宋拓《华严经入法界品善财参问变相经》中的家具图像研究

在描述宋拓《华严经入法界品善财参问变相经》并探讨其图像作者以及创作诸问题的基础上,对其中的家具图像进行了系统研究,认为它们体现了高坐家具在中国开始普及时的基本特征,具有重要的研究价值。

敦煌文献S3441“明众生入法界”探析

本文以敦煌S3441“明众生入法界”的部分为中心,首先对于S3441作了简要地考察,认为其大致出现的时间为公元592—626年。其次,本文依据S3441底本,参照日本学者青木隆的录文,对S3441“明众生入法界”部分做重新校录和注释。最后,依据新校录文,对于S3441文献中的“众生界义”、“入法界义”进行详细地分析和探讨,发现S3441所论述的众生界与法界同体无二、不出不入、不增不灭的理论依据,就是建立在“地论学派”之大乘通宗圆教的教判,及自体缘集说等最具“地论学派”代表性的学说之上。通过分析发现,S3441强调众生界与法界的无二、生灭与不生灭的无二,是从众生如何成佛的方法论的角度进行论述,也就是因圆顿众生界与法界同一无二、因圆顿生灭与不生灭无二,而不是从现象与本体的关系进行论述,这其中有佛教界话语转移的问题。

《入法界品》研究史考察

《华严经.入法界品》可看作是整部经文的缩影,历史上曾出现过很多它的相关论著。立足于史料的考察,我们对这些论著从研究方法上加以整理,并说明由早期注疏、语言学研究发展到"六经注我",所表现出的研究态度是基于不同的理论立场;而对《入法界品》的义理研究最终失音于实利追求,也是中国佛教义学发展的现实写照。

瞿昙寺善财童子五十三参壁画初探

瞿昙寺壁画分为两大系统,即藏传佛教密宗图像和汉传佛教传记、经变图像,技法上也体现出汉藏两种风格。其中该寺瞿昙殿善财童子五十三参壁画为明代汉式风格,是研究善财童子五十三参图像流变和明代河湟地区汉藏文化交往交流交融关系的珍贵资料。文章通过文献对照和实物分析对瞿昙寺善财童子五十三参壁画做了初步探讨。首先对壁画内容进行了详细解读,其次对相关问题展开讨论,认为瞿昙寺善财童子五十三参壁画出自北宋惟白撰写的《文殊指南图赞》,跟山西崇善寺善财童子五十三参壁画一脉相承。由于画面人物不多,瞿昙寺善财童子五十三参壁画更多地将精力放在画面场景的设计上,讲究画面的构图均衡和空间处理,整个画面充满田园情调,带有浓郁的“人文画”气息。根据瞿昙殿及其他主要建筑的具体建成时间,初步判断瞿昙寺善财童子五十三参壁画绘制年代应在1391年至1430年之间。至于画师身份,从壁画图像范式、人物造型、场景风物和笔墨技法看,应该是汉族画师,可能来自河湟地区周边。

NOVEL IMMERSED BOUNDARY-LATTICE BOLTZMANN METHOD BASED ON FEEDBACK LAW

The lattice Boltzmann method （LBM） and the immersed boundary method （IBM） are alternative, com- putational techniques for solving complex fluid dynamics systems, and can take the place of the Navier-Stokes（N- S） equation. This paper proposes a novel immersed boundary-lattice Boltzmann method （IB-LBM） based on the feedback law. The method uses the immersed boundary concept in the LBM framework to capture the coupling between a body with complex geometry and a uniform fluid, Then, the flows around a stationary circular cylinder and two circular cylinders in a side by side arrangement are simulated by using the method. Results are agreed well with the benchmark data, so, the capability of the method for complex geometry is demonstrated. Different from the conventional IB-LBM, which uses the Hook＇s law or the direct forcing method to compute the interae- tion force, the method uses the feedback law--the feedback of velocity field and displacement information to calculate the force, thus ensuring the method has advantages of easy implementation and full parallelism.

炳灵寺上寺第4窟主尊身份与壁画研究

炳灵寺上寺第4窟是明代藏传佛教壁画的精品,内容丰富,至今学界还没有系统研究,通过对炳灵寺上寺第4窟壁画内容比对分析,发现第4窟正壁展现的是华严经入法界变,及由《普贤行愿品》引导出的西方净土变。根据正壁主尊头光及两侧文殊、普贤配置,判断正壁主尊身份应为十一面观音,由此形成了文殊、十一面观音、普贤三大士题材。艺师匠心独具,把入法界经变、三大士、西方净土变贯穿起来,营造出圣神庄严的佛国世界。

2.5D scattering of incident plane SH waves by a canyon in layered half-space

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green's functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free field and from the fictitious uniform moving loads have to be added to obtain the whole motion. The numerical results are carried out for the cases of a canyon in homogenous and in one layer over bedrock. The results show that the 2.5D wave scattering problem is essentially different from the 2D case, and there exist distinct differences between the wave amplification by a canyon in layered half-space and that in homogeneous half-space. The reasons for the distinct difference are explored, and the effects of the thickness and stiffness of the layer on the amplification are discussed.

Numerical Simulation for Water Entry of a Wedge at Varying Speed by a High Order Boundary Element Method

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.

An extended iterative direct-forcing immersed boundary method in thermo-fluid problems with Dirichlet or Neumann boundary conditions

An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.

