Shape algorithms

Alternative structures have been proposed by Liu and Wentzcovitch [180], Wentz-covitch and Martins [181] and Wentzcovitch [182], proposing a cubic zinc blende structure with one carbon vacancy per unit cell, and a structure resembling graphitic CN with one carbon vacancy per four nitrogen sites. This study was based on an ab initio molecular dynamics scheme with a variable cell shape algorithm. 

Zhou Jianbin, Zhou Wei, et al. 2012. Study of time-domain digital pulse shaping algorithms for nuclear signals. Nuclear Science and Techniques 23(1) 150-155. 

In shape optimization, the availability of finite element methods has enabled the optimization of very general structural shapes. Algorithms utilizing variational approaches and perturbation techniques have successfully been developed by Tada and Seguchi[13] and Banichuk[14], respectively. The applications of the perturbation method are not restricted to cases where the basic relations of the problems contain the small parcuneter in explicit form. One basic part of optimal structural design is sensitivity analysis. Perturbation method provides a tool in investigating design sensitivity analysis on optimum solutions. 

The algorithm for sizing of eraeks with complex cross-sections and unknown shapes based on the method was used in for sizing of cracks oriented perpendicularly to the applied field. This algoritlim is presented in Fig.3. In this paper, the same algorithm is applied readily to sizing of cracks with non-perpendicular orientation with respect to the applied field. 

Fig.3 The algorithm for sizing of cracks with complex cross-sections and unknown shapes. The five minimisation procedures are numbered consecutively.

The data from Table 2 show that the algorithm developed in allows sizing of different cracks with complex cross-sections and unknown shapes for orientation angles not exceeding 45°. It is seen that the width 2a and the parameter c (or the surface density of charge m=4 r // e at the crack walls) are determined with 100% accuracy for all of the Case Symbols studied. The errors in the computation of the depths dj and di are less than 4% while the errors in the computation of d, dj, d, and d are less than 20% independent of the shape of the investigated crack and its orientation angle O <45°. 

Two macromolecular computational problems are considered (i) the atomistic modeling of bulk condensed polymer phases and their inherent non-vectorizability, and (ii) the determination of the partition coefficient of polymer chains between bulk solution and cylindrical pores. In connection with the atomistic modeling problem, an algorithm is introduced and discussed (Modified Superbox Algorithm) for the efficient determination of significantly interacting atom pairs in systems with spatially periodic boundaries of the shape of a general parallelepiped (triclinic systems). 

Most drug-like molecules adopt a number of conformations through rotations about bonds and/or inversions about atomic centers, giving the molecules a number of different three-dimensional (3D) shapes. To obtain different energy minimized structures using a force field, a conformational search technique must be combined with the local geometry optimization described in the previous section. Many such methods have been formulated, and they can be broadly classified as either systematic or stochastic algorithms. 

---