Computational methods Models

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

The 3D structure of a raolectile can be derived either from experiment or by computational methods. Regardless of the origin of the 3D model of the molecule under consideration, the user should alway.s be aware of how the data were obtain-... 

The Born model is based on electrostatic interactions, dielectric permitivity, and orbital overlaps. It has the advantage of being fairly straightforward and adaptable to computational methods. The free energy for the polarization of the solute is expressed as... 

As mentioned above, the preferred computational methods for modeling crystals have changed over the years. Below is a list of basis function schemes, with the most often used appearing first ... 

If these elements are included in an organic molecule, the choice of computational method can be made based on the organic system with deference to the exceptions listed in this section. If completely inorganic calculations are being performed, use a method that tends to correctly model the property of interest in organic systems. 

There is a growing interest in modeling transition metals because of its applicability to catalysts, bioinorganics, materials science, and traditional inorganic chemistry. Unfortunately, transition metals tend to be extremely difficult to model. This is so because of a number of effects that are important to correctly describing these compounds. The problem is compounded by the fact that the majority of computational methods have been created, tested, and optimized for organic molecules. Some of the techniques that work well for organics perform poorly for more technically difficult transition metal systems. 

This last definition should be carefully appHed as either an interpolation or an extrapolation, particularly for empirical computational methods based on diverse observations. It is critical that users of molecular modeling tools understand where it is appropriate to apply a technique and where it is not, and what degree of accuracy can be expected. 

E. San2,J. Giraldo, andE. lsl. 2ia2LU., QSAR and Molecular Modeling Concepts, Computational Methods and Biological Applications,]. R. Prous Science Pubhshers,... 

The development of mathemafical models is described in several of the general references [Giiiochon et al., Rhee et al., Riithven, Riithven et al., Suzuki, Tien, Wankat, and Yang]. See also Finlayson [Numerical Methods for Problems with Moving Front.s, Ravenna Park, Washington, 1992 Holland and Liapis, Computer Methods for Solving Dynamic Separation Problems, McGraw-Hill, New York, 1982 Villadsen and Michelsen, Solution of Differential Equation Models by... 

Zannetti, Paolo, Air Pollution Modeling Theories, Computational Methods, and Available Software, Van Nostrand, Beinhold, New York, 1990. 

At present, conformational searches provide for the most important application of computer molecular modeling in biology. In contrast, in statistical physics, from which MC and MD methods were originally borrowed, they are primarily used for studying... 

Zannetti, P., "Air Pollution Modeling Theories, Computational Methods and Available Software." Van Nostrand Reinhold, Florence, KY, 1990. 

Very recently, people who engage in computer simulation of crystals that contain dislocations have begun attempts to bridge the continuum/atomistic divide, now that extremely powerful computers have become available. It is now possible to model a variety of aspects of dislocation mechanics in terms of the atomic structure of the lattice around dislocations, instead of simply treating them as lines with macroscopic properties (Schiotz et al. 1998, Gumbsch 1998). What this amounts to is linking computational methods across different length scales (Bulatov et al. 1996). We will return to this briefly in Chapter 12. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

The bond fluctuation model (BFM) [51] has proved to be a very efficient computational method for Monte Carlo simulations of linear polymers during the last decade. This is a coarse-grained model of polymer chains, in which an effective monomer consists of an elementary cube whose eight sites on a hypothetical cubic lattice are blocked for further occupation (see... 

In this chapter we present various computational methods for studying the structure and stability regions of various phases within the basic and the extended LG models of the ternary surfactant mixtures. In particular we use ... 

A. Karma, W.-J. Rappel. Phase field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys Rev E 55 R3017, 1996 A. Karma, W.-J. Rappel. Quantitative phase field modeling of dendritic growth in two and three dimensions. Phys Rev E 57 4111, 1998. 

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