Statistical methods lattice design

Statistical mechanics methods such as Cluster Variation Method (CVM) designed for working with lattice statics are based on the assumption that atoms sit on lattice points. We extend the conventional CVM [1] and present a method of taking into account continuous displacement of atoms from their reference lattice points. The basic idea is to treat an atom which is displaced by r from its reference lattice point as a species designated by r. Then the summation over the species in the conventional CVM changes into an integral over r. An example of the 1-D case was done successfully before [2]. The similar treatments have also been done for... 

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, / , (,r)108. Hermans describes the loss of correlation along the series of rods by a convolution polynomial . One of Hermans lattice statistics is namedparacrystalby Hosemann [5,117]. Hosemann shows that the field of distorted structure is concisely treated by the methods of complex analysis. A controversial subject is Hosemann s extension of ID statistics to 3D [63,131,227,228],... 

Initially, the protein-like HP sequences were generated in [18] for the lattice chains of N = 512 monomeric units (statistical segments), using for simulations a Monte Carlo method and the lattice bond-fluctuation model [34], When the chain is a random (quasirandom) heteropolymer, an average over many different sequence distributions must be carried out explicitly to produce the final properties. Therefore, the sequence design scheme was repeated many times, and the results were averaged over different initial configurations. 

Statistical optimisation was carried out by Mallick and co-workers [25] for the bacterium Nostoc muscorum to optimise the physical and chemical parameters. A five-level four-factorial central composite design was employed to determine the interactions between the variables for the production of PHA. A second-order polynomial equation was obtained using RSM, which resulted in an increase of product yield along with a decreased use of acetate and propionate. Yang and co-workers [27] reported the optimisation of Cupriavidus necator HI 6 for CDW, PITA content and 3HV monomer composition. A simplex lattice method was formulated using the Minitab V14 program. Optimisation in this study resulted in a 4-fold increase in cell growth and PHA production. 

---