A comparison between a shakedown design approach and the analytical design approach in the UK for flexible road pavements

Recently a shakedown approach has been proposed for structural design of flexible road pavements (Wang and Yu, 2013a). This new approach makes use of both elastic and plastic properties of materials, and therefore represents an advance from the existing analytical design approach in the UK where pavement life is related with elastic strains at critical locations using empirical equations. However, no direct comparison between designs using these two approaches has been made to date. In this paper, following a brief review of both approaches, the shakedown approach based on Wang and Yu (2013a) is used to design layer thicknesses for a typical asphalt pavement considered in the analytical approach TRRL Report LR1132. Typical values of plastic parameters are chosen for pavement materials at temperature 20°C, while stiffness moduli of materials are kept identical with the analytical design. The resulting shakedown designs are then compared with the thickness design chart using the analytical design approach. And the influence of temperature on the shakedown-based thickness design is also discussed in detail. It is found that if the shakedown design approach is conducted against the maximum wheel pressure at a relatively high temperature, the resulting pavement structure will probably not fail due to excessive rutting within the service life

Jacobian Methods for Dynamic Polarization Control in Optical Applications

Dynamic polarization control (DPC) is beneficial for many optical applications. It uses adjustable waveplates to perform automatic polarization tracking and manipulation. Efficient algorithms are essential to realizing an endless polarization control process at high speed. However, the standard gradientbased algorithm is not well analyzed. Here we model the DPC with a Jacobian-based control theory framework that finds a lot in common with robot kinematics. We then give a detailed analysis of the condition of the Stokes vector gradient as a Jacobian matrix. We identify the multi-stage DPC as a redundant system enabling control algorithms with null-space operations. An efficient, reset-free algorithm can be found. We anticipate more customized DPC algorithms to follow the same framework in various optical systems