DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME(Ⅲ)

The Hamiltonian mechanics in Newtonian-Riemannian space-time and its application to hydromechanics are discussed. Biography: Zhang Rong-ye (1938-), Professor     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME (Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ (Ⅰ ) (ｓｅｅ:ＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ (ＥｎｇｌｉｓｈＥｄｉｔｉｏｎ) ,2 0 0 0 ,2 1 (7) :82 5-83 5) ,ｗｅｈａｖｅｅｓｔａｂｌｉｓｈｅｄｔｈｅｄｙｎａｍｉｃｓｉｎＮｅｗｔｏｎｉａｎ＿Ｒｉｅｍａｎｎｉａｎｓｐａｃｅ＿ｔｉｍｅ,ａｎｄｇｉｖｅｉｔｓａｐｐｌｉｃａｔｉｏｎｔｏＨｙｄｒｏｍｅｃｈａｎｉｃｓ.ＴｈｅｒｅｉｓＧａｌｉｌｅｏ’ｓｐｒｉｎｃｉｐｌｅｏｆｒｅｌａｔｉｖｉｔｙｉｎＣｌａｓｓｉｃａｌＮｅｗｔｏｎ’ｓｍｅｃｈａ…     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME(Ⅱ)

The relativity of motion and covariance of equation of motion in Newtonian-Riemannian space-time, some relationship between Newton’s mechanics in N-R space-time and the general relativity, their difference and identity are discussed.     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME (Ⅳ)

ＩｎｔｒｏｄｕｃｔｉｏｎＬａｇｒａｎｇｉａｎｍｅｃｈａｎｉｃｓｉｓａｎｉｍｐｏｒｔａｎｔｐａｒｔｏｆａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ.ＩｔｉｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆＮｅｗｔｏｎｉａｎｍｅｃｈａｎｉｃｓ.Ｎｅｗｔｏｎｉａｎｍｅｃｈａｎｉｃｓｉｓｅｓｔａｂｌｉｓｈｅｄｏｎｔｈｅｃｏｎｆｉｇｕｒａｔｉｏｎｓｐａｃｅ—Ｒｉｅｍａｎｎｉａｎｍａｎｉｆｏｌｄ .Ｌａｇｒａｎｇｉａｎｍｅｃｈａｎｉｃｓｉｓｅｓｔａｂｌｉｓｈｅｄｏｎｉｔｓｔａｎｇｅｎｔｂｕｎｄｌｅ ,Ｈａｍｉｌｔｏｎｉａｎｍｅｃｈａ…     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME(Ⅳ)

Lagrangian mechanics in Newtonian-Riemannian space-time and relationship between Lagrangian mechanics and Newtonian mechanics, and between Lagrangian mechanics and Hamiltonian mechanics in N-R space-time are discussed.     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACETIME (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＴｉｍｅａｎｄｓｐａｃｅｉｓａｂａｓｉｃｆｏｒｍｉｎｗｈｉｃｈｔｈｅｍａｔｔｅｒｓｅｘｉｓｔ.Ａｌｌｍａｔｔｅｒｓａｎｄｔｈｉｎｇｓｉｎｔｈｅｗｏｒｌｄｏｃｃｕｒ,ｅｘｉｓｔ,ｍｏｖｅ ,ｄｅｖｅｌｏｐａｎｄｖａｒｉａｔｅｉｎｔｈｅｓｐａｃｅｔｉｍｅ.Ａｌｌｐｒｏｃｅｓｓｅｓｉｎｔｈｅｍａｔｅｒｉａｌｗｏｒｌｄａｒｅｔｈｅｐｒｏｃｅｓｓｅｓｏｆｔｈｅｍｏｔｉｏｎ ,ｄｅｖｅｌｏｐｍｅｎｔａｎｄｖａｒｉａｔｉｏｎｏｆｍａｔｔｅｒｓ.Ｔｏｓｔｕｄｙｔｈｅｏｂｊｅｃｔｓｔｈａｔｏｃｃｕ…     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACETIME (Ⅰ)

By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian-Galilean spacetime is generalized to Newtonian-Riemannian Spacetime, and the dynamics in N-R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued. CLC number: 0313.1 Document code: A     

MASS TRANSPORT IN SOLID TUMORS (Ⅰ)──FLUID DYNAMICS

I.IntroductionCancerhasbeenthekillerinmanywesterncountriesonlysecondtothecardiovasculardiseaseformanyyears.Ditficultiesinearlydiagnosisisoneofthemajorobstaclesincancertreatment.However,recentlyitisreportedthatthetumorphysiologicalbarrier,whichpreventsdrugsfrompenetratingintothecoreoftumor,'mayconstituteanothermajorobstacleinkillingcancercallseffectivelyl'].Therefore,tostudythemasstransp.ortprocessintumorbecomesimportantinthatitmayprovidesomecriteriafordrugdesignanddrug-giningstrategies.Tradit…     

MASS TRANSPORT IN SOLID TUMORS (Ⅰ)──FLUID DYNAMICS

A three-porous-medium model for transvascular exchange and extravascular transport of fluid and macromolecules in a spherical solid tumor is developed. The microvasculature, lymphatics, and tissue space are each treated as a porous medium with the flow of blood. lymph, and interstitial fluid obeying Darcy’s law and Starling’s assumption. In this part, the role of interstitial pressure and fluid convection are studited. The analytical soiutions are obtained for foe isolated tumor and the normal-tissue-surrounded tumor respectively. The calculated interstitial pressure profue are consistent with the experimental observation that the elevated interstitial pressure is a major barrier in the penetration of macromolecular drug into tumors. The factors which may reduce the interstitial pressure are analyzed in details.     

CHAPLYGIN EQUATION IN THREE-DIMENSIONAL NON-CONSTANT ISENTROPIC FLOW-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅲ)

This work is the continuation of the discussion of Ref.[1].In this Paper we resoive theequations of isentropic gas dynamics into two problems:the three-dimensional non-constant irrotational flow (thus the isentropic flow,too),and the three-dimensional non-constant indivergent flow (i.e.the in compressible isentropic flow).We apply the theory offunctions of a complex variable under Dirac-Pauli representation and the Legendretransformation,transform these equations of two problems from physical space intovelocity space,and obtain two general Chaplygin equations in this paper.The generalChaplygin equation is a linear difference equation,and its general solution can be expressedat most by the hypergeometric functions.Thus we can obtain the general solution of generalproblems for the three-dimensional non-constant isentropic flow of gas dynamics.     

CHAPLYGIN EQUATION IN THREE-DIMENSIONAL NON-CONSTANT ISENTROPIC FLOW-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅲ)

This work is the continuation of the discussion of Ref. [1]. In this paper we resolve the equations of isentropic gas dynamics into two problems: the three-dimensional non-constant irrotational flow (thus the isentropic flow, too), and the three-dimensional non-constant indivergent flow (i. c. the in compressible isentropic flow). We apply the theory of functions of a complex variable under Dirac-Pauli representation and the Legendre transformation, transform these equations of two problems from physical space into velocity space, and obtain two general Chaplygin equations in this paper. The general Chaplygin equation is a linear difference equation, and its general solution can be expressed at most by the hypergeometric functions. Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics.     

ON PATH-INDEPENDENT INTEGRALS AND FRACTURE CRITERIA IN NONLINEAR FRACTURE DYNAMICS

In this paper,we consider path-independent integrals and frac-ture criteria in nonlinear fracture dynamics.The dynamic effectand crack propagation are included in the discussion.Both nonlinearelastic and elastic-plastic case for crack propagation have been con-sidered.and the related path-independent integrals are proposed.Asan example,the steady state propagation of crack has been discussed.Lastly,we give the mechanical meaning of this path-independent inte-grals as the crack extension force,and make it possible to use thepath-independent integrals(as fracture criterion in nonlinear frac-ture dynamics).     

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

A three-dimensional discrete element model of the connective type is presented. Moreover, a three- dimensional numerical analysis code, which can carry out the transitional process from connective model (for continuum) to contact model (for non-continuum), is developed for simulating the mechanical process from continuum to non-continuum. The wave propagation process in a concrete block (as continuum) made of cement grout under impact loading is numerically simulated with this code. By comparing its numerical results with those by LS-DYNA, the calculation accuracy of the model and algorithm is proved. Furthermore, the failure process of the concrete block under quasi-static loading is demonstrated, showing the basic dynamic transitional process from continuum to non-continuum. The results of calculation can be displayed by animation. The damage modes are similar to the experimental results. The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum. It also shows that the discrete element method (DEM) will have broad prospects for development and application.     

流体物理学(Ⅲ)

5.2 时兴学科领域5.2.1 空气动力学通过渐近方法达到新的理论认识,加上作为研究方法的对理论的数值仿真,计算机在数据的取得和分析中的应用,以及对湍流过程物理机理的更好了解,这些加快了空气动力学的前进步伐。由于紧迫需要和以上这些知识进步的激励,人们已在提高民航运输机效率,改进直升机和有人驾驶再入飞行器的性能,以及加强军用飞机与武器装备的效能等方面取得很大      

MOLECULAR DYNAMICS SIMULATION OF SELF-ORGANIZED STRUCTURE IN MICRO-PHASE SEPARATION OF NANO-SCALE FILM

Self-organization in thin micro-films has shown potential for the production of microelements with specific structures and functions; however, little is known about its mechanism of formation. A 2-D molecular dynamics (MD) simulation on this process is carried out in this paper for films between two parallel walls (substrates) under different initial conditions. The films consist of two immiscible components (A and B). The simulation results in altemative columns perpendicular to the walls, which are rich either in A or in B molecules, respectively, apparently owing to their different interactions with the walls. The characteristic breadths of the columns depend on the distance between the two walls. By providing microscopic details of the self-organization processes and the resulted structures, MD simulation proves itself as a unique way for analyzing the dynamics of thin films.     

THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC—PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅰ)

In this paper:(A) We cast aside the traditional quaternion theory and build up the theory offunctions of a complex variable under Dirac-Pauli representation. Thus the multivariateand multidimensional problems become rather simple problems.(B) We simplify the Navier-Stokes equation of incompressible viscous fluid dynamicsand the equations group of isentropic aerodynamics by theory of functions of a complexvariable under Dirac-Pauli representation. And the above-equations, as central problems offluid dynamics, are classified as the nonlinear equation with only one complex unknownfunction.So the changes are the Great Pole, and give birth to the Two Bearings; the TwoBearings give birth to the Four Quadrants, and the Four Quadrants give birth to the EightDiagrams.——Commentaries on Changes,Copula(Ⅰ)     

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS (Ⅰ)——BASIC THEORY

Under the basis of physiological data, a nonlinear and unsteady comprehensive mathematical model of microcirculatory dynamics with distributed parameters is developed. Hemodynamics, interstitium dynamics, lymph dynamics, dynamics of protein transport, oxygen dynamics, dynamics of heat transfer, and myogenic and metabolic regulation procedures are included. The interactions between these factors were comprehensively exhibited. The influences of arteriolar vasomotion and nonlinear viscoelasticity of blood in arteriole are considered. A simplified vessel network consisting of arteriole, open and reserved capillaries, venule, initial lymphatics and arteriole-venule anastomose is adopted as the geometrical model. This kind of comprehensive mathematical model is helpful in analyzing clinical data and developing a “numerical experiment method” in microcirculation research.     

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS (Ⅰ)——BASIC THEORY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｂａｓｉｃｆｕｎｃｔｉｏｎｏｆｔｈｅｍｉｃｒｏｃｉｒｃｕｌａｔｉｏｎｉｓｔｏａｌｌｏｗｒａｐｉｄｅｘｃｈａｎｇｅｏｆｗａｔｅｒ，ｇａｓｅｓ，ｎｕｔｒｉｅｎｔｓａｎｄｗａｓｔｅｐｒｏｄｕｃｔｓｂｅｔｗｅｅｎｔｈｅｂｌｏｏｄａｎｄｔｉｓｓｕｅｃｅｌｌｓ．Ａｍｉｃｒｏｃｉｒｃｕｌａｔｉｏｎｕｎｉｔｔｈｅｒｅｆｏｒｅｃｏｎｓｉｓｔｓｏｆｍｉｃｒｏｖｅｓｓｅｌｓ（ａｒｔｅｒｉｏｌｅｓ，ｃａｐｉｌｌａｒｉｅｓ，ｖｅｎｕｌｅｓ，ｔｈｏｒｏｕｇｈｆａｒｅｓａｎｄａｒｔｅｒｉｏｌｅ＿…     

EXISTENCE AND UNIQUENESS OF GLOBAL STRONG SOLUTIONS OF TWO MODELS IN ATMOSPHERIC DYNAMICS

In this paper,the author proves by the methode of energy estimates the existence anduniqueness of global strong solutions of barotopic nondivergent model and baroclinicquasi-geostrophic quasi-nondivergent model.The two models are fundamental ones inatmospheric dynamics.The results here generalize the outcome given by the author in[3]-[5]and verify a conjecture posed by Zeng Qing-cun in[1].     

SOLUTIONS OF MAGNETOHYDRODYNAMICS EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅳ)

This work is the continuation of the discussion of Refs.[1 3].(A) We turn the Magnetohydrodynamics equaitons of isentropic compresible andnon-dissipative magneto-flow into the form of the ideal hydrodynamics equations in thispaper;we can obtain the general Chaplygin equation from Ref.[3],and the generalsduction of this equation.(B)We apply the theory of functions of a complex rariable under Dirac-paulirepresentation,turn the general Magnetohydrodyamics equations of incompressiblemageto-flow into two nonlinear equaitons for flow function and"magneto-flow function",and obtain the exact stable solution of incompressible magnetohydrodynamics equationsunder the condition of stable magnetic field(i.e.under conditon of equality for kinematicalviscid coefficient or viscid diffusion coefficient with magnetic diffusion coefficient).