APPLICATION OF TIME-TEMPERATURE SUPERPOSITION PRINCIPLE TO EVALUATION OF SCATTERING INTENSITY EVOLUTION IN PHASE SEPARATION FOR PMMA/SAN BLENDS

Spinodal phase separation behavior of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) blends was investigated by the time-resolved small angle light scattering (SALS) technique. It was found that the influence of temperature on the scattering intensity evolution followed the time-temperature superposition principle. The relationship between temperature and the relaxation ti me of scattering intensity I(t) can be well described by the Williams-Landel-Ferry (WLF) function.

ZONAL DISINTEGRATION MECHANISM OF DEEP CRACK-WEAKENED ROCK MASSES UNDER DYNAMIC UNLOADING

Size and quantity of fractured zone and non-fractured zone are controlled by cracks contained in deep rock masses. Zonal disintegration mechanism is strongly dependent on the interaction among cracks. The strong interaction among cracks is investigated using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. It is found from numerical results that crack nucleation, growth and coalescence lead to failure of deep crack- weakened rock masses. The stress redistribution around the surrounding rock mass induced by unloading excavation is studied. The effect of the excavation time on nucleation, growth, interaction and coalescence of cracks was analyzed. Moreover, the influence of the excavation time on the size and quantity of fractured zone and non-fractured zone was given. When the excavation time is short, zonal disintegration phenomenon may occur in deep rock masses. It is shown from numerical results that the size and quantity of fractured zone increase with decreasing excavation time, and the size and quantity of fractured zone increase with the increasing value of in-situ geostress.

Analysis on the stability of the single weld pool formed during the triple-electrode high speed CO2 welding

The pinch instability theory with free surface and wave superposition principle was applied to understanding the critical disturbance wavelength and the theoretical bead width for the single weld pool formed during the triple-electrode high speed CO2 welding. In addition, the reason for higher stability in the single weld pool was analyzed. Then single-, twin-, and triple-electrode overlaying experiments were conducted. It was found that triple-electrode CO2 welding can improve welding efficiency greatly without reducing the weld quality. The results indicated that the oscillation frequcncy of the weld pool increased, oscillation wavelength decreased, and bead width increased with the increase of welding electrodes under the same disturbance circumstances.

COMPLEX FUNDAMENTAL SOLUTIONS FOR SEMI-INFINITEPLANE AND INFINITE PLANE WITH HOLE UNDER VARIOUS BOUNDARY CONDITIONS

A general method of finding the complex fundamental solutions for semi-infinite plane and infinite plane with hole under various boundary conditions has be established by using Riemann-Schwarz symmetric principle and superposition principle of the solutions of elasticity. More than ten solutions have been derived respectively.

Multiple Debye Spherical Layers and Universe —Gravitation Originates from Electric Force

Electric field superposition principle and Gauss’s law are the basis of electrostatics. By extended analysis on the electric field lines of a charge, it is shown that electric field superposition principle and Gauss’s law are not tenable in some states, involving the electric field of ion atmosphere that is a key concept in Debye-Hückel theory of electrolyte solution and plasma. Unveiling Debye shield, ion atmosphere (Debye spherical layer 1) actually is equivalent to continue to transmit the electric field originated from the central ion, just changing the direction of the electric field. Debye spherical layer 2 and multiple Debye spherical layers generate in the transmission. Due to the effect of the multiple Debye spherical layers of charged particles in the universe, gravitation originates from electric force.

EIT Image Reconstruction by Modified Data

Electrical impedance tomography (EIT) is a radiation-free imaging method. Canoni-cally, in lung EIT, 16 electrodes are placed horizontally on the thorax skin. By inject-ing currents through electrodes attached to the skin, a set of induced voltage measure-ments can be collected. The conductivity distribution on the chest plane can be ob-tained from these electrical boundary conditions. It has been reported that the adjacent current injection pattern is sub-optimal for EIT reconstruction. However, this adjacent current injection pattern is commonly used in commercially available EIT devices. In this study, we modify the boundary conditions according to the superposition principle of the electrical field. As a result, boundary conditions of the adjacent current pattern will be transformed to those corresponding to “skip-3” current injection pattern. Simulation results indicated that reconstruction benefits from the modified boundary conditions.

Interaction between cracks and effect of microcrack zone on main crack tip

Mechanism interaction between cracks with different orientation angles is analyzed based on the principle of superposition and a flattening method. It is found that the maximum interaction effect does not occur when the microcrack is along the direction parallel or perpendicular to the principal tensile stress, which is different from the conclusion drawn by Ortiz （1987）. The mechanism of microcrack generation and the effect of the microcrack zone on the main crack tip are studied. It is concluded that the microcrack zone has effect on the main crack tip, which increases with the increase of microcrack density and length.

Trilinear equations, Bell polynomials, and resonant solutions

A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables.

Strip distortion generator for simulating inlet flow distortion in gas turbine engine ground test facilities

A methodology has been developed to generate a non-uniform/distoited inlet flow field to test a gas turbine engine in ground test facilities.The distorted flow field is generated by positioning radial and circumferential strips of varying widths upstream of the Aerodynamic Interface Plane.The interacting wakes from these strips are used to generate a given target flow field.The approximate superposition of these wakes is investigated and used to construct the strip arrangement which is subsequently validated by computing the flow field by solving the Navier-Stokes equations.The strip geometry designed using the present methodology is able to produce the target Mach number distribution with a root-mean-square error of 5.06%.

