Determination of a Drawing Die's Cone Angle at a Small Compression Ratio Based on the Upper Bound Theory

The value of a drawing die＇s cone angle has great influence on wire drawing. In order to determine the optimum value of a drawing die＇ s cone angle, the plastic deformation power Wi, shear deformation power Wi and friction power of contact surface Wf were calculated using the upper bound theory with a reasonable and movement permitted velocity field according to the related characteristics. Then the relation between half cone angle and unit drawing force was obtained and it was compared with the result with the spherical velocity field. The relative error of the two near the optimal value is only about 0. 26% through comparing with existing calculated results. Finally, in an ABAQUS environment the finite element modal of the wire rod with 12. 5 mm diameter in first drawing pass was established and the axial drawing force in different cone angles was obtained using the ABAQUS/Explicit explicit integration method. The finite element method （FEM） results verify the results using the upper bound theory and this indicated that the velocity field and the relation between half cone angle and unit drawing force reasonable.

Modeling commuters' route choice behavior under pre-trip information system

Research about the auto commuter＇s pre-trip route choice behavior ignores the combined influence of the real-time information and all respondents＇ historical information in the existing documents.To overcome this shortcoming,an approach to describing the pre-trip route choice behavior with the incorporation of the real-time and historical information is proposed.Two types of real-time information are investigated,which are quantitative information and prescriptive information.By using the bounded rationality theory,the influence of historical information on the real-time information reference process is examined first.Estimation results show that the historical information has a significant influence on the quantitative information reference process,but not on the prescriptive information reference process.Then the route choice behavior is modeled.A comparison is also made among three route choice models,one of which does not incorporate the real-time information reference process,while the others do.Estimation results show that the route choice behavior is better described with the consideration of the reference process of both quantitative and prescriptive information.

Theoretical Calculations of Transition Probabilities and Oscillator Strengths for Sc（Ⅲ） and Y（Ⅲ）

The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc（Ⅲ） and Y（Ⅲ）. In this method, by solving the SchrSdinger equation of the weakest bound electron, the expressions of energy eigenvalue and the radial function can be obtained. And a coupled equation is used to determine the parameters which are needed in the calculations. The ob- tained results of Sc（III） from this work agree very well with the accepted values taken from the National Institute of Standards and Technoligy （NIST） data base, most deviations are within the accepted level. For Y（Ⅲ） there are no accepted values reported by the NIST data base. So we compared our results of Y（Ⅲ） with other theoretical results, good agreement is also obtained.

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.

Calculation of Rydberg energy levels for the francium atom

Based on the weakest bound electron potential model theory, the Rydberg energy levels and quantum defects of the nP^2P^o1/2 （n=7-50） and np^2P^o3/2 （n=7-50） spectrum series for the francium atom are calculated. The calculated results are in excellent agreement with the 48 measured levels, and 40 energy levels for highly excited states are predicted.

Temperature and hydrogen-like impurity effects on the excited state of the strong coupling bound polaron in a CsI quantum pseudodot

With hydrogen-like impurity（HLI） located in the center of Cs I quantum pseudodot（QPD） and by using the variational method of Pekar type（VMPT）, we investigate the first-excited state energy（FESE）, excitation energy and transition frequency of the strongly-coupled bound polaron in the present paper. Temperature effects on bound polaron properties are calculated by employing the quantum statistical theory（QST）. According to the present work＇s numerical results, the FESE, excitation energy and transition frequency decay（amplify） with raising temperature in the regime of lower（higher）temperature. They are decreasing functions of Coulomb impurity potential strength.

Base stability analysis of braced deep excavation in undrained anisotropic clay with upper bound theory

It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay.Based on previously published field monitoring data and finite element analyses of ground settlements of deep excavation in soft clay,an assumed plastic deformation mechanism proposed here gives upper bound solutions for base stability of braced deep excavations.The proposed kinematic mechanism is optimized by the mobile depth(profile wavelength).The method takes into account the influence of strength anisotropy under plane strain conditions,the embedment of the retaining wall,and the locations of the struts.The current method is validated by comparison with published numerical study of braced excavations in Boston blue clay and two other cases of excavation failure in Taipei.The results show that the upper bound solutions obtained from this presented method is more accurate as compared with the conventional methods for basal heave failure analyses.