions were aridity index and precipitation,respectively.Eco-geographical regions were mapped over China using these rules and the gridded indicators.Both the temperature zones and humidity regions mapped by the rules show≥85%consistency with the existing regionalization,which is higher than values for mapping by the commonly used simplified method that uses the classification of one indicator.This study demonstrates that the proposed rough set method can establish eco-geographical regionalization that is quantitative and repeatable and able to dynamically updated.展开更多
文摘The geochemical characteristics of two sections—the Permian–Triassic boundary(PTB) Guryul Ravine section, Kashmir Valley, Jammu and Kashmir,India; and the Attargoo section, Spiti Valley, Himachal Pradesh, India—have been studied in the context of provenance, paleo-weathering, and plate tectonic setting.These sections represent the siliciclastic sedimentary sequence from the Tethys Himalaya. The PTB siliciclastic sedimentary sequence in these regions primarily consists of sandstones and shales with variable thickness. Present studied sandstones and shales of both sections had chemical index of alteration values between 65 and 74; such values reveal low-to-moderate degree of chemical weathering. The chemical index of weathering in studied samples ranged from 71 to 94, suggesting a minor K-metasomatism effect on these samples. Plagioclase index of alteration in studied sections ranged from 68 to 92, indicating a moderate degree of weathering of plagioclase feldspars. The provenance discriminant function diagram suggests that the detritus involved in the formation of present studied siliciclastic sedimentary rocks fall in quartzose sedimentary and felsic igneous provenances. These sediments were deposited in a passive continental margin plate tectonic setting according to their location on a Si_2 O versus K_2O/Na_2 O tectonic setting diagram.
文摘For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.
基金supported by the National Natural Science Foundation of China (Grant No.12072114)the National Key Research and Development Plan (Grant No.2020YFB1709401)the Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology (2021B1212040003).
文摘In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relatively smooth level set function with a local optimality condition.The objective of topology optimization is tond an optimal conguration of theuid and solid materials that minimizes power dissipation under a prescribeduid volume fraction constraint.An articial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition.Although a great deal of work has been carried out for topology optimization ofuidow in recent years,there are few researches on the topology optimization ofuidow with physical body forces.To simulate theuidow in reality,the constant body force(e.g.,gravity)is considered in this paper.Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design,and demonstrate the feasibility and superiority of the proposed method in dealing with unstructuredmesh problems.Three 3D numerical examples demonstrate the proposedmethod is feasible in three-dimensional.
文摘During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions for the numerical solution of Partial Differential Equations (PDEs). A level set method is a promising design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. In the conventional level set methods, the level set equation is solved to evolve the interface using a capturing Eulerian approach. The solving procedure requires an appropriate choice of the upwind schemes, reinitialization, etc. Our goal is to include Multiquadric Radial Basis Functions (MQ RBFs) into the level set method to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm. This paper presents an alternative approach to the conventional level set methods for solving moving-boundary problems. The solution was compared to the solution calculated by the exact explicit lime integration scheme. The examples show that MQ RBFs and adaptive greedy algorithm is a very promising calculation scheme.
文摘目的:探讨体质量指数(body mass index,BMI)对乳腺癌患者治疗中位移误差的影响,为乳腺癌放射治疗中计划靶区外放边界提供数据支持。方法:回顾性分析本中心乳腺癌治疗的患者153例,利用CBCT获取摆位误差,并对数据进行挖掘,计算出两组因BMI的不同而导致的误差和PTV外放的差别。结果:从左乳和右乳的摆位误差分析计算得出:在考虑BMI情况下,左乳在腹背Z方向的摆位误差随BMI的增大而略有增大。右乳在Rx方向的摆位误差随BMI的增大而增大。左乳中,腹背Z方向外扩边界随BMI增大而逐渐增大。右乳中,头脚Y方向外扩边界随BMI增大而增大。结论:医师可根据乳腺癌的左右位置和BMI的大小来判断Mptv的扩大或者缩小,从而为患者提供更个性化精准化治疗。
基金Project supported by the National Natural Science Foundation of China (No. 10871096)the Foun-dation of Major Project of Science and Technology of Chinese Education Ministry (No. 205056)+2 种基金the Project of Graduate Education Innovation of Jiangsu Province (No. CX09B_284Z)the Foundation for Outstanding Doctoral Dissertation of Nanjing Normal Universitythe Foundation for Young Teachers of Jiangnan University (No. 2008LQN008)
文摘This paper is a sequel to a previous paper (Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69(2), 1364-1375 (2008)) in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.
文摘Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.
文摘Let Ω R d and ξ∈Ω. Let E be any non tangential subset of Ω.We prove that if E is internal thin at ξ, then it is minimal thin at any minimal Martin boundary point of Ω.
基金Supported by the National Natural Science Foundation of China(10771024,11101060,11171048)
文摘This paper deals with the quenching behavior of positive solutions to the Newton filtration equations coupled with boundary singularities.We determine quenching rates for non-simultaneous quenching at first,and then establish the criteria to identify the simultaneous and non-simultaneous quenching in terms of the parameters involved.
基金Under the auspices of the Key Program of National Natural Science Foundation of China(No.41530749)。
文摘Eco-geographical regionalization involves dividing land into regions by considering both intra-regional consistency and interregional disparity and is based on the pattern of differentiation of eco-geographical elements.Owing to the complexity of the land surface,and the limitation of data and appropriate methods,regions in China have hitherto been mapped manually,meaning that the process of mapping was non-repeatable.To make the regionalization technique repeatable,this study aimed to extract and quantify the expert knowledge of regionalization using an automated method.The rough set method was adopted to extract rules of regionalization based on the existing eco-geographical regionalization map of China,as well as its corresponding meteorological and geological datasets.Then,the rules for regionalization were obtained hierarchically for each natural domain,each temperature zone,and each humidity region.Owing to differences in zonal differentiation,the rule extraction sequence for the eastern monsoon zone and Tibetan Alpine zone was temperature zone first followed by humidity region,with the reverse order being applied for the northwest arid/semi-arid zone.Results show that the extracted indicators were similar to those of the existing(expert-produced)regionalization scheme but more comprehensive.The primary indicator for defining temperature zones was the≥10℃ growing season,and the secondary indicators were the January and July mean temperatures.The primary and secondary indicators for identifying humid regions were aridity index and precipitation,respectively.Eco-geographical regions were mapped over China using these rules and the gridded indicators.Both the temperature zones and humidity regions mapped by the rules show≥85%consistency with the existing regionalization,which is higher than values for mapping by the commonly used simplified method that uses the classification of one indicator.This study demonstrates that the proposed rough set method can establish eco-geographical regionalization that is quantitative and repeatable and able to dynamically updated.