The ICM method with objective function transformed by variable discrete condition for continuum structure

ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.

A feasible method for comparing the power dependent photostability of fluorescent proteins

A feasible method of combining the concept of fluorescence half-life and the power dependent photo- bleaching rate for characterizing the practical photostability of fluorescent proteins （FPs） was introduced. Furthermore, by using a fluorescent photostability standard, a relative comparison of the photostabilty of FPs from different research groups was proposed, which would be of great benefit for developing novel FPs with optimized emission wavelength, better brightness, and improved photostability. We used rho- damine B as an example to verify this method and evaluate the practical photostability of a far-red FP, mKate-S158C. Experimental results indicated good potential of this method for further study.

A high order numerical manifold method and its application to linear elastic continuous and fracture problems

The numerical manifold method(NMM) is a partition of unity(PU) based method. For the purpose of obtaining better accuracy with the same mesh, high order global approximation can be adopted by increasing the order of local approximations(LAs). This,however, will cause the "linear dependence"(LD) issue, where the global matrix is rank deficient even after sufficient constraints are enforced. In this paper, through quadrilateral mesh to form the mathematical cover, a high order numerical manifold method called Quad4-COLS(NMM) is developed, where the constrained and orthonormalized least-squares method(CO-LS) is used to construct the LAs. The developed Quad4-COLS(NMM) does not need extra nodes or DOFs to construct high order global approximations, while is free from the LD issue. Nine numerical tests including five tests for linear elastic continuous problems and four tests for linear elastic fracture problems are carried out to validate the accuracy and robustness of the proposed Quad4-COLS(NMM).