Study on characteristics of well-test type curves for composite reservoir with sealing faults

The pressure response for the composite reservoirs with a sealing fault locating in inner and outer region is different,which neglected by previous researchers,would cause significant errors during well-test interpretations.Based on seepage theory,a well-test model of two-region radial composite reservoir with infinite outer boundary has been built in this study considering wellbore storage and skin effects.The solutions for this model and characteristics of the type curves have been analyzed by applying the method of mirror image,Laplace transformation and superposition principle,including a straight fault,a perpendicular fault and parallel faults cases.The study shows that the dimensionless pressure derivative curves would be obviously different in two cases:the well to fault distance is larger,and smaller than the half length of the inner-region radius.Therefore,type curves are presented with reasonable parameters to analyze the distance effect on the dynamic pressure response.The results in this study are of great significance。

Shape-changed propagations and interactions for the(3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids

In this article,we consider the(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP)equation in fluids.We show that a variety of nonlinear localized waves can be produced by the breath wave of the GKP model,such as the(oscillating-)W-and M-shaped waves,rational W-shaped waves,multi-peak solitary waves,(quasi-)Bell-shaped and W-shaped waves and(quasi-)periodic waves.Based on the characteristic line analysis and nonlinear superposition principle,we give the transition conditions analytically.We find the interesting dynamic behavior of the converted nonlinear waves,which is known as the time-varying feature.We further offer explanations for such phenomenon.We then discuss the classification of the converted solutions.We finally investigate the interactions of the converted waves including the semi-elastic collision,perfectly elastic collision,inelastic collision and one-off collision.And the mechanisms of the collisions are analyzed in detail.The results could enrich the dynamic features of the high-dimensional nonlinear waves in fluids.

Universal Concentration Scaling on Rheometric Properties of Polydisperse and High Molecular Weight Polyacrylamide Aqueous Solutions

A great progress has been made over the last decades in studying concentration scaling on rheometric properties of monodisperse polymer solutions.However,the effects of polydisperse polymer solutions on such a concentration scaling remain elusive.In this work,rheometric properties of industrially relevant polydisperse and high molecular weight polyacrylamide(PAAm)aqueous solution have been studied.The results show a concentration scaling of the characteristic relaxation time,the plateau modulus and the zero-shear viscosity across a concentration range from 10c^(*)to 250c^(*).The time-concentration superposition principle is validated and extended in the data analysis of the terminal dynamic regime.The concentration scaling exponent of their shifting factors is significantly smaller than the results of monodisperse polymer solutions in good andθsolvents reported in the literature.The steady shear viscosity and shear stress of 18M PAAm aqueous solutions with relatively lower concentration(≤35c^(*))could also be superimposed into a master curve with the shear-thinning exponent of 0.73±0.03 and0.27±0.03,respectively,over a wide range of shear rates in about six orders of magnitudes.However,for 18M PAAm aqueous solutions with higher concentration(≥48c^(*))in an intermediate shear thinning regime,the scaling exponent shows a pronounced concentration dependence.The shear thinning exponent of steady shear viscosity varies from 0.73 to 0.57 as concentration is increased,and then increases from 0.57 to 0.90from sufficiently high shear rate.Further increasing shear rate,the shear-thinning exponent of 18M PAAm aqueous solutions at all concentrations converges to the lower bounded value observed in the relatively less concentrated(≤35c^(*))18M PAAm aqueous solutions,i.e.,0.73±0.02 for shear viscosity and 0.27±0.02 for steady shear stress,respectively.It reveals that the concentration effects of polydisperse polymer solutions could be greatly reduced by the dynamic"molecular individualism”in strong shear flow.

A Two-Scale Asymptotic Analysis of a Time-Harmonic Scattering Problem with a Multi Layered Thin Periodic Domain

The scope of this paper is to show how a two-scale asymptotic analysis,based on a superposition principle,allows us to derive high order approximate boundary conditions for a scattering problem of a time-harmonic wave by a thin and tangentially periodic multi-layered domain.The periods are assumed of the same order of the thickness.New terms like memory effect and variance-covariance ones are observed contrarily to the laminar case.As a result,optimal error estimates are obtained.

Understanding the Reinforcement and Dissipation of Natural Rubber Compounds Filled with Hybrid Filler Composed of Carbon Black and Silica

The performance of reinforced rubber compounds depends on the filler composition while the reinforcement and dissipation mechanisms still remain unclear. Herein linear and nonlinear dynamic rheological responses of carbon black/silica hybrid filler filling nature rubber compounds are investigated. The rheological contributions of dynamically retarded bulk phase and filler network are revealed to be crucial at high and low frequencies, respectively, and the bulk phase is shown to be of vital importance for the occurrence of nonlinear Payne effect at mediate frequencies. A framework for simultaneously solving reinforcement and dissipation varying with filler composition and content is suggested, providing a new perspective in understanding the filling effect for manufacturing high-performance rubber materials.

AN ACCURATE SOLUTION OF SEISMIC PRESSURE ON DAM BY LIQUID OF VARIABLE DENSITY

In this paper an accurate solution of seismic pressure on dam by liquid of vari- able density according to the principle of superposition is given.It can be extended to general two-demensional plate's problems and darn with inclined upstrearm face.