Computer models to analyze

Maximemko, A.L. and Olevsky, E.A. (2004) Effective diffusion coefficients in solid-state sintering, Acta Mater. 52, 2953. An example of the use of computer modeling to analyze the role of different diffusion processes in the various stages of sintering. 

Recently, Yu et al. [6] provided a comprehensive review of existing computational models to analyze trends in mechanical properties, e.g., yield Stress CTc or tensile strength. The following analytical expression for the modified rule of mixture model is most coimnonly used to relate stress values to contemporary concepts of glass fiber structure and polymer property relationships ... 

There are several important difficulties in the application of such numerical models to analyze the chromatographic data for extracting the kinetic parameters. First, the computer package needed to describe adequately the chromatographic process has to be available. Second, long computer times are often required to fit the theoretical model to the experimental profiles. Third, with many variables used in a model, any combination may fit well the experimental measurements but may not be adequate to represent the physical reality of the process. Therefore it is important to design a chromatographic system that permits simplifications for the applicability of the model. 

Luss and Amundson (LI 3) employed this model to analyze reactor stability and control for segregated two-phase systems. The Monte Carlo simulation was employed to model the age distribution of segregated drops in the vessel. Conditions of operation under which heat-transfer effects may control the design of the reactor were given. It was shown that some steady states may be obtained in which the temperature of some drops greatly exceeds the average dispersed-phase temperature. The coalescence-redispersion problem was not considered here because of unreasonable computation times. 

K. Wang, K. Yau, and A. Lee, A zero-inflated Poisson mixed model to analyze diagnosis related groups with majority of same-day hospital stays. Comput Methods Programs Biomed 68 195-203 (2002). 

Morgenstern and co-workers (263) used interactive computer graphics to analyze the binding of a set of substituted phenylhippurates 35 to chymotry-psin. A model of these substituted phenylhippurates in the active site of... 

Musical Acoustics. A conjunction of music, craftsmanship, auditory science, and vibration physics, musical acoustics analyzes musical instruments to better understand how the instruments are crafted, the physical principles of their tone production, and why each instrument has a unique timbre. Musical instruments are studied by analyzing their tones and then creating computer models to synthesize these sounds. When the sounds can he recreated with minimal software comphcations, a synthesizer featuring realistic orchestral tones may he constructed. The second method of study is to assemble an instrument or modify an existing instrument to perform nondestructive (or on occasion destructive) testing so that the effects of various modifications may be gauged. 

Studies using computer-based compartmental modeling to analyze plasma retinol kinetics have shown that each molecule of retinol circulates through the plasma compartment several times before it is irreversibly degraded (see Tissue Retinoid Metabolism ). In a young man who consumed... 

A series of monographs and correlation tables exist for the interpretation of vibrational spectra [52-55]. However, the relationship of frequency characteristics and structural features is rather complicated and the number of known correlations between IR spectra and structures is very large. In many cases, it is almost impossible to analyze a molecular structure without the aid of computational techniques. Existing approaches are mainly based on the interpretation of vibrational spectra by mathematical models, rule sets, and decision trees or fuzzy logic approaches. 

Once a PES has been computed, it is often fitted to an analytic function. This is done because there are many ways to analyze analytic functions that require much less computation time than working directly with ah initio calculations. For example, the reaction can be modeled as a molecular dynamics simulation showing the vibrational motion and reaction trajectories as described in Chapter 19. Another technique is to fit ah initio results to a semiempirical model designed for the purpose of describing PES s. 

Although much as been done, much work remains. Improved material models for anisotropic materials, brittle materials, and chemically reacting materials challenge the numerical methods to provide greater accuracy and challenge the computer manufacturers to provide more memory and speed. Phenomena with different time and length scales need to be coupled so shock waves, structural motions, electromagnetic, and thermal effects can be analyzed in a consistent manner. Smarter codes must be developed to adapt the mesh and solution techniques to optimize the accuracy without human intervention. 

Other models (or combinations of them) are often employed when computers are used to analyze dispersal. These can give an acceptable degree of accuracy when combined with detailed weather data. Short-exposure modeling is the most difficult and is liable to the greatest degree of error. It is for this reason that such models are not accurate when dealing with odor nuisances. The problem of modeling odor dispersal is dealt with below. 

Moreover, molecular modeling is one key method of a wide range of computer-assisted methods to analyze and predict relationships between protein sequence, 3D-molecular structure, and biological function (sequence-structure-function relationships). In molecular pharmacology these methods focus predominantly on analysis of interactions between different proteins, and between ligands (hormones, drugs) and proteins as well gaining information at the amino acid and even to atomic level. 

The Field of Numerical Analysis.—As used here, numerical analysis will be taken to represent the art and science of digital computation. The art is learned mainly by experience hence, this chapter will be concerned with explicit techniques and the mathematical principles that justify them. Digital computation is to be contrasted with analog computation, which is the use of slide rules, differential analyzers, model basins, and other devices in which such physical magnitudes as lengths, voltages, etc., represent the quantities under consideration. 

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