Mesoscale, and Macroscale

In principle, we could find the minimum-energy crystal lattice from electronic structure calculations, determine the appropriate A-body interaction potential in the presence of lattice defects, and use molecular dynamics methods to calculate ab initio dynamic macroscale material properties. Some of the problems associated with this approach are considered by Wallace [1]. Because of these problems it is useful to establish a bridge between the micro- 

As a suceessful example of a mesoseale eoncept we eonsider the disloeation. Gilman [2] presents an exeellent intermediate-level diseussion of erystal dis-loeations. On a somewhat higher mathematieal level is the textbook of Hirth and Lothe [3]. 

A mesoseale variable deseribing a eolleetion of atomie disloeations is the total length of dislocation line per unit volume in metallurgieal publieations 

Orowan [7] has shown that when disloeations move with average veloeity V under the influenee of a shear stress r, the rate at whieh plastie shear strain is aeeumulated is given by 

The definition of N as the total length of mobile disloeation per unit volume takes us from the mieroseale (atoms in a erystal lattiee) to the meso-seale (a sealar quantity N. Equation (7.1) then takes us from the mesoseale to the maeroseale in whieh we aetually make measurement of the rate at whieh materials aeeumulate plastie strain. The quantity may also have its own evolutionary law involving yet another mesoseale variable. When the number of evolutionary equations (ealled the material eonstitutive deserip-tion) equals the number of variables, we ean perform a ealeulation of expeeted material response by eombination of the evolutionary law with equations of mass, momentum, and energy eonservation. 

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Much of what we currently understand about the micromechanics of shock-induced plastic flow comes from macroscale measurement of wave profiles (sometimes) combined with pre- and post-shock microscopic investigation. This combination obviously results in nonuniqueness of interpretation. By this we mean that more than one micromechanical model can be consistent with all observations. In spite of these shortcomings, wave profile measurements can tell us much about the underlying micromechanics, and we describe here the relationship between the mesoscale and macroscale. 

Papers originally presented at the Analytical Chemistry Division Symposium Analytics for Mesoscale and Macroscale Processes —Pref. 

Society. Division of Analytical Chemistry. III. American Chemical Society. Meeting (185th 1983 Seattle, Wash.) IV. Analytical Chemistry Division Symposium Analytics for Mesoscale and Macroscale Processes (1983 Seattle, Wash.) V. Series. 

The mathematical modeling of polymerization reactions can be classified into three levels microscale, mesoscale, and macroscale. In microscale modeling, polymerization kinetics and mechanisms are modeled on a molecular scale. The microscale model is represented by component population balances or rate equations and molecular weight moment equations. In mesoscale modeling, interfacial mass and heat transfer... 

Nanoparticles in relatively small amounts, through their high surface area, affect not only the mesoscale and macroscale physical properties, but electrical properties and magnetic properties as well. 

The stability of foams in constraining media, such as porous media, is much more complicated. Some combination of surface elasticity, surface viscosity and disjoining pressure is still needed, but the specific requirements for an effective foam in porous media remain elusive, partly because little relevant information is available and partly because what information is there appears to be somewhat conflicting. For example, both direct [63] and inverse [64] correlations have been found between surface elasticity and foam stability and performance in porous media. Overall, it is generally found that the effectiveness of foams in porous media is not reliably predicted based on bulk physical properties or on bulk foam measurements. Instead, it tends to be more useful to study the foaming properties in porous media at various laboratory scales microscale, mesoscale and macroscale. 

Olefin polymerization reactors will now be modeled using a bottom-up approach, from microscale to macroscale. In this section polymerization kinetic models will be introduced to describe polymerization rates and polymer microstructures, ignoring any phenomena that may take place in the mesoscale and macroscale. These models depend on the concentration of reagents and temperatures at the active site. As explained in the previous... 

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