Surface Motion of Alluvial Valley in Layered Half-Space for Incident Plane P-Waves

The indirect boundary element method (IBEM) is used to study the surface motion of an alluvial valley in layered half-space for incident plane P-waves based on Wolf’s theory. Firstly, the free field response can be solved by the direct stiffness method, and the scattering wave response is calculated by Green’s functions of distributed loads acting on inclined lines in a layered half-space. The method is verified by comparing its results with literature and numerical analyses are performed by taking the amplification of incident plane P-waves by an alluvial valley in one soil layer resting on bedrock as an example. The results show that there exist distinct differences between the wave amplification by an alluvial valley embedded in layered half-space and that in homogeneous half-space and there is interaction between the valley and the soil layer. The amplitudes are relatively large when incident frequencies are close to the soil layer’s resonant frequencies.

Three-dimensional Scattering of Obliquely Incident Plane SH Waves by an Alluvial Valley in a Layered Half-space

The indirect boundary element method （IBEM） is used to study three-dimensional scattering of obliquely incident plane SH waves by an alluvial valley embedded in a layered half-space. The free-field response of the layered half-space is calculated by the direct stiffness method, and dynamic Green＇s functions of moving distributed loads acting on inclined lines in a layered half-space are calculated to simulate the scattering wave field. The presented method yields very accurate results since the three-dimensional dynamic stiffness matrix is exact and the moving distributed loads can act directly on the valley boundary without singularity. Numerical results and analyses are performed for amplification of obliquely incident plane SH waves around an alluvial valley in a uniform half-space and in single layer over half-space. The results show that the three-dimensional responses are distinctly different from the two-dimensional responses, and the displacement amplitudes around alluvial valleys in a uniform haft-space are obviously different from those in a layered half-space.

论善财童子"五十三参"的内涵及其对中国佛教的影响

《入法界品》是整部《华严经》的点睛之笔,“深入法界、随顺法界”,这一《华严经》的核心旨趣在此得到了升华。善财童子奔赴各地向善知识求法问道,而各位善知识的指点既为善财童子指明了层层递进的阶梯,又堪称《华严经》思想的形象化图解。从表面上看,善财童子之所以得名是因为其出生时显现出财宝,而且一般都容易从物质财富角度解释。其实,此名以及《入法界晶》的描述是大有深意的,并非为表面的有形财宝,具有深刻的象征意义。善财童子奔走各地寻访善知识求取成佛之道的修行历程,对于中国佛教产生了深远的影响,这突出体现在信众对于善财童子的崇拜以及中国佛教的参学参访风气的兴起等方面。

б-sharpen immersed boundary method(б-SIBM)—New method for solving the horizontal pressure-gradient force(PGF) problem of б-coordinate

Although G-coordinate is one of the most popular methods used in marine and estuarine modeling, it has long suffered from the so-called ＂steep boundary problem＂, namely, the PGF problem. In this paper, a new method called the ＂σ-sharpen immersed boundary method＂ （σ-SIBM） is put forward. In this method, the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain. By this, OH/Ox of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem, which is, in turn, solved by the SIBM. The accuracy and efficiency of the σ-sharpen immersed boundary method （σ-SIBM） has been showed by both comparative theoretical analysis and classical numerical tests. First, it is shown that the σ-SIBM is more effective than the z-level method, in that σ-SIBM needs special treatment only in the steep section, but the z-level method needs the special treatment in each grid note. Second, it is superior to the p-method in that it is not restricted by the density distribution. This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force （PGFE） and their long-term effects on circulation. It can be seen that, as for the maximum erroneous velocity and kinetic energy, the value of σ-SIBM is much less than that of the z-level method and the traditional σ-method.

Compliant mechanisms design based on pairs of curves

The success of compliant mechanism design by structural topology optimization approach depends,to a large extent,on its structural geometry representation scheme.In this work,a novel representation scheme based on pairs of curves is presented.In the representation,the structure is characterized by a set of input/output(I/O) regions.While it is still unknown how the rest of the design space will be occupied by the structure,the I/O regions must exist somewhere because any structure must have parts which interact with its surroundings by way of at least one loading region,one support region,and one output region.For a valid structural design,pairs of Bezier curves are used to connect I/O regions in order to form one single connected load-bearing structure.The boundary is explicitly described,so the need for smoothening of the blurred and jagged edges can be avoided by developing such a representation scheme to directly generate smooth boundary structures.With the scheme,shape and topology can be optimized simultaneously,and the obtained topology solutions have no check-board phenomena nor intermediate zones.A multi-objective genetic algorithm is then applied to couple with the representation scheme for defining and encoding the structural geometry in the form of graph.The solution framework is integrated with a nonlinear fixed grid finite element method(FG-FEM) code for large-displacement analyses of the compliant structures.Simulation results from a displacement inverter indicated that the proposed representation scheme is appropriate.

Numerical analysis on shock-cylinder interaction using immersed boundary method

The problem of shock interaction with a rigid circular cylinder has been investigated using a compressible immersed boundary method coupled with high-order weighted-essentially non-oscillatory(WENO) scheme.First,the accuracy of the developed code is validated.Then,influences of the incident shock Mach number on the flow-field structure and dynamic drag coefficient,as well as time evolution of the flow field are studied.For different shock Mach number,the flow structure shows very different features.At a given dimensionless time,both the normalized shock detachment distance and the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder decreases with increasing shock Mach number.However,location of the upper triple point varies non-monotonically with shock Mach number.For a case with given shock Mach number,the trajectory of the upper triple point and the time evolution of the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder can both be predicted by linear correlation.Nevertheless,the time evolution of the normalized shock detachment distance is biased to be non-linear.Meanwhile,time evolution of force exerted on the cylinder is quite unsteady for a case with given shock Mach number and given cylinder diameter.For small shock Mach number,there exists a negative valley,and it disappears when the incident shock Mach number increases to a large value,e.g.,1.7.Furthermore,correlations to predict the occurrence of the peak drag and its value under different shock Mach numbers have been proposed.