On the quantization of folded strings in non-critical dimensions

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

Optimization design and experimental study of vortex pump based on orthogonal test

To study the effects of the performance of different types of impeller on the vortex pump, orthogonal test design, which is carried out by combining experimental test and numerical calculation, is adopted to optimize the type of design structure for the impeller in vortex pump. To find out the folding blade angle, the position of the folding point in the whole blade, and whether to wedge folding blade, an orthogonal test scheme with three factors and two levels is designed. A numerical simulation test is conducted for each scheme by analyzing the performance curve of orthogonal test plan to find the optimal performance of the program and analyzing the test data of each scheme to obtain the primary and secondary orders of the impact performance in the angle of folding blades of the vortex pump, the position of folding point of blades, and the wedge shape of blades. The results show that the optical blade type combination is the blade angle R30F60, the folding point is at 2/3 of the whole blade, and the blade does not adopt radial wedge. The optimal combination scheme is 36% higher than the design value at the rated flow head, the efficiency is 18.75% higher than the design value, the high-efficiency zone of the vortex pump is wider, and the performance meets the design requirements. Through orthogonal experimental design, the design cycle of vortex pump can be shortened effectively, the design level of vortex pump can be improved, and the hydraulic model with superior performance can be obtained.

Extendability of Equilibria of Nematic Polymers

The purpose of this paper is to study the extendability of equilibrium states of rodlike nematic polymers with the Maier-Saupe intermolecular potential. We formulate equilibrium states as solutions of a nonlinear system and calculate the determinant of the Jacobian matrix of the nonlinear system. It is found that the Jacobian matrix is nonsingular everywhere except at two equilibrium states. These two special equilibrium states correspond to two points in the phase diagram. One point is the folding point where the stable prolate branch folds into the unstable prolate branch; the other point is the intersection point of the nematic branch and the isotropic branch where the unstable prolate state becomes the unstable oblate state. Our result establishes the existence and uniqueness of equilibrium states in the presence of small perturbations away from these two special equilibrium states.