Shear induced phase transitions in highly dilute aqueous detergent solutions

Aqueous solutions of some cationic detergents show rheopectic behaviour at very low concentrations. Rheological measurements and the electrical anisotropy of the streaming solutions indicate that the rheopectic behaviour of the solutions is due to a shear induced phase transition.     

Sharp Estimates of Bounded Solutions to Some Second-order Forced Dissipative Equations

Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A ^* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A ^1/2) et λ, c sont des constantes positives, tandis que . By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A ^* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A ^1/2) and λ, c are positive constants, while .

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Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

Optimal Control of Deployment of a Tethered Subsatellite

One of the most important operations during a tethered satellite system mission is the deployment of a subsatellite from a space ship. We restrict tothe simple but practically important case that the system ismoving on a circular orbit around the Earth. The main problem duringdeployment due to gravity gradient is that the two satellites do not move along the straight radial relative equilibrium position which is stable for a tether of constant length. Instead, deploymentleads to an unstable motion with respect to the radial relativeequilibrium configuration. Therefore we introduce an optimal control strategy using theMaximum Principle to achieve a force controlled deployment of the tethered subsatellite from the radial relative equilibrium position close to the space ship to the radial relative equilibrium position far away from the space ship.     

Inertial contributions to the pressure in the truncated-cone-and-plate apparatus with application to dilute polymer solutions

New measurements of the pressure distribution generated by two Newtonian liquids in the Truncated Cone-and-Plate Apparatus are presented, in order to evaluate the exact form of the inertial contribution for a range of Reynolds numbers (Re) fromRe = 140 toRe = 36,000;Re = R ² /, where and are the liquid density and viscosity respectively,R is the plate radius, and is the angular velocity of the cone. The Walters equation for lowRe, p ^w = 0.15 ² (r² – R²), is shown to be in excellent agreement with the measurements up toRe = 1000, provided an appropriate correction for the Newtonian hole pressure is made. Up toRe = 1000, the measured slope is within 1% of the theoretical value of 0.15 given by the Walters equation; as the Reynolds number increases above 1000, the data become increasingly nonlinear inr ². Other theoretical predictions made especially for largeRe begin to disagree with the data even belowRe = 1000. The application of the experimentally determined additive inertial contribution to measurements of pressure distribution in four dilute polymer solutions is found to reproduce adequately the expected form of the viscoelastic pressure distribution, even at highRe where the Walters equation is not valid. Measurements of a combination of normal-stress differencesN ₁ + 2N ₂ for polymer solutions involving specific polymer/solvent interaction sites show a difference of 45% with change of solvent, while no difference is observed in solutions of polymers without the interaction sites. The normal-stress ratio —N ₂/N ₁ for a 5% solution of cis-polybutadiene is 0.24 at a shear rate of 100 s^–1, and it appears to approach the zero shear limit of 2/7 given by the Doi-Edwards theory. The Higashitani-Pritchard-Baird-Lodge equation relating the elastic hole pressure to the normal-stress differenceN ₁ –N ₂ gives a qualitative agreement betweenN ₁ –N ₂ from the TCP Apparatus and the hole pressure from the Stressmeter; the percent difference is 0 at shear stress < 25 Pa, 35% at = 45 Pa, and 18% at the highest = 63 Pa.     

沿垂等温平板的自然对流问题的近似解析解

本文用加权残值得到了沿垂等温平板的自然对流问题的近似解析解。和已有准确解的比较表明，在平板表面附近，近似解有很好的精度，而且速度场的精度比温度场更好一些。文末还对配域法的准收敛问题作了说明。     

SOLVING THE FREE BOUNDARY PROBLEM IN CONTINUOUS CASTING BY USING BOUNDARY ELEMENT METHOD

ＳＯＬＶＩＮＧＴＨＥＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＩＮＣＯＮＴＩＮＵＯＵＳＣＡＳＴＩＮＧＢＹＵＳＩＮＧＢＯＵＮＤＡＲＹＥＬＥＭＥＮＴＭＥＴＨＯＤＬｉＹａｏｙｏｎｇ（李耀勇）；ＺｈａｎｇＺｈｉｌｉ（张自立）（ＲｅｃｅｉｖｅｄＪｕｎｅ，１８，１９...     

旋转圆盘受均布压力作用时的摄动分析

本文对中心带轴匀速旋转圆盘在均布压力作用下的受力及变形问题进行了摄动分析，得到了受载条件为Ｊ＾２／ＪＨ＜＜１时，圆盘应力及形变的渐近解。其形变渐近解为Ｗｈｉｔａｋｅｒ函数形式比较表明，渐近解与Ｃｈｅｂｙｓｈｅｖ数值解有较好的一致性。     

Higher order asymptotic solution of mode I crack growth in elastic-perfectly plastic media

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given. The project supported by National Natural Science Foundation of China     

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.