A Perfect Shape Factor Corresponding States Principle for Pure Non-Polar and Polar Fluids

In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called 'a' fluid) and the reference fluid(called 'o' fluid) must be identical. This is not generally observed in nature. To overcome this limitation, a perfect shape factor CSP is proposed in which the compressibility factors of 'a' and 'o' fluids are corresponded perfectly by introducing a new pressure shape factor 8. Using methane as the 'o' fluid, the shape factors of many fluids are calculated from PVT properties at saturation state and the second virial coefficients. Models are also formulated for the shape factors with the assumption of is a function of temperature and volume while 6 and 5 are temperature dependent only. The models described the shape factors satisfactorily in whole region including vapor, liquid and their co-existing phases. The perfect shape factor CSP could be applied for both polar and non-polar fluids.

On calculating glacial isostatic adjustment

Modeling the earth's fluid and elastic response to the melting of the glaciers of the last ice age is the most direct way to infer the earth's radial viscosity profile.Here,we compare two methods for calculating the viscoelastic response to surface loading.In one,the elastic equation of motion is converted to a viscoelastic equation using the Correspondence Principle.In the other,elastic deformation is added to the viscous flow as isostatic adjustment proceeds.The two modeling methods predict adjustment histories that are different enough to potentially impact the interpretation of the observed glacial isostatic adjustment(GIA).The differences arise from buoyancy and whether fluid displacements are subjected to hydrostatic pre-stress.The methods agree if they use the same equations and boundary conditions.The origin of the differences is determined by varying the boundary conditions and pre-stress application.

3-D rheologic model of earthquake preparation (I)—Displacement field

Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelas-tic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model.

Calculation of Transport Properties of CF4＋Noble Gas Mixtures

The present work is concerned with determining the viscosity,diffusion,thermal diffusion factor and thermal conductivity of five equimolar binary gas mixtures including:CF4-He,CF4-Ne,CF4-Ar,CF4-Kr,CF4-Xe from the principle of corresponding states of viscosity by the inversion technique.The Lennard-Jones (12-6) model potential is used as the initial model potential.The calculated interaction potential energies obtained from the inversion procedure is employed to reproduce the viscosities,diffusions,thermal diffusion factors,and thermal conductivities.The accuracies of the calculated viscosity and diffusion coefficients were 1% and 4%,respectively.

Twin Prime Distribution Problem

The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is discussed. Through the corresponding prime distribution rate of integers and composite numbers, it is found that the corresponding prime distribution rate of composite numbers approaches the corresponding prime distribution rate of integers. The distribution principle of corresponding prime number of composite number is proved. The twin prime distribution theorem is obtained. The number of twin prime numbers is thus obtained. It provides a practical way to study the conjecture of twin prime numbers.

POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS

The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.

Determination of Transport Properties for Dilute Gas Mixtures Involving Carbon Tetrafluoride

In our previous work,we calculated transport properties of pure gaseous polyatomic carbon tetrafluoride(CF4) and five equimolar binary gas mixtures of CF4 with noble gases through inversion technique.The present work is a continuation of our studies on determining the transport properties of binary gas mixtures CF4 with some gases including three diatomic molecules CO,N2,and O2,a linear polyatomic CO2,and two non-linear polyatomic molecules SF6 and CH4.The Chapman-Enskog and Vesovic-Wakeham methods as well as inversion procedure are used to determine the viscosities,diffusivities,and thermal conductivities,which deviates from the literature values within 1%,4%,and 5%,respectively.

A MICROMECHANICAL FRAMEWORK WITH AGGREGATE-MASTIC INTERFACE EFFECT FOR PREDICTING UNIAXIAL COMPRESSION CREEP OF ASPHALT MIXTURE

According to the elastic-viscoelastic correspondence principle, an elastic microme- chanical framework taking the inclusion-matrix interface effect into account is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded in a viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different temperature and stress conditions in order to determine the matrix constitutive parameters, the framework presented is validated by comparison with the experiment, and then some predictions of uniaxial compression creep behavior of asphalt mixture in different temperature and stress conditions are given.