Macroscopic computational models

More than 20 years ago, Matsushita et al. observed macroscopic patterns of electrodeposit at a liquid/air interface [46,47]. Since the morphology of the deposit was quite similar to those generated by a computer model known as diffusion-limited aggregation (D LA) [48], this finding has attracted a lot of attention from the point of view of morphogenesis in Laplacian fields. Normally, thin cells with quasi 2D geometries are used in experiments, instead of the use of liquid/air or liquid/liquid interfaces, in order to reduce the effect of convection. 

When the mutation of interest involves a significant rearrangement of charge, it is critical to treat electrostatic interactions accurately. Since the systems of interest are macroscopic, a finite computer model is not normally sufficient bulk solvent must be explicitly included at some stage of the calculation. This is especially important if a charge is introduced into or removed from the system. 

This computer model depicts a molecular bearing that performs the same functions as a macroscopic scale bearing, the only difference being the number of atoms contained within the device. (Alfred Pasieka/Photo Researchers, Inc.)... 

In the case of complex crystallization cycles of cocoa butter, the two preceding examples have shown that the macroscopic approach of the FEM-TTT model allowed a satisfactory prediction of the crystallization kinetics. The model simply needs to first establish the TTT diagrams corresponding to the experimental conditions used. Therefore, computer modeling can become a tool for quantitative simulation of the crystallization kinetics of fat (e.g., estimation of percentage of phases formed and crystallization times) under complex cooling and shear conditions. 

One of the methods of synthesis of clusters of uniform size consisting of just several atoms is the intrusion of liquid phase (e.g., mercury) under high pressure into zeolites with voids of different volume. High pressure is necessary for overcoming the capillary pressure in order to achieve filling of small voids with a liquid. When the pressure drops, the column of liquid in the thin capillary ruptures, similarly to the column of mercury in the thermometer upon cooling, and monodispersed clusters become trapped in the zeolite voids. Computer modeling and experimental studies of such small clusters both indicated that they form unique crystalline structures, impossible in the case of macroscopic crystals. For example, such structures may contain the axes of symmetry of fifth order. 

Chemistry seeks to explain the submicroscopic events that lead to macroscopic observations. One way this can be done is by making a model. A model is a visual, verbal, or mathematical explanation of experimental data. Scientists use many types of models to represent things that are hard to visualize, such as the structure and materials used in the construction of a building and the computer model of the airplane shown in Figure 1.8. Chemists also use several different types of models to represent matter, as you will soon learn. 

It is widely presumed that in the vicinity of insertion the elastic properties must differ from the macroscopic limit [76,89]. However, this notion has not previously been implemented in a computational model. 

Fig. 4.20a shows a variety of deformation mechanisms at the equator of the spherulite, due to differing orientations of the lamellar stacks relative to the tensile stress axis. Computer models are needed to consider the variety of lamellar stack orientations, and calculate the macroscopic stresses. Using an axisymmetric model of a spherulite (in a regular array), the tensile yield stress was predicted to be a nearly linear function of the crystallinity (Fig. 4.20b), and in the same range as experimental data. 

The first section deals specifically with the spectroscopic/ microscopic tools that can be used in concert with macroscopic techniques. The second section emphasizes computer models that are used to elucidate surface mediated reaction mechanisms. The remainder of the volume is organized around reaction type. Sections are included on sorption/desorption of inorganic species sorption/desorption of organic species precipitation/dissolution processes heterogeneous electron transfer reactions photochemically driven reactions and microbially mediated reactions. What follows are a few highlights taken from the work presented in this volume. 

In recent years, there has been great interest in developing physically inspired computational models based on the idea that the dynamics of the motion of fluid and interfaces can be represented in terms of the collective behavior of interactions of quasi-particle populations at scales smaller than macroscopic, but larger than molecular scales. These models fall in the class of mesoscopic methods - the LBM [6, 42, 45] being one. The LBM is generally based on minimal discrete kinetic models whose emergent behavior, under appropriate constraints, corresponds to the... 

As shown in Figure 26.1, the wide gap opens up between the particle and continuum paradigms. This gap cannot be spanned using statistical mechanical methods only. The existing theoretical models to be applied in the mesoscale are based on heuristics obtained via downscaling of macroscopic models and upscaling particle approach. Simphfied theoretical models of complex fluid flows, e.g., flows in porous media, non-Newtonian fluid dynamics, thin film behavior, flows in presence of chemical reactions, and hydrodynamic instabilities formation, involve not only vah-dation but should be supported by more accurate computational models as well. However, until now, there has not been any precisely defined computational model, which operates in the mesoscale, in the range from 10 A to tens of microns. 

The connections between molecular level characteristics and the macroscopic properties of materials are not always easy to discern, but current research in materials science and computer modeling are advancing our ability to make them. In this chapter, we will introduce ideas that can be used to infer the molecular scale explanations of why materials behave the way they do. Along the way, we will be able to answer at least some of the questions we have raised about carbon-based materials and the emerging field of nanotechnology. 

Mayer, B. P. Lewicki, J. P. Weisgraber, T. H. Small, W. Chinn, S. C. Maxwell, R. S., Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling. Macromolecules 2011,44,8106-8115. 

In this chapter, the current status and several major aspects of PEFC component modeling are described and discussed. Mathematical and computational modeling (both analytical and numerical) play important roles in the technology development and optimal operation of PEFCs from a fundamental understanding of underlying phenomena to engineering design and optimization that can lead to cost reductions and durability improvements. At present, the macroscopic descriptions of phenomena in the individual fuel-cell components have been formulated and... 

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