Computational approaches categories

Computational approaches to potential energy may be divided into two broad categories quantum mechanics (Hehre et al, 1986) and molecular mechanics (Berkert and Allinger, 1982). The basis for this division depends on the incorporation of the Schrodinger equation or its matrix equivalent. It is now widely recognized that both methods reinforce one another in an attempt to understand chemical and biological behavior at the molecular level. From a purely practical standpoint, the complexity of the problem, time constraints, computer size, and other limiting factors typically determine which method is feasible. 

We attempted to survey the knowledge acquired in studies of the category (i) by presenting some typical examples and general trends. These are hoped to be useful for selecting the computational approach that would be compatible with the requirements involved in applications of the ty.pes tii) and (iii). 

AI techniques can be roughly divided into two categories symbolic AI and computational intelhgence. The former focuses on development of knowledge-based systems while the latter focuses on development of a set of nature-inspired computational approaches. The latter primarily includes evolutionary computations, artificial nemal networks and fuzzy logic systems. A brief introduction to these techniques begins on the next page. 

In general, computational approaches to modelling a molecular system may be divided into two broad categories quantum mechanics (QM) [44] and molecular... 

Due to the difTiculties encountered in experimental characterization of nanomaterial, theoretical approaches in determining the CNT-based composite properties have attracted a great interest. A tremendous amount of research has been developed to understand the mechanical behavior of CNTs and their composites. According to the literature, the theoietieal and computational approaches can be mainly classified into two categories i) atomistic modeling, and ii) continuum mechanics approaches [152-164] (see Fig. 23.12). 

Eliminating the basic MCS as a realistic alternative for large structural systems with relatively moderate probability of failure events, the available computational approaches can be broadly divided into two categories (i) the... 

To resolve the problems associated with structured and unstructured grids, these fundamentally different approaches may be combined to generate mesh types which partially posses the properties of both categories. This gives rise to block-structured , overset and hybrid mesh types which under certain conditions may lead to more efficient simulations than the either class of purely structured or unstructured grids. Detailed discussions related to the properties of these classes of computational grid.s can be found in specialized textbooks (e.g, see Liseikin, 1999) and only brief definitions are given here. 

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development... 

While there are plenty of methods to predict 1-octanol-water partition coefficients, logP (see Chapters 14 and 15), the number of approaches to predict 1-octanol-water distribution coefficients is rather limited. This is due to a lower availability of log D data and, in general, higher computational complexity of this property compared to that of log P. The approaches to predict log D can be roughly classified into two major categories (i) calculation of log D at an arbitrary pH and (ii) calculation of log D at a fixed pH. 

The report made by Yang et al. [23] determines the amount and composition of the e-waste flow in China (i.e. the quantity and the type of products that it includes). The document distinguishes among TVs, computers, mobile phones, air-conditioners, refrigerators, etc. Nevertheless, as aforementioned, this approach focuses on televisions (category 4) and computers (category 3). 

In order to follow the same line of the category approach, the content of Lead and BFRs is estimated. Due to the lack of data on the content of TBBPA in televisions and computers, this additive is removed from the single appliance approach. Therefore this section focuses on the content of Pb and PBDEs. 

The other technique which has poved valuable in this area is computer simulation. When the kinetic data become very complicated, as with oscillating reactions involving two elementary steps, it is still possible to obtain rate constants from the data by doing computer simulation. That is actually not as outlandish as it might appear. It is really in the same category as the Fourier transform approach. I think this is an area that will make a considerable impact upon inorganic kinetic studies in the future. 

However, it is more appropriate to provide theoretical justifications for such use. In this respect, first, we introduce the third category of decoupling of positive and negative states commonly known as the direct perturbation theory . This approach does not suffer from the singularity problems described previously. However, the four-component form of the Dirac equation remains intact. The new Hamiltonian requires identical computational effort as for the Dirac equation itself, hence it is not an attractive alternative to the Dirac equation. However, it is useful to assess the accuracy of approximate two-component forms derived from the Dirac equation such as Pauli Hamiltonian. Consider the transformation... 

Some computer programs draw the equiprobability circles at a selected confidence level. So it is possible to evaluate how close an imknown object is to a category in this way LDA approaches the modelling methods. Gilbert et al. used 95% confidence circles to show the separation between honeys from the United Kingdom, Australia, Argentina and Canada. 